8 June - Practice Questions - Liability Driven and Index-based strategies

Doug, the newly hired chief financial officer for the City of Radford, asks the deputy financial manager, Hui, to prepare an analysis of the current investment portfolio and the city’s current and future obligations. The city has multiple liabilities of different amounts and maturities relating to the pension fund, infrastructure repairs, and various other obligations.

Hui observes that the current fixed-income portfolio is structured to match the duration of each liability. Previously, this structure caused the city to access a line of credit for temporary mismatches resulting from changes in the term structure of interest rates.

Doug asks Hui for different strategies to manage the interest rate risk of the city’s fixed-income investment portfolio against one-time shifts in the yield curve. Hui considers two different strategies:

• Strategy 1: Immunization of the single liabilities using zero-coupon bonds held to maturity.

• Strategy 2: Immunization of the single liabilities using coupon-bearing bonds while continuously matching duration.

Q.

A disadvantage of Strategy 1 is that:

1. A.price risk still exists.

2. B.interest rate volatility introduces risk to effective matching.

3. C.there may not be enough bonds available to match all liabilities.

Solution

C is correct. It may be impossible to acquire zero-coupon bonds to precisely match liabilities because the city’s liabilities have varying maturities and amounts. In many financial markets, zero-coupon bonds are unavailable.

https://chatgpt.com/c/1c8ba3bf-193c-47a1-8436-248a2acdced3

Q.

Which duration measure should be matched when implementing Strategy 2?

1. A.Key rate

2. B.Modified

3. C.Macaulay

Solution

C is correct. An investor having an investment horizon equal to the bond’s Macaulay duration is effectively protected, or immunized, from the first change in interest rates, because price and coupon reinvestment effects offset for either higher or lower rates.

Q.

An upward shift in the yield curve on Strategy 2 will most likely result in the:

1. A.price effect cancelling the coupon reinvestment effect.

2. B.price effect being greater than the coupon reinvestment effect.

3. C.coupon reinvestment effect being greater than the price effect.

Solution

A is correct. An upward shift in the yield curve reduces the bond’s value but increases the reinvestment rate, with these two effects offsetting one another. The price effect and the coupon reinvestment effect cancel each other out in the case of an upward shift in the yield curve for an immunized liability.

Q.

The effects of a non-parallel shift in the yield curve on Strategy 2 can be reduced by:

1. A.minimizing the convexity of the bond portfolio.

2. B.maximizing the cash flow yield of the bond portfolio.

3. C.minimizing the difference between liability duration and bond-portfolio duration.

Solution

A is correct. Minimizing the convexity of the bond portfolio minimizes the dispersion of the bond portfolio.

A non-parallel shift in the yield curve may result in changes in the bond portfolio’s cash flow yield.

In summary, the characteristics of a bond portfolio structured to immunize a single liability are that it (1) has an initial market value that equals or exceeds the present value of the liability,

(2) has a portfolio Macaulay duration that matches the liability’s due date, and

(3) minimizes the portfolio convexity statistic.

The city also manages a separate, smaller bond portfolio for the Radford School District. During the next five years, the school district has obligations for school expansions and renovations. The funds needed for those obligations are invested in the Bloomberg Barclays US Aggregate Index. Doug asks Hui which portfolio management strategy would be most efficient in mimicking this index.

Q.

Hui’s response to Doug’s question about the most efficient portfolio management strategy should be:

1. A.full replication.

2. B.active management.

3. C.an enhanced indexing strategy.

Solution

C is correct. Under an enhanced indexing strategy, the index is replicated with fewer than the full set of index constituents but still matches the original index’s primary risk factors. This strategy replicates the index performance under different market scenarios more efficiently than the full replication of a pure indexing approach.

Keywords - Small bond portfolio, can't afford for full replication

A Radford School Board member has stated that she prefers a bond portfolio structure that provides diversification over time, as well as liquidity. In addressing the board member’s inquiry, Hui examines a bullet portfolio, a barbell portfolio, and a laddered portfolio.

QuestionQ.

Which portfolio structure should Hui recommend that would satisfy the school board member’s preference?

1. A.Bullet portfolio

2. B.Barbell portfolio

3. C.Laddered portfolio

Solution

C is correct. The laddered approach provides both diversification over time and liquidity. Diversification over time offers the investor a balanced position between two sources of interest rate risk: cash flow reinvestment and market price volatility. In practice, perhaps the most desirable aspect of a laddered portfolio is liquidity management, because as time passes, the portfolio will always contain a bond close to maturity.

Serena is a risk management specialist with Liability Protection Advisors. Trey, CFO of Kiest Manufacturing, enlists Serena’s help with three projects. The first project is to defease some of Kiest’s existing fixed-rate bonds that are maturing in each of the next three years. The bonds have no call or put provisions and pay interest annually. Exhibit 1 presents the payment schedule for the bonds.

Exhibit 1:

Kiest Manufacturing Bond Payment Schedule (as of beginning of Year 1)

Maturity Date	Payment Amount
End of Year 1	$9,572,000
End of Year 2	$8,392,000
End of Year 3	$8,200,000

Q.

Based on Exhibit 1, Kiest’s liabilities would be classified as:

1. A.Type I.

2. B.Type II.

3. C.Type III.

Solution

A is correct. Type I liabilities have cash outlays with known amounts and timing. The dates and amounts of Kiest’s liabilities are known; therefore, they would be classified as Type I liabilities.

The second project for Serena is to help Trey immunize a $20 million portfolio of liabilities. The liabilities range from 3.00 years to 8.50 years with a Macaulay duration of 5.34 years, cash flow yield of 3.25%, portfolio convexity of 33.05, and basis point value (BPV) of $10,505. Serena suggested employing a duration-matching strategy using one of the three AAA rated bond portfolios presented in Exhibit 2.

Exhibit 2:

Possible AAA Rated Duration-Matching Portfolios

	Portfolio A	Portfolio B	Portfolio C
Bonds (term, coupon)	4.5 years, 2.63% 7.0 years, 3.50%	3.0 years, 2.00% 6.0 years, 3.25% 8.5 years, 3.88%	1.5 years, 1.25% 11.5 years, 4.38%
Macaulay duration	5.35	5.34	5.36
Cash flow yield	3.16%	3.33%	3.88%
Convexity	31.98	34.51	50.21
BPV	$10,524	$10,506	$10,516

Q.

Based on Exhibit 2, the portfolio with the greatest structural risk is:

1. A.Portfolio A.

2. B.Portfolio B.

3. C.Portfolio C.

Solution

C is correct. Structural risk arises from the design of the duration-matching portfolio. It is reduced by minimizing the dispersion of the bond positions, going from a barbell structure to more of a bullet portfolio that concentrates the component bonds’ durations around the investment horizon. With bond maturities of 1.5 and 11.5 years, Portfolio C has a definite barbell structure compared with those of Portfolios A and B, and it is thus subject to a greater degree of risk from yield curve twists and non-parallel shifts. In addition, Portfolio C has the highest level of convexity, which increases a portfolio’s structural risk.

Q.

Which portfolio in Exhibit 2 fails to meet the requirements to achieve immunization for multiple liabilities?

1. A.Portfolio A

2. B.Portfolio B

3. C.Portfolio C

Solution

A is correct. The two requirements to achieve immunization for multiple liabilities are

• for the money duration (or BPV) of the asset and liability to match and

• for the asset convexity to exceed the convexity of the liability.

Although all three portfolios have similar BPVs, Portfolio A is the only portfolio to have a lower convexity than that of the liability portfolio (31.98, versus 33.05 for the $20 million liability portfolio), and thus, it fails to meet one of the two requirements needed for immunization.

Q.

Based on Exhibit 2, relative to Portfolio C, Portfolio B:

1. A.has higher cash flow reinvestment risk.

2. B.is a more desirable portfolio for liquidity management.

3. C.provides less protection from yield curve shifts and twists.

Solution

B is correct. Portfolio B is a laddered portfolio with maturities spread more or less evenly over the yield curve. A desirable aspect of a laddered portfolio is liquidity management. Because there is always a bond close to redemption, the soon-to-mature bond can provide emergency liquidity needs. Barbell portfolios, such as Portfolio C, have maturities only at the short-term and long-term ends and thus are much less desirable for liquidity management.

Serena explains to Trey that the underlying duration-matching strategy is based on the following three assumptions.

1. Yield curve shifts in the future will be parallel.

2. Bond types and quality will closely match those of the liabilities.

3. The portfolio will be rebalanced by buying or selling bonds rather than using derivatives.

Q.

Serena’s three assumptions regarding the duration-matching strategy indicate the presence of:

1. A.model risk.

2. B.spread risk.

3. C.counterparty credit risk.

Solution

A is correct. Serena believes that any shift in the yield curve will be parallel. Model risk arises whenever assumptions are made about future events and approximations are used to measure key parameters. The risk is that those assumptions turn out to be wrong and the approximations are inaccurate. A non-parallel yield curve shift could occur, resulting in a mismatch of the duration of the immunizing portfolio versus the liability.

chose B - spread risk coz buying selling bonds involves spread cost.

ChatGPT (Correct) - https://chatgpt.com/c/1f0a9113-6155-4571-823f-3cb08a76abc5

Serena's three assumptions regarding the duration-matching strategy indicate the presence of:

A. Model risk.

Here's the reasoning for each option:

1. Model risk: This is the risk that the assumptions and models used to estimate the duration and match assets to liabilities may be incorrect or incomplete. Serena's assumptions about parallel yield curve shifts, matching bond types and quality to liabilities, and rebalancing the portfolio by buying or selling bonds all suggest reliance on a specific model for duration matching. If these assumptions do not hold true, the model may fail, leading to potential mismatches and financial losses.

2. Spread risk: This refers to the risk that the difference (spread) between the yields on different types of bonds (e.g., corporate vs. government bonds) will change. While Serena's assumption about matching bond types and quality to liabilities touches on spread considerations, it does not directly address changes in spreads between different bond types.

3. Counterparty credit risk: This is the risk that the counterparty in a financial transaction will not fulfill its obligations. Serena’s assumptions do not explicitly mention or rely on counterparty relationships or creditworthiness, so this risk is not directly indicated by the assumptions given.

Therefore, Serena's three assumptions primarily point to the presence of model risk.

The third project for Serena is to make a significant direct investment in broadly diversified global bonds for Kiest’s pension plan. Kiest has a young workforce, and thus, the plan has a long-term investment horizon. Trey needs Serena’s help to select a benchmark index that is appropriate for Kiest’s young workforce. Serena discusses three benchmark candidates, presented in Exhibit 3.

Exhibit 3:

Global Bond Index Benchmark Candidates

Index Name	Effective Duration	Index Characteristics
Global Aggregate	7.73	Market cap weighted; Treasuries, corporates, agency, securitized debt
Global Aggregate GDP Weighted	7.71	Same as Global Aggregate, except GDP weighted
Global High Yield	4.18	GDP weighted; sovereign, agency, corporate debt

Q.

The global bond benchmark in Exhibit 3 that is least appropriate for Kiest to use is the:

1. A.Global Aggregate Index.

2. B.Global High Yield Index.

3. C.Global Aggregate GDP Weighted Index.

Solution

B is correct. Kiest has a young workforce and thus a long-term investment horizon. The Global Aggregate and Global Aggregate GDP Weighted Indexes have the highest durations (7.73 and 7.71, respectively) and would be appropriate for this group. Global High Yield is the least appropriate due to its relatively shorter duration.

With the benchmark selected, Trey provides guidelines to Serena directing her to (1) use the most cost-effective method to track the benchmark and (2) provide low tracking error.

After providing Trey with advice on direct investment, Serena offered him additional information on alternative indirect investment strategies using (1) bond mutual funds, (2) exchange-traded funds (ETFs), and (3) total return swaps. Trey expresses interest in using bond mutual funds rather than the other strategies for the following reasons.

Reason 1	Total return swaps have much higher transaction costs and initial cash outlay than bond mutual funds.
Reason 2	Unlike bond mutual funds, bond ETFs can trade at discounts to their underlying indexes, and those discounts can persist.
Reason 3	Bond mutual funds can be traded throughout the day at the net asset value of the underlying bonds.

Q.

To meet both of Trey’s guidelines for the pension’s bond fund investment, Serena should recommend:

1. A.pure indexing.

2. B.enhanced indexing.

3. C.active management.

Solution

B is correct. Low tracking error requires an indexing approach. A pure indexing approach for a broadly diversified bond index would be extremely costly because it requires purchasing all the constituent securities in the index. A more efficient and cost-effective way to track the index is an enhanced indexing strategy, whereby Serena would purchase fewer securities than the index but would match primary risk factors reflected in the index. Closely matching these risk factors could provide low tracking error.

Q.

Which of Trey’s reasons for choosing bond mutual funds as an investment vehicle is correct?

1. A.Reason 1

2. B.Reason 2

3. C.Reason 3

Solution

B is correct. Although a significant spread between the market price of the underlying fixed-income securities portfolio and an ETF’s NAV should drive an authorized participant to engage in arbitrage, many fixed-income securities are either thinly traded or not traded at all. This situation might allow such a divergence to persist.

Chose B coz 1 - total return swaps don't change initial outlay? only currency swap does? 3 - ETV can be traded all day, not a benefit to choose mutual fund

SD&R Capital (SD&R), a global asset management company, specializes in fixed-income investments. Molly, chief investment officer, is meeting with a prospective client, Leah of DePuy Financial Company (DFC).

Leah informs Molly that DFC’s previous fixed-income manager focused on the interest rate sensitivities of assets and liabilities when making asset allocation decisions. Molly explains that, in contrast, SD&R’s investment process first analyzes the size and timing of client liabilities, and then it builds an asset portfolio based on the interest rate sensitivity of those liabilities.

Q.

The investment process followed by DFC’s previous fixed-income manager is best described as:

1. A.asset-driven liabilities.

2. B.liability-driven investing.

3. C.asset–liability management.

Solution

C is correct. Asset–liability management strategies consider both assets and liabilities in the portfolio decision-making process. Leah notes that DFC’s previous fixed-income manager attempted to control for interest rate risk by focusing on both the asset and the liability side of the company’s balance sheet. The previous manager thus followed an asset–liability management strategy.

Molly notes that SD&R generally uses actively managed portfolios designed to earn a return in excess of the benchmark portfolio. For clients interested in passive exposure to fixed-income instruments, SD&R offers two additional approaches.

Approach 1	Seeks to fully replicate a small range of benchmarks consisting of government bonds.
Approach 2	Follows an enhanced indexing process for a subset of the bonds included in the Bloomberg Barclays US Aggregate Bond Index. Approach 2 may also be customized to reflect client preferences.

Q.

Relative to Approach 1 of gaining passive exposure, an advantage of Approach 2 is that it:

1. A.minimizes tracking error.

2. B.requires less risk analysis.

3. C.is more appropriate for socially responsible investors.

Solution

C is correct. Enhanced indexing is especially useful for investors who consider environmental, social, or other factors when selecting a fixed-income portfolio. Environmental, social, and corporate governance (ESG) investing, also called socially responsible investing, refers to the explicit inclusion or exclusion of some sectors, which is more appropriate for an enhanced index strategy relative to a full index replication strategy. In particular, Approach 2 may be customized to reflect client preferences.

To illustrate SD&R’s immunization approach for controlling portfolio interest rate risk, Molly discusses a hypothetical portfolio composed of two non-callable, investment-grade bonds. The portfolio has a weighted average yield-to-maturity of 9.55%, a weighted average coupon rate of 10.25%, and a cash flow yield of 9.85%.

Q.

The two-bond hypothetical portfolio’s immunization goal is to lock in a rate of return equal to:

1. A.9.55%.

2. B.9.85%.

3. C.10.25%.

Solution

B is correct. Immunization is the process of structuring and managing a fixed-income portfolio to minimize the variance in the realized rate of return and to lock in the cash flow yield (internal rate of return) on the portfolio, which in this case is 9.85%.

ChatGPT (Correct) - https://chatgpt.com/c/cdfca09e-b8d3-4fe8-a8c0-89e91ce4d77e

To answer the question, we need to understand what the immunization approach aims to achieve. In finance, immunization is a strategy to shield a portfolio from interest rate risk by ensuring that the portfolio's duration matches the investor's investment horizon. This strategy locks in a rate of return for the investor.

Given the information:

• Weighted average yield-to-maturity (YTM): 9.55%

• Weighted average coupon rate: 10.25%

• Cash flow yield: 9.85%

The rate of return that an immunization strategy aims to lock in is typically the cash flow yield, as it represents the yield on the portfolio's cash flows taking into account the timing of those cash flows. Therefore, the immunization goal for the two-bond hypothetical portfolio would be to lock in a rate of return equal to:

B. 9.85%.

While YTM is an important measure of a bond's return, it does not directly account for the timing of the bond's cash flows in the context of the entire portfolio. The immunization strategy focuses on locking in the return based on the cash flows, which is more accurately represented by the cash flow yield.

The coupon rate does not account for the bond's price or the reinvestment of interest payments. It simply represents the bond's interest payments as a percentage of its face value, not the actual return an investor earns if the bond is purchased at a price different from its face value.

Leah informs Molly that DFC has a single $500 million liability due in nine years, and she wants SD&R to construct a bond portfolio that earns a rate of return sufficient to pay off the obligation. Leah expresses concern about the risks associated with an immunization strategy for this obligation. In response, Molly makes the following statements about liability-driven investing:

Statement 1	Although the amount and date of SD&R’s liability is known with certainty, measurement errors associated with key parameters relative to interest rate changes may adversely affect the bond portfolios.
Statement 2	A cash flow matching strategy will mitigate the risk from non-parallel shifts in the yield curve.

Q.

Which of Molly’s statements about liability-driven investing is (are) correct?

1. A.Statement 1 only.

2. B.Statement 2 only.

3. C.Both Statement 1 and Statement 2.

Solution

C is correct.

Molly is correct that measurement error can arise even in immunization strategies for Type 1 cash flows, which have set amounts and set dates. Also, a parallel shift in yield curves is a sufficient but not a necessary condition to achieve the desired outcome.

Non-parallel shifts as well as twists in the yield curve can change the cash flow yield on the immunizing portfolio; however, minimizing the dispersion of cash flows in the asset portfolio mitigates this risk. As a result, both statements are correct.

Cash flow matching, here only 1 timing so there's no dispersion of cash flows so statement 2 is correct in the context of the single liability

Molly provides the four US dollar–denominated bond portfolios in Exhibit 1 for consideration. Molly explains that the portfolios consist of non-callable, investment-grade corporate and government bonds of various maturities because zero-coupon bonds are unavailable.

Exhibit 1:

Proposed Bond Portfolios to Immunize SD&R Single Liability

	Portfolio 1	Portfolio 2	Portfolio 3	Portfolio 4
Cash flow yield	7.48%	7.50%	7.53%	7.51%
Average time to maturity	11.2 years	9.8 years	9.0 years	10.1 years
Macaulay duration	9.8	8.9	8.0	9.1
Market value-weighted duration	9.1	8.5	7.8	8.6
Convexity	154.11	131.75	130.00	109.32

Q.

Based on Exhibit 1, which of the portfolios will best immunize SD&R’s single liability?

1. A.Portfolio 1

2. B.Portfolio 2

3. C.Portfolio 3

Solution

B is correct. In the case of a single liability, immunization is achieved by matching the bond portfolio’s Macaulay duration with the horizon date. DFC has a single liability of $500 million due in nine years. Portfolio 2 has a Macaulay duration of 8.9, which is closer to 9 than that of either Portfolio 1 or 3. Therefore, Portfolio 2 will best immunize the portfolio against the liability.

ChatGPT said portfolio 4 but it's not given. but matching macD is legit.

https://chatgpt.com/c/65b729cc-07cd-46fa-b6e1-2c31de3b9bbd

To determine which bond portfolio is best suited to immunize SD&R’s single $500 million liability due in nine years, we need to consider the following factors:

1. Matching Duration: The Macaulay duration of the bond portfolio should be close to the liability duration (nine years) to effectively immunize against interest rate changes.

2. Yield: Higher yields can generate more income to meet the liability.

3. Convexity: Lower convexity can be preferable because it indicates less sensitivity to interest rate changes, leading to a more stable bond portfolio.

Q.

Which of the portfolios in Exhibit 1 best minimizes the structural risk to a single-liability immunization strategy?

1. A.Portfolio 1

2. B.Portfolio 3

3. C.Portfolio 4

Solution

C is correct. Structural risk to immunization arises from twists and non-parallel shifts 📍 in the yield curve. Structural risk is reduced by minimizing the dispersion of cash flows in the portfolio, which can be accomplished by minimizing the convexity for a given cash flow duration level. Because Portfolio 4 has the lowest convexity compared with the other two portfolios and also has a Macaulay duration close to the liability maturity of nine years, it minimizes structural risk.

The discussion turns to benchmark selection. DFC’s previous fixed-income manager used a custom benchmark with the following characteristics:

Characteristic 1	The benchmark portfolio invests only in investment-grade bonds of US corporations with a minimum issuance size of $250 million.
Characteristic 2	Valuation occurs on a weekly basis, because many of the bonds in the index are valued weekly.
Characteristic 3	Historical prices and portfolio turnover are available for review.

Q.

Which of the custom benchmark’s characteristics violates the requirements for an appropriate benchmark portfolio?

1. A.Characteristic 1

2. B.Characteristic 2

3. C.Characteristic 3

Solution

B is correct. The use of an index as a widely accepted benchmark requires clear, transparent rules for security inclusion and weighting, investability, daily valuation, availability of past returns, and turnover. Because the custom benchmark is valued weekly rather than daily, this characteristic would be inconsistent with an appropriate benchmark.

ChatGPT (Correct)

https://chatgpt.com/c/a870e6b6-093b-41a7-8c97-49cf17a902b0

Characteristic 1: The benchmark portfolio invests only in investment-grade bonds of US corporations with a minimum issuance size of $250 million.

• This characteristic ensures that the benchmark is focused on a specific and relevant segment of the market (investment-grade US corporate bonds) and has a reasonable level of liquidity (issuance size of at least $250 million). This criterion does not violate the requirements for an appropriate benchmark.

Characteristic 2: Valuation occurs on a weekly basis, because many of the bonds in the index are valued weekly.

• Benchmarks should ideally provide timely and frequent pricing information to reflect current market conditions. Weekly valuation may not be frequent enough for a benchmark, as it can lead to stale pricing and misalignment with more frequently valued portfolios. Therefore, this characteristic could be problematic if daily valuations are standard in the market.

Characteristic 3: Historical prices and portfolio turnover are available for review.

• Transparency regarding historical prices and turnover is crucial for evaluating and understanding the benchmark's performance and risk profile. This characteristic is essential for an appropriate benchmark and does not violate any requirements.

Molly explains that, in order to evaluate the asset allocation process, fixed-income portfolios should have an appropriate benchmark. Leah asks for benchmark advice regarding DFC’s portfolio of short-term and intermediate-term bonds, all denominated in US dollars. Molly presents three possible benchmarks in Exhibit 2.

Exhibit 2:

Proposed Benchmark Portfolios

Benchmark	Index	Composition	Duration
1	Bloomberg Barclays US Bond Index	80% US government bonds 20% US corporate bonds	8.7
2 Index Blend	50% Bloomberg Barclays US Corporate Bond Index	100% US corporate bonds	7.5
	50% Bloomberg Barclays Short-Term Treasury Index	100% short-term US government debt	0.5
3	Bloomberg Barclays Global Aggregate Bond Index	60% EUR-denominated corporate bonds 40% US-denominated corporate debt	12.3

Q.

Based on DFC’s bond holdings and Exhibit 2, Molly should recommend:

1. A.Benchmark 1.

2. B.Benchmark 2.

3. C.Benchmark 3.

Solution

B is correct. DFC has two types of assets, short term and intermediate term. For the short-term assets, a benchmark with a short duration is appropriate. For the intermediate-term assets, a benchmark with a longer duration is appropriate. In this situation, DFC may wish to combine several well-defined sub-benchmark categories into an overall blended benchmark (Benchmark 2). The Bloomberg Barclays Short-Term Treasury Index is an appropriate benchmark for the short-term assets, and SD&R uses a 50% weight for this component. The longer-duration Bloomberg Barclays US Corporate Bond Index is an appropriate benchmark for the intermediate-term assets, and SD&R uses a 50% weight for this component. As a result, Molly should recommend proposed Benchmark 2.

ChatGPT (Correct by calculating the duration. benchmark 2 duration is ard 4. duration > 7 years are considered long-term by it)

https://chatgpt.com/c/a870e6b6-093b-41a7-8c97-49cf17a902b0

Chaopraya is an investment advisor for high-net-worth individuals. One of her clients, Schuylkill, plans to fund her grandson’s college education and considers two options:

Option 1	Contribute a lump sum of $300,000 in 10 years.
Option 2	Contribute four level annual payments of $76,500 starting in 10 years.

The grandson will start college in 10 years. Schuylkill seeks to immunize the contribution today.

For Option 1, Chaopraya calculates the present value of the $300,000 as $234,535. To immunize the future single outflow, Chaopraya considers three bond portfolios given that no zero-coupon government bonds are available. The three portfolios consist of non-callable, fixed-rate, coupon-bearing government bonds considered free of default risk. Chaopraya prepares a comparative analysis of the three portfolios, presented in Exhibit 1.

Exhibit 1:

Results of Comparative Analysis of Potential Portfolios

	Portfolio A	Portfolio B	Portfolio C
Market value	$235,727	$233,428	$235,306
Cash flow yield	2.504%	2.506%	2.502%
Macaulay duration	9.998	10.002	9.503
Convexity	119.055	121.498	108.091

Chaopraya evaluates the three bond portfolios and selects one to recommend to Schuylkill.

Q.

Recommend the portfolio in Exhibit 1 that would best achieve the immunization.

Template for Question 23

Recommend the portfolio in Exhibit 1 that would best achieve the immunization. (circle one)	Justify your response.
Portfolio A
Portfolio B
Portfolio C

Justification:

Portfolio A is the most appropriate portfolio because it is the only one that satisfies the three criteria for immunizing a single future outflow (liability), given that the cash flow yields are sufficiently close in value:

1. Market Value: Portfolio A's initial market value of $235,727 exceeds the outflow's present value of $234,535. Portfolio B is not appropriate because its market value of $233,428 is less than the present value of the future outflow of $234,535. A bond portfolio structured to immunize a single liability must have an initial market value that equals or exceeds the present value of the liability.

2. Macaulay Duration: Portfolio A’s Macaulay duration of 9.998 closely matches the 10-year horizon of the outflow. Portfolio C is not appropriate because its Macaulay duration of 9.503 is furthest away from the investment horizon of 10 years.

3. Convexity: Although Portfolio C has the lowest convexity at 108.091, its Macaulay duration does not closely match the outflow amount. Of the remaining two portfolios, Portfolio A has the lower convexity at 119.055; this lower convexity will minimize structural risk.

Default risk (credit risk) is not considered because the portfolios consist of government bonds that presumably have default probabilities approaching zero.

Criteria for liability immunization (single liability)

• market value > liability outflow PV (B failed)

• macD match liability horizon (C failed)

• Lower convexity

Q.

Schuylkill and Chaopraya now discuss Option 2. Chaopraya estimates the present value of the four future cash flows as $230,372, with a money duration of $2,609,700 and convexity of 135.142. She considers three possible portfolios to immunize the future payments, as presented in Exhibit 2.

Exhibit 2: Data for Bond Portfolios to Immunize Four Annual Contributions

	Portfolio 1	Portfolio 2	Portfolio 3
Market value	$245,178	$248,230	$251,337
Cash flow yield	2.521%	2.520%	2.516%
Money duration	2,609,981	2,609,442	2,609,707
Convexity	147.640	139.851	132.865

Template for Question 24

Determine the most appropriate immunization portfolio in Exhibit 2. (circle one)	Justify your decision.
Portfolio 1
Portfolio 2
Portfolio 3	lower convexity; closest money duration

Justification: Portfolio 2 is the most appropriate immunization portfolio because it is the only one that satisfies the following two criteria for immunizing a portfolio of multiple future outflows:

1. Money Duration: Money durations of all three possible immunizing portfolios match or closely match the money duration of the outflow portfolio. Matching money durations is useful because the market values and cash flow yields of the immunizing portfolio and the outflow portfolio are not necessarily equal.

2. Convexity: Given that the money duration requirement is met by all three possible immunizing portfolios, the portfolio with the lowest convexity that is above the outflow portfolio’s convexity of 135.142 should be selected.

The dispersion, as measured by convexity, of the immunizing portfolio should be as low as possible subject to being greater than or equal to the dispersion of the outflow portfolio. This will minimize the effect of non-parallel shifts in the yield curve.

Portfolio 3’s convexity of 132.865 is less than the outflow portfolio’s convexity, so Portfolio 3 is not appropriate.

Both Portfolio 1 and Portfolio 2 have convexities that exceed the convexity of the outflow portfolio, but Portfolio 2’s convexity of 139.851 is lower than Portfolio 1’s convexity of 147.640. Therefore, Portfolio 2 is the most appropriate immunizing portfolio.

The immunizing portfolio needs to be greater than the convexity (and dispersion) of the outflow portfolio. But, the convexity of the immunizing portfolio should be minimized in order to minimize dispersion and reduce structural risk.

For multiple liability outflow

1) Matching money duration

2) lowest convexity that above outflow portfolio's convexity

Chaopraya is an investment advisor for high-net-worth individuals. One of her clients, Schuylkill, plans to fund her grandson’s college education and considers two options:

Option 1	Contribute a lump sum of $300,000 in 10 years.
Option 2	Contribute four level annual payments of $76,500 starting in 10 years.

The grandson will start college in 10 years. Schuylkill seeks to immunize the contribution today.

For Option 1, Chaopraya calculates the present value of the $300,000 as $234,535. To immunize the future single outflow, Chaopraya considers three bond portfolios given that no zero-coupon government bonds are available. The three portfolios consist of non-callable, fixed-rate, coupon-bearing government bonds considered free of default risk. Chaopraya prepares a comparative analysis of the three portfolios, presented in Exhibit 1.

Exhibit 1:

Results of Comparative Analysis of Potential Portfolios

	Portfolio A	Portfolio B	Portfolio C
Market value	$235,727	$233,428	$235,306
Cash flow yield	2.504%	2.506%	2.502%
Macaulay duration	9.998	10.002	9.503
Convexity	119.055	121.498	108.091

Chaopraya evaluates the three bond portfolios and selects one to recommend to Schuylkill.

Q.

After selecting a portfolio to immunize Schuylkill's multiple future outflows, Chaopraya prepares a report on how this immunization strategy would respond to various interest rate scenarios. The senario analysis is presented in Exhibit 3.

Exhibit 3: Projected Portfolio Response to Interest Rate Scenarios

	Immunizing Portfolio	Outflow Portfolio	Difference
Upward parallel shift
Δ Market value	-6,410	-6,427	18
Δ Cash flow yield	0.250%	0.250%	0.000%
Δ Portfolio BPV	-9	-8	-1
Downward parallel shift
Δ Market value	6,626	6,622	4
Δ Cash flow yield	-0.250%	-0.250%	0.000%
Δ Portfolio BPV	9	8	1
Steepening twist
Δ Market value	-1,912	347	-2,259
Δ Cash flow yield	0.074%	-0.013%	0.087%
Δ Portfolio BPV	-3	0	-3
Flattening twist
Δ Market value	1,966	-343	2,309
Δ Cash flow yield	-0.075%	0.013%	-0.088%
Δ Portfolio BPV	3	0	3

Discuss the effectiveness of Chaopraya's immunization strategy in terms of duration gaps.

Solution

Chaopraya’s strategy immunizes well for parallel shifts, with little deviation between the outflow portfolio and the immunizing portfolio in market value and BPV.

Because the money durations are closely matched, the differences between the outflow portfolio and the immunizing portfolio in market value are small and the duration gaps (as shown by the difference in Δ Portfolio BPVs) between the outflow portfolio and the immunizing portfolio are small for both the upward and downward parallel shifts.

Chaopraya’s strategy does not immunize well for the non-parallel steepening and flattening twists (i.e., structural risks) shown in Exhibit 3. In those cases, the outflow portfolio and the immunizing portfolio market values deviate substantially and the duration gaps between the outflow portfolio and the immunizing portfolio are large.

Chosovi Puhuyesva is the chief investment officer of Abiquia Mutual Assurance Company, a provider of life insurance, which is headquartered in Albuquerque, New Mexico. Puhuyesva manages an asset portfolio of fixed-income securities designed to fund Abiquia’s insurance liabilities and grow its surplus so as to protect members from premium increases or possibly allow for premium reductions.

Puhuyesva’s approach matches the interest rate sensitivity of the asset portfolio to that of the liabilities. If she has reasonably strong beliefs about how interest rates will change in the near future and the surplus exceeds her threshold of 4% of assets, she will adjust the interest rate sensitivity of the asset portfolio to attempt to increase the surplus. She typically uses derivatives positions to adjust the asset portfolio’s interest rate sensitivity, rather than buying and selling securities.

Puhuyesva’s approach to asset/liability management would least likely be characterized as:

1. A.contingent immunization.

2. B.cash flow matching.

3. C.derivatives overlay.

LEAST LIKELY!

Solution

B is correct. Puhuyesva matches interest rate sensitivities of the asset portfolio to the insurance liability portfolio. This is a duration-matching approach, not a cash flow–matching approach. She makes portfolio decisions based on whether she has strong views about future interest rate movements; therefore, contingent immunization could be used to describe her approach. She uses derivatives to adjust portfolio duration; therefore, derivatives overlay could partly be used to describe her approach.

A is incorrect because Puhuyesva will alter the duration of the asset portfolio if she has strong views on future interest rate changes, which is a contingent immunization strategy.

C is incorrect because Puhuyesva uses derivatives to alter the asset portfolio’s duration, which is a derivatives overlay approach.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Compare strategies for a single liability and for multiple liabilities, including alternative means of implementation

ChatGPT

https://chatgpt.com/c/f80fa1c3-a590-473d-aa3b-3675ff0147e0

B. cash flow matching.

Here's the reasoning:

• Contingent immunization: This is a strategy where a portfolio is actively managed to outperform a certain benchmark or required return, but if the surplus drops below a certain level, the strategy switches to immunization to ensure the liabilities are met. Puhuyesva’s approach of adjusting the interest rate sensitivity and managing the surplus threshold aligns with contingent immunization principles.

• Derivatives overlay: This refers to using derivatives to adjust the risk profile of a portfolio without altering the underlying securities. Puhuyesva’s use of derivatives to manage interest rate sensitivity directly fits this description.

• Cash flow matching: This involves structuring a portfolio so that its cash flows (from interest and principal payments) match the expected outflows to meet liabilities. Puhuyesva’s strategy of managing interest rate sensitivity through derivatives rather than structuring specific cash flows indicates that cash flow matching is not the primary method used.

Puhuyesva believes interest rates will fall over the next three months and wants to position the asset portfolio accordingly. She intends to use futures contracts on the 10-year Treasury bond. The three-month contract has a par value of USD100,000 and a basis point value of USD102.30 per contract. Exhibit 1 provides current information about the asset and liability portfolios.

Exhibit 1

Abiquia’s Assets and Liabilities

	Assets	Liabilities
Value	USD217.3 million	USD206.8 million
Modified duration	11.2 years	14.5 years
Basis point value (BPV)	USD243,376	USD299,860

The most appropriate action given Puhuyesva’s views on interest rates and the information in Exhibit 1 would be to buy:

1. A.492 contracts.

2. B.614 contracts.

3. C.552 contracts.

how to determine buy or sell? also why value of asset (4% higher) matter?

ChatGPT (Incorrect - calculated 552 but didn't consider value of assers)

https://chatgpt.com/c/c404e5df-b597-480e-b599-ef8cc462c66e

Additional Consideration

Because the value of the assets is more than 4% greater than the value of the liabilities (calculated as 217.3206.8−1=5.1%\frac{217.3}{206.8} - 1 = 5.1\%206.8217.3​−1=5.1%) and Puhuyesva believes interest rates will fall, the duration of assets should be greater than the duration of liabilities to ensure the surplus increases if interest rates fall. Therefore, buying slightly more than 552 contracts would be more appropriate.

Conclusion

B is correct. To fully remove the duration gap, 552 futures contracts should be bought. However, because Puhuyesva expects interest rates to fall and wants the surplus to increase, buying more than 552 contracts is advisable. Hence, the correct answer is:

B. 614 contracts.

The benchmark of the Abiquia asset portfolio is complex and is composed of fixed weights of a variety of global fixed-income indexes. Recently, a decision was made to add South American debt to the benchmark at a 6% weight. Puhuyesva’s assistant, Alo Honanie, is tasked with finding an appropriate index for South American debt securities. He narrows his choices to three: Deuda Sudamericana (DS), Renta Fija Sudamericana (RFS), and Bonos de Sur y Centro America (BSCA). All three contain similar mixtures of corporate and government debt with credit rating weightings that are essentially the same. Summary information for these indexes is found in Exhibit 2.

Exhibit 2:

South American Debt Indexes

	DS	RFS	BSCA
Current duration	9.2 years	10.8 years	8.7 years
Number of securities	312	187	263
Weighting scheme	Value weighted	Value weighted	Equally weighted

If Puhuyesva’s focus is avoiding credit quality deterioration, which of the South American debt indexes should most likely be chosen on the basis of the information in Exhibit 2?

1. A.RFS

2. B.DS

3. C.BSCA

olution

C is correct. Compared with other weighting schemes, such as equally weighted, value-weighted indexes are tilted toward issuers with higher levels of debt. The more an issuer or sector borrows, the greater the tilt toward that issuer in the index. Leverage and creditworthiness are negatively correlated, so a value-weighted index will be more susceptible to credit quality deterioration than an equally weighted index will be. BSCA is an equally weighted index, whereas the others are value weighted.

A is incorrect because RFS is a value-weighted index.

B is incorrect because DS is a value-weighted index.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Discuss criteria for selecting a benchmark and justify the selection of a benchmark

ChatGPT (Correct)

https://chatgpt.com/c/97573380-cfe7-48d0-b1ee-e6863b3bc078

Value-weighted means that more money is put into debts from bigger issuers (companies or governments with more debt). This can be risky because if one of these bigger issuers starts having problems, it affects the index more heavily.

Equally weighted means that each debt in the basket is given the same importance, no matter how big the issuer is. This is safer because it spreads the risk more evenly. If one issuer has problems, it doesn't affect the index as much.

Honanie and Puhuyesva meet to discuss the choice of debt indexes. Puhuyesva expresses her concerns about the difficulties they will face in trying to purchase securities to match the index chosen: “Whatever index we choose, my goal is to match it as closely as possible while minimizing costs. We will need to focus on minimizing tracking risk. One advantage we have over equity portfolio managers is that fixed-income valuation models are much more reliable than those for equities; therefore, it is much easier to determine the value of a fixed-income portfolio than an equity portfolio.”

Is Puhuyesva most likely correct in her comments to Honanie regarding South American debt indexes?

1. A.No. She is incorrect regarding valuation.

2. B.Yes

3. C.No. She is incorrect regarding tracking risk.

Solution

A is correct. Puhuyesva is incorrect regarding valuation. Equity securities typically trade much more frequently than debt securities, so current market valuations are available. Many fixed-income securities are very illiquid, trading very infrequently. Therefore, pricing and valuation are difficult, and such estimations as matrix pricing, which are subject to error, must be used.

B is incorrect because Puhuyesva is incorrect regarding valuation.

C is incorrect because tracking error (tracking risk) is a good way to measure how well a portfolio is mimicking its benchmark index.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Discuss bond indexes and the challenges of managing a fixed-income portfolio to mimic the characteristics of a bond index

Honanie responds, “Because of the intended size of our South American debt portfolio, it would be too expensive to attempt full replication of any of these indexes. The two choices available to us are purchasing securities that, together, match the primary risk characteristics of the chosen index or purchasing pooled investments, such as mutual funds or exchange-traded funds. A synthetic strategy cannot be pursued because there are no exchange-traded derivative contracts for these indexes.”

Are Honanie’s comments to Puhuyesva regarding replicating a South American debt index most likely correct?

1. A.Yes.

2. B.No. He is incorrect regarding synthetic strategies.

3. C.No. He is incorrect regarding full replication.

Solution

B is correct. Honanie is incorrect regarding synthetic strategies because an active futures market is not required. A total return swap could be entered into in the over-the-counter market to achieve exposure to the desired index.

A is incorrect because Honanie is incorrect regarding synthetic strategies.

C is incorrect because Honanie is correct regarding the prohibitive costs of a full replication strategy for a relatively small portfolio; 6% of $217.3 million is only $13.0 million.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Compare alternative methods for establishing bond market exposure passively

ChatGPT

https://chatgpt.com/c/a25edfa1-fa74-4866-a850-0e70514715ea

The Abiquia asset portfolio benchmark has a US Treasury debt component. Puhuyesva asks Honanie to explore choices for that piece of the portfolio and provide an executive summary to her. Honanie’s summary compares laddered, bullet, and barbell portfolio structures, assuming the same portfolio value and duration, and highlights three key differences.

• Difference 1: The laddered portfolio would have lower convexity than the other portfolio styles.

• Difference 2: The laddered portfolio would provide for better liquidity management relative to the other portfolio styles.

• Difference 3: The laddered portfolio would provide better diversification over the interest rate cycle compared with the other portfolio styles.

Of the differences between a laddered strategy for fixed-income portfolios and bullet and barbell strategies described by Honanie, which is least likely correct?

1. A.Difference 3

2. B.Difference 2

3. C.Difference 1

Solution

C is correct. Given the same value and duration, of the three types, the bullet portfolio would have the lowest convexity and the barbell portfolio would have the highest. The laddered portfolio would have a convexity in between the two.

A is incorrect because the laddered portfolio would regularly buy new long-term securities to replace maturing securities on the short end. To the extent interest rates are volatile, the laddered portfolio would eventually contain a mixture (diversity) of high- and low-yielding securities.

B is incorrect because the laddered portfolio would always have some securities with little time remaining before maturity. These would be good collateral for a repo or loan or would shortly turn into cash (upon maturity), thus providing high liquidity.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Describe construction, benefits, limitations, and risk–return characteristics of a laddered bond portfolio

bullet portfolio would have the lowest convexity and the barbell portfolio would have the highest. The laddered portfolio would have a convexity in between the two.

At a second meeting, Ruelas tells Maestre about a EUR22 million bond issue Cávado would like to retire. The issue is currently rated A–, and credit spreads for that rating are relatively high. Ruelas expects spreads to narrow in the future as the economy improves and as Cávado’s performance for the coming year is factored into markets.

The bond is closely held by two investment funds, and Ruelas feels they would be willing to sell their bond exposure at a small premium over the market price.

Ruelas also feels Cávado’s auditors would permit accounting defeasement if Cávado purchased a portfolio of high-quality government bonds whose cash flow characteristics closely matched the Cávado bonds or

if it purchased a portfolio of corporate bonds with similar duration and convexity characteristics and higher yields. Maestre recommends a strategy for retiring the bond.

Which of the following strategies would Maestre most likely recommend for retiring the Cávado bond?

1. A.Bond tender offer

2. B.Cash flow matching with government bonds

3. C.Duration matching with corporate bonds

Solution

A is correct. Because the outstanding bond issue can likely be purchased for a small premium over market value, there is no reason to engage in a more complicated and likely more expensive retirement process using a cash flow-matching or duration-matching strategy.

B is incorrect because there is no need to engage in the more complicated process when the outstanding bond issue can be purchased at little premium.

C is incorrect because there is no need to engage in the more complicated process when the outstanding bond issue can be purchased at little premium.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Compare strategies for a single liability and for multiple liabilities, including alternative means of implementation

ChatGPT (Incorrect, but done pretty well explaining clearer)

https://chatgpt.com/c/4559c303-b5b1-4f77-82a6-79079034496f

The Goal

Cávado wants to pay off (retire) these bonds early. This means they want to buy back the bonds from the investors who currently hold them.

Possible Strategies

1. Bond tender offer (Option A):

   • This means offering to buy back the bonds from the investors at a specific price.

   • It's like saying, "Hey, we'll pay you a little more than the current price if you sell us your bonds now."

   • Simple and direct approach.

2. Cash flow matching with government bonds (Option B):

   • This means buying a set of government bonds (very safe bonds) that pay out money at the same times and in the same amounts as the Cávado bonds.

   • This is more complicated because you need to find and buy the right set of government bonds.

3. Duration matching with corporate bonds (Option C):

   • This involves buying a set of corporate bonds (issued by other companies) that have similar characteristics to the Cávado bonds.

   • This is also complicated and involves finding the right bonds to match.

As Maestre continues, she discusses an example of a single liability owed by Cávado, a EUR2.3 million balloon payment due to the former CEO of the company in approximately six and a half years as a part of her deferred compensation package.

Maestre tells the group, “Suppose you wanted to immunize this liability. One way to do so would be to purchase zero-coupon bonds with essentially zero credit risk that mature in six-and-a-half years and have a face value of EUR2.3 million.

Unfortunately, no zero-coupon bonds are available with this maturity.

Therefore, a portfolio of high-quality government bonds with a duration of approximately six-and-a-half years could be used, although this portfolio might have to be adjusted over time to maintain a matched duration with the liability.” She proposes to select one of the three portfolios shown in Exhibit 2.

Exhibit 2

German Euro-Denominated Government Bond Portfolios

	Portfolio A	Portfolio B	Portfolio C
Cash Flow Yield	2.18%	2.14%	2.16%
Macaulay Duration	6.50	6.52	6.47
Convexity	102.64	86.16	129.43

Which of the portfolios described in Exhibit 2 would most likely be recommended by Maestre?

1. A.Portfolio A

2. B.Portfolio B

3. C.Portfolio C

Solution

B is correct. The three portfolios have essentially the same cash flow yield. They also have Macaulay durations very close to the horizon for the liability (i.e., 6.5 years). Therefore, the question is one of convexity, and the differences in convexity are meaningful.

Although more (positive) convexity is generally desired by fixed-income investors,

💡 the goal of ALM is to minimize the dispersion of cash flows around the Macaulay duration and make the portfolio more like the zero-coupon liability it is attempting to immunize.

Therefore, Portfolio B should be recommended because it has the lowest convexity. Minimizing the portfolio convexity (i.e., the dispersion of cash flows around the Macaulay duration) makes the portfolio closer to the zero-coupon bond that would provide perfect immunization.

A is incorrect because Portfolio A has a substantially larger convexity than Portfolio B.

C is incorrect because Portfolio C has a substantially larger convexity than Portfolio B.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Evaluate strategies for managing a single liability

Immunize Single Liability

1) Close MacD duration

2) low convexity

Ruelas also tells Maestre that he has considered moving to a passively managed bond portfolio. He is not convinced it is

worth his or his staff’s time and effort to try to beat the broad market bond index. (does it worth my time to trade trying to beat S&P500 ? )

He is concerned, however, that it may be no less expensive either in time or transaction costs to replicate an index than to actively manage a portfolio. Maestre recommends a bond-indexing strategy.

What bond indexing strategy would Maestre least likely recommend?

1. A.A stratified sampling approach

2. B.An index mutual fund

3. C.A synthetic strategy using a total return swap

Solution

A is correct. Given that bonds typically trade in large blocks (in excess of USD1 million), attempting to build a bond index fund, even with a stratified sampling approach, would be difficult given the small size of the portfolio. Although mutual funds require payment of expenses, index funds benefit from economies of scale that are passed on to investors. A synthetic approach using a total return swap and holding cash would work. Although it would require finding a counterparty for a relatively small swap, conducting due diligence to control counterparty risk, and dealing with occasional rollover risk, it would still have lower costs than building the portfolio directly.

B is incorrect because an index mutual fund would be very easy to implement compared to stratified sampling and given the relatively small size of the portfolio would likely have lower costs.

C is incorrect because a synthetic approach using a total return swap would be easier and cheaper to implement than stratified sampling because of the small size of the portfolio.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Compare alternative methods for establishing bond market exposure passively

ChatGPT Explained why TRS is cheaper

https://chatgpt.com/c/9d3b62da-0e23-47c7-b591-935c8682f002

• Lower Transaction Costs:

  • When you use a total return swap, you're not buying the actual bonds. Instead, you're entering into an agreement where you pay a counterparty a fixed or floating rate, and in return, you receive the total return of a bond index. This means you avoid the costs associated with buying and selling large blocks of bonds.

• Reduced Trading Volume:

  • Buying individual bonds, especially in large quantities, involves significant transaction costs, including broker fees, bid-ask spreads, and sometimes high minimum purchase amounts. With a swap, you avoid these high trading volumes and the associated costs.

• Simplified Management:

  • Managing a bond portfolio involves ongoing tasks like reinvesting coupons (interest payments), dealing with maturing bonds, and maintaining the portfolio's alignment with the index. A swap simplifies this because the counterparty manages these details, and you just deal with the net payments of the swap.

• Avoiding Illiquidity Issues:

  • Some bonds can be hard to buy or sell (illiquid), especially in smaller quantities, which can drive up costs. A swap mitigates this issue since the agreement is based on the index performance rather than direct bond transactions.

• Counterparty Risk Management:

  • Although you need to manage counterparty risk (the risk that the other party in the swap may default), this can be less costly than managing the operational complexities and costs of a diversified bond portfolio. Proper due diligence and choosing a reliable counterparty can mitigate this ri

Ruelas tells Maestre he is concerned about the many risks Cávado faces both in managing the pension fund and in managing the derivatives overlay. He asks if any risks can be avoided. Maestre names a risk that is not faced in managing the portfolio and would be virtually eliminated through careful selection of the type of derivatives used in the overlay.

In her response to Ruelas regarding risks, Maestre is most likely referring to:

1. A.spread risk.

2. B.model risk.

3. C.counterparty credit risk.

Solution

C is correct. Counterparty credit risk is essentially absent from exchange-traded derivatives, such as futures contracts, and can be essentially eliminated from over-the-counter derivatives, such as swaps, through inclusion of a Credit Support Annex.

In contrast, model risk is implicit in the management of a defined-benefit pension plan, which is made up of Type IV liabilities (uncertain amount and uncertain timing).

Further, most fixed-income derivatives contracts trade on credit risk–free government securities, and the pension plan’s assets consist of both investment-grade and speculative-grade corporate securities, making spread risk difficult to eliminate from the management of the portfolio.

A is incorrect because spread risk is very difficult to eliminate for a fixed-income portfolio containing a variety of investment grade and speculative grade corporate securities.

B is incorrect because model risk cannot be eliminated for a defined-benefit pension plan’s liabilities.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Explain risks associated with managing a portfolio against a liability structure

ChatGPT (Correct - and explained further)

https://chatgpt.com/c/7c7513c3-68a7-4f55-9b49-0124f78ebd8e

1. Ruelas and Maestre's Conversation: Ruelas is worried about different risks involved in managing both a pension fund and some special financial tools called derivatives. He asks Maestre if any of these risks can be avoided.

2. What Are Derivatives?: Derivatives are financial contracts that derive their value from an underlying asset, like stocks, bonds, or interest rates. They can be used to manage or "hedge" risk.

3. Maestre's Response: Maestre mentions a specific risk that isn't a problem when managing the main portfolio but can be a concern with derivatives. She says this risk can almost be eliminated if they choose the right type of derivatives.

4. Understanding Risks:

   • Spread Risk: This is the risk that the difference between the buying and selling price of assets will change unfavorably.

   • Model Risk: This is the risk that the mathematical models used to value assets or manage risk might be wrong.

   • Counterparty Credit Risk: This is the risk that the other party in a financial contract (like a derivative) might not fulfill their obligations.

5. The Best Answer:

   • The risk Maestre is referring to is counterparty credit risk.

   • Why? Because when you choose the right kind of derivatives, especially those cleared through central counterparties (organizations that act as middlemen to ensure the deal goes smoothly), you can almost eliminate the risk of the other party defaulting.

So, Maestre is most likely talking about counterparty credit risk because it can be avoided through careful selection of derivatives.

During the meeting, Maestre presents some information about Cávado’s pension fund, which is primarily invested in corporate bonds with a mixture of investment-grade and speculative-grade issues. This information is presented in Exhibit 1.

Exhibit 1

Cávado Pension Fund Liabilities and Assets

	Liabilities	Assets
Value	EUR47.3 million	EUR49.8 million
Modified Duration	12.6 years	18.4 years
Basis Point Value (BPV)	EUR59,598	EUR91,632

Ruelas explains that he uses futures contracts on euro-denominated German government bonds to reduce the duration gap between assets and liabilities. However, because the pension fund has only a small surplus and he would like to increase this surplus through active management of the portfolio, he employs a contingent immunization strategy. The fund is currently short 254 contracts based on a 10-year bond with a par value of EUR100,000 and a basis point value (BPV) of EUR97.40 per contract.

Given the futures position entered into by the pension fund, Ruelas most likely believes interest rates will:

1. A.fall.

2. B.rise.

3. C.remain the same.

supposedly

amt = (59598 - 91632) / 97.40 = -329

but short 254 only, so

when short less, means buy, means he think... bond price up, interests fall

TOTALLY CORRECT !

In their first face-to-face meeting, Ruelas gathers a group of his employees and asks Maestre to explain the methods Cávado uses to manage interest rate risk. Maestre starts by discussing the nature of pension fund management.

She tells the group, “With a defined-benefit pension fund, the assets are structured to match the expected cash outflows required to meet the liabilities, making it a form of liability-driven investing (LDI).

Pension funds can be difficult to manage, because neither the timing nor the amount of the liabilities is known in advance with certainty.

With LDI, interest rate risk management efforts focus on changes in the values of the assets because the liabilities, while uncertain, aren’t affected by changes in interest rates.”

Is Maestre’s description of pension fund management as a form of LDI most likely correct?

1. A.Yes.

2. B.No, she is incorrect regarding the focus of interest rate risk management.

3. C.No, she is incorrect regarding the difficulty of managing pension funds.

Solution

B is correct. Liability-driven investing (LDI) is a form of asset/liability management (ALM). All ALM strategies require the manager to incorporate the interest rate sensitivity of both the assets and the liabilities in the portfolio management process. The amount and timing of pension fund liabilities may be sensitive to changes in interest rates if retirement decisions are based on other savings or salaries change with market interest rates. Further, the value of the liability portfolio would change with changes in interest rates because of a discount rate effect, even if the amount or timing of the payments do not change.

A is incorrect because LDI must take into account the net interest rate sensitivity of both the asset and liability portfolios.

C is incorrect because defined-benefit pension fund liabilities are Type IV liabilities (timing and amount of cash flows is uncertain), and these are the most difficult liabilities to manage.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Describe liability-driven investing

ChatGPT

https://chatgpt.com/c/82148f4c-5f2a-4490-9f32-11de4af2f3bb

Maestre is explaining how pension funds work, specifically a type called a defined-benefit pension fund. Here’s what that means:

• Pension Fund: This is money set aside by companies to pay their employees after they retire.

• Defined-Benefit: This means the company promises to pay a certain amount to retirees, no matter what happens with the investments.

Maestre says that managing these pension funds is a type of strategy called Liability-Driven Investing (LDI).

Liability-Driven Investing (LDI): This is a strategy where the investments (assets) are chosen to match the expected payments (liabilities) that need to be made to retirees. The goal is to ensure there’s enough money to pay retirees when they need it.

Maestre explains two main points:

1. Pension funds are hard to manage: This is because we don’t know exactly when retirees will need the money or how much they’ll need. This is true and accurate.

2. Interest rate risk management focuses on the assets: Here’s where she makes a mistake. She says that changes in interest rates don’t affect the liabilities (the payments to retirees). But actually, interest rates do affect the liabilities. If interest rates change, the value of the liabilities (how much money the company needs to have) changes too. Effective LDI strategies focus on managing this interest rate risk for both assets and liabilities to ensure the company can meet its future payment obligations.

Adams replies to Berendsen, “We focus on the ability of the portfolio to meet future cash flow needs and seek to immunize the liabilities as an objective in the management of the portfolio.

If the fixed-income portfolio achieves an average annual investment return of at least 4% for the next four years, the proceeds of its liquidation will be enough to purchase an annuity sufficient to provide the funds needed to supplement your Social Security benefits. Until then, we will observe the following principles for managing the portfolio:

Principle I	Our investment strategy is structured to address a Type I liability.
Principle II	The strategy should begin by analyzing the size and timing of liabilities.
Principle III	The solution will require an asset-driven liability framework as opposed to a liability-driven investing one.

Which of Adams’s three principles is least likely relevant for managing Berendsen’s fixed-income portfolio?

1. A.Principle I

2. B.Principle II

3. C.Principle III

Solution

C is correct. Managing the portfolio to Berendsen’s retirement needs is an example of a liability-driven investment, not an asset-driven liability. The aim of a liability-driven investment is to manage the assets to meet the liabilities. The liabilities are given and not driven by the assets.

A is incorrect because this is an example of a Type 1 liability. The price of the annuity and the timing of its purchase are both known.

B is incorrect because analyzing the size and timing of the liabilities is relevant to managing Berendsen’s portfolio.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Describe liability-driven investing

I have summarized your fixed-income portfolio consisting of three government bonds in Exhibit 1. The yield curve has steepened since the bonds were purchased, which can be seen by comparing their respective yield to maturities (YTMs) of the purchase price yield to today’s yield.”

Exhibit 1

Berendsen Fixed-Income Portfolio Characteristics

	Bond A	Bond B	Bond C
Coupon rate	0.50%	9.00%	4.45%
Maturity date	15-Feb-2021	15-Aug-2023	15-Feb-2027
YTM at time of purchase	2.95%	4.72%	4.97%
YTM at current price	1.85%	4.70%	5.07%
Market value	USD732,412	USD930,720	USD986,100
Allocation	28%	35%	37%
Macaulay duration	1.49	3.48	6.43

Note 1: Interest earned on cash: 1.00%

Note 2: Portfolio cash flow yield: 4.15%

According to the information in Exhibit 1 and assuming Berendsen retires in four years, the fixed-income portfolio most likely:

1. A.should have a shorter duration.

2. B.needs a higher cash flow yield.

3. C.has currently achieved zero replication.

mv1 = 732412

mv2 = 930720

mv3 = 986100

w1 = 28%

w2 = 35%

w3 = 37%

macD = 1.49; 3.48; 6.43

0.28*1.49 + 0.35 * 3.48 + 0.37*6.43 = 4.0143, but approximately 4 also

when weighted MacD == duration of single liability

return == same

Zero Replication

(But I'm not sure how to measure the return part

Adams states, “Generally when we evaluate similar situations, we will use a passive, as opposed to an active, management strategy for the fixed-income portfolio, which means the risk of measurement error will be greater than asset liquidity risk.”

Is Adams is most likely correct in her assessment of measurement error?

1. A.Yes

2. B.No, because passive management would preclude measurement error

3. C.No, because asset liquidity risk is greater than the risk of measurement error

Solution

A is correct. Measurement error for Asset BPV can arise even in the classic passive immunization strategy for Type I cash flows, which have set amounts and dates. Asset liquidity can become a risk factor in strategies that add active investing to otherwise passive fixed-income portfolios and would not be applicable here.

B and C are incorrect.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Explain risks associated with managing a portfolio against a liability structure

Later, Adams and junior portfolio manager Frank Neeson review the fixed-income portfolios of two new defined benefit plan clients, Lawson Doors & Cabinets, Inc., and Wharton Farms.

Lawson’s plan has 30 participants, who are mostly experienced craftsmen and machinists, whereas

Wharton has over 100 participants in its plan.

The average participant age is 15 years younger for the Wharton plan compared with the Lawson plan.

In both plans, participants receive a monthly benefit upon retirement based on average final pay and have no option for a lump sum distribution.

The two plans’ portfolio characteristics are shown in Exhibit 2.

Exhibit 2

Selected Plan Portfolio Statistics

	Lawson	Wharton
Market value of assets	USD15,498,000	USD8,351,000
Duration of assets	7.79	7.82
Duration of liabilities	7.78	10.01
Semiannual portfolio dispersion	46.07	147.22
Accumulated benefit obligation	USD14,389,000	USD7,470,000
Portfolio cash flow yield	4.47%	4.51%

Which of the following three strategies is least likely appropriate for the plans in Exhibit 2?

1. A.Duration matching

2. B.Cash flow matching

3. C.Contingent immunization

Solution

B is correct. Cash flow matching is least appropriate for both plans. In both the Lawson and Wharton plans, participants are entitled to receive a monthly benefit. Cash flow matching entails building a dedicated portfolio of zero-coupon or fixed-income bonds to ensure there are sufficient cash inflows to pay the scheduled cash outflows. However, such a strategy is impractical and can lead to large cash flow holdings between payment dates, resulting in reinvestment risk and forgone returns on cash holdings.

C is incorrect. Contingent immunization is an appropriate strategy for both plans. Contingent immunization allows for active bond portfolio management until a minimum threshold in the surplus is reached. The threshold of 5% (of assets greater than liabilities) is exceeded in both plans; the Lawson portfolio has a surplus of 7.7%, and the Wharton portfolio has a surplus of 11.8%.

A is incorrect. Duration management is also appropriate for both the Lawson and Wharton plans. In this case, however, because they enjoy a surplus of assets to liabilities, the contingent immunization strategy is most appropriate. Since the plans are in the process of being advised by Pavonia, Wharton would likely be advised to eliminate the duration gap in similar form to Lawson.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Compare strategies for a single liability and for multiple liabilities, including alternative means of implementation

Monthly benefit -> Not suitable using cash flow matching (?)

such a strategy is impractical and can lead to large cash flow holdings between payment dates, resulting in reinvestment risk and forgone returns on cash holdings.

Adams states to Neeson, “For the Lawson and Wharton plans, we can consider one of three alternative strategies to manage the multiple liabilities associated with these plans. Whenever a plan’s surplus is less than 5%, we favor passive management strategies. We could also use a derivatives strategy, and I prefer derivatives strategies that protect the portfolio against an increase in interest rates but will not produce large losses if rates decrease.”

Which of the following strategies most likely meets Adams’ preferences?

1. A.Buy a payer swaption.

2. B.Write a receiver swaption.

3. C.Enter into a pay fixed swap.

Solution

A is correct. Adams would most likely buy a payer swaption. Although all three choices would hedge against rising interest rates, the potential losses on a payer swaption if rates fell would be limited to the option premium and would not be potentially large with uncertain timing.

B is incorrect because the potential loss on writing a receiver swaption if rates fell would be contingent on the interest rate and would be uncertain until termination of the contract.

C is incorrect because the amount of the potential loss if interest rates fell is contingent on the interest rate and would be uncertain until termination of the contract with a pay fixed swap.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Evaluate liability-based strategies under various interest rate scenarios and select a strategy to achieve a portfolio’s objectives

ChatGPT (Correct)

https://chatgpt.com/c/137d6393-b1c7-46b0-9ff4-9106292276ee

Neeson comments, “The durations for almost half of the bonds in the Wharton portfolio are clustered around 4 years, and the durations of the remainder around 12 years, while the durations of the Lawson portfolio bonds are clustered between 6 years and 8 years. In general, a laddered bond portfolio approach would improve liquidity management for both, although the Lawson portfolio would experience an increase in cash flow reinvestment risk and the Wharton portfolio would experience a decrease in convexity.”

Is Neeson most likely correct in his assessment of the effects of a laddered bond portfolio approach on the Wharton and Lawson portfolios?

1. A.Yes

2. B.No, because the Lawson portfolio is a bullet portfolio where the duration of its assets are matched to the duration of its liabilities

3. C.No, because the duration of the Wharton liabilities is greater than that of the Lawson liabilities owing to the younger age of its participants

Solution

A is correct. A laddered portfolio has lower convexity and dispersion than a barbell portfolio but more than a bullet portfolio, given comparable duration and cash flow yields. Lower convexity and dispersion are desirable aspects in liquidity management. In a laddered portfolio, there is always a bond close to redemption enhancing liquidity. As bonds mature, the final coupon and principal are available for distribution or can be reinvested in a long-term bond at the back of the ladder. The Wharton portfolio is more of a barbell, has higher convexity than the Lawson portfolio, and would see a larger reduction in cash flow reinvestment risk with the reduction of convexity.

B and C are incorrect. Neither duration nor the projected life of the plan reveal the convexity or dispersion characteristics of the portfolio.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Describe construction, benefits, limitations, and risk–return characteristics of a laddered bond portfolio

Rumson Shrewsbury and Sandy Silver are field consultants with Fair Haven Advisers, LLC, an investment consultant firm specializing in fixed-income investing. They plan to expand their practice to focus on such clients as retirement schemes, insurance companies, and others that require solutions to meet liability streams. They meet to discuss Fair Haven’s approach to this new business segment, and Shrewsbury makes the following points to Silver.

• Point 1: Life-insurance companies and defined benefit (DB) pension schemes both use liability-driven investing (LDI), which is a special form of asset–liability management (ALM). In both cases, the liabilities are defined and assets are managed in a way that considers the profile and characteristics of the liability.

• Point 2: Asset-driven liabilities (ADLs), like LDI, are special cases of ALM. Financing companies accumulate assets as a result of their underlying business. They use ADLs to structure their assets in a way that matches the maturities of the liabilities.

• Point 3: An LDI strategy requires estimating the amount and timing of cash outlays in order to estimate the interest rate sensitivity of the liabilities.

Shrewsbury is least likely correct on which point?

1. A.Point 1

2. B.Point 2

3. C.Point 3

Solution

B is correct. Shrewsbury is incorrect with regard to Point 2. Financing companies that accumulate such assets as loans as a result of their underlying business use ADLs to structure their liabilities in a way that matches the maturities of the assets. In this manner, the debt manager is seeking to minimize interest rate risk by better matching the duration of assets and liabilities. With LDI, the liabilities are given and the assets are managed in a way that considers the structure of the liabilities, as Shrewsbury correctly states in Point 1. An LDI strategy requires that the liabilities be modeled to measure their interest rate sensitivity, as he correctly states in Point 3.

A is incorrect. With LDI, the liabilities are given and the assets are managed in a way that considers the structure of the liabilities, as Shrewsbury correctly states in Point 1.

C is incorrect. An LDI strategy requires that the liabilities be modeled to measure their interest rate sensitivity, as he correctly states in Point 3.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Describe liability-driven investing

ChatGPT (Correct)

https://chatgpt.com/c/13c2d944-afe3-4c35-86a1-ea00ebcacc7a

Shrewsbury is least likely correct on Point 2.

Here’s why:

• Point 1: Life-insurance companies and defined benefit (DB) pension schemes indeed use liability-driven investing (LDI) as part of their asset-liability management (ALM) strategy. This involves managing assets in a way that considers the characteristics of the liabilities, which is a well-established practice.

• Point 2: Asset-driven liabilities (ADLs) are not typically considered a form of ALM. Instead, ALM usually focuses on managing assets to meet specific liabilities (as in LDI), whereas ADLs involve structuring assets based on the business model rather than matching liabilities. This makes the characterization of ADLs as a form of ALM somewhat inaccurate.

• Point 3: An LDI strategy does indeed require estimating the amount and timing of cash outlays to assess the interest rate sensitivity of the liabilities. This is a fundamental aspect of implementing an LDI approach.

Silver tells Shrewsbury, “Managing fixed-income portfolios to meet obligations requires an understanding of the nature of the liabilities. Clients with liability types such as those listed in Exhibit 1 use yield statistics, such as Macaulay duration, modified duration, money durations, and the present value of a basis point (PVBP), when implementing immunization strategies.”

Exhibit 1

Classification of Liabilities

Liability Type	Example	Cash Outlay Amount	Timing
I	Bond with no options	Known	Known
II	Callable bond	Known	Uncertain
III	Structured notes	Uncertain	Known
IV	Defined benefit plan	Uncertain	Uncertain

Shrewsbury responds, “Only Type I clients can measure the interest rate sensitivity of liabilities using yield statistics. Those with Type II, III, and IV liabilities must use a curve duration statistic, such as effective duration, to estimate interest rate sensitivity.”

Who is least likely correct with regard to the measures that clients in Exhibit 1 use when immunizing their liabilities?

1. A.Shrewsbury regarding Type I investors

2. B.Silver regarding Type I, II, III, and IV investors

3. C.Shrewsbury regarding Type II, III, and IV investors

Solution

B is correct. Silver is correct in that Type I clients can use a yield statistic for immunizing their liabilities, but he is incorrect in stating that Type II, III, and IV investors can use the same approach. An advantage to knowing the size and timing of cash flows is that yield duration statistics—that is, Macaulay duration, modified duration, money duration, and PVBP—can be used to measure the interest rate sensitivity of the liabilities. With Type II, III, and IV liabilities, a curve duration statistic known as effective duration is needed to estimate interest rate sensitivity. This statistic is calculated using a model for the uncertain amount and/or timing of the cash flows and an initial assumption about the yield curve.

A is incorrect because Shrewsbury is correct regarding Type I clients.

C is incorrect because Shrewsbury is correct regarding II, III, and IV clients.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Evaluate strategies for managing a single liability

Silver and Shrewsbury begin discussing a client that sponsors a US DB plan. The client wants to immunize the liabilities such that changes in interest rates under various scenarios will not cause a deterioration in funded status. Key data for the plan assets and liabilities are provided in Exhibit 2. Silver’s forecast is that interest rates will rise in a non-parallel fashion. In fact, he expects a bear steepening of the curve as inflation accelerates because of rising wages.

Exhibit 2

Defined Benefit Plan Characteristics

Description	Assets	Liabilities
Market Value in USD	517,342,000
Liability, PBO* in USD		500,000,000
Macaulay Modified Duration	12.66	13.10
Convexity	21.40	22.51
Dispersion	6.48	6.70
Cash Flow Yield (%)	4.90	4.50
PV01	654,281	684,276

Based on the data in Exhibit 2, will the client discussed most likely be able to immunize its DB plan given the interest rate scenario described by Silver?

1. A.Yes

2. B.No, because of the differences in money duration

3. C.No, because of the differences in convexity and dispersion

Solution

C is correct. The money duration of the assets and liabilities are equal: 517,342,000 × 12.66 = 6,548,381,000, and 500,000,000 × 13.10 = 6,548,381,000. For parallel changes, the equal money durations and PV01 imply that assets and liabilities would move in tandem. Silver expects a bear steepener; that is, long rates will rise faster than short rates. In a bear steepener, long rates rise faster than short rates in a non-parallel fashion. Given that the assets have lower convexity and dispersion than the liabilities, they will underperform; that is, the liabilities would change by a greater amount than the assets.

A is incorrect because Silver expects a bear steepener; that is, long rates will rise faster than short rates. In a bear steepener, long rates rise faster than short rates in a non-parallel fashion. Given that the assets have lower convexity and dispersion than the liabilities, they will underperform.

B is incorrect because the differences in convexity and dispersion are unfavorable; that is, they are lower for the assets than for the liabilities. If the opposite were the case, then the liabilities would be immunized.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Evaluate liability-based strategies under various interest rate scenarios and select a strategy to achieve a portfolio’s objectives

ChatGPT (Correct)

https://chatgpt.com/c/63bfe85e-698b-4a78-b397-221d68176d83

Analysis:

1. Duration Matching:

   • The modified durations of the assets (12.66) and liabilities (13.10) are close but not identical. Ideally, for perfect immunization, the durations should match. The difference indicates a mismatch in the sensitivity of assets and liabilities to changes in interest rates.

2. Convexity and Dispersion: <--

   • The convexity of assets (21.40) is slightly lower than that of liabilities (22.51). Similarly, the dispersion of assets (6.48) is slightly lower than that of liabilities (6.70). This implies that the assets and liabilities do not react similarly to changes in interest rates. Higher convexity means that the value of liabilities will increase at a faster rate than assets as interest rates decline, which could lead to a deterioration in funded status.

3. Bear Steepening Scenario:

   • In a bear steepening scenario, long-term interest rates rise more than short-term rates. This typically increases the liabilities more than the assets, especially if the durations and convexities are not well matched. The given data shows that liabilities have higher duration and convexity than the assets, implying that the liabilities will be more sensitive to changes in interest rates, especially in a steepening scenario.

Silver and Shrewsbury continue their discussion regarding hedging the economic and market risks for a DB plan. Shrewsbury explains that any hedging program can fall short of its objective owing to a number of risks. Silver believes they can use various instruments to hedge interest rate risk but that certain risks can be more difficult to address. He tells Silver, “One risk you face in hedging the liabilities is that the yield of high-quality bonds is used in the discounting process, whereas most investment solutions use a more diversified and lower-quality portfolio of corporate bonds. Conversely, you can face the opposite problem, if you use Treasury futures or interest rate swaps to hedge the liabilities.”

The risk that Silver describes to Shrewsbury in hedging the liabilities is most likely:

1. A.model risk.

2. B.spread risk.

3. C.liquidity risk.

Solution

B is correct. Silver is referring to spread risk in his discussion with Shrewsbury regarding risks in hedging DB plan liabilities. The liabilities are estimated—that is, calculation of the PBO—using high-quality corporate bonds. The typically wider spreads of lower-quality bonds may underperform the spreads of higher-quality bonds in a market sell-off. Conversely, hedging the liabilities with swaps may not provide enough of a spread risk hedge relative to using corporate bonds such that if spreads tighten, high-quality corporate bonds (used to discount liabilities) may outperform swaps. Model risk refers to making incorrect assumptions regarding future liabilities or approximations being inaccurate. Liquidity risk is associated with exhausting available collateral funds to meet margin calls on derivative positions or to pay benefits.

A is incorrect because model risk refers to making incorrect assumptions regarding future liabilities or approximations being inaccurate.

C is incorrect because liquidity risk is associated with exhausting available collateral funds to meet margin calls on derivative positions or to pay benefits.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Explain risks associated with managing a portfolio against a liability structure

ChatGPT (Correct)

https://chatgpt.com/c/01619379-908d-4430-885a-102024f9c4f4

The risk that Silver describes to Shrewsbury in hedging the liabilities is most likely:

B. spread risk.

Explanation: Spread risk refers to the risk that the yield spread between different types of bonds (such as high-quality bonds and lower-quality corporate bonds) will change. This change in spread can affect the effectiveness of the hedging strategy. Silver points out that the yield of high-quality bonds is used in the discounting process, but many investment solutions use a more diversified and lower-quality portfolio of corporate bonds, which have different yield spreads. Conversely, using Treasury futures or interest rate swaps might not perfectly hedge liabilities if those instruments do not match the yield characteristics of the liabilities being hedged. Hence, spread risk is the most relevant risk in this context.

Silver considers alternatives to a cash bond portfolio for hedging the liabilities because he is concerned that as time passes and market conditions change, the initially established hedging program may drift from target levels. Some of his clients with DB plans are underfunded and have interest rate hedge ratios well below 100%. These clients expect rates to rise, and should their view prove correct, the duration gap will improve funded status. He believes these clients should at least consider a costless derivative position to protect from rates falling further if their view is incorrect while also increasing the hedge ratio if rates rise.

What contingent strategies would Shrewsbury’s DB clients most likely enter into under the scenario he outlines?

1. A.Short a receiver swap

2. B.Long a payer swaption, short a receiver swaption

3. C.Long a receiver swaption, short a payer swaption

Solution

C is correct. The plan is not fully funded and is also not fully hedged; that is, the money durations of the assets and liabilities are not matched. If the clients’ view is incorrect and rates fall further, the mismatch will result in the liabilities increasing in value while the assets will appreciate by a lesser amount. Swaptions are a contingent security on interest rate swaps. A receiver swaption would allow the plan to receive a fixed (higher) rate if rates rally, but at the cost of the swaption premium. To finance this receiver swaption, the DB plan can sell a payer swaption to collect a premium that finances the receiver swaption. If rates rise above some level, the plan would increase its duration by virtue of being put a swap. The plan may have anticipated closing the duration gap at higher interest rate levels, so being put a swap is in line with an LDI program.

A is incorrect because a receiver swap is not a contingent security.

B is incorrect because it is the reverse of the correct solution—long a receiver swaption, short a payer swaption.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Compare strategies for a single liability and for multiple liabilities, including alternative means of implementation

ChatGPT (wrong but can see)

https://chatgpt.com/c/2755b81e-4d73-445b-9e8b-44534df4c9dd

Scenario

You have a pension plan (DB plan) that is not fully funded and not fully hedged. This means:

• Not fully funded: The assets (money) you have aren't enough to cover all the future liabilities (money you owe).

• Not fully hedged: The interest rate sensitivity (how much their value changes with interest rates) of your assets and liabilities don't match.

Goal

Your goal is to protect your pension plan from the risk of interest rates falling further, which would increase your liabilities more than your assets. At the same time, you want to benefit if interest rates rise, improving your funding status.

Swaptions

A swaption is like an option (a choice) to enter into an interest rate swap at a future date:

• Receiver swaption: Gives you the right to receive fixed interest payments and pay floating (variable) interest payments.

• Payer swaption: Gives you the right to pay fixed interest payments and receive floating interest payments.

Strategy: Long a Receiver Swaption, Short a Payer Swaption

C. Long a receiver swaption, short a payer swaption

1. Long a Receiver Swaption:

   • Why?: If interest rates fall, this option lets you enter into a swap to receive fixed payments, which would be higher than new lower rates. This helps offset the increase in your liabilities, protecting your plan.

   • Cost: You have to pay a premium (like an insurance premium) for this option.

2. Short a Payer Swaption:

   • Why?: By selling this option, you collect a premium (money) which helps cover the cost of the receiver swaption. If interest rates rise, the buyer of this swaption will exercise their option, and you’ll enter into a swap where you pay fixed and receive floating, which is beneficial since you expected rates to rise.

   • Risk: If rates rise too high, you’ll have to pay fixed rates, but this fits your plan’s goal because it increases your asset duration, matching liabilities bette

Shrewsbury knows that some of his clients do not favor active portfolio management strategies, particularly given their higher fee structures relative to passive strategies. He evaluates alternate ways to establish passive bond market exposure. His preference is to select an instrument that hedges not only the interest rate component of the liability’s discount rate but also the credit component. The obligation should reference a corporate bond index but be structured as a synthetic secured financing transaction.

Shrewsbury would most likely choose which instrument to achieve his alternate investment objective?

1. A.Creation units

2. B.Interest rate swap

3. C.Total return swap

Solution

C is correct. A total return swap (TRS) is an over-the-counter portfolio derivative strategy that combines elements of interest rate swaps and credit derivatives. There is an exchange of cash flows between the two parties over the tenure of the contract, based on a reference obligation that is an underlying equity, commodity, or bond index. In this case, the reference obligation would be a corporate bond index. Creation units are large blocks of exchange-traded fund (ETF) shares traded against a basket of underlying securities; this transaction typically occurs between the ETF distributor and a broker/dealer. Entering into a creation unit transaction is done to facilitate trading but does not establish a passive bond position. The DB plan could use also use the actual ETF as an alternate passive instrument.

A is incorrect because creation units are large blocks of ETF shares traded against a basket of underlying securities.

B is incorrect because the DB plan needs to establish passive interest rate and credit exposure.

Liability-Driven and Index-Based Strategies Learning Outcome

1. Compare alternative methods for establishing bond market exposure passively

ChatGPT (Correct)

https://chatgpt.com/c/2ad62358-119e-44d2-b8ec-a2c5c838ee16

To achieve his alternate investment objective of establishing passive bond market exposure that hedges both the interest rate component and the credit component of the liability's discount rate, Shrewsbury would most likely choose:

C. Total return swap

Here's why:

• Creation units: These are typically used in the creation and redemption process of ETFs and do not inherently provide a hedge for interest rate or credit components.

• Interest rate swap: While an interest rate swap can hedge interest rate risk, it does not address credit risk.

• Total return swap: A total return swap can provide exposure to the total return of a corporate bond index, including both interest rate and credit risk components. It allows Shrewsbury to synthetically replicate the performance of the bond index, making it suitable for his objective.