Practice Questions

Q. Jo Akumba’s portfolio is invested in a range of developed markets fixed income securities. She asks her adviser about the possibility of diversifying her investments to include emerging and frontier markets government and corporate fixed income securities. Her adviser makes the following comment regarding risk:

“All emerging and frontier market fixed income securities pose economic, political and legal risk. Economic risks arise from the fact that emerging market countries have poor fiscal discipline, rely on foreign borrowing, have less diverse tax base and significant dependence on specific industries. They are susceptible to capital flight. Their ability to pay is limited. In addition, weak property rights, weak enforcement of contract laws and political instability pose hazard for emerging markets debt investors.”

Discuss the statement made.

Solution

The statement correctly identifies economic, political and legal risk. The adviser has correctly identified some of the characteristics typically associated with emerging and frontier markets that may affect their governments’ and corporate borrowers’ ability and willingness to pay bondholders. However, the assertion that all emerging and frontier market fixed income securities pose such risk is incorrect, as many countries classified as “emerging” are considered to be healthy and prosperous economies.

By ChatGPT

The adviser's statement encompasses a range of risks associated with investing in emerging and frontier market fixed income securities. Here's a breakdown and discussion of the statement, focusing on economic, political, and legal risks:

1. Economic Risks:

   • Poor fiscal discipline: Emerging market countries may have less disciplined fiscal policies, potentially leading to higher inflation, currency devaluation, and default risk.

   • Dependence on foreign borrowing: Heavy reliance on external debt can lead to currency mismatches (debt in foreign currency while revenue is in local currency) and vulnerability to global liquidity conditions.

   • Less diverse tax base: A narrow tax base can lead to volatile government revenues, especially if it's heavily dependent on specific industries like commodities.

   • Industry dependence: Overreliance on specific sectors (like natural resources) makes these economies vulnerable to sector-specific downturns and global commodity price fluctuations.

   • Susceptibility to capital flight: In times of global or local stress, investors may rapidly withdraw their capital, leading to currency and liquidity crises.

   • Limited ability to pay: Emerging markets may have limited fiscal space to service debt, especially during economic downturns, increasing the risk of default.

2. Political Risks:

   • Political instability: Governments may change frequently or unpredictably, leading to changes in policies that can affect the investment climate, such as sudden alterations in tax laws, expropriation of assets, or changes in regulations.

   • Policy unpredictability: Inconsistent economic policies can lead to an unstable investment environment, making long-term planning and investment difficult.

3. Legal Risks:

   • Weak property rights: Inadequately defined or enforced property rights can lead to uncertainty regarding the ownership of assets, diminishing their value and attractiveness to investors.

   • Weak enforcement of contract laws: If contracts are not reliably upheld, the risk to lenders and investors increases, as the mechanisms to enforce agreements or resolve disputes may be ineffective or biased.

In conclusion, while emerging and frontier markets can offer diversification and potentially higher returns, they come with heightened risks. Investors need to carefully consider these risks and weigh them against the potential benefits. It's also crucial for investors to conduct thorough due diligence, understand local market dynamics, and possibly seek expert advice when considering investments in these markets.

Link: https://chat.openai.com/c/dcc8d4a7-b716-42f0-a55d-2f1716be48ea

Risks in Emerging Market Bonds

Q.

Identify risks faced by investors in emerging market equities over and above those that are faced by fixed income investors in such markets.

Solution

In addition to the economic, political and legal risks faced by fixed income investors, equity investors in emerging markets face corporate governance risks. Their ownership claims may be by corporate insiders, dominant shareholders or the government. Interested parties may misuse the companies’ assets. Weak disclosure and accounting standards may result in limited transparency that favors insiders. Weak checks and balances on governmental actions may bring about regulatory uncertainty, seizure of property or nationalization.

ChatGPT

Investors in emerging market equities face a unique set of risks, some of which are amplified compared to those faced by fixed income investors in these markets. Here are the additional risks predominantly associated with emerging market equities:

1. Market Volatility:

   • Higher volatility: Equity markets in emerging countries tend to be more volatile than their fixed income counterparts and developed market equities, due to factors such as lower liquidity, less mature markets, and economic instability.

2. Equity-Specific Risks:

   • Corporate governance risk 🟢 : There may be a higher prevalence of issues related to corporate governance, including transparency, accountability, and shareholder rights, which can impact stock performance.

   • Limited investor protection: Legal frameworks may be less developed, offering less protection to minority shareholders against malpractices like expropriation or unfair related-party transactions.

3. Liquidity Risk:

   • Lower liquidity: Emerging market stocks may have lower liquidity compared to developed markets, making it harder to enter or exit positions without impacting the market price significantly.

4. Regulatory and Reporting Standards:

   • Inconsistent reporting standards 🟢: Accounting, auditing, and financial reporting standards may be less rigorous or enforced less stringently than in developed markets, leading to issues with transparency and reliability of financial information.

5. Currency Risk:

   • Greater currency fluctuation: While this affects both equities and fixed income, the impact on equities can be more pronounced due to the longer-term nature of equity investments and the direct impact of currency movements on companies' operational results.

6. Economic and Political Risks:

   • Sensitivity to global commodity prices: Many emerging markets are commodity-driven economies, and their equities are particularly sensitive to global commodity price fluctuations.

   • Expropriation and nationalization 🟢: There's a higher risk of government actions like nationalization or expropriation of assets, which can directly affect equity valuations.

7. Performance and Valuation Risk:

   • Valuation discrepancies: Emerging market equities may be subject to mispricing due to factors such as less analyst coverage, leading to potential overvaluation or undervaluation.

   • Growth expectation and performance risk: Equity investments are often made with growth expectations, which can be significantly impacted by the country's economic performance, policy changes, or global economic conditions.

8. Information and Transparency Risk:

   • Access to information 🟢: Investors may have less access to reliable and timely information, making it difficult to make informed investment decisions or assess the true value of a company.

While investing in emerging market equities can offer high return potential and diversification benefits, it's crucial for investors to understand and manage these additional risks carefully. Strategies such as thorough due diligence, diversification across sectors and countries, and a focus on quality and governance can help mitigate some of these risks.

Forecasting Equity Return

Q.

Describe the main issues that arise when conducting historical analysis of real estate returns.

Solution

Properties trade infrequently so there is no data on simultaneous periodic transaction prices for a selection of properties. Analysis therefore relies on appraisals.

Secondly, each property is different, it is said to be heterogenous. The returns calculated from appraisals represent weighted averages of unobservable returns. Published return series is too smooth and the sample volatility understates the true volatility of returns. It also distorts estimates of correlations.

ChatGPT

• Data Availability: Historical real estate data can be scarce, incomplete, or inconsistent, making analysis challenging.

• Market Heterogeneity: Real estate markets vary significantly by location and property type, complicating broad analyses.

• Valuation Challenges: Accurately assessing property values over time is difficult due to factors like depreciation and renovations.

• Economic and Regulatory Influence: Changes in economic conditions, interest rates, and regulations can significantly impact real estate returns.

• Inflation Effects: Adjusting for inflation is crucial for comparing real returns over time but can be complex due to varying inflation rates.

• Illiquidity and Transaction Costs: Real estate is relatively illiquid with high transaction costs, affecting investment returns and market dynamics.

• Subjectivity in Appraisals: Property appraisals can be subjective, introducing variability in return calculations.

• Lack of Standardization: Unlike stocks and bonds, real estate lacks standardization, making it difficult to aggregate and compare data.

Forecasting Real Estate Returns

Question

An analyst at a real estate investment management firm seeks to establish expectations for rate of return for properties in the industrial sector over the next year. She has obtained the following information:

Current industrial sector capitalization rate (“cap” rate)	5.7%
Expected cap rate at the end of the period	5.5%
NOI growth rate (real)	1%
Inflation expectation	1.5%

Estimate the expected return from the industrial sector properties based on the data provided.

Solution

The expected change in the cap rate from 5.7% to 5.5% represents a (5.5% − 5.7%)/5.7% = 3.5% decrease.

Using the expression E(Rre) = CapRate + NOI growth rate − %ΔCapRate = 5.7% + (1% + 1.5%) − (−3.5%) = 11.7%.

Note: As the cap rate is expected to decrease, property values are expected to increase, hence the cap rate change contributes to the expected return.

ChatGPT

To estimate the expected return from the industrial sector properties, we can use the following components:

1. Income Return: Based on the current capitalization rate and NOI growth.

2. Capital Appreciation: Driven by the change in the capitalization rate.

3. Inflation Impact: To reflect the real purchasing power of the returns.

Let's break it down:

1. Income Return:

   • Current Cap Rate = 5.7%.

   • NOI Growth Rate = 1% (real, not nominal).

   • Income Return = Current Cap Rate + NOI Growth Rate = 5.7% + 1% = 6.7%.

2. Capital Appreciation:

   • The capital appreciation is influenced by the change in the cap rate.

   • Current Cap Rate = 5.7%, Expected Cap Rate at end of the period = 5.5%.

   • A decrease in the cap rate typically indicates an increase in property values (inverse relationship).

   • We can estimate the price change due to cap rate change by the formula: Price Change % = (New Cap Rate / Old Cap Rate - 1).

   • Price Change % = (5.5 / 5.7 - 1) = -3.51%.

3. Inflation Impact:

   • Expected Inflation = 1.5%.

   • The real return should be adjusted for inflation to reflect the real purchasing power.

Now, let's calculate the expected return, considering both the income return and capital appreciation:

\text{Expected Return} = \text{Income Return} + \text{Price Change %} - \text{Inflation Impact} $Expected Return=6.7$

Now, we'll compute the actual value:

The expected return from the industrial sector properties, based on the provided data, is approximately 1.69%.

Q.

A client has asked his adviser to explain the key considerations in forecasting exchange rates. The adviser’s firm uses two broad complementary approaches when setting expectations for exchange rate movements, namely focus on trade in goods and services and, secondly, focus on capital flows. Identify the main considerations that the adviser should explain to the client under the two approaches.

Solution

Under the first approach analysts focus on flows of export and imports to establish what the net trade flows are and how large they are relative to the economy and other, potentially larger financing and investment flows.

The approach also considers differences between domestic and foreign inflation rates that relate to the concept of purchasing power parity. Under PPP, the expected percentage change in the exchange rate should equal the difference between inflation rates. The approach also considers the sustainability of current account imbalances, reflecting the difference between national saving and investment.

Under the second approach the analysis focuses on capital flows and the degree of capital mobility. It assumes that capital seeks the highest risk-adjusted return. The expected changes in the exchange rate will reflect the differences in the respective countries’ assets’ characteristics such as relative short-term interest rates, term, credit, equity and liquidity premiums.

The approach also considers hot money flows and the fact that exchange rates provide an across the board mechanism for adjusting the relative sizes of each country’s portfolio of assets.

ChatGPT

When explaining the key considerations in forecasting exchange rates, the adviser should outline the main factors under the two broad approaches: focus on trade in goods and services, and focus on capital flows.

1. Focus on Trade in Goods and Services:

• Balance of Trade: The difference between a country's exports and imports. A trade surplus or deficit can influence the demand for a nation's currency.

• Price Competitiveness: Changes in relative prices or inflation rates can affect the competitiveness of a nation's goods and services, thereby influencing trade balances and exchange rates.

• Exchange Rate Pass-Through: The extent to which the prices of imported and exported goods change as a result of exchange rate movements. This can affect trade volumes and the trade balance.

• Trade Agreements and Barriers: Tariffs, quotas, and trade agreements can alter trade flows and impact the demand for currencies.

• Elasticity of Demand: The responsiveness of export and import volumes to changes in price and exchange rates. High elasticity could mean larger impacts on the trade balance from exchange rate changes.

2. Focus on Capital Flows:

• Interest Rate Differentials: Differences in interest rates between countries can influence investment flows. Higher interest rates typically attract foreign capital, increasing demand for the currency.

• Investor Sentiment and Risk Appetite: Global investor sentiment and preference for risk can shift capital flows. In times of uncertainty, investors might prefer safe-haven currencies.

• Political and Economic Stability: Stable political and economic environments attract foreign investment, supporting the currency. Conversely, instability can lead to capital outflows.

• Capital Controls: Restrictions on the flow of capital into or out of a country can significantly affect exchange rates by limiting supply and demand dynamics.

• Expectations of Future Economic Performance: Investors’ expectations about a country's future economic performance can drive capital flows. Positive expectations can attract foreign investment, supporting the currency.

The adviser should explain that these factors interplay in complex ways and that forecasting exchange rates involves analyzing both current data and expectations about future conditions under these two approaches.

Looking independently at each of the economic observations below, indicate the country where an analyst would expect to see a strengthening currency for each observation.

	Country X	Country Y
Expected inflation over next year	2.0%	3.0%
Short-term (1-month) government rate	Decrease	Increase
Expected (forward-looking) GDP growth over next year	2.0%	3.3%
New national laws have been passed that enable foreign direct investment in real estate/financial companies	Yes	No
Current account surplus (deficit)	8%	−1%

Solution

	Country X	Country Y
Expected inflation over next year	2.0%	3.0%
Short-term (1-month) government rate	Decrease	Increase
Expected (forward-looking) GDP growth over next year	2.0%	3.3%
New national laws have been passed that enable foreign direct investment in real estate/financial companies	Yes	No
Current account surplus (deficit)	8%	−1%

Note: The shaded cells represent the comparatively stronger measure, where an analyst could expect to see a strengthening currency based on the factor being independently reviewed.

ChatGPT

Let's analyze each economic observation independently and determine which country (Country X or Country Y) would likely see a strengthening currency based on each individual factor:

1. Expected Inflation over Next Year:

   • Lower inflation is generally positive for a currency's value.

   • Country X: 2.0% (Lower)

   • Country Y: 3.0% (Higher)

   • Expected to Strengthen: Country X

2. Short-term (1-month) Government Rate:

   • Higher interest rates can attract foreign capital, strengthening the currency.

   • Country X: Decrease

   • Country Y: Increase

   • Expected to Strengthen: Country Y

3. Expected (forward-looking) GDP Growth over Next Year:

   • Higher GDP growth expectations can lead to increased investment and a stronger currency.

   • Country X: 2.0%

   • Country Y: 3.3% (Higher)

   • Expected to Strengthen: Country Y

4. New National Laws that Enable Foreign Direct Investment in Real Estate/Financial Companies:

   • Laws that encourage foreign investment can strengthen a currency due to increased demand.

   • Country X: Yes (New laws passed)

   • Country Y: No

   • Expected to Strengthen: Country X

5. Current Account Surplus (Deficit):

   • A current account surplus indicates that a country is a net lender to the rest of the world, often leading to a stronger currency.

   • Country X: 8% (Surplus)

   • Country Y: -1% (Deficit)

   • Expected to Strengthen: Country X

Based on these observations, Country X is expected to see a strengthening currency in the cases of lower expected inflation, new laws enabling foreign investment, and a current account surplus. On the other hand, Country Y is expected to see a strengthening currency in the cases of an increase in short-term government rates and higher expected GDP growth.

Forecasting Exchange Rates

Q.

Fap is a small country whose currency is the Fip. Three years ago, the exchange rate was considered to be reflecting purchasing power parity (PPP). Since then, the country’s inflation has exceeded inflation in the other countries by about 5% per annum. The Fip exchange rate, however, remained broadly unchanged.

What would you have expected the Fip exchange rate to show if PPP prevailed?

Are Fips over or undervalued, according to PPP?

Solution

According to PPP, to offset the effect of the higher inflation in Fap, the Fip should have depreciated against the other currencies by approximately the difference between Fap inflation and that in the other countries.

According to PPP, Fip is overvalued.

ChatGPT

If Purchasing Power Parity (PPP) prevailed, the exchange rate of the Fip should have adjusted to offset the inflation differential between Fap and the other countries. Let's analyze the situation:

1. Expected Exchange Rate Adjustment under PPP:

   • Inflation in Fap has exceeded inflation in other countries by about 5% per annum for three years.

   • If PPP held true, the Fip should have depreciated by approximately 5% each year relative to the currencies of the other countries to maintain purchasing power equivalence.

   • The cumulative depreciation over three years, considering compound effect, would be more than just 15% (because each year's depreciation is on a new, lower base).

2. Actual Exchange Rate Movement:

   • The Fip exchange rate remained broadly unchanged over the three years.

3. Valuation of Fips According to PPP:

   • Given that the Fip did not depreciate to offset the higher inflation in Fap, the Fip is likely overvalued according to PPP.

   • An overvalued Fip means that goods and services in Fap are relatively more expensive compared to other countries when considering the unchanged exchange rate and higher domestic inflation.

In conclusion, if PPP prevailed, one would expect the Fip exchange rate to show a significant depreciation over the three years. However, since the Fip exchange rate remained broadly unchanged despite higher inflation in Fap, the Fip appears to be overvalued according to PPP principles.

An analyst is reviewing various asset alternatives and is presented with the following information relating to the broad equity market of Switzerland and various industries within the Swiss market that are of particular investment interest.

Expected risk premium for overall global investable market (GIM) portfolio	3.5%
Expected standard deviation for the GIM portfolio	8.5%
Expected standard deviation for Swiss Healthcare Industry equity investments	12.0%
Expected standard deviation for Swiss Watch Industry equity investments	6.0%
Expected standard deviation for Swiss Consumer Products Industry equity investments	7.5%

Assume that the Swiss market is perfectly integrated with the world markets.

Swiss Healthcare has a correlation of 0.7 with the GIM portfolio.

Swiss Watch has a correlation of 0.8 with the GIM portfolio.

Swiss Consumer Products has a correlation of 0.8 with the GIM portfolio.

Q.

Basing your answers only upon the data presented in the table above and using the international capital asset pricing model—in particular, the Singer–Terhaar approach—estimate the expected risk premium for the following:

1. Swiss Health Care Industry

2. Swiss Watch Industry

3. Swiss Consumer Products Industry

Solution

ChatGPT

The Singer-Terhaar approach to the International Capital Asset Pricing Model (ICAPM) suggests that expected risk premiums for specific industries or markets can be estimated based on their correlation with the global market, their own volatility (standard deviation), and the risk premium and volatility of the global market.

The formula for estimating the risk premium for a specific industry or market is:

$Expected Risk Premium for Specific Industry=Correlation with GIM×Standard Deviation of Specific Industry×Expected Risk Premium for GIMStandard Deviation of GIMExpected Risk Premium for Specific Industry=Correlation with GIM×Standard Deviation of Specific Industry×Standard Deviation of GIMExpected Risk Premium for GIM​$

Given the data provided, we can calculate the expected risk premiums for the Swiss Healthcare, Swiss Watch, and Swiss Consumer Products industries as follows:

1. Swiss Healthcare Industry:

   • Correlation with GIM = 0.7

   • Standard Deviation for Swiss Healthcare = 12.0%

   • Expected Risk Premium for GIM = 3.5%

   • Standard Deviation for GIM = 8.5%

2. Swiss Watch Industry:

   • Correlation with GIM = 0.8

   • Standard Deviation for Swiss Watch = 6.0%

   • Expected Risk Premium for GIM = 3.5%

   • Standard Deviation for GIM = 8.5%

3. Swiss Consumer Products Industry:

   • Correlation with GIM = 0.8

   • Standard Deviation for Swiss Consumer Products = 7.5%

   • Expected Risk Premium for GIM = 3.5%

   • Standard Deviation for GIM = 8.5%

Now let's calculate the expected risk premiums for each industry using the provided data:

Based on the Singer–Terhaar approach to the International Capital Asset Pricing Model, the estimated expected risk premiums for the specific industries are:

• Swiss Healthcare Industry: Approximately 3.46%

• Swiss Watch Industry: Approximately 1.98%

• Swiss Consumer Products Industry: Approximately 2.47% ​

An analyst is reviewing various asset alternatives and is presented with the following information relating to the broad equity market of Switzerland and various industries within the Swiss market that are of particular investment interest.

Expected risk premium for overall global investable market (GIM) portfolio	3.5%
Expected standard deviation for the GIM portfolio	8.5%
Expected standard deviation for Swiss Healthcare Industry equity investments	12.0%
Expected standard deviation for Swiss Watch Industry equity investments	6.0%
Expected standard deviation for Swiss Consumer Products Industry equity investments	7.5%

Assume that the Swiss market is perfectly integrated with the world markets.

Swiss Healthcare has a correlation of 0.7 with the GIM portfolio.

Swiss Watch has a correlation of 0.8 with the GIM portfolio.

Swiss Consumer Products has a correlation of 0.8 with the GIM portfolio.

QuestionQ.

Judge which industry is most attractive from a valuation perspective.

Solution

Based on the above analysis, the Swiss Healthcare Industry would have the highest expected return. However, that expected return reflects compensation for systematic risk. Based on the data provided we cannot conclude which industry is most attractive from a valuation standpoint.

ChatGPT

To judge which industry is most attractive from a valuation perspective based on the provided data, we need to consider both the expected risk premium (as a measure of expected return) and the risk associated with each industry (measured by standard deviation and correlation with the GIM portfolio). The attractiveness of an investment can be gauged by the reward-to-risk ratio, often estimated as the risk premium per unit of risk.

Let's calculate the reward-to-risk ratio for each industry using the expected risk premium and the standard deviation:

Reward-to-Risk Ratio = Expected Risk Premium / Standard Deviation

From the previous calculations, we have the expected risk premiums:

• Swiss Healthcare Industry: 3.46%

• Swiss Watch Industry: 1.98%

• Swiss Consumer Products Industry: 2.47%

And the standard deviations:

• Swiss Healthcare Industry: 12.0%

• Swiss Watch Industry: 6.0%

• Swiss Consumer Products Industry: 7.5%

Let's compute the reward-to-risk ratios for each industry:

Based on the reward-to-risk ratios, the attractiveness of each industry is as follows:

• Swiss Healthcare Industry: Reward-to-Risk Ratio = 0.29

• Swiss Watch Industry: Reward-to-Risk Ratio = 0.33

• Swiss Consumer Products Industry: Reward-to-Risk Ratio = 0.33

Both the Swiss Watch Industry and the Swiss Consumer Products Industry have the highest reward-to-risk ratios (0.33), indicating that they are more attractive from a valuation perspective compared to the Swiss Healthcare Industry, which has a lower ratio (0.29).

Between the Swiss Watch Industry and the Swiss Consumer Products Industry, the attractiveness is the same based on the calculated reward-to-risk ratio. However, other factors not included in the data (such as industry trends, market stability, growth potential, etc.) might influence the final investment decision. If only considering the calculated reward-to-risk ratio, the Swiss Watch and Swiss Consumer Products industries are equally the most attractive from a valuation perspective.

Forecasting Equity Return

Judith Bader is a senior analyst for a company that specializes in managing international developed and emerging markets equities. Next week, Bader must present proposed changes to client portfolios to the Investment Committee, and she is preparing a presentation to support the views underlying her recommendations.

Bader begins by analyzing portfolio risk. She decides to forecast a variance–covariance matrix (VCV) for 20 asset classes, using 10 years of monthly returns and incorporating both the sample statistics and the factor-model methods. To mitigate the impact of estimation error, Bader is considering combining the results of the two methods in an alternative target VCV matrix, using shrinkage estimation.

Bader asks her research assistant to comment on the two approaches and the benefits of applying shrinkage estimation. The assistant makes the following statements:

Statement 1	Shrinkage estimation of VCV matrices will decrease the efficiency of the estimates versus the sample VCV matrix.
Statement 2	Your proposed approach for estimating the VCV matrix will not be reliable because a sample VCV matrix is biased and inconsistent.
Statement 3	A factor-based VCV matrix approach may result in some portfolios that erroneously appear to be riskless if any asset returns can be completely determined by the common factors or some of the factors are redundant.

Bader then uses the Singer–Terhaar model and the final shrinkage-estimated VCV matrix to determine the equilibrium expected equity returns for all international asset classes by country. Three of the markets under consideration are located in Country A (developed market), Country B (emerging market), and Country C (emerging market). Bader projects that in relation to the global market, the equity market in Country A will remain highly integrated, the equity market in Country B will become more segmented, and the equity market in Country C will become more fully integrated.

Next, Bader applies the Grinold–Kroner model to estimate the expected equity returns for the various markets under consideration. For Country A, Bader assumes a very long-term corporate earnings growth rate of 4% per year (equal to the expected nominal GDP growth rate), a 2% rate of net share repurchases for Country A’s equities, and an expansion rate for P/E multiples of 0.5% per year.

In reviewing Countries B and C, Bader’s research assistant comments that emerging markets are especially risky owing to issues related to politics, competition, and accounting standards. As an example, Bader and her assistant discuss the risk implications of the following information related to Country B:

• Experiencing declining per capita income

• Expected to continue its persistent current account deficit below 2% of GDP

• Transitioning to International Financial Reporting Standards, with full convergence scheduled to be completed within two years

Bader shifts her focus to currency expectations relative to clients’ base currency and summarizes her assumptions in Exhibit 1.

Exhibit 1:

Baseline Assumptions for Currency Forecasts

	Country A	Country B	Country C
Historical current account	Persistent current account deficit of 5% of GDP	Persistent current account deficit of 2% of GDP	Persistent current account surplus of 2% of GDP
Expectation for secular trend in current account	Rising current account deficit	Narrowing current account deficit	Rising current account surplus
Long-term inflation expectation relative to global inflation	Expected to rise	Expected to keep pace	Expected to fall
Capital flows	Steady inflows	Hot money flowing out	Hot money flowing in

During a conversation about Exhibit 1, Bader and her research assistant discuss the composition of each country’s currency portfolio and the potential for triggering a crisis. Bader notes that some flows and holdings are more or less supportive of the currency, stating that investments in private equity make up the majority of Country A’s currency portfolio, investments in public equity make up the majority of Country B’s currency portfolio, and investments in public debt make up the majority of Country C’s currency portfolio.

Bader asks her research assistant to comment on the two approaches and the benefits of applying shrinkage estimation. The assistant makes the following statements:

Statement 1	Shrinkage estimation of VCV matrices will decrease the efficiency of the estimates versus the sample VCV matrix.
Statement 2	Your proposed approach for estimating the VCV matrix will not be reliable because a sample VCV matrix is biased and inconsistent.
Statement 3	A factor-based VCV matrix approach may result in some portfolios that erroneously appear to be riskless if any asset returns can be completely determined by the common factors or some of the factors are redundant.

Question

Which of the following statements made by Bader’s research assistant is correct?

1. A.Statement 1

2. B.Statement 2

3. C.Statement 3

C is correct. Statement 3 is correct. As long as none of the factors used in a factor-based VCV model are redundant and none of the asset returns are completely determined by the common factors, there will not be any portfolios that erroneously appear to be riskless. Therefore, a factor-based VCV matrix approach may result in some portfolios that erroneously appear to be riskless if any asset returns can be completely determined by the common factors or some of the factors are redundant.

A is incorrect because shrinkage estimation of VCV matrices will increase the efficiency of the estimates versus the sample VCV matrix, because its mean squared error (MSE) will in general be smaller than the MSE of the (unbiased) sample VCV matrix. Efficiency in this context means a smaller MSE.

B is incorrect because, although the proposed approach is not reliable, the reason is not that the sample VCV matrix is biased and inconsistent; on the contrary, it is unbiased and consistent. Rather, the estimate of the VCV matrix is not reliable because the number of observations is not at least 10 times the number of assets (i.e., with 10 years of monthly return data, there are only 120 observations, but the rule of thumb suggests there should be at least 200 observations for 20 asset classes).

ChatGPT

Statement 1:

• "Shrinkage estimation of VCV (Variance-Covariance) matrices will decrease the efficiency of the estimates versus the sample VCV matrix."

• This statement is incorrect. Shrinkage estimation aims to improve the estimation of the VCV matrix by combining the sample VCV matrix with a structured estimator (like an identity matrix) to address the problem of estimation error in the sample VCV, especially when the dimension of the data is high relative to the number of observations. Shrinkage estimation generally increases the efficiency and stability of the VCV estimates.

Statement 2:

• "Your proposed approach for estimating the VCV matrix will not be reliable because a sample VCV matrix is biased and inconsistent."

• This statement is also incorrect. While it's true that the sample VCV matrix can have estimation errors, especially in a high-dimensional context (more assets than observations), it doesn't mean that the approach is always unreliable. Techniques like shrinkage estimation and other regularization methods are specifically designed to address these issues and improve the reliability of the sample VCV matrix.

Statement 3:

• "A factor-based VCV matrix approach may result in some portfolios that erroneously appear to be riskless if any asset returns can be completely determined by the common factors or some of the factors are redundant."

• This statement is correct. In a factor-based VCV matrix approach, if the asset returns are perfectly explained by the common factors, or if there are redundant factors (i.e., factors that provide the same information), it may lead to an underestimation of risk. This can give the false impression that a portfolio is riskless when, in fact, it may not be.

Based on the analysis, the correct statement is:

C. Statement 3

Bader then uses the Singer–Terhaar model and the final shrinkage-estimated VCV matrix to determine the equilibrium expected equity returns for all international asset classes by country. Three of the markets under consideration are located in Country A (developed market), Country B (emerging market), and Country C (emerging market). Bader projects that in relation to the global market, the equity market in Country A will remain highly integrated, the equity market in Country B will become more segmented, and the equity market in Country C will become more fully integrated.

Q.

Based on expectations for changes in integration with the global market, all else being equal, the Singer–Terhaar model implies that Bader should shift capital from Country A to:

A. only Country B.

B. only Country C.

C. both Countries B and C.

Solution

B is correct. Bader expects the equity market in Country C (an emerging market) to become more fully integrated with the global market while Country A (a developed market) remains highly integrated. All else being equal, the Singer–Terhaar model implies that when a market becomes more globally integrated (segmented), its required return should decline (rise). As prices adjust to a lower (higher) required return, the market should deliver an even higher (lower) return than was previously expected or required by the market. Therefore, the allocation to markets that are moving toward integration should be increased. If a market is moving toward integration, its increased allocation will come at the expense of markets that are already highly integrated. This will typically entail a shift from developed markets to emerging markets.

ChatGPT

My initial analysis missed an important aspect of the Singer–Terhaar model related to market integration and its impact on expected returns:

• Increased Integration: When a market becomes more globally integrated, its risk and return characteristics start resembling those of the global market. The required return decreases as local, non-diversifiable risks diminish. Consequently, as the market adjusts to this lower required return, assets might deliver higher returns than previously expected.

• Decreased Integration/Increased Segmentation: Conversely, when a market becomes more segmented from the global market, its required return increases due to the retention of local, non-diversifiable risks. The market might deliver lower returns than previously expected as it adjusts to this higher required return.

In the context of the question:

• Country B: Expected to become more segmented. According to the model, this would typically increase the required return due to higher local risks. However, the price adjustment to a higher required return might lead to lower actual returns in the short term.

• Country C: Expected to become more integrated. This would decrease the required return as the market's risk profile aligns more closely with the global market, potentially leading to higher actual returns in the short term as prices adjust.

The key point I initially missed is the impact of changing levels of integration on the required return and how prices adjust to these changes, thereby affecting actual returns. The correct strategy, according to the Singer–Terhaar model, would be to shift capital to markets that are becoming more integrated (Country C in this case), as they are expected to offer better returns due to the adjustment of prices to a lower required return.

Hence, the correct answer is B: only Country C, as it is expected to become more fully integrated with the global market, implying an increase in allocation to benefit from the expected decrease in required return and subsequent price adjustment.

1. Integration Increases (e.g., Country C):

   • Required Return Decreases: As a market becomes more integrated with the global market, the risks specific to that market (country-specific risks) decrease. Investors then require a lower return for holding assets from that market because the perceived risk is lower.

   • Price Adjustment and Actual Returns: When the required return decreases, the prices of assets in that market tend to increase (since lower required returns make the assets more attractive). This price increase can lead to higher actual returns in the short term because the market is adjusting to a new, lower level of risk.

2. Integration Decreases/Segmentation Increases (e.g., Country B):

   • Required Return Increases: As a market becomes more segmented from the global market, the risks specific to that market increase. Investors then require a higher return for holding assets from that market to compensate for the higher perceived risk.

   • Price Adjustment and Actual Returns: When the required return increases, the prices of assets in that market tend to decrease (since higher required returns make the assets less attractive). This price decrease can lead to lower actual returns in the short term because the market is adjusting to a new, higher level of risk.

In the context of the question, Country C is becoming more integrated with the global market. According to the Singer–Terhaar model, this would lead to a decrease in the required return for assets in Country C. As the market adjusts to this new, lower level of risk, the prices of assets are likely to increase, potentially leading to higher actual returns in the short term. Therefore, it makes sense to shift capital to Country C, as it is expected to offer better returns due to the adjustment in prices following the decrease in required return.

Next, Bader applies the Grinold–Kroner model to estimate the expected equity returns for the various markets under consideration. For Country A, Bader assumes a very long-term corporate earnings growth rate of 4% per year (equal to the expected nominal GDP growth rate), a 2% rate of net share repurchases for Country A’s equities, and an expansion rate for P/E multiples of 0.5% per year.

Q.

Using the Grinold–Kroner model, which of the following assumptions for forecasting Country A’s expected equity returns is plausible for the very long run?

A.Rate of net share repurchases

B.Corporate earnings growth rate

C.Expansion rate for P/E multiples

Solution

B is correct. Country A’s long-term corporate earnings growth rate of 4% per year is equal to the expected nominal GDP growth rate of 4%, which is an economically plausible long-run assumption. The only very long-run assumptions that are consistent with economically plausible relationships are %ΔE = Nominal GDP growth, %ΔS = 0, and %ΔP/E = 0, where %ΔE is the expected nominal earnings growth rate, %ΔS is the expected percentage change in shares outstanding, and %ΔP/E is the expected percentage change in the price-to-earnings ratio.

A is incorrect because a 2% rate of net share repurchases would eventually eliminate all shares, which is not an economically plausible very long-run assumption. The only very long-run assumptions that are consistent with economically plausible relationships are %ΔE = Nominal GDP growth, %ΔS = 0, and %ΔP/E = 0, where %ΔE is the expected nominal earnings growth rate, %ΔS is the expected percentage change in shares outstanding, and %ΔP/E is the expected percentage change in the price-to-earnings ratio.

C is incorrect because Country A’s perpetually rising P/E would lead to an arbitrarily high price per currency unit of earnings per share. The only very long-run assumptions that are consistent with economically plausible relationships are %ΔE = Nominal GDP growth, %ΔS = 0, %ΔP/E = 0, where %ΔE is the expected nominal earnings growth rate, %ΔS is the expected percentage change in shares outstanding, and %ΔP/E is the expected percentage change in the price-to-earnings ratio.

ChatGPT (correct)

The Grinold–Kroner model is used to estimate the expected return on a stock or stock market based on several components. The formula for the Grinold–Kroner model is:

$E(R)=(D/P)+g+ΔS−ΔP/E+ΔY$

Where:

• $E(R)$ = Expected return
• $D/P$ = Dividend yield
• $g$ = Real growth rate of earnings per share
• $ΔS$ = Change in shares outstanding (reflecting net share repurchases or issuance)
• $ΔP/E$ = Change in the price-to-earnings ratio (reflecting changes in investor sentiment or required returns)
• $ΔY$ = Change in yield (reflecting changing inflation expectations or required real returns)

In the case of Country A, Bader assumes:

• Corporate earnings growth rate (g) of 4% per year

• Rate of net share repurchases ($ΔS$) of 2% per year
• Expansion rate for P/E multiples ($ΔP/E$) of 0.5% per year

Let's analyze the plausibility of each component for forecasting Country A’s expected equity returns in the very long run:

A. Rate of Net Share Repurchases:

• A 2% rate of net share repurchases is plausible if companies in Country A are consistently buying back more shares than they are issuing. This would increase the earnings per share and potentially the stock price. However, maintaining a 2% rate of net share repurchases in the very long run can be challenging, as it depends on corporate financial policies and market conditions.

B. Corporate Earnings Growth Rate:

• A 4% corporate earnings growth rate, equal to the expected nominal GDP growth rate, is quite plausible for the very long run. It's reasonable to assume that corporate earnings growth would be in line with the overall economic growth of the country.

C. Expansion Rate for P/E Multiples:

• An expansion rate of 0.5% per year for P/E multiples implies that investors are willing to pay progressively more for each dollar of earnings. This could be due to improved investor sentiment, lower required returns, or other factors. While possible, expecting P/E ratios to expand consistently in the very long run can be optimistic, as P/E expansion is often influenced by cyclical factors and may not persist indefinitely at a constant rate.

Based on these considerations, the most plausible assumption for forecasting Country A’s expected equity returns in the very long run is:

B. Corporate Earnings Growth Rate

This component aligns well with the expectation of earnings growth keeping pace with the country's overall economic growth, making it a reasonable and sustainable assumption in the very long term.

In reviewing Countries B and C, Bader’s research assistant comments that emerging markets are especially risky owing to issues related to politics, competition, and accounting standards. As an example, Bader and her assistant discuss the risk implications of the following information related to Country B:

• Experiencing declining per capita income

• Expected to continue its persistent current account deficit below 2% of GDP

• Transitioning to International Financial Reporting Standards, with full convergence scheduled to be completed within two years

Q.

Based only on the emerging markets discussion, developments in which of the following areas most likely signal increasing risk for Country B’s equity market?

1. A.Politics
2. B.Competitiveness
3. C.Accounting standards

Solution

A is correct. Per capita income for Country B has been falling, which is a potential source of political stress.

B is incorrect because the persistent current account deficit has been below 2% of GDP. Persistent current account deficits greater than 4% of GDP probably indicate a lack of competitiveness.

C is incorrect because Country B has been transitioning to International Financial Reporting Standards, with full convergence expected within two years, which is a positive development for better accounting standards.

ChatGPT (wrong)

Let's analyze each area in relation to the information provided about Country B:

A. Politics:

• While the provided information does not directly mention political developments, declining per capita income can sometimes be associated with political risk if it leads to social unrest or policy uncertainty. However, without explicit information about political instability or changes, it's not the most direct link to the information given.

B. Competitiveness:

• The persistent current account deficit below 2% of GDP indicates that the country is importing more than it's exporting. While not excessively large, a persistent deficit could signal issues related to the country's international competitiveness. If a country consistently spends more on foreign goods than it earns from its exports, it might suggest that its industries are struggling to compete on the global stage.

C. Accounting Standards:

• Country B is transitioning to International Financial Reporting Standards (IFRS), with full convergence scheduled to be completed within two years. This move is generally seen as a positive development, aiming to improve transparency and comparability of financial statements. It suggests an improvement, rather than an increase, in risk concerning accounting standards.

Based on the discussion of emerging markets and the specific information about Country B, the most likely signal of increasing risk for Country B’s equity market, in this case, seems to be related to B. Competitiveness. The persistent current account deficit could indicate competitiveness issues, potentially making the country's industries and, by extension, its equity market riskier. The other options, while important, do not directly align with the information provided about Country B as signals of increasing risk in this context.

(Corrected after posting solution)

• A (Politics) is indeed the correct choice. The declining per capita income in Country B is a significant indicator that can lead to political stress or instability. Economic challenges often translate into political risk, especially in emerging markets, where institutions might be less robust, and the social fabric might be more vulnerable to economic downturns.

• B (Competitiveness) is not considered the most significant risk in this context, especially given that the persistent current account deficit is below 2% of GDP, which is not excessively high and not necessarily indicative of severe competitiveness issues.

• C (Accounting Standards) is not a signal of increasing risk. In fact, the transition to International Financial Reporting Standards is a positive development, likely to improve transparency and reliability in financial reporting, which would be a positive factor for investors.

The key insight here is that while economic indicators like current account deficits and changes in accounting standards are important, the direct impact of declining per capita income on the socio-political landscape can be a more immediate and significant source of risk, especially in the context of emerging markets. Therefore, A (Politics) is the correct answer.

Me: doesn't current account deficit counted as politics, and per capital income counted as competitiveness?

ChatGPT:

Your question touches on the interconnected nature of economic indicators and their broader implications. Let's clarify the typical associations of these indicators:

1. Current Account Deficit:

   • This is primarily viewed as an economic indicator. A current account deficit means the country is importing more than it exports, which can relate to its competitiveness in international markets.

   • However, persistent and large current account deficits can also lead to political issues, especially if they result in economic policies that are unpopular or lead to dependence on foreign capital.

2. Per Capita Income:

   • This indicator is usually associated with the economic well-being of the average citizen in a country. Declining per capita income can signal worsening economic conditions, such as rising unemployment or declining wages.

   • While it's an economic indicator, declining per capita income can indeed lead to competitiveness issues if it reflects broader economic malaise. However, it's more directly and immediately connected to political risk because it can lead to social unrest, dissatisfaction with the government, and political instability.

In the context of the question, the declining per capita income was considered a direct signal of potential political stress because it can quickly translate into social unrest and political instability, especially in emerging markets where economic downturns can rapidly lead to political crises.

On the other hand, the current account deficit, while important, was below the threshold (2% of GDP) that typically indicates severe competitiveness issues or immediate political concern. Hence, it wasn't considered the primary signal of increasing risk in this scenario.

The categorization of these indicators can depend on the context and the specific economic, social, and political dynamics of a country. The solution provided is based on the immediate and direct implications of the indicators presented, with declining per capita income seen as a more direct signal of potential political stress in the context of Country B.

Exhibit 1:

Baseline Assumptions for Currency Forecasts

	Country A	Country B	Country C
Historical current account	Persistent current account deficit of 5% of GDP	Persistent current account deficit of 2% of GDP	Persistent current account surplus of 2% of GDP
Expectation for secular trend in current account	Rising current account deficit	Narrowing current account deficit	Rising current account surplus
Long-term inflation expectation relative to global inflation	Expected to rise	Expected to keep pace	Expected to fall
Capital flows	Steady inflows	Hot money flowing out	Hot money flowing in

Q.

Based on Bader’s expectations for current account secular trends as shown in Exhibit 1, Bader should reallocate capital, all else being equal, from:

A.Country A to Country C.

B.Country B to Country A.

C.Country C to Country A.

Solution

A is correct. Bader should reallocate capital from Country A, which is expected to have a secularly rising current account deficit, to Country C, which is expected to have a secularly rising current account surplus. A rising current account deficit will tend to put upward pressure on real required returns and downward pressure on asset prices, whereas a rising current account surplus (or narrowing deficit) will put downward pressure on real required returns and upward pressure on asset prices. Analysts should consider reallocation of portfolio assets from countries with secularly rising current account deficits to those with secularly rising current account surpluses (or narrowing deficits).

ChatGPT (correct)

Let's analyze the implications of the secular trends in the current accounts and other economic factors for each country:

Country A:

• Historical current account: Persistent deficit of 5% of GDP.

• Secular trend: Rising current account deficit.

• Inflation: Expected to rise relative to global inflation.

• Capital flows: Steady inflows.

Country B:

• Historical current account: Persistent deficit of 2% of GDP.

• Secular trend: Narrowing current account deficit.

• Inflation: Expected to keep pace with global inflation.

• Capital flows: Hot money flowing out.

Country C:

• Historical current account: Persistent surplus of 2% of GDP.

• Secular trend: Rising current account surplus.

• Inflation: Expected to fall relative to global inflation.

• Capital flows: Hot money flowing in.

Analysis:

• Country A is showing signs of increasing economic vulnerability with a rising current account deficit and inflation expected to rise, which can lead to currency depreciation.

• Country B shows some potential for improvement with a narrowing current account deficit, but hot money flowing out can be a sign of instability or lack of investor confidence.

• Country C appears to be in a strong position with a rising current account surplus, falling inflation expectations (relative to global inflation), and hot money flowing in, indicating strong investor confidence and potential for currency appreciation.

Conclusion: Given the expectations for current account secular trends and other economic indicators, Bader should reallocate capital from countries showing signs of economic vulnerability or instability to those showing signs of strength and stability.

Answer: A. Country A to Country C.

• Moving capital from Country A (rising current account deficit and rising inflation) to Country C (rising current account surplus, falling inflation, and hot money inflows) seems prudent based on the data. Country C's indicators suggest a strengthening economic position and potentially stronger currency, making it a more attractive investment destination compared to Country A.

During a conversation about Exhibit 1, Bader and her research assistant discuss the composition of each country’s currency portfolio and the potential for triggering a crisis. Bader notes that some flows and holdings are more or less supportive of the currency, stating that investments in private equity make up the majority of Country A’s currency portfolio, investments in public equity make up the majority of Country B’s currency portfolio, and investments in public debt make up the majority of Country C’s currency portfolio.

Q.

Based on Bader’s inflation expectations as shown in Exhibit 1, purchasing power parity implies that which of the following countries’ currencies should depreciate, all else being equal?

A.Country A

B.Country B

C.Country C

Solution

A is correct. Purchasing power parity implies that the value of Country A’s currency will decline. Inflation for Country A is expected to rise relative to global inflation. Purchasing power parity implies that the expected percentage change in Country A’s exchange rate should be equal to the difference in expected inflation rates. If Country A’s inflation is rising relative to global inflation, then the currency will be expected to depreciate.

B is incorrect because purchasing power parity implies that the value of Country B’s currency will remain stable. Inflation for Country B is expected to keep pace with global inflation. Purchasing power parity implies that the expected percentage change in Country B’s exchange rate should be equal to the difference in expected inflation rates. If Country B’s inflation is keeping pace with global inflation, then the exchange rate will be expected to stay the same, corresponding to a stable value of Country B’s currency.

C is incorrect because purchasing power parity implies that the value of Country C’s currency will rise. Inflation for Country C is expected to fall relative to global inflation. Purchasing power parity implies that the expected percentage change in Country C’s exchange rate should be equal to the difference in expected inflation rates. If Country C’s inflation is falling relative to global inflation, then the currency will be expected to appreciate.

ChatGPT (correct)

Purchasing Power Parity (PPP) implies that currencies should adjust to equalize the price of a basket of goods between countries. If a country's inflation rate is higher than that of its trading partners, its currency should depreciate to maintain PPP. Let's analyze the inflation expectations for each country as per Exhibit 1:

Country A:

• Long-term inflation expectation relative to global inflation: Expected to rise.

• Investments in private equity make up the majority of the currency portfolio.

Country B:

• Long-term inflation expectation relative to global inflation: Expected to keep pace.

• Investments in public equity make up the majority of the currency portfolio.

Country C:

• Long-term inflation expectation relative to global inflation: Expected to fall.

• Investments in public debt make up the majority of the currency portfolio.

Based on PPP and the inflation expectations:

• Country A is expected to have rising inflation relative to global inflation. According to PPP, this should lead to the depreciation of Country A's currency, as higher inflation reduces the purchasing power of the currency relative to other currencies.

• Country B is expected to keep pace with global inflation, implying that its currency's value should remain relatively stable compared to other currencies if inflation rates are similar.

• Country C is expected to have falling inflation relative to global inflation, which could lead to the appreciation of its currency, as lower inflation increases the purchasing power of the currency relative to other currencies.

Answer: A. Country A

Based on Bader’s inflation expectations and the concept of PPP, Country A’s currency should depreciate, all else being equal, due to its higher inflation rate relative to global inflation.

Me: why If a country's inflation rate is higher than that of its trading partners, its currency should depreciate to maintain PPP.ChatGPTChatGPT

ChatGPT

If a country's inflation rate is higher than that of its trading partners, its currency should depreciate to maintain Purchasing Power Parity (PPP) because of the relative changes in price levels between the two countries. Here's how it works:

1. Higher Inflation Leads to Higher Prices:

   • When a country experiences higher inflation, the prices of goods and services in that country tend to increase more rapidly compared to a country with lower inflation.

   • This means that, over time, the same amount of money buys fewer goods and services in the country with higher inflation.

2. Need for Currency Adjustment to Maintain Purchasing Power:

   • If the exchange rate remained the same, goods and services in the high-inflation country would become relatively more expensive than those in the low-inflation country.

   • For example, if $1 could buy a loaf of bread in both Country A (high inflation) and Country B (low inflation) initially, and then prices in Country A rise faster due to higher inflation, $1 would eventually buy less than a loaf of bread in Country A but still a loaf in Country B.

3. Currency Depreciation to Equalize Prices:

   • To maintain the purchasing power between the two countries (PPP), the currency of the high-inflation country (Country A) should depreciate relative to the currency of the low-inflation country (Country B).

   • This means that you would need more of Country A's currency to buy the same amount of goods and services as before, relative to Country B's currency.

   • The depreciation compensates for the higher price levels in Country A, making its exports competitively priced on the global market and ensuring that a unit of currency has a similar purchasing power in both countries.

In essence, currency depreciation in the high-inflation country is a mechanism to balance the purchasing power of currencies and ensure that trade remains fair and balanced between countries with different inflation rates. It's a natural adjustment process to ensure that goods and services have similar prices when expressed in a common currency, maintaining the principle of Purchasing Power Parity.

Q.

Based on Exhibit 1, which country’s central bank is most likely to buy domestic bonds near term to sterilize the impact of money flows on domestic liquidity?

A.Country A

B.Country B

C.Country C

Solution

B is correct. Hot money is flowing out of Country B; thus, Country B’s central bank is the most likely to sell foreign currency (thereby draining domestic liquidity) to limit/avoid depreciation of the domestic currency and buy government securities (thereby providing liquidity) to sterilize the impact on bank reserves and interest rates.

A is incorrect because Country A is not experiencing hot money flows and, therefore, would not need to sterilize the impact of money flows on domestic liquidity.

C is incorrect because hot money is flowing into Country C; thus, Country C’s central bank is most likely to sell government securities to limit the growth of bank reserves and/or maintain a target level of interest rates.

ChatGPT (wrong)

Corrected:

Thank you for providing the solution. Based on the information:

• B (Country B) is the correct answer. The outflow of hot money from Country B would likely lead to a decrease in domestic liquidity and potential depreciation of the domestic currency. To counteract this, Country B's central bank might sell foreign currency reserves to support the domestic currency. Additionally, to sterilize the impact on domestic liquidity and prevent an increase in interest rates due to tighter liquidity conditions, the central bank could buy government securities. This action would inject liquidity back into the banking system, offsetting the liquidity drain caused by the capital outflow.

• A (Country A) is incorrect as Country A is not experiencing hot money flows that would necessitate sterilization.

• C (Country C) is incorrect in this context. While hot money is flowing into Country C, increasing domestic liquidity, the most likely central bank action would be to sell government securities to absorb this excess liquidity, rather than buying them. Selling securities would help to limit the growth of bank reserves and maintain target interest rates, countering the effects of the inflows.

The key point in sterilization activities is to balance the domestic money supply and maintain control over domestic interest rates in the face of significant capital flows. In the case of Country B, the outflow of hot money creates a need for liquidity injection, hence the likelihood of the central bank buying government securities to sterilize the impact on domestic liquidity.

(wrong response initially)

Let's analyze the situation of each country based on Exhibit 1 and determine which country's central bank is most likely to buy domestic bonds near term to sterilize the impact of money flows on domestic liquidity:

Country A:

• Historical current account: Persistent deficit of 5% of GDP.

• Expectation for secular trend in current account: Rising current account deficit.

• Long-term inflation expectation relative to global inflation: Expected to rise.

• Capital flows: Steady inflows.

• Investments in private equity make up the majority of the currency portfolio.

Country B:

• Historical current account: Persistent deficit of 2% of GDP.

• Expectation for secular trend in current account: Narrowing current account deficit.

• Long-term inflation expectation relative to global inflation: Expected to keep pace.

• Capital flows: Hot money flowing out.

• Investments in public equity make up the majority of the currency portfolio.

Country C:

• Historical current account: Persistent surplus of 2% of GDP.

• Expectation for secular trend in current account: Rising current account surplus.

• Long-term inflation expectation relative to global inflation: Expected to fall.

• Capital flows: Hot money flowing in.

• Investments in public debt make up the majority of the currency portfolio.

Analysis:

• Sterilization is a monetary policy action taken by a country's central bank to counteract unwanted fluctuations in money supply caused by foreign exchange operations. It typically involves the central bank engaging in open market operations, like buying or selling domestic bonds, to offset the impact of foreign capital inflows or outflows on domestic liquidity.

• Country A is experiencing steady capital inflows, but also a rising current account deficit and expected inflation rise. While it may need to manage liquidity, the steady nature of inflows and the potential need to address inflation might not prompt immediate sterilization.

• Country B is experiencing hot money flowing out, which can lead to a decrease in domestic liquidity. The central bank might intervene to stabilize the currency and liquidity levels, but the primary focus might be on managing the currency's value and addressing the capital outflow, rather than sterilizing the outflow per se.

• Country C is experiencing hot money flowing in, leading to an increase in domestic liquidity. This situation often prompts central banks to sterilize the inflows to maintain control over the money supply and prevent excess liquidity from leading to inflation. The central bank may buy domestic bonds to absorb the excess liquidity and stabilize the money supply.

Conclusion: C. Country C

Based on the information in Exhibit 1, Country C's central bank is most likely to buy domestic bonds near term to sterilize the impact of hot money inflows on domestic liquidity, thereby preventing excess liquidity from potentially leading to inflation.

During a conversation about Exhibit 1, Bader and her research assistant discuss the composition of each country’s currency portfolio and the potential for triggering a crisis. Bader notes that some flows and holdings are more or less supportive of the currency, stating that investments in private equity make up the majority of Country A’s currency portfolio, investments in public equity make up the majority of Country B’s currency portfolio, and investments in public debt make up the majority of Country C’s currency portfolio.

Q.

Based on the composition of each country’s currency portfolio, which country is most vulnerable to a potential crisis?

A.Country A

B.Country B

C.Country C

Solution

C is correct. Public debt makes up the majority of Country C’s currency portfolio, which is the least supportive flow (or holding) to a currency. Public debt is less supportive because it has to be serviced and must be either repaid or refinanced, potentially triggering a crisis. Some types of flows and holdings are considered to be more or less supportive of the currency. Investments in private equity represent long-term capital committed to the market and are most supportive of the currency. Public equity would likely be considered the next most supportive of the currency. Debt investments are the least supportive of the currency.

ChatGPT (wrong)

The composition of a country's currency portfolio can significantly influence its vulnerability to a potential crisis. Different types of investments have different levels of risk and liquidity, which can affect the stability of the currency and the broader financial system in times of stress. Let's analyze each country:

Country A:

• Investments in private equity make up the majority of the currency portfolio.

• Private equity investments are typically illiquid and have a longer investment horizon. They can be highly profitable but also carry significant risk, especially in times of economic downturn or market stress. The illiquidity can be a major issue during a crisis, as selling these assets quickly to raise cash can be difficult and might lead to substantial losses.

Country B:

• Investments in public equity (stock market) make up the majority of the currency portfolio.

• Public equities are more liquid than private equity but can be highly volatile. A significant portion of the currency portfolio in public equities means that the country's financial stability can be closely tied to the performance of the stock market, which can fluctuate widely based on economic conditions, investor sentiment, and other factors.

Country C:

• Investments in public debt (government bonds) make up the majority of the currency portfolio.

• Public debt is typically considered a safer investment compared to equities, as it is generally less volatile and offers fixed interest payments. However, a heavy concentration in public debt could be a concern if the country's fiscal health deteriorates or if there's a rise in global interest rates, which can reduce the value of existing bonds.

Conclusion:

• Country A seems the most vulnerable to a potential crisis due to the illiquidity and high risk associated with a currency portfolio heavily weighted in private equity. In times of crisis, the inability to quickly liquidate these assets without incurring significant losses can pose a serious financial risk.

• Country B also faces vulnerability due to the volatility of public equity markets, but the liquidity of these assets is generally better than that of private equity.

• Country C appears to be the least vulnerable among the three, as investments in public debt are generally considered safer and less volatile, although not entirely without risk.

Based on the composition of each country's currency portfolio, the answer is:

A. Country A

(After sharing solution)

Thank you for the clarification. Based on the composition of the currency portfolios and the nature of the investments:

• C (Country C) is correct. The majority of Country C's currency portfolio being in public debt makes it the most vulnerable to a potential crisis. Public debt investments, while generally considered safer in terms of volatility compared to equities, have to be serviced (interest payments) and eventually repaid or refinanced. In a scenario where the country faces economic challenges or there are significant shifts in global interest rates, servicing and refinancing the debt can become burdensome, potentially triggering a financial crisis. The need to constantly manage debt obligations can put significant pressure on a country's currency, especially if the market perceives a risk of default or restructuring.

• Country A, with investments predominantly in private equity, is considered less vulnerable in this context because private equity represents long-term capital committed to the market, providing more stability and support to the currency.

• Country B, with investments predominantly in public equity, is also considered less vulnerable compared to Country C, as public equity is generally more supportive of the currency than public debt, despite its volatility.

The key insight is that while private equity and public equity investments can provide support to the currency due to their nature of representing equity stakes in companies, public debt, especially if it makes up a large portion of the currency portfolio, can be less supportive and more vulnerable to crisis conditions due to the constant need for debt service and refinancing. Hence, Country C, with a majority in public debt investments, is considered the most vulnerable to a potential crisis.

An investor is considering adding three new securities to her internationally focused fixed income portfolio. She considers the following non-callable securities:

• 1-year government bond

• 10-year government bond

• 10-year BBB rated corporate bond

She plans to invest equally in all three securities being analyzed or will invest in none of them at this time. She will only make the added investment provided that the expected spread/premium of the equally weighted investment is at least 1.5 percent (150bp) over the 1-year government bond. She has gathered the following information:

Risk free interest rate (1-year, incorporating 0.6% inflation expectation)	1.0%
Term premium (10-year vs. 1-year government bond)	1%
10-year BBB credit premium (over 10-year government bond)	75bp
Estimated liquidity premium on 10-year corporate bonds	55bp

Using only the information given, address the following problems using the risk premium approach:

QuestionQ.

Calculate the expected return that an equal-weighted investment in the three securities could provide.

Solution

Solution

	Risk free interest rate (nominal) (%)	+	Premiums (%)	=	Expected annual fixed-income return (%)
1-year government bond	1	+	0	=	1
10-year government bond	1	+	1	=	2
10-year corporate bond	1	+	1 + 0.75 + 0.55	=	3.3

Estimate of the expected return of an equal-weighted investment in the three securities: (1% + 2% + 3.3%)/3 = 2.1%.

ChatGPT (Correct)

https://chat.openai.com/c/109ee777-8dd1-4178-a477-6217174791a6

To calculate the expected return of an equal-weighted investment in the three securities, we'll break down the return of each security based on the given information and then average them.

1. 1-year government bond:

   • Risk-free rate: 1.0%

   • No additional premiums are applicable.

2. 10-year government bond:

   • Risk-free rate: 1.0%

   • Term premium (for the additional 9 years): 1.0%

3. 10-year BBB rated corporate bond:

   • Risk-free rate: 1.0%

   • Term premium (for the additional 9 years): 1.0%

   • Credit premium (for BBB rating over government bond): 0.75% (75bp)

   • Liquidity premium: 0.55% (55bp)

Now, let's calculate the yield for each bond:

1. 1-year government bond yield:

   • Yield = Risk-free rate = 1.0%

2. 10-year government bond yield:

   • Yield = Risk-free rate + Term premium = 1.0% + 1.0% = 2.0%

3. 10-year BBB rated corporate bond yield:

   • Yield = Risk-free rate + Term premium + Credit premium + Liquidity premium

   • Yield = 1.0% + 1.0% + 0.75% + 0.55% = 3.3%

Finally, we'll calculate the expected return of an equal-weighted investment in these three securities:

Now, let's compute the exact value:

The expected return of an equal-weighted investment in the three securities would be 2.1%. ​

Q.

Calculate the expected total risk premium of the three securities and determine the investor’s probable course of action.

Solution

The average spread (over 1-year government bond) at issue is [0 + 1 + (1 + 0.75 + 0.55)] = 3.3%/3 = 1.1%.

As the 1.1% is less than 1.5%, the investor will not make the investment.

ChatGPT (Correct)

To calculate the expected total risk premium of the three securities, we'll sum up the individual premiums for each bond over the risk-free rate (1-year government bond yield). Then, we'll determine if the investor should proceed with the investment based on her criterion (the expected spread/premium of the equally weighted investment must be at least 1.5 percent or 150bp over the 1-year government bond).

Let's break down the premiums for each security:

1. 1-year government bond:

   • No premium as it's the risk-free rate.

2. 10-year government bond:

   • Term premium: 1.0%

3. 10-year BBB rated corporate bond:

   • Term premium: 1.0%

   • Credit premium: 0.75%

   • Liquidity premium: 0.55%

Now, calculate the total risk premium for each bond, and then compute the average to determine the expected total risk premium for the equally weighted portfolio.

1. Total risk premium for 1-year government bond:

   • 0.0% (it's the risk-free security, so no premium)

2. Total risk premium for 10-year government bond:

   • Term premium only: 1.0%

3. Total risk premium for 10-year BBB rated corporate bond:

   • Sum of Term, Credit, and Liquidity premiums: 1.0% + 0.75% + 0.55% = 2.3%

Now, calculate the expected total risk premium of the portfolio and then determine the investor's probable course of action based on the 1.5% criterion:

After calculating the value, we'll compare it against the investor's minimum requirement of 1.5% to determine her course of action. If the expected total risk premium is at least 1.5%, she will proceed with the investment; otherwise, she won't. Let's compute this:

The expected total risk premium of the equally weighted investment in the three securities is approximately 1.10%.

Given that the investor's requirement is that the expected spread/premium of the investment must be at least 1.5% (150bp) over the 1-year government bond, and the calculated risk premium (1.10%) does not meet this threshold, the investor would likely decide not to proceed with the investment at this time.

Richard Martin is chief investment officer for the Trunch Foundation (the foundation), which has a large, globally diversified investment portfolio. Martin meets with the foundation’s fixed-income and real estate portfolio managers to review expected return forecasts and potential investments, as well as to consider short-term modifications to asset weights within the total fund strategic asset allocation.

Martin asks the real estate portfolio manager to discuss the performance characteristics of real estate. The real estate portfolio manager makes the following statements:

Statement 1	Adding traded REIT securities to an equity portfolio should substantially improve the portfolio’s diversification over the next year.
Statement 2	Traded REIT securities are more highly correlated with direct real estate and less highly correlated with equities over multi-year horizons.

Martin looks over the long-run valuation metrics the manager is using for commercial real estate, shown in Exhibit 1.

Exhibit 1:

Commercial Real Estate Valuation Metrics

Cap Rate	GDP Growth Rate
4.70%	4.60%

The real estate team uses an in-house model for private real estate to estimate the true volatility of returns over time. The model assumes that the current observed return equals the weighted average of the current true return and the previous observed return. Because the true return is not observable, the model assumes a relationship between true returns and observable REIT index returns; therefore, it uses REIT index returns as proxies for both the unobservable current true return and the previous observed return.

Martin asks the fixed-income portfolio manager to review the foundation’s bond portfolios. The existing aggregate bond portfolio is broadly diversified in domestic and international developed markets. The first segment of the portfolio to be reviewed is the domestic sovereign portfolio. The bond manager notes that there is a market consensus that the domestic yield curve will likely experience a single 20 bp increase in the near term as a result of monetary tightening and then remain relatively flat and stable for the next three years. Martin then reviews duration and yield measures for the short-term domestic sovereign bond portfolio in Exhibit 2.

Exhibit 2:

Short-Term Domestic Sovereign Bond Portfolio

Macaulay Duration	Modified Duration	Yield to Maturity
3.00	2.94	2.00%

The discussion turns to the international developed fixed-income market. The foundation invested in bonds issued by Country XYZ, a foreign developed country. XYZ’s sovereign yield curve is currently upward sloping, and the yield spread between 2-year and 10-year XYZ bonds is 100 bps.

The fixed-income portfolio manager tells Martin that he is interested in a domestic market corporate bond issued by Zeus Manufacturing Corporation (ZMC). ZMC has just been downgraded two steps by a major credit rating agency. In addition to expected monetary actions that will raise short-term rates, the yield spread between three-year sovereign bonds and the next highest-quality government agency bond widened by 10 bps.

Although the foundation’s fixed-income portfolios have focused primarily on developed markets, the portfolio manager presents data in Exhibit 3 on two emerging markets for Martin to consider. Both economies increased exports of their mineral resources over the last decade.

Exhibit 3:

Emerging Market Data

Factor	Emerging Republic A	Emerging Republic B
Fiscal deficit/GDP	6.50%	8.20%
Debt/GDP	90.10%	104.20%
Current account deficit	5.20% of GDP	7.10% of GDP
Foreign exchange reserves	90.30% of short-term debt	70.10% of short-term debt

The fixed-income portfolio manager also presents information on a new investment opportunity in an international developed market. The team is considering the bonds of Xdelp, a large energy exploration and production company. Both the domestic and international markets are experiencing synchronized growth in GDP midway between the trough and the peak of the business cycle. The foreign country’s government has displayed a disciplined approach to maintaining stable monetary and fiscal policies and has experienced a rising current account surplus and an appreciating currency. It is expected that with the improvements in free cash flow and earnings, the credit rating of the Xdelp bonds will be upgraded. Martin refers to the foundation’s asset allocation policy in Exhibit 4 before making any changes to either the fixed-income or real estate portfolios.

Exhibit 4:

Trunch Foundation Strategic Asset Allocation—Select Data

Asset Class	Minimum Weight	Maximum Weight	Actual Weight
Fixed income—Domestic	40.00%	80.00%	43.22%
Fixed income—International	5.00%	10.00%	6.17%
Fixed income—Emerging markets	0.00%	2.00%	0.00%
Alternatives—Real estate	2.00%	6.00%	3.34%

Martin asks the real estate portfolio manager to discuss the performance characteristics of real estate. The real estate portfolio manager makes the following statements:

Statement 1	Adding traded REIT securities to an equity portfolio should substantially improve the portfolio’s diversification over the next year.
Statement 2	Traded REIT securities are more highly correlated with direct real estate and less highly correlated with equities over multi-year horizons.

QuestionQ.

Which of the real estate portfolio manager’s statements is correct?

1. A.Only Statement 1
2. B.Only Statement 2
3. C.Both Statement 1 and Statement 2

Solution

B is correct. Statement 2 is correct because traded REIT securities are more highly correlated with direct real estate and less highly correlated with equities over multi-year horizons. Thus, although REITs tend to act like stocks in the short run, they act like real estate in the longer run.

A and C are incorrect because Statement 1 is not correct. Traded REIT securities have relatively high correlations with equity securities over short time horizons, such as one year. The higher correlations suggest that traded REIT securities will not act as a good diversifier for an equity portfolio over a one-year period.

ChatGPT (Correct)

Let's analyze both statements in the context of real estate investment trusts (REITs) and their correlation with other asset classes:

Statement 1: "Adding traded REIT securities to an equity portfolio should substantially improve the portfolio’s diversification over the next year."

• REITs are indeed a different asset class compared to traditional equities. They represent investment in real estate and may provide diversification benefits due to their different market drivers. However, the statement is somewhat absolute in claiming substantial improvement in diversification over the next year. While REITs can offer diversification, the extent of this diversification can vary based on market conditions, the specific equity portfolio in question, and the types of REITs added. It's important to note that the correlation between REITs and equities can fluctuate over time, and there might be periods where REITs move more in tandem with the equity market.

Statement 2: "Traded REIT securities are more highly correlated with direct real estate and less highly correlated with equities over multi-year horizons."

• This statement is generally accurate. REITs, being a representation of real estate investment, tend to show a higher correlation with the direct real estate market. Although they are traded on stock exchanges and subject to some of the same market forces as equities, REITs' primary underlying value is driven by real estate markets. Over longer periods, this characteristic tends to make them behave more like the real estate market than like the broader equity market. However, it's important to recognize that traded REITs, due to their liquidity and market presence, can still show a notable correlation with the broader equity market, especially in the short term or during market events where liquidity and market sentiment drive asset prices across the board.

In summary, Statement 2 is generally correct, recognizing the inherent characteristics of REITs and their correlation with direct real estate and equities over multi-year horizons. Statement 1 has a grain of truth regarding diversification but might be overly optimistic or absolute without considering the nuances of market conditions and the specific composition of the equity portfolio in question. Therefore, the more accurate statement here is:

Only Statement 2.

Martin looks over the long-run valuation metrics the manager is using for commercial real estate, shown in Exhibit 1.

Exhibit 1:

Commercial Real Estate Valuation Metrics

Cap Rate	GDP Growth Rate
4.70%	4.60%

Q.

Based only on Exhibit 1, the long-run expected return for commercial real estate:

1. A.is approximately double the cap rate.
2. B.incorporates a cap rate greater than the discount rate.
3. C.needs to include the cap rate’s anticipated rate of change.

Solution

A is correct. An estimate of the long-run expected or required return for commercial real estate equals the sum of the capitalization rate (cap rate) plus the growth rate (constant) of net operating income (NOI). An approximation of the steady-state NOI growth rate for commercial real estate is equal to the growth rate in GDP. Thus, from Equation 7 and the information provided in Exhibit 1, E(Rre) = Cap rate + NOI growth rate = 4.70% + 4.60% = 9.30%, which is approximately double the cap rate.

B is incorrect because the discount rate (expected or required return) equals the sum of the cap rate and the NOI growth rate. Based on the information in Exhibit 1, the 4.70% cap rate is less than (not greater than) the 9.30% discount rate.

C is incorrect because the discount rate over finite horizons (not long-run horizons) needs to include the anticipated rate of change in the cap rate. For long-run expected return calculations, the anticipated rate of change in the cap rate is not included.

ChatGPT (Wrong)

Let's break down the elements in Exhibit 1 and their implications for long-run expected returns in commercial real estate:

• Cap Rate: This is a measure used to estimate the investor's potential return on a real estate investment, calculated as the Net Operating Income (NOI) divided by the property asset value or sale price. A cap rate of 4.70% implies that the investor expects a 4.70% return on the property, assuming the property is purchased in cash without financing.

• GDP Growth Rate: The GDP growth rate of 4.60% is an indicator of the overall economic growth, which can impact the real estate market by influencing factors like rental income growth, property demand, and valuation changes.

Now, let's analyze each statement:

A. "is approximately double the cap rate."

• This statement seems to suggest that the expected return is around 9.4% (double the cap rate of 4.70%), which doesn't have a direct logical or empirical basis in the data provided. The cap rate alone does not imply that the expected return would be double its value.

B. "incorporates a cap rate greater than the discount rate."

• This statement implies that the cap rate (4.70%) is being compared to a discount rate (not provided in the exhibit). Generally, in valuation, if the cap rate is greater than the discount rate, it indicates a potentially higher return. However, without knowing the actual discount rate or having it explicitly mentioned in the exhibit, this statement is speculative and not directly supported by the information provided.

C. "needs to include the cap rate’s anticipated rate of change."

• This statement recognizes that the cap rate is not the only factor in determining the long-run expected return on commercial real estate. The long-run return would also be influenced by the growth or change in the net operating income (which could be influenced by economic factors like the GDP growth rate), as well as any changes in the cap rate itself over time (due to changes in market conditions, interest rates, etc.). This approach aligns with a more comprehensive view of real estate valuation, considering both current yield (cap rate) and the potential for capital appreciation or depreciation (change in property value and cap rate).

Based on the information provided in Exhibit 1 and the understanding of how these factors play into real estate valuation, option C ("needs to include the cap rate’s anticipated rate of change") seems to be the most reasonable statement. It acknowledges the need to consider more than just the current cap rate for estimating long-run expected returns, incorporating the dynamics of the real estate market and economic factors.

Question 5 of 13

Review Answer On Off30.8% complete

Richard Martin is chief investment officer for the Trunch Foundation (the foundation), which has a large, globally diversified investment portfolio. Martin meets with the foundation’s fixed-income and real estate portfolio managers to review expected return forecasts and potential investments, as well as to consider short-term modifications to asset weights within the total fund strategic asset allocation.

Martin asks the real estate portfolio manager to discuss the performance characteristics of real estate. The real estate portfolio manager makes the following statements:

Statement 1	Adding traded REIT securities to an equity portfolio should substantially improve the portfolio’s diversification over the next year.
Statement 2	Traded REIT securities are more highly correlated with direct real estate and less highly correlated with equities over multi-year horizons.

Martin looks over the long-run valuation metrics the manager is using for commercial real estate, shown in Exhibit 1.

Exhibit 1:

Commercial Real Estate Valuation Metrics

Cap Rate	GDP Growth Rate
4.70%	4.60%

The real estate team uses an in-house model for private real estate to estimate the true volatility of returns over time. The model assumes that the current observed return equals the weighted average of the current true return and the previous observed return. Because the true return is not observable, the model assumes a relationship between true returns and observable REIT index returns; therefore, it uses REIT index returns as proxies for both the unobservable current true return and the previous observed return.

Q.

Based on the private real estate model developed to estimate return volatility, the true variance is most likely:

1. A.lower than the variance of the observed data.
2. B.approximately equal to the variance of the observed data.
3. C.greater than the variance of the observed data.

Solution

C is correct. The in-house model assumes that the current observed return equals the weighted average of the current true return and the previous observed return. The model uses REIT index returns as proxies for the returns in the model. The smoothed nature of most published (observed) real estate returns is a major contributor to the appearance of low correlation with financial assets. This smoothing dampens the volatility of the observed data and distorts correlations with other assets. Thus, the raw observable data tend to understate the risk and overstate the diversification benefits of these asset classes. It is generally accepted that the true variance of real estate returns is greater than the variance of the observed data.

ChatGPT (Incorrect)

The model described uses an in-house approach to estimate the true volatility of private real estate returns by blending current and past observed returns and aligning them with REIT index returns. The key is that the current observed return is a weighted average of the current true return (which is not directly observable) and the previous observed return, and REIT index returns are used as proxies for these unobservable true returns.

Given the nature of this smoothing technique (taking a weighted average of the current and past returns), the model tends to dampen the volatility of the observed data. This happens because when returns are averaged over time, extreme values (both high and low) are mitigated, leading to a series of data that exhibits less fluctuation than the actual observed data.

Here's how each statement holds up:

A. "lower than the variance of the observed data."

• This option is consistent with the effect of the smoothing technique described. By averaging returns over time, the model likely underestimates the true variance or volatility of returns. The model's approach to smoothing can buffer the effect of short-term fluctuations, leading to an estimation of volatility that is lower than what would be observed in the actual, more volatile data.

B. "approximately equal to the variance of the observed data."

• This would be the case if the model accurately captured the true variance of the returns without any smoothing or other modifications. However, given the description of the model, it's specifically designed to use a weighted average approach, which inherently alters the variance from what is purely observed.

C. "greater than the variance of the observed data."

• This outcome is unlikely given the model's methodology. Averaging past and current returns typically reduces observed variance rather than increases it.

Given the model's approach to smoothing the data by averaging current and past returns, the most likely scenario is that the true variance is underestimated by the model. Therefore, the correct answer is:

A. "lower than the variance of the observed data."

Martin asks the fixed-income portfolio manager to review the foundation’s bond portfolios. The existing aggregate bond portfolio is broadly diversified in domestic and international developed markets. The first segment of the portfolio to be reviewed is the domestic sovereign portfolio. The bond manager notes that there is a market consensus that the domestic yield curve will likely experience a single 20 bp increase in the near term as a result of monetary tightening and then remain relatively flat and stable for the next three years. Martin then reviews duration and yield measures for the short-term domestic sovereign bond portfolio in Exhibit 2.

Exhibit 2:

Short-Term Domestic Sovereign Bond Portfolio

Macaulay Duration	Modified Duration	Yield to Maturity
3.00	2.94	2.00%

Q.

Based on Exhibit 2 and the anticipated effects of the monetary policy change, the expected annual return over a three-year investment horizon will most likely be:

1. A.lower than 2.00%.
2. B.approximately equal to 2.00%.
3. C.greater than 2.00%.

Solution

B is correct. If the investment horizon equals the (Macaulay) duration of the portfolio, the capital loss created by the increase in yields and the reinvestment effects (gains) will roughly offset, leaving the realized return approximately equal to the original yield to maturity. This relationship is exact if (a) the yield curve is flat and (b) the change in rates occurs immediately in a single step. In practice, the relationship is only an approximation. In the case of the domestic sovereign yield curve, the 20 bp increase in rates will likely be offset by the higher reinvestment rate, creating an annual return approximately equal to 2.00%.

ChatGPT (Incorrect)

To determine the expected annual return over a three-year investment horizon for the short-term domestic sovereign bond portfolio based on the anticipated effects of the monetary policy change, we need to consider the information provided:

1. The bond portfolio's yield to maturity (YTM) is 2.00%.

2. The market consensus anticipates a single 20 basis point (bp) increase in the near term due to monetary tightening.

3. The portfolio's modified duration is 2.94.

The expected impact of interest rate changes on a bond's price can be estimated using the bond's modified duration. Modified duration provides an estimate of the percentage change in a bond's price for a 1% change in yield. Here, the anticipated change in yield is 20 basis points, or 0.20%.

The formula to estimate the price change of a bond given a yield change is:

$ΔP/P=−Dmod×ΔP/P=−Dmod​×ΔY$

Where:

• $ΔP/P$ is the percentage change in the bond's price,
• $modD​$ is the modified duration of the bond,
• is the change in yield (in decimal form).

Let's calculate the expected percentage change in the bond's price given the 20 bp increase in interest rates.

$ΔP/P=−2.94×0.0020ΔP/P=−2.94×0.0020$

After calculating this, we can discuss the impact on the bond's expected annual return over the three-year horizon.

The expected percentage change in the bond's price due to a 20 basis point increase in yield is approximately -0.588%. This indicates that the bond's price is expected to decrease by this percentage as a result of the anticipated monetary policy change.

Given that the yield to maturity (YTM) of the portfolio is 2.00%, and considering the price decrease due to the anticipated increase in interest rates, the total return of the bond over the next year would be the sum of the yield to maturity and the price change. However, since the interest rate change is expected to happen once in the near term and then remain stable, the initial negative price impact would be somewhat offset by the bond's YTM over the three-year horizon. Yet, this price decrease at the onset needs to be recovered through the bond's coupon payments and the reinvestment of these coupons at the new higher rates over the remaining investment period.

Considering the relatively flat and stable interest rate environment expected after the initial increase, and without specific calculations to account for the reinvestment of coupons at potentially higher rates following the rate hike, the most straightforward assessment would be that the expected annual return would likely be slightly lower than the initial YTM of 2.00%, primarily due to the immediate negative price impact not being fully offset over the three-year horizon. This is because the initial loss from the price decline due to the rate increase would detract from the overall return, even though the YTM suggests an annual return of 2.00% if rates had remained unchanged.

Therefore, the expected annual return over a three-year investment horizon will most likely be lower than 2.00% (Option A), mainly due to the immediate impact of the anticipated rate increase. ​

https://chat.openai.com/c/23608fec-d706-4d4d-8adb-69830ddfe815

ChatGPT (After corrected, and MacD & investment horizon explanation)

Given the explanation that if the investment horizon equals the Macaulay duration of the portfolio, the capital loss due to an increase in yields and the reinvestment gains will roughly offset, leading to a realized return approximately equal to the original yield to maturity, the correct answer is indeed B. approximately equal to 2.00%.

This understanding relies on the principle that the Macaulay duration represents the weighted average time until a bond's cash flows are repaid and acts as a measure of the bond's sensitivity to interest rate changes. In this scenario, the Macaulay duration is 3.00 years, which matches the three-year investment horizon mentioned. Under these conditions, the initial capital loss from the yield increase is expected to be counterbalanced by the gains from reinvesting at higher rates, assuming the yield change happens immediately and in a single step.

Although in real-world situations, this relationship serves more as an approximation due to yield curve shapes and the timing of interest rate changes, the concept holds that for an investment horizon matching the Macaulay duration, the realized return should approximate the original yield to maturity, given a flat yield curve and an immediate rate change. Therefore, despite the initial decrease in bond prices due to the anticipated 20 basis point increase in yields, the overall expected annual return over the investment period is anticipated to be roughly equal to the bond portfolio's initial yield to maturity of 2.00%, accounting for the higher reinvestment rate following the rate increase.

If the investment horizon does not match the Macaulay duration of the bond portfolio, the relationship between interest rate changes, capital gains or losses, and reinvestment rates affecting the realized return will differ. The impact of interest rate changes on a bond portfolio's return is closely tied to the concept of duration:

1. When the Investment Horizon is Shorter than the Macaulay Duration: If the investment horizon is shorter than the bond's Macaulay duration, the investor is more exposed to price volatility and less able to benefit from reinvestment at potentially higher rates. In this scenario, a rise in interest rates would likely lead to a capital loss that is not fully offset by the higher reinvestment rates for the shorter period, potentially resulting in a realized return that is lower than the original yield to maturity.

2. When the Investment Horizon is Longer than the Macaulay Duration: If the investment horizon is longer than the Macaulay duration, the initial capital loss from a rise in interest rates can be more than offset by the gains from reinvesting the bond's coupons (and possibly the principal) at higher rates over the longer period. This situation could lead to a realized return that is higher than the initial yield to maturity, as the investor benefits more from the compounding of these reinvested earnings at the new, higher interest rates.

The exact impact also depends on the shape of the yield curve and the timing of the interest rate changes. A steeper yield curve or a gradual change in interest rates over time might affect the realized return differently, compared to a flat yield curve or an immediate, one-time adjustment in rates.

In summary, the alignment of the investment horizon with the bond portfolio's Macaulay duration is crucial for predicting the impact of interest rate changes on realized returns. Deviations from this alignment can lead to realized returns that are either higher or lower than the original yield to maturity, depending on whether the investment horizon is longer or shorter than the portfolio's duration and on the dynamics of interest rate movements and reinvestment rates.

In my own words

if interests rise

• MacD == investment horizon - price drop offsets reinvestment

• MacD < investment horizon - price drop lower than reinvestment, more return

• macD > investment horizon - price drop higher than reinvestment, less return

The discussion turns to the international developed fixed-income market. The foundation invested in bonds issued by Country XYZ, a foreign developed country. XYZ’s sovereign yield curve is currently upward sloping, and the yield spread between 2-year and 10-year XYZ bonds is 100 bps.

Q.

Based on the building block approach to fixed-income returns, the dominant source of the yield spread for Country XYZ is most likely the:

1. A.term premium.
2. B.credit premium.
3. C.liquidity premium.

Solution

A is correct. From the building block approach to fixed-income returns, the required return for fixed-income asset classes has four components: the one-period default-free rate, the term premium, the credit premium, and the liquidity premium. Since sovereign bonds are considered the highest-quality bonds, they likely do not have a significant credit premium nor are they likely to have a significant premium for illiquidity. The slope of the yield curve is useful information on which to base forecasts of the term premium. Therefore, the dominant source of the yield spread is most likely the term premium for XYZ’s sovereign bond.

ChatGPT (correct) - interestingly I dunno where to refer for this answer, then...

https://chat.openai.com/c/0d262ae7-548a-4c22-9544-7b709bcb945e

Based on the information provided about Country XYZ, where the sovereign yield curve is currently upward sloping and the yield spread between 2-year and 10-year XYZ bonds is 100 basis points (bps), the dominant source of the yield spread for Country XYZ is most likely the A. term premium.

The term premium refers to the extra yield that investors require to hold longer-maturity bonds instead of shorter-term bonds. This premium compensates investors for the additional risks associated with the longer time horizon, such as interest rate risk and the uncertainty of economic conditions over a longer period. The fact that the yield curve is upward sloping—meaning that longer-term bonds have higher yields than shorter-term bonds—is indicative of a positive term premium. This is because investors demand higher returns for locking in their money for a longer period due to the greater risk of interest rate changes over time.

In contrast, a credit premium compensates investors for the risk of default, which is more relevant when comparing bonds of different credit qualities rather than the same issuer's bonds across different maturities. A liquidity premium, on the other hand, compensates investors for holding securities that are less easily sold without a significant change in price. The scenario described does not provide specific details that would suggest the yield spread is primarily due to credit risk differences or liquidity concerns within the same country's sovereign bonds.

Therefore, the upward sloping yield curve and the yield spread between 2-year and 10-year bonds being highlighted without mention of differing credit qualities or liquidity issues suggest that the term premium is the most likely dominant source of the yield spread for Country XYZ.

The relevant information to this question is specifically related to the characteristics of Country XYZ's bond market as provided in the scenario:

• "The discussion turns to the international developed fixed-income market. The foundation invested in bonds issued by Country XYZ, a foreign developed country. XYZ’s sovereign yield curve is currently upward sloping, and the yield spread between 2-year and 10-year XYZ bonds is 100 bps."

This part of the text directly relates to the question regarding the dominant source of the yield spread for Country XYZ, highlighting the upward sloping nature of the yield curve and the specific yield spread between shorter-term (2-year) and longer-term (10-year) bonds. The mention of an "upward sloping" yield curve and the specific spread indicates that the term premium is a critical factor, as it reflects the extra yield that investors demand for holding longer-term debt securities due to the risks associated with longer durations, such as interest rate risk.

Let me explain why this specific information is key to determining that the term premium is the most likely source:

1. Yield Curve Description: The text states that Country XYZ's sovereign yield curve is "upward sloping." An upward-sloping yield curve is a typical market phenomenon where longer-term debt instruments have a higher yield compared to shorter-term ones. This shape of the yield curve is often interpreted as normal because it reflects the expectation of investors that they should receive higher yields for taking on the additional risk of lending money over a longer period. This additional risk includes the uncertainty about future interest rates, inflation, and the overall economic outlook over the time horizon of the bond.

2. Yield Spread Information: The specific detail that the yield spread between 2-year and 10-year bonds in Country XYZ is 100 basis points (1%) further supports the significance of the term premium. The yield spread is the difference in yields between two bonds, which, in this context, is determined by their differing maturities. A 100 bps spread indicates a significant difference in yields based on the maturity length, which is a classic indication of a term premium at work. The term premium compensates investors for the risks associated with the longer duration of the 10-year bond compared to the 2-year bond.

The term premium is relevant here because it directly addresses the risk and return expectations associated with the time value of money and interest rate risks over different maturities. In contrast, a credit premium would be relevant if we were comparing bonds of different credit qualities, and a liquidity premium would be discussed if there were significant differences in the ease of buying or selling the bonds without affecting their price. Since the information provided centers on the yield differences between bonds of different maturities rather than their credit quality or liquidity, it points to the term premium as the dominant source of the yield spread in Country XYZ.

Comparing A, B, C

To clarify why the dominant source of the yield spread for Country XYZ is most likely not the credit premium or the liquidity premium, let's examine what each of these terms means and how they relate to the information provided about Country XYZ:

B. Credit Premium

• Definition: The credit premium (or credit spread) compensates investors for the issuer's default risk—the higher the risk of default, the higher the credit premium. It reflects the difference in yield between a risk-free bond (usually government bonds) and a bond with some risk of default (corporate bonds, for instance).

• Why Not Relevant: The scenario discusses the yield spread between 2-year and 10-year bonds issued by the same sovereign entity, Country XYZ. Since both bonds are issued by the same entity, their default risk is essentially the same. The difference in yields is not attributed to different levels of credit risk but rather to the duration of the bonds. Hence, the credit premium is not the focus here.

C. Liquidity Premium

• Definition: The liquidity premium compensates investors for holding a bond that is harder to sell quickly without substantial price concessions. Bonds that are less liquid (harder to sell) will offer a higher yield to attract buyers.

• Why Not Relevant: The information given does not mention anything about the liquidity of the 2-year vs. the 10-year bonds. The liquidity premium would be relevant if there were indications that one bond is significantly less liquid than the other, affecting its yield. However, the discussion centers on the yield spread due to maturity differences, not liquidity concerns.

Why Term Premium Is the Focus

The term premium is highlighted because the yield spread is explicitly associated with different maturities (2-year vs. 10-year bonds) within the same country's sovereign debt. The scenario points to an upward-sloping yield curve, which naturally suggests that longer-term bonds are yielding more than shorter-term bonds. This situation is typical of a term premium, where the extra yield on longer-term bonds compensates investors for the added risks over a longer horizon, such as interest rate risk, inflation risk, and the uncertainty regarding future economic conditions.

Therefore, given the context and the details provided, the term premium is the most plausible explanation for the yield spread between the 2-year and 10-year bonds of Country XYZ, rather than differences attributed to credit risk (credit premium) or liquidity concerns (liquidity premium).

The fixed-income portfolio manager tells Martin that he is interested in a domestic market corporate bond issued by Zeus Manufacturing Corporation (ZMC). ZMC has just been downgraded two steps by a major credit rating agency. In addition to expected monetary actions that will raise short-term rates, the yield spread between three-year sovereign bonds and the next highest-quality government agency bond widened by 10 bps.

Q.

Using the building block approach, the required rate of return for the ZMC bond will most likely:

1. A.increase based on the change in the credit premium.
2. B.decrease based on the change in the default-free rate.
3. C.decrease based on the change in the liquidity premium.

Solution

A is correct. The credit premium is the additional expected return demanded for bearing the risk of default losses. A credit downgrade two steps lower will increase the credit premium and the required rate of return. The change in the default-free rate associated with the monetary tightening will increase (not decrease) the required rate of return. The widening of the spread between the sovereign bond and the next highest-quality government agency security indicates an increase in the liquidity premium, which will increase (not decrease) the required rate of return.

B is incorrect because the required rate of return would increase (not decrease) based on the change in the default-free rate associated with the monetary tightening.

C is incorrect because the rate of return would increase (not decrease) based on a change in the liquidity premium. The liquidity premium can be estimated from the yield spread between the highest-quality issuer (typically a sovereign bond) and the next highest-quality large issuer of similar bonds (often a government agency). A widening yield spread indicates an increase in the liquidity premium and required rate of return.

ChatGPT (Correct)

https://chat.openai.com/c/0d262ae7-548a-4c22-9544-7b709bcb945e

Using the building block approach to determine the required rate of return for bonds, we consider various components such as the default-free rate, credit premium, liquidity premium, and other factors that might affect the yield. Let's analyze the scenario provided for Zeus Manufacturing Corporation (ZMC) and the given options:

• ZMC Bond Downgrade: The scenario mentions that ZMC has just been downgraded two steps by a major credit rating agency. A downgrade in credit rating typically indicates a perceived increase in the risk of default by the issuer. This increased risk would necessitate a higher yield to compensate investors for taking on additional risk.

Given this information, let's evaluate the options:

A. Increase based on the change in the credit premium.

• Rationale: A downgrade in credit rating directly affects the credit premium, which is the additional yield above the default-free rate that investors require to compensate for the risk of default. When a bond is downgraded, its credit risk is perceived to be higher, and thus, the credit premium increases. An increase in the credit premium would lead to an increase in the required rate of return for the bond.

B. Decrease based on the change in the default-free rate.

• Not Supported by Information Provided: There is no specific mention of a change in the default-free rate (typically represented by government bond yields) in the scenario that would justify a decrease in the required rate of return for the ZMC bond. The scenario does not provide information suggesting that the default-free rate is decreasing.

C. Decrease based on the change in the liquidity premium.

• Not Supported by Information Provided: Similar to option B, there is no mention in the scenario of changes in the liquidity of the ZMC bond that would suggest a decrease in the required rate of return based on the liquidity premium. The liquidity premium compensates investors for the risk associated with the ease of buying or selling the bond without affecting its price significantly. The scenario does not address liquidity changes.

Given the details provided, the most likely outcome is:

A. Increase based on the change in the credit premium.

The credit downgrade of ZMC suggests an increased perception of credit risk, which would naturally lead to an increased credit premium and, consequently, an increased required rate of return for the ZMC bond.

Although the foundation’s fixed-income portfolios have focused primarily on developed markets, the portfolio manager presents data in Exhibit 3 on two emerging markets for Martin to consider. Both economies increased exports of their mineral resources over the last decade.

Exhibit 3:

Emerging Market Data

Factor	Emerging Republic A	Emerging Republic B
Fiscal deficit/GDP	6.50%	8.20%
Debt/GDP	90.10%	104.20%
Current account deficit	5.20% of GDP	7.10% of GDP
Foreign exchange reserves	90.30% of short-term debt	70.10% of short-term debt

Q.

Based only on Exhibit #3, the foundation would most likely consider buying bonds issued by:

1. A.only Emerging Republic A.
2. B.only Emerging Republic B.
3. C.neither Emerging Republic A nor Emerging Republic B.

Solution

C is correct. Emerging market debt requires an analysis of economic and political/legal risks. Based on the macroeconomic factors, the risk of a bond investment in either Republic A or Republic B appears to be high. Thresholds such as the risk guidelines listed in the table below can be used to assess the attractiveness of the two emerging market (EM) opportunities in Republic A and Republic B. Most notably, both republics raise concern based solely on their fiscal deficit-to-GDP ratios greater than 4.00% (Republic A’s is 6.50% and Republic B’s is 8.20%).

Emerging Market Analysis

Country Political/Economic Risk	Emerging Market Risk Guidelines	Emerging Republic A	Emerging Republic B
Fiscal deficit/GDP	4.00%	Negative	Negative
Debt/GDP	70.00%	Negative	Negative
Current account deficit	4.00% of GDP	Negative	Negative
Foreign exchange reserves	100.00% of short-term debt	Negative	Negative

Analysis of the economic and political risks associated with the two EM opportunities is suggestive of the need for further scrutiny; therefore, the foundation should not invest in Emerging Republic A or Emerging Republic B based only on the information provided.

ChatGPT (Wrong)

https://chat.openai.com/c/37b312a4-814e-476b-bd36-8e771fa42815

Based solely on the data provided in Exhibit 3, which presents various financial metrics for Emerging Republic A and Emerging Republic B, we can evaluate the attractiveness of bonds issued by these countries using their fiscal and economic indicators.

Emerging Republic A:

• Fiscal deficit/GDP: 6.50%

• Debt/GDP: 90.10%

• Current account deficit: 5.20% of GDP

• Foreign exchange reserves: 90.30% of short-term debt

Emerging Republic B:

• Fiscal deficit/GDP: 8.20%

• Debt/GDP: 104.20%

• Current account deficit: 7.10% of GDP

• Foreign exchange reserves: 70.10% of short-term debt

Analysis:

• Fiscal Deficit/GDP: A lower fiscal deficit as a percentage of GDP indicates better fiscal health. Republic A has a lower fiscal deficit compared to Republic B.

• Debt/GDP: A lower debt to GDP ratio indicates a country is in a better position to manage its debt. Republic A has a lower debt to GDP ratio than Republic B.

• Current Account Deficit: A lower current account deficit as a percentage of GDP suggests a country is better at managing its external trade and investment relations. Republic A has a lower current account deficit than Republic B.

• Foreign Exchange Reserves to Short-term Debt: A higher ratio indicates a country is in a better position to manage its short-term external debt obligations. Republic A has a higher ratio than Republic B.

Given these indicators, Emerging Republic A appears to be in a relatively better fiscal and economic position than Emerging Republic B. Republic A has a lower fiscal deficit and debt relative to its GDP, a smaller current account deficit, and higher foreign exchange reserves relative to its short-term debt. These factors suggest that Republic A might be considered more creditworthy or less risky compared to Republic B.

Therefore, the foundation would most likely consider buying bonds issued by:

A. only Emerging Republic A.

(added the solution) The explanation you provided highlights the importance of a comprehensive analysis of both economic and political/legal risks when considering investments in emerging market debt. The assessment against the emerging market risk guidelines indicates that both Emerging Republic A and Emerging Republic B exhibit high risk levels based on their fiscal deficit/GDP ratios, debt/GDP ratios, current account deficits, and foreign exchange reserves as percentages of short-term debt. Given that both countries exceed the specified risk thresholds in all these categories, it underscores the high risk of bond investment in these nations.

Such an analysis is crucial for investment decisions, especially for an institution like the foundation, which must carefully manage its risk exposure. The fiscal deficit/GDP ratios being greater than the 4.00% guideline, debt/GDP ratios exceeding the 70.00% threshold, current account deficits surpassing the 4.00% guideline, and foreign exchange reserves falling short of covering 100.00% of short-term debt for both republics, signal significant economic vulnerabilities.

Therefore, the correct answer to the question, based on a prudent analysis of economic and political/legal risks and considering the provided emerging market risk guidelines, is:

C. neither Emerging Republic A nor Emerging Republic B.

This conclusion is reached because both countries present high investment risks that do not align with the foundation's likely risk tolerance and investment criteria for emerging market debt.

Q.

Based only on Exhibits 3 and 4 and the information provided by the portfolio managers, the action most likely to enhance returns is to:

1. A.decrease existing investments in real estate by 2.00%.
2. B.initiate a commitment to emerging market debt of 1.00%.
3. C.increase the investments in international market bonds by 1.00%.

Solution C is correct. An investment in the bonds of the international energy exploration and production company (Xdelp) looks attractive. The international market benefits from positive macroeconomic fundamentals: point in the business cycle, monetary and fiscal discipline, rising current account surplus, and an appreciating currency. The anticipated credit rating improvement will add to the potential for this to become a profitable investment and enhance returns. An increase in the investments within the international fixed-income segment by 1.00% (existing weight is 6.17%) would take advantage of this opportunity and remain in compliance with the foundation’s 5.00%–10.00% strategic asset allocation limits.

A is incorrect because a decrease in the existing weight of real estate by 2.00% would put the portfolio weight below the minimum threshold of 2.00% (i.e., 3.34% ̶ 2.00% = 1.34%) of the foundation’s strategic asset allocation.

B is incorrect because the information presented in Exhibit 3 would lead the chief investment officer to avoid the two opportunities in emerging market debt (Emerging Republic A and Emerging Republic B) and not initiate a commitment to emerging market debt of 1.00% (i.e., increase the existing weight above 0.00%).

ChatGPT (Wrong)

To determine the action most likely to enhance returns based on Exhibits 3 and 4 and the additional information provided, let's analyze the given options:

A. Decrease existing investments in real estate by 2.00%

• The current allocation to real estate is 3.34%, which is within the strategic asset allocation range of 2.00% to 6.00%. Reducing the allocation by 2.00% would bring the investment to the minimum threshold of the policy range. There's no specific information provided that suggests real estate investments are underperforming or that decreasing this allocation would enhance returns, especially without knowing the performance or opportunities within the real estate sector.

B. Initiate a commitment to emerging market debt of 1.00%

• The current allocation to emerging markets debt is 0.00%, with the policy allowing for up to 2.00%. Given the data in Exhibit 3, both Emerging Republic A and B have shown significant increases in exports of mineral resources, suggesting potential economic growth. However, both also have high fiscal deficits and debt-to-GDP ratios, which could indicate risk. Despite these risks, emerging markets can offer higher yields compared to developed markets, potentially enhancing returns. Given the foundation's current lack of exposure to emerging markets and the strategic allocation allowance, this option could diversify the portfolio and possibly increase returns, assuming the higher risks associated with emerging market debt are acceptable and well-managed.

C. Increase the investments in international market bonds by 1.00%

• The current allocation to international fixed income is 6.17%, with the policy allowing for up to 10.00%. The description of the international market, particularly the bonds of Xdelp, suggests a positive outlook with expected improvements in free cash flow, earnings, and a potential upgrade in credit rating. This indicates a strong case for investment in international market bonds, especially considering the disciplined fiscal and monetary policies, current account surplus, and appreciating currency in the foreign country.

Given the strategic asset allocation ranges and the information provided, Option B, initiating a commitment to emerging market debt of 1.00%, could be considered the action most likely to enhance returns. This option takes advantage of the current zero allocation to emerging markets within the allowed policy range and the potential for higher yields, despite the higher risks. Emerging markets can offer diversification benefits and the possibility of higher returns due to their growth potential, especially if the foundation's portfolio is currently underexposed to these markets. However, this action should be balanced against the risk profile and long-term investment strategy of the foundation.

(after adjustment) Given the solution, it's clear that the correct answer is C. Increase the investments in international market bonds by 1.00%. This decision aligns with the favorable macroeconomic fundamentals in the international market where Xdelp operates. The positive macroeconomic indicators—such as the point in the business cycle, monetary and fiscal discipline, rising current account surplus, and an appreciating currency—coupled with the anticipated credit rating improvement for Xdelp's bonds, present a strong case for enhancing returns through an increased investment in international bonds. This move would also adhere to the foundation's strategic asset allocation limits for international fixed income, which allows for a maximum weight of 10.00%, with the existing allocation at 6.17%.

The explanation clarifies why options A and B are less suitable:

• A is incorrect because reducing real estate investments by 2.00% would breach the minimum threshold set by the strategic asset allocation, potentially compromising the diversification and stability provided by real estate investments within the overall portfolio.

• B is incorrect because, despite the potential high yields in emerging markets, the specific circumstances and risks highlighted for Emerging Republic A and B in Exhibit 3 (such as high fiscal deficits and debt-to-GDP ratios) suggest a cautious approach. It indicates that the chief investment officer might view these opportunities as too risky or not aligned with the foundation's strategic goals or risk tolerance, thus advising against initiating a new commitment to emerging market debt at this time.

The rationale for selecting C emphasizes the importance of aligning investment decisions with the foundation's strategic asset allocation framework, macroeconomic analysis, and potential for credit rating improvement, all of which point towards a promising opportunity to enhance returns through a carefully considered increase in international bond investments.

An Australian investor currently holds a A$240 million equity portfolio. He is considering rebalancing the portfolio based on an assessment of the risk and return prospects facing the Australian economy. Information relating to the Australian investment markets and the economy has been collected in the following table:

10-Year Historical	Current	Capital Market Expectations
Average government bond yield: 2.8%	10-year government bond yield: 2.3%
Average annual equity return: 4.6%	Year-over-year equity return: −9.4%
Average annual inflation rate: 2.3%	Year-over-year inflation rate: 2.1%	Expected annual inflation: 2.3%
Equity market P/E (beginning of period): 15×	Current equity market P/E: 14.5×	Expected equity market P/E: 14.0×
Average annual dividend income return: 2.6%		Expected annual income return: 2.4%
Average annual real earnings growth: 6.0%		Expected annual real earnings growth: 5.0%

Using the information in the table, address the following problems:

Q.

Calculate the historical Australian equity risk premium using the “equity-vs-bonds” premium method.

Answer (ChatGPT correct)

Your Answer:To calculate the historical Australian equity risk premium using the "equity-vs-bonds" premium method, we follow the formula: Equity Risk Premium=Average Annual Equity Return−Average Government Bond YieldEquity Risk Premium=Average Annual Equity Return−Average Government Bond Yield Based on the information provided: Average annual equity return = 4.6% Average government bond yield = 2.8% Let's calculate the equity risk premium: Equity Risk Premium=4.6%−2.8%Equity Risk Premium=4.6%−2.8% The historical Australian equity risk premium, using the "equity-vs-bonds" premium method, is approximately 1.8%.

---

Solution

The historical equity risk premium is 1.8%, calculated as follows:Historical equity returns − Historical 10-year government bond yield = Historical equity risk premium4.6% − 2.8% = 1.8%

// Some code
# Given data
average_annual_equity_return = 4.6  # in percent
average_government_bond_yield = 2.8  # in percent

# Calculating the equity risk premium
equity_risk_premium = average_annual_equity_return - average_government_bond_yield
equity_risk_premium

Q.

Calculate the expected annual equity return using the Grinold–Kroner model (assume no change in the number of shares outstanding).

Solution

The Grinold–Kroner model states that the expected return on equity is the sum of the expected income return (2.4%), the expected nominal earnings growth return (7.3% = 2.3% from inflation + 5.0% from real earnings growth) and the expected repricing return (−3.45%). The expected change in market valuation of −3.45% is calculated as the percentage change in the P/E level from the current 14.5× to the expected level of 14.0×: (14 − 14.5)/14.5 = −3.45%. Thus, the expected return is 2.4% + 7.3% − 3.45% = 6.25%.

// Some code
# Given data for the Grinold-Kroner model
current_pe = 14.5
expected_pe = 14.0
expected_dividend_yield = 2.4  # D/Y
expected_inflation = 2.3  # i
expected_real_earnings_growth = 5.0  # g

# Calculating the expected change in P/E
delta_pe = ((expected_pe - current_pe) / current_pe) * 100

# Calculating the expected annual equity return using the Grinold-Kroner model
expected_annual_equity_return = delta_pe + expected_dividend_yield + expected_inflation + expected_real_earnings_growth
expected_annual_equity_return

ChatGPT (Correct)

The Grinold-Kroner model provides a way to estimate the expected annual equity return by considering several components. Assuming no change in the number of shares outstanding, the formula simplifies to:

$E(R)=ΔP/E+D/Y+i+g$

where:

• $E(R)$ is the expected annual equity return,
• $ΔP/E$ is the expected change in the price-to-earnings ratio,
• $D/Y$ is the dividend yield,
• $i$ is the expected inflation rate, and
• $g$ is the expected real earnings growth rate.

Given the information:

• Current equity market P/E: 14.5×

• Expected equity market P/E: 14.0×, implying a $ΔP/E$ = $(14 - 14.5)/14.5$,
• Expected annual dividend income return (which can serve as the $�/�D/Y$): 2.4%,
• Expected annual inflation: 2.3%,

• Expected annual real earnings growth: 5.0%.

Let's calculate each component and then the expected annual equity return using the Grinold-Kroner model.

The expected annual equity return, using the Grinold-Kroner model and assuming no change in the number of shares outstanding, is approximately 6.25%.

Grinold-Korner model (with share outstanding)

When there's a change in the number of shares outstanding, the Grinold-Kroner model incorporates an additional term to account for the effect of share repurchases or issuance. The revised formula becomes:

$E(R)=ΔP/E+D/Y+i+g−ΔS$

where:

• $E(R)$ is the expected annual equity return,
• $ΔP/E$ is the expected change in the price-to-earnings ratio,
• $D/Y$ is the dividend yield,
• $i$ is the expected inflation rate,
• $g$ is the expected real earnings growth rate,
• $ΔS$ represents the change in the number of shares outstanding, expressed as a percentage. A positive $ΔS$ indicates share issuance (which is dilutive and thus subtracts from returns), and a negative $ΔS$ indicates share repurchases (which is accretive and thus adds to returns).

However, you've mentioned to assume no change in the number of shares outstanding. This implies $Δ�=0ΔS=0$, making it unnecessary to adjust our previous calculation for the expected annual equity return using the Grinold-Kroner model.

If there were changes in the number of shares outstanding, we would need specific information on the rate of share issuance or repurchase to accurately incorporate it into the Grinold-Kroner model calculation. Without those details, we can't precisely calculate the impact of changes in the number of shares outstanding on the expected annual equity return.

Q.

Using your answer to Part B, calculate the expected annual equity risk premium.

Solution

Using the results from Part B, the expected equity return is 6.25 percent.Expected equity return − Current 10-year government bond yield = Expected equity risk premium6.25% − 2.3% = 3.95%.

ChatGPT (Correct)

The expected annual equity risk premium can be calculated by subtracting the expected government bond yield from the expected annual equity return. From the information provided earlier:

• Expected annual equity return (from the Grinold-Kroner model) = 6.25%

• Current 10-year government bond yield = 2.3%

Using these values, we can calculate the expected annual equity risk premium as follows:

$Expected Equity Risk Premium=Expected Annual Equity Return−Current Government Bond YieldExpected Equity Risk Premium=Expected Annual Equity Return−Current Government Bond Yield$

$Expected Equity Risk Premium=6.25$

The expected annual equity risk premium, based on the expected annual equity return calculated using the Grinold-Kroner model, is approximately 3.95%.

At the start of the meeting, Fiske asks the analysts, Len Tuoc, Kim Spenser, and Pier Poulsen, to describe and justify their different approaches to economic forecasting. They reply as follows.

• Tuoc: I prefer econometric modeling. Robust models built with detailed regression analysis can help predict recessions well because the established relationships among the variables seldom change.

• Spenser: I like the economic indicators approach. For example, the composite of leading economic indicators is based on an analysis of its forecasting usefulness in past cycles. They are intuitive, simple to construct, require only a limited number of variables, and third-party versions are also available.

• Poulsen: The checklist approach is my choice. This straightforward approach considers the widest range of data. Using a simple statistical method, such as time-series analysis, an analyst can quickly assess which measures are extreme. This approach relies less on subjectivity and is less time-consuming.

Regarding the approaches to economic forecasting, the statement by which analyst is most accurate?

1. A.Poulsen
2. B.Tuoc
3. C.Spenser

Solution

C is correct. Spenser’s statement is most accurate. In the economic indicators approach, for example, the composite of leading economic indicators is based on an analysis of its forecasting usefulness in past cycles. The indicators are intuitive, simple to construct, require only a limited number of variables, and third-party versions are also available.

A is incorrect. Contrary to Poulson’s statement, the checklist approach is highly subjective and time-consuming.

B is incorrect. Contrary to Tuoc’s statement, the relationships between variables are likely to change. In practice, model-based forecasts rarely forecast recessions well, although they have a better record of anticipating upturns.

Capital Market Expectations, Part 1: Framework and Macro Considerations Learning Outcome

1. Compare major approaches to economic forecasting

ChatGPT (wrong)

The accuracy of each analyst's statement regarding economic forecasting approaches depends on the context in which "accuracy" is considered. Each analyst advocates for a different methodology based on their perceived strengths and weaknesses of each approach. Here's a breakdown:

1. Len Tuoc (Econometric Modeling): Tuoc argues that econometric modeling, which relies on regression analysis to establish relationships among variables, is effective in predicting recessions. This approach is indeed powerful for understanding complex economic dynamics due to its reliance on historical data and statistical methods to forecast future trends. The claim that "the established relationships among the variables seldom change" might be overly optimistic, as economic relationships can evolve over time due to structural changes in the economy or unforeseen events.

2. Kim Spenser (Economic Indicators): Spenser prefers using economic indicators, specifically the composite of leading economic indicators, which has been empirically tested for its forecasting usefulness. This approach is praised for its intuitiveness, simplicity, and reliance on a limited number of variables. Economic indicators are indeed widely used for forecasting due to their ability to provide early signals of economic turning points. However, the effectiveness of this approach can vary depending on which indicators are chosen and how they are interpreted.

3. Pier Poulsen (Checklist Approach): Poulsen's preference for the checklist approach, which involves a broad consideration of data and simple statistical methods like time-series analysis, emphasizes speed and a reduction in subjectivity. This approach can be effective for quickly assessing economic conditions without the complexity of building and maintaining detailed models. However, its reliance on identifying "extreme" measures could potentially miss subtle shifts in economic trends.

Each approach has its merits and limitations. The most accurate statement cannot be universally determined without additional context regarding the specific forecasting needs, the availability and quality of data, and the economic environment in which the forecasting is taking place. Thus, the accuracy of Tuoc, Spenser, and Poulsen's statements is contingent upon the specific objectives and constraints of the forecasting exercise. However, in terms of providing a comprehensive analysis that balances depth with practicality, Poulsen's approach might be seen as more universally applicable for general economic forecasting due to its flexibility and efficiency.

The analysts think that adding to US Treasuries would fit portfolio objectives, but they are concerned that the US Federal Reserve Board is likely to raise the real fed funds rate soon. They assemble the data in Exhibit 1 in order to use the Taylor rule (giving equal weights to inflation and output gaps) to help predict the Fed’s next move with respect to interest rates.

Exhibit 1

Current Data and Forecasts from the Fed

Statistic	Status	Value (%)
Fed funds rate	Current	3
Neutral	2.5
GDP growth rate	Trend	4.5
Forecast	3
Inflation	Target	2.5
Forecast	3.2

Using the data in Exhibit 1 and the investment team’s approach to predict the Fed’s next move, the new real fed funds rate will most likely be:

1. A.2.9%.
2. B.2.6%.
3. C.2.1%.

Solution

C is correct. The Taylor rule is

Roptimal = Rneutral + [0.5 × (GDPgforecast – GDPgtrend)] + [0.5 × (Iforecast – Itarget)]

= 2.5 + [0.5 × (3.0 – 4.5)] + [0.5 × (3.2 – 2.5)]

= 2.5 – 0.75 + 0.35

= 2.10%

A is incorrect. It incorrectly reversed the terms within the parentheses:

2.5 + [0.5 × (4.5 – 3.0)] + [0.5 × (2.5 – 3.2)] = 2.5 + 0.75 – 0.35 = 2.9

B is incorrect. It incorrectly uses the current rate of 3.0 for the first term instead of the neutral rate of 2.5%.

Capital Market Expectations, Part 1: Framework and Macro Considerations Learning Outcome

1. Discuss the effects of monetary and fiscal policy on business cycles

ChatGPT (Correct)

https://chat.openai.com/c/da50c698-f5e6-49ce-b8a9-6c9f5f725fed To predict the Federal Reserve's next move with respect to interest rates using the Taylor Rule, we can use the formula that incorporates both inflation and output gaps, giving them equal weights. The Taylor Rule is generally represented as follows:

$Taylor Rule Interest Rate=Neutral Rate+0.5×Inflation Gap+0.5×Output GapTaylor Rule Interest Rate=Neutral Rate+0.5×Inflation Gap+0.5×Output Gap$

where:

• Neutral Rate is the Fed funds rate that is considered neither stimulative nor restrictive.

• Inflation Gap is the difference between the current inflation rate and the target inflation rate.

• Output Gap is the difference between the actual GDP growth rate and the trend or potential GDP growth rate.

Given data:

• Neutral Rate: 2.5%

• Current Inflation Rate: 3.2%

• Target Inflation Rate: 2.5%

• Actual GDP Growth Rate: 3%

• Trend GDP Growth Rate: 4.5%

We can calculate the Inflation Gap and the Output Gap as follows:

• Inflation Gap = Current Inflation Rate - Target Inflation Rate = 3.2% - 2.5%

• Output Gap = Actual GDP Growth Rate - Trend GDP Growth Rate = 3% - 4.5%

Let's calculate the new real fed funds rate according to the Taylor Rule formula.

According to the Taylor Rule calculation, the new real fed funds rate will most likely be 2.1%. Therefore, the correct answer is:

C. 2.1%. ​

neutral_rate = 2.5
current_inflation_rate = 3.2
target_inflation_rate = 2.5
actual_gdp_growth_rate = 3
trend_gdp_growth_rate = 4.5

# Calculating gaps
inflation_gap = current_inflation_rate - target_inflation_rate
output_gap = actual_gdp_growth_rate - trend_gdp_growth_rate

# Taylor Rule calculation
taylor_rule_interest_rate = neutral_rate + 0.5 * inflation_gap + 0.5 * output_gap

taylor_rule_interest_rate

Result

2.1

To assess the attractiveness of emerging market equities, Fiske suggests that they use the data in Exhibit 2 and determine the expected return of small-cap emerging market equities using the Singer–Terhaar approach.

Exhibit 2

Data for Analyzing Emerging Markets

Asset Class	Standard Deviation	Correlation with GIM	Degree of Integration with GIM
Emerging small-cap equity	23%	0.85	65%
Global investable market (GIM)	7.00%

Additional information
Risk-free rate: 2.5%
Illiquidity premium: 60 bps
Sharpe ratio for GIM and emerging small-cap equity: 0.31

Using the data in Exhibit 2 and Fiske’s suggested approach, the forecast of the expected return for small-cap emerging market equities is closest to:

1. A.8.9%.
2. B.9.9%.
3. C.9.5%.

My calculation

Sharpe Ratio = 0.31 = RP / standard deviation; so given SD of each

RP (Global) = 0.07 * 0.31 = 0.0217 = 2.17% (not needed**)

RP (Small cap equity- segmented) = 0.23 * 0.31 = 0.0713 = 7.13%

RP (Small cap E - Integrated) = 7.13% * 0.85 = 0.060605 = 6.06%

RP = 6.06 * 0.65 + 0.35 * 7.13 = 6.43% , + 3.1 = 9.53

Premiums: 2.5 + 0.6 = +3.1

essentially we need

RP (segmented)

degree of correlation with GIM

degree of integration with GIM

Solution

C is correct. The Singer and Terhaar approach for determining the expected return on an asset class involves determining the risk premium arising from systematic risk as a weighted average of the risk premiums arising from a fully integrated market and fully segmented market, where the weights for the fully integrated market is the degree of integration of the markets.

• The risk premium for the fully integrated market is given by:RPi = σiρi,M(RPM/σM) where (RPM/σM) is the Sharpe ratio for the world market portfolio

• The risk premium for the fully segmented market is given by: RPi = σi(RPM/σM)

• In addition, if there are market imperfections such as illiquidity premiums, they must be added in

• Finally, the expected return on the asset class is determined by adding these risk premiums to the risk-free rate, in the classical CAPM fashion.

• Systematic risk premium in fully integrated market

  Risk Premium: RPi = σiρi,M(RPM/σM)

  = [23% × 0.85 × 0.31]

  = 6.06%

• Systematic risk premium in fully segmented market

  Risk Premium: RPi = σi(RPM/σM)

  = [23% × 0.31]

  = 7.13%

• Weight systematic risk premiums by degree of integration:0.65 × 6.06 + 0.35 × 7.13 = 6.43%

• Add the illiquidity premium6.43% + 0.60% = 7.03%

• Add the risk-free rate:2.5% + 7.03% = 9.53%

A is incorrect. It omits the liquidity premium.

Step 1	Systematic risk premium in fully integrated market Risk Premium: RPi = σiρi,M(RPM/σM) = [23% × 0.85 × 0.31] = 6.06%
Step 2	Systematic risk premium in fully segmented market Risk Premium: RPi = σi(RPM/σM) = [23% × 0.31] = 7.13%
Step 3	Weight systematic risk premiums by degree of integration:0.65 × 6.06 + 0.35 × 7.13 = 6.43%
Step 4	Error: Omit the illiquidity premium6.43%
Step 5	Add the risk-free rate:2.5% + 6.43% = 8.93%

B is incorrect. It incorrectly reverses weights: apply 0.65 weighting to 7.73% and 0.35 weighting to 6.06.

Step 1	Systematic risk premium in fully integrated market Risk Premium: RPi = σiρi,M(RPM/σM) = [23% × 0.85 × 0.31] = 6.06%
Step 2	Systematic risk premium in fully segmented market Risk Premium: RPi = σi(RPM/σM) = [23% × 0.31] = 7.13%
Step 3	Error: reverse weights of systematic risk premiums by degree of integration:0.35 × 6.06 + 0.65 × 7.13 = 6.76%Step 4: Add the illiquidity premium6.76% + 0.60% = 7.36%
Step 5	Add the risk-free rate:2.5% + 7.36% = 9.86%

Capital Market Expectations, Part 2: Forecasting Asset Class Returns Learning Outcome

1. Discuss approaches to setting expectations for equity investment market returns

ChatGPT (Wrong)

https://chat.openai.com/c/ea0fa469-f3c8-4238-90ff-44e5d6495220

Thank you for providing the detailed solution and clarification on how to calculate the expected return for small-cap emerging market equities using the Singer–Terhaar approach. This method involves accounting for the risk premiums from both fully integrated and fully segmented markets, weighting them by the degree of market integration, and adjusting for any market imperfections such as illiquidity premiums. Finally, adding these risk premiums to the risk-free rate yields the expected return on the asset class in the classical CAPM fashion.

The steps you provided clearly break down the process into manageable parts, demonstrating how to calculate each component of the expected return:

1. Systematic Risk Premium in a Fully Integrated Market: Calculated using the formula $σi​ρi,M​(RPM/σM​)$, which considers the standard deviation of the asset class, its correlation with the market, and the Sharpe ratio of the world market portfolio.
2. Systematic Risk Premium in a Fully Segmented Market: Calculated using the formula $σi​(RPM/σM​)$, which only takes into account the standard deviation of the asset class and the Sharpe ratio of the world market portfolio.
3. Weighting Systematic Risk Premiums by Degree of Integration: The calculated premiums are then weighted according to the degree of market integration.

4. Adjusting for Illiquidity Premiums: Any market imperfections, such as illiquidity premiums, are added to the weighted risk premium.

5. Final Expected Return: The risk-free rate is added to the adjusted risk premium to determine the final expected return on the asset class.

The correct answer, as you've shown, is (C) 9.53%, which is derived from adding the calculated risk premium (adjusted for the degree of integration and illiquidity premium) to the risk-free rate.

This explanation not only clarifies the correct answer but also provides a comprehensive overview of how the Singer–Terhaar approach is applied in practice to forecast asset class returns, specifically for emerging small-cap equities in this case. It's an effective methodology for considering both global market integration levels and specific market segment characteristics when estimating expected returns.

https://chat.openai.com/c/ea0fa469-f3c8-4238-90ff-44e5d6495220

o calculate the expected return of small-cap emerging market equities using the Singer–Terhaar approach, we follow these steps:

1. Calculate the global market risk premium (GMRP): This is the difference between the expected return on the global investable market (GIM) and the risk-free rate. Since we don't have the expected return on GIM directly, we use the Sharpe ratio for GIM to find it. The Sharpe ratio is defined as $(Expected Return−Risk-Free Rate)/Standard Deviation(Expected Return−Risk-Free Rate)/Standard Deviation$.
2. Determine the risk premium for emerging small-cap equity: We adjust the global market risk premium for the specific risk and integration level of emerging small-cap equity. This involves scaling the GMRP by the correlation with GIM and the degree of integration with GIM.

3. Add the risk-free rate and any applicable premiums (e.g., illiquidity premium): To get the final expected return, we add the risk-free rate and any specific premiums that apply to small-cap emerging market equities.

Given Data:

• Standard Deviation of GIM: 7%

• Correlation of Emerging Small-Cap Equity with GIM: 0.85

• Degree of Integration with GIM for Emerging Small-Cap Equity: 65%

• Risk-Free Rate: 2.5%

• Illiquidity Premium: 0.6% (60 bps)

• Sharpe Ratio for GIM: 0.31

Let's start by calculating the Global Market Risk Premium (GMRP) using the Sharpe ratio formula. We rearrange the formula to solve for the expected return on GIM:

Solving for the expected return on GIM gives us:

Next, we calculate the risk premium for emerging small-cap equity, adjusting it for correlation and degree of integration, and then find the expected return for emerging small-cap equity. Let's proceed with these calculations.

The forecast of the expected return for small-cap emerging market equities, based on the Singer–Terhaar approach and the provided data, is closest to 4.3%.

It seems there might have been a misunderstanding in the calculation or the interpretation of the options provided (A. 8.9%, B. 9.9%, C. 9.5%). Given the calculation follows the outlined steps correctly with the provided data, let's reassess to ensure accuracy and alignment with the expected outcomes.

Given the discrepancy and the unexpected result, it's possible that a mistake was made in interpreting the question or in the calculation process. The expected answers suggest a higher return, indicating a possible oversight in calculating the global market risk premium (GMRP) or its application. Let's reevaluate the approach and assumptions:

1. Reevaluate the Sharpe Ratio application: The calculation of the expected return on GIM might need adjustment based on a more precise interpretation of the Sharpe ratio and the global market risk premium.

2. Integration and Correlation Adjustments: Ensure the correct application of the degree of integration and correlation in adjusting the GMRP for emerging small-cap equity.

3. Illiquidity Premium Addition: Confirm that the addition of the illiquidity premium is correctly applied in the context of the expected return calculation.

Given the options and the methodology outlined, it seems there was an error in my interpretation or calculation. The expected return should indeed reflect an outcome closer to the options provided (A. 8.9%, B. 9.9%, C. 9.5%). The calculation provided does not align with these options due to an error in the calculation process.

Let's correct the process and ensure the calculation aligns with the expected methodology and outcome options. ​​

Upon revisiting the calculation and understanding the methodology more carefully, it's clear that my previous approach to calculating the expected return for small-cap emerging market equities contained an error. The calculation did not align with the expected options (A. 8.9%, B. 9.9%, C. 9.5%), indicating a significant oversight in applying the Singer–Terhaar approach correctly.

To correctly forecast the expected return for small-cap emerging market equities using the Singer–Terhaar approach, one should:

1. Calculate the global market risk premium (GMRP) using the Sharpe ratio and standard deviation of the global investable market (GIM), then applying this to find the expected return on GIM.

2. Adjust this premium for the specific risk characteristics of the emerging small-cap equities, such as their correlation with the GIM and their degree of integration with the global market.

3. Finally, add any specific premiums (like the illiquidity premium) to this adjusted risk premium, along with the risk-free rate, to find the expected return on emerging small-cap equities.

Given the error in the initial calculation, and without re-executing the precise mathematical steps here, it's important to note that the calculation should correctly account for these factors to align with the Singer–Terhaar method. The correct expected return should indeed fall within the range provided by the options (A. 8.9%, B. 9.9%, C. 9.5%), reflecting a proper application of the method to the data given in Exhibit 2.

I encourage revisiting the calculation with careful application of the Singer–Terhaar formula, considering all aspects like the global market risk premium, the degree of market integration, correlation factors, and any specific premiums applicable to the asset class in question. This corrected approach should yield an expected return that matches one of the provided options.

Finally, after examining data pertaining to the European equity markets, the investment team believes that there are attractive investment opportunities in selected countries. Specifically, they compare the recent economic data with long-term average trends in three different countries, shown in Exhibit 3.

Exhibit 3

Relationship of Current Economic Data to Historical Trends: Selected European Countries

	Ireland	Spain	Hungary
Output gap	Above trend	Closing	Well above trend
Money market rates	Moving up at accelerated pace	Above average and rising	Bottoming, expecting to rise over short horizon
Other	Housing demand strong	Boom mentality	Confidence rising
Fiscal/monetary policies	Removing stimulus	Restrictive	Stimulative

Among the three countries examined by the investment team, which is in the most attractive phase of the business cycle for equity returns?

1. A.Hungary
2. B.Ireland
3. C.Spain

Solution

A is correct. The most favorable phases when considering equity returns are initial recovery and early upswing; the late upswing, slowdown, and recession phases carry the greater risk for equities.

Hungary has the combination of factors consistent with the initial recovery/early upswing phases of the business cycle—increasing production, low inflation, improving confidence, stimulatory fiscal/monetary policies, and abundant capacity. These indicators point to strongly rising stock prices and therefore most attractive for equity returns.

C is incorrect as discussed above. Spain appears to be in late upswing with high production, exuberant confidence and rising inflation, and restrictive fiscal/monetary policies. Stocks would be topping out and often volatile.

B is incorrect as discussed above. Ireland is likely at risk of entering a recession with production, utilization and inflation each above long-term averages while confidence is weakening. Fiscal/monetary policies are on a cautionary note. Stocks would be in bottoming/starting to rise stage.

Capital Market Expectations, Part 1: Framework and Macro Considerations Learning Outcome

1. Discuss how business cycles affect short- and long-term expectations

ChatGPT (Correct)

https://chat.openai.com/c/42335650-c3ee-496e-82a7-6f99464c1a72

To determine which country is in the most attractive phase of the business cycle for equity returns, let's analyze the economic indicators provided in Exhibit 3 for each country:

Ireland

• Output gap: Above trend, indicating that the economy is likely operating above its potential, which could lead to inflationary pressures.

• Money market rates: Moving up at an accelerated pace, suggesting tightening monetary policy to combat potential inflation.

• Other: Strong housing demand, indicating robust consumer confidence and economic activity.

• Fiscal/monetary policies: Removing stimulus, which could slow down the economy but is aimed at preventing overheating.

Spain

• Output gap: Closing, indicating that the economy is moving towards its potential output level.

• Money market rates: Above average and rising, suggesting tightening monetary policy, possibly in response to improving economic conditions.

• Other: Boom mentality, which could indicate optimism and investment growth but also the risk of overheating or asset bubbles.

• Fiscal/monetary policies: Restrictive, aimed at controlling growth to sustainable levels.

Hungary

• Output gap: Well above trend, suggesting significant economic activity above potential output, which is often seen during the expansion phase of the business cycle.

• Money market rates: Bottoming, expecting to rise over the short horizon, indicating that monetary policy may start to tighten but is currently supportive of growth.

• Other: Confidence rising, which supports consumer spending and investment.

• Fiscal/monetary policies: Stimulative, aimed at encouraging economic growth.

Based on this analysis, Hungary appears to be in the most attractive phase of the business cycle for equity returns. It is characterized by an economy well above trend (expansionary phase), with monetary policy still supportive (though expected to tighten), rising confidence, and stimulative fiscal/monetary policies. These factors typically create favorable conditions for equity markets as corporate earnings growth tends to be strong during such phases.

Ted Rogers Case Scenario

Ted Rogers is the director of a research team that analyzes traditional and non-traditional sources of energy for investment purposes. For traditional energy sources, a number of high-frequency historical data series are available. For non-traditional energy sources, the data are generally quarterly and tend to hide a great deal of the volatility that Rogers knows to exist because appraised values are used instead of market values.

The quarterly data available for non-traditional energy sources are best described as data with a:

1. A.smoothing bias.
2. B.survivorship bias.
3. C.time-period bias.

Solution

A is correct. Smoothed, or appraisal, data arise when appraised values are used instead of market values, which tends to make correlation magnitudes smaller and underestimate volatility.

B is incorrect because survivorship bias is when a data series only reflects companies that exist at a given moment in time and not companies that may have left prior to the given moment in time (i.e., only the surviving firms are in the data). There is no evidence of such a bias here.

C is incorrect because a time-period bias is a temporary trend that appears in data of which there is no evidence.

Capital Market Expectations, Part 1: Framework and Macro Considerations Learning Outcome

1. Discuss challenges in developing capital market forecasts

ChatGPT (Correct)

https://chat.openai.com/c/9a898947-1432-423b-8c72-90d295531a1c The scenario with Ted Rogers and his research team dealing with the analysis of traditional and non-traditional sources of energy for investment purposes involves dealing with data of varying frequencies and reliability. The quarterly data for non-traditional energy sources, as mentioned, tend to hide a great deal of the volatility because appraised values are used instead of market values. This approach to data reporting, where the inherent volatility and fluctuations are not fully captured due to the nature of the data collection and reporting intervals, leads to a specific type of bias.

Given the description, the quarterly data for non-traditional energy sources are best described as having a smoothing bias. This is because the use of appraised values over market values and the infrequent reporting interval (quarterly) tend to smooth out the short-term fluctuations and volatility that actually exist. By relying on less frequent and more stable appraised values, the data presents a less volatile and possibly more stable outlook than what might be the case if market values and more frequent data points were used. This can lead to underestimating the risk and volatility inherent in these non-traditional energy investments.

• Smoothing Bias occurs when the data collection or reporting method systematically understates the volatility of the metric being measured. This is a common issue with appraised values, which are often based on models or expert judgments that may not reflect the immediate market conditions or the latest trends accurately.

The other options, survivorship bias and time-period bias, do not as directly apply to the situation described. Survivorship bias would imply that only the successful firms or investments are being considered, ignoring those that have failed, while time-period bias refers to the distortion that can arise from using data from a specific time period that may not be representative of other periods. In this case, the primary issue is the understatement of volatility due to the nature of the data collection and reporting process, thus making smoothing bias the most accurate description.

For non-traditional energy sources, the data are generally quarterly and tend to hide a great deal of the volatility that Rogers knows to exist because appraised values are used instead of market values. To supplement the quarterly data, Rogers’s team uses an index of the top 30 firms in new and experimental technologies, called the “NEXT Index.” Although not all of the firms in the NEXT are energy firms, the index is available as a weekly series. However, the NEXT does change its composite mix of firms frequently as firms in the index fail or are sold to larger firms that are not in the index.

The NEXT Index data most likely reflects:

1. A.volatility clustering.
2. B.transcription errors.
3. C.survivorship bias.

Solution

C is correct. Survivorship bias arises when a data series only reflects companies that exist at a given moment in time and not companies that may have left prior to the given moment in time (i.e., only the surviving firms are in the data). The NEXT Index has survivorship bias as evidenced by the frequent change in its component firms because of failure and acquisition by larger non-index firms.

A is incorrect because there is no evidence of this time series phenomenon.

B is incorrect because there is no evidence of improperly recorded data.

Capital Market Expectations, Part 1: Framework and Macro Considerations Learning Outcome

1. Discuss challenges in developing capital market forecasts

ChatGPT (Correct)

https://chat.openai.com/c/9a898947-1432-423b-8c72-90d295531a1c

The NEXT Index, which tracks the top 30 firms in new and experimental technologies, changes its composite mix frequently as firms in the index fail or are sold to larger firms not in the index. This characteristic of the NEXT Index suggests that it most likely reflects C. survivorship bias.

Survivorship bias occurs when an analysis is conducted on the remaining subjects or entities (in this case, firms) without taking into account those that have failed or no longer exist. Since the NEXT Index frequently updates its composition to remove firms that fail or are acquired, it inherently focuses on the firms that have "survived" or are currently successful enough to be included. This can lead to a distorted view of the market or sector's performance, as the index does not account for the total universe of firms, including those that did not succeed, potentially overestimating the overall performance and health of the sector.

• Volatility clustering refers to the phenomenon where large price movements are followed by large price movements (of either direction), and small price movements follow small price movements. While the NEXT Index might exhibit volatility, the description provided does not specifically indicate that volatility clustering is a characteristic reflected by the NEXT Index data.

• Transcription errors refer to mistakes made in recording data. There is no information given in the scenario that suggests transcription errors are a feature of the NEXT Index data.

Therefore, given the description of how the NEXT Index operates, survivorship bias is the most appropriate choice among the options provided.

Which of the following psychological traps best describes Rogers’s team’s decision to give historical correlation more weight in the correlation matrix?

1. A.Prudence trap
2. B.Overconfidence trap
3. C.Anchoring trap

Solution

A is correct. Rogers’s team views giving more weight to the historical correlations as a safety measure and as a way to manage client expectations. They do not want to appear extreme. The prudence trap is the tendency to be cautious when making decisions that could be potentially expensive or damaging to the decision maker’s career.

B is incorrect because the overconfidence trap is when an individual overestimates the accuracy of their forecast by not considering the possibility of bad events.

C is incorrect because the anchoring trap occurs when there is a particular initial point of view that dominates an analysis.

Capital Market Expectations, Part 1: Framework and Macro Considerations Learning Outcome

1. Discuss challenges in developing capital market forecasts

The approach taken by Rogers’s team to calculate the correlation matrix is best described as which type of estimator?

1. Shrinkage

2. Time series

3. Historical

Solution

A is correct. To determine the correlation matrix in the different energy sectors, Rogers’s team relies on a weighted average of correlations derived from multifactor models and historical correlations. A shrinkage estimator is a weighted average of correlation (or covariance) matrices created from at least two different correlation (or covariance) matrices generated from different sources.

C is incorrect because historical estimators are not reduced on analyst opinion; shrinkage estimators are.

B is incorrect because time-series estimators are not reduced based on analyst opinion; shrinkage estimators are.

Capital Market Expectations, Part 2: Forecasting Asset Class Returns Learning Outcome

1. Discuss approaches to setting expectations for fixed- income returns

ChatGPT (Correct)

The approach taken by Rogers's team to calculate the correlation matrix, where they rely on a weighted average of correlations derived from multifactor models and historical correlations, with a greater weight given to historical correlations to purposefully understate the expected future performance of investment models, is best described as a A. Shrinkage estimator.

Shrinkage involves adjusting a more complex model (e.g., one based on multifactor models that could be more sensitive to recent data or specific assumptions) towards a simpler model or a more stable historical baseline to improve its robustness and predictive accuracy. This technique is used to prevent overfitting and to manage the risk of making overly optimistic forecasts based on less reliable or more volatile data sources. By emphasizing historical correlations, Rogers's team is effectively applying a shrinkage technique, as they are moving their estimates towards a more stable, historical perspective that likely incorporates a broader range of market conditions over time.

• Time series analysis involves methods for analyzing time series data to extract meaningful statistics and other characteristics of the data. While Rogers's team likely uses time series data (such as the weekly series of the NEXT Index), the description focuses more on how they integrate different types of data to calculate the correlation matrix, rather than on the analysis of time series data per se.

• Historical estimators would rely solely on historical data without the integration of other models or weighting approaches. Although Rogers's team does emphasize historical data, their method goes beyond simple historical analysis by incorporating multifactor models and applying a specific weighting strategy, aligning more closely with shrinkage techniques.

Therefore, the approach described aligns most closely with a shrinkage estimator, which is aimed at improving the estimator's performance by reducing its variance, at the cost of introducing some bias, in a manner intended to produce more reliable and conservative forecasts.