12 June - YC Strategies practices

An analyst manages an active fixed-income fund that is benchmarked to the Bloomberg Barclays US Treasury Index. This index of US government bonds currently has a modified portfolio duration of 7.25 and an average maturity of 8.5 years. The yield curve is upward-sloping and expected to remain unchanged. Which of the following is the least attractive portfolio positioning strategy in a static curve environment?

Solution

B is correct. The 30-year pay-fixed swap is a “short” duration position and also results in negative carry (that is, the fixed rate paid would exceed MRR received) in an upward-sloping yield curve environment; therefore, it is the least attractive static curve strategy.

In the case of a.), the manager enters a “buy-and-hold” strategy by purchasing the 10-year zero-coupon bond and extends duration, which is equal to 9.80 = 10/1.02 since the Macaulay duration of a zero equals its maturity, and ModDur = MacDur/(1+r) versus 7.25 for the index.

Under c.), the manager introduces leverage by purchasing a long-term bond and financing it at a lower short-term repo rate.

An investment manager is considering decreasing portfolio duration versus a benchmark index given her expectations of an upward parallel shift in the yield curve. If she has a choice between a callable bond which is unlikely to be called, a putable bond which is likely to be put, or an option-free bond with otherwise comparable characteristics, the most profitable position would be to:

Solution

B is correct. The value of a bond with an embedded option is equal to the sum of the value of an option-free bond plus the value to the embedded option. With a putable bond, the embedded put option is owned by the bond investor, who can exercise the option if yields-to-maturity increase, as in this scenario. Under A, the embedded call option is owned by the bond issuer, who is more likely to exercise if yields-to-maturity decrease (that is, the bond investor is short the call option). As for C, the option-free bond underperforms the putable bond given the rise in value of the embedded put option.

ChatGPT (Correct)

Interest Rates and Bond Prices: When interest rates go up, the prices of bonds generally go down. Think of it like this: if new bonds are being issued with higher interest rates, the older bonds (with lower rates) become less attractive, so their prices drop.
Types of Bonds:
- Callable Bond: This type of bond can be "called" back by the issuer before it matures. Imagine you lend money to someone, and they have the option to repay you early if they want to. When interest rates go up, the issuer won't call the bond because they don't want to borrow at higher rates. But the bond's price will still go down with rising rates.
- Putable Bond: This type of bond can be "put" back to the issuer by you (the bondholder) before it matures. Imagine you can demand your money back if you want to. If interest rates go up and bond prices go down, you can use this option to sell the bond back to the issuer at a set price, protecting yourself from the price drop.
- Option-Free Bond: This is a regular bond with no special features. It will lose value if interest rates rise, with no additional protection or benefits.
Which Bond to Choose?: If you think interest rates are going to rise (which means bond prices will fall), the putable bond is the best choice. Why? Because it gives you the option to sell it back to the issuer at a set price, helping you avoid losses when other bond prices are falling.

So, in a situation where you expect interest rates to go up, owning the putable bond (Option B) is the most profitable because it protects you from the negative effects of rising rates.

so when yield higher, putable bond value more than normal bond;

callable bond price rises lesser when yield got low

An active fixed-income manager holds a portfolio of commercial and residential mortgage-backed securities that tracks the Bloomberg Barclays US Mortgage-Backed Securities Index. Which of the following choices is the most relevant portfolio statistic for evaluating the first-order change in his portfolio’s value for a given change in benchmark yield?

Solution

A is correct. Effective duration is a yield duration statistic that measures interest rate risk using a parallel shift in the benchmark yield curve (ΔCurve), as in Equation 8.

Effective duration measures interest rate risk for complex bonds whose future cash flows are uncertain because they are contingent on future interest rates.

Both Macaulay duration (B) and modified duration (C) are relevant statistics only for option-free bonds.

An active fund trader seeks to capitalize on an expected steepening of the current upward-sloping yield curve using option-based fixed-income instruments. Which of the following portfolio positioning strategies best positions her to gain if her interest rate view is realized?

Solution

C is correct. A steepening of the yield curve involves an increase in the slope, or the difference between long-term and short-term yields-to-maturity. An optimal portfolio positioning strategy is one which combines a short duration exposure to long-term bonds and a long duration exposure to short-term bonds.

Portfolio C involves the right (but not the obligation) to purchase a 2-year bond, which will increase in value as short-term yields fall with the right to pay-fixed on a 30-year swap, which increases in value if long-term yields rise. Portfolio A involves the sale of two options. Although they will expire unexercised in a steeper curve environment, the investor’s return is limited to the two option premia. Portfolio B is the opposite of Portfolio C, positioning the investor for a flattening of the yield curve.

ChatGPT (Correct)

Swaptions: These are options on interest rate swaps (a swap is a financial agreement to exchange future interest payments).
- Payer Swaption: Gives you the right to enter a swap where you pay a fixed interest rate and receive a variable rate.
- Receiver Swaption: Gives you the right to enter a swap where you receive a fixed interest rate and pay a variable rate.

so if i up, you wanna pay fixed and receive float - payer swaption

A Dutch investor considering a 5-year EUR government bond purchase expects yields-to-maturity to decline by 25 bps in the next six months. Which of the following statements about the rolldown return is correct?

Solution

C is correct.

Rolldown return is the difference between the price of the 5-year bond and that of a 4.5-year bond at the same yield-to-maturity.

A 5-year zero-coupon bond trading at a premium has a negative yield. As the price “pulls to par” over time, the premium amortization will be a loss to the investor.

A reflects the full price appreciation since it is calculated using the lower yield-to-maturity, while B equals E (Δ Price due to investor’s view of benchmark yield).

ChatGPT (Incorrect but for reference

An active investor enters a duration-neutral yield curve flattening trade that combines 2-year and 10-year Treasury positions. Under which of the following yield curve scenarios would you expect the investor to realize the greatest portfolio loss?

Solution

C is correct. A duration-neutral flattening trade involves a short 2-year bond position and a long 10-year bond position, which have a “matched” duration or portfolio duration of zero. This portfolio will realize a loss if the slope of the yield curve—that is, the difference between short-term and long-term yields—increases. The bear steepening in A involves a rise in the 10-year yield-to-maturity more than in the 5-year yield-to-maturity, causing a portfolio loss.

Should be A - bear steepening? explanation correct.

A financial analyst at an in-house asset manager fund has created the following spreadsheet of key rate durations to compare her active position to that of a benchmark index so she can compare the rate sensitivities across maturities.

Tenor

KeyRateDurActive

KeyRateDurIndex

Difference

−0.532

0.738

−1.270

0.324

1.688

−1.364

10y

5.181

2.747

2.434

30y

1.142

2.162

−1.020

Portfolio

6.115

7.335

−1.220

QuestionQ.

Which of the following statements is true if yield levels increase by 50 bps?

Solution

A is correct. Recall from Equation 11 that the sum of the key rate durations equals the effective portfolio duration. The approximate (first-order) change in portfolio value may be estimated from the first (modified) term of Equation 3, namely (−EffDur × ΔYield). Solving for this using the −1.22 effective duration difference multiplied by 0.005 equals 0.0061, or 61 bps.

Equation 11

I see, simply use the keyRateDur diff (-1.22) * 0.005 = -0.0061 = -61 bps

Tenor

KeyRateDurActive

KeyRateDurIndex

Difference

−0.532

0.738

−1.270

0.324

1.688

−1.364

10y

5.181

2.747

2.434

30y

1.142

2.162

−1.020

Portfolio

6.115

7.335

−1.220

QuestionQ.

Which of the following statements best characterizes how the active portfolio is positioned for yield curve changes relative to the index portfolio?

Solution

B is correct. A positive butterfly indicates a decrease in the butterfly spread due to an expected rise in short- and long-term yields-to-maturity combined with a lower medium-term yield-to-maturity. Since the active portfolio is short duration versus the index in the 2-year, 5-year, and 30-year maturities and long duration in the 10-year, it will generate excess return if the butterfly spread falls.

An heuristic

so if Active Portfolio diff is - - + -, so positive butterfly movement would win; vice versa

ChatGPT (Correct)

Tenor

KeyRateDurActive

KeyRateDurIndex

Difference

−0.532

0.738

−1.270

0.324

1.688

−1.364

10y

5.181

2.747

2.434

30y

1.142

2.162

−1.020

Portfolio

6.115

7.335

−1.220

QuestionQ.

Which of the following derivatives strategies would best offset the yield curve exposure difference between the active and index portfolios?

A.Add a pay-fixed 10-year swap and long 2-year, 5-year, and 30-year bond futures positions to the active portfolio.
B.Add a receive-fixed 30-year swap, a pay-fixed 10-year swap, and short positions in 2-year and 5-year bond futures to the active portfolio.
C.Add a pay-fixed 10-year swap, a short 30-year bond futures, and long 2-year and 5-year bond futures positions to the active portfolio.

Solution

A is correct. A net positive key rate duration difference indicates a long duration position relative to the index, while a net negative duration difference indicates a short position. Relative to the index, the active portfolio is “short” in the 2-year, 5-year, and 30-year maturities and “long” the 10-year maturity versus the index. The pay-fixed 10-year swap and long 2-year, 5-year, and 30-year bond futures positions best offset these differences.

ChatGPT (Correct)

Tenor

KeyRateDurActive

KeyRateDurIndex

Difference

−0.532

0.738

−1.270

0.324

1.688

−1.364

10y

5.181

2.747

2.434

30y

1.142

2.162

−1.020

Portfolio

6.115

7.335

−1.220

Which of the following statements best describes the forward rate bias?

Solution

C is correct. Forward rate bias is defined as an observed divergence from interest rate parity conditions under which active investors seek to benefit by borrowing in a lower-yield currency and investing in a higher-yield currency.

A is incorrect since lower-yielding currencies trade at a forward premium.

B is incorrect due to covered interest rate parity; fully hedged foreign currency fixed-income investments will tend to yield the domestic risk-free rate.

ChatGPT (Correct)

The best description of the forward rate bias in the context of fixed-income investments is:

C. Investors tend to favor unhedged fixed-income investments in higher-yielding currencies that are sometimes enhanced by borrowing in lower-yielding currencies.

This statement captures the essence of the forward rate bias, where investors are inclined to invest in higher-yielding currencies without hedging their currency risk, and they may also leverage their positions by borrowing in currencies with lower yields.

A Sydney-based fixed-income portfolio manager is considering the following Commonwealth of Australia government bonds traded on the ASX (Australian Stock Exchange):

Tenor

Coupon

Yield

Price

Modified Duration

Convexity

5.75%

0.28%

110.90

1.922

4.9

4.5y

3.25%

0.55%

111.98

4.241

22.1

2.50%

1.10%

111.97

8.175

85.2

The manager is considering portfolio strategies based upon various interest rate scenarios over the next 12 months. She is considering three long-only government bond portfolio alternatives, as follows:

Bullet: Invest solely in 4.5-year government bonds
Barbell: Invest equally in 2-year and 9-year government bonds
Equal weights: Invest equally in 2-year, 4.5-year, and 9-year bonds

QuestionQ.

The portfolio alternative with the highest modified duration is the:

Solution

B is correct. The modified duration of a fixed-income portfolio is approximately equal to the market value-weighted average of the bonds in the portfolio, so the barbell has a modified duration of 5.049, or (1.922 + 8.175)/2), which is larger than that of either the bullet (4.241) or the equally weighted portfolio (4.779, or (1.922 + 4.241 + 8.175)/3.

The manager estimates that accelerated economic growth in Australia will increase the level of government yields-to-maturity by 50 bps. Under this scenario, which of the three portfolios experiences the smallest decline in market value?

Assume the manager is able to extend her mandate by adding derivatives strategies to the three portfolio alternatives. The best way to position her portfolio to benefit from a bear flattening scenario is to combine a:

A.2-year receive-fixed Australian dollar (AUD) swap with the same modified duration as the bullet portfolio.
B.2-year pay-fixed AUD swap with twice the modified duration as the 2-year government bond in the barbell portfolio.
C.9-year receive-fixed AUD swap with twice the modified duration as the 9-year government bond position in the equally weighted portfolio.

ChatGPT (Totally correct)

Solution

B is correct. A bear flattening scenario is a decrease in the yield spread between long- and short-term maturities driven by higher short-term rates. The manager must therefore position her portfolio to benefit from rising short-term yields. Under A, the receive-fixed 2-year swap is a synthetic long position, increasing portfolio duration that will result in an MTM loss under bear flattening. The receive-fixed swap in answer C will increase duration in long-term maturities. In the case of B, the pay-fixed swap with twice the modified duration of the barbell will more than offset the existing long position, resulting in net short 2-year and long 9-year bond positions in the overall portfolio and a gain under bear flattening.

So, bear flattening -> ST rates rise; so want to receive float at ST (== pay fixed)

if bull flattening -> LT rates falls; you want to receive fixed at LT swap (C is correct)

In her market research, the manager learns that ASX 3-year and 10-year Treasury bond futures are the most liquid products for investors trading and hedging medium- to long-term Australian dollar (AUD) interest rates. Although neither contract matches the exact characteristics of the cash bonds of her choice, which of the following additions to a barbell portfolio best positions her to gain under a bull flattening scenario?

bull flattening -> LT rates falls -> you want to receive fixed long term

not sure man, C?

coz LT rates fall -> LT bond prices rise -> so LT bond futures would benefit from the price rise

Earlier example - pay / receive swaps, so price doesn't matter

Solution

C is correct. A bull flattening is a decrease in the yield spread between long- and short-term maturities driven by lower long-term yields-to-maturity. Both A and B involve changes in portfolio exposure to short-term rates, while C increases the portfolio exposure to long-term rates to benefit from a fall in long-term yields-to-maturity.

ChatGPT (For reference)

A Sydney-based fixed-income portfolio manager is considering the following Commonwealth of Australia government bonds traded on the ASX (Australian Stock Exchange):

Tenor

Coupon

Yield

Price

Modified Duration

Convexity

5.75%

0.28%

110.90

1.922

4.9

4.5y

3.25%

0.55%

111.98

4.241

22.1

2.50%

1.10%

111.97

8.175

85.2

The manager is considering portfolio strategies based upon various interest rate scenarios over the next 12 months. She is considering three long-only government bond portfolio alternatives, as follows:
Bullet: Invest solely in 4.5-year government bonds
Barbell: Invest equally in 2-year and 9-year government bonds
Equal weights: Invest equally in 2-year, 4.5-year, and 9-year bonds

An economic slowdown is expected to result in a 25 bp decline in Australian yield levels. Which portfolio alternative will experience the largest gain under this scenario?

ChatGPT (Totally Correct)

The portfolio alternative with the least exposure to convexity is the:

A.bullet portfolio.
B.barbell portfolio.
C.equally weighted portfolio.

Solution

A is correct. The bullet portfolio has the same convexity as the 4.5-year bond, or 22.1. The barbell portfolio in B has portfolio convexity of 45.05, = (4.9 + 85.2)/2, while the equally weighted portfolio has portfolio convexity of 37.4, = (4.9 + 22.1 + 85.2)/3.

The calculation of convexity is really simple - just weighted average convexity, so don't be lazy

A Sydney-based fixed-income portfolio manager is considering the following Commonwealth of Australia government bonds traded on the ASX (Australian Stock Exchange):

Tenor

Coupon

Yield

Price

Modified Duration

Convexity

5.75%

0.28%

110.90

1.922

4.9

4.5y

3.25%

0.55%

111.98

4.241

22.1

2.50%

1.10%

111.97

8.175

85.2

The manager is considering portfolio strategies based upon various interest rate scenarios over the next 12 months. She is considering three long-only government bond portfolio alternatives, as follows:
Bullet: Invest solely in 4.5-year government bonds
Barbell: Invest equally in 2-year and 9-year government bonds
Equal weights: Invest equally in 2-year, 4.5-year, and 9-year bonds

The current butterfly spread for the Australian government yield curve based upon the manager’s portfolio choices is:

Solution

C is correct. The butterfly spread is equal to twice the medium-term yield minus the short-term and long-term yields, as in Equation 2, or −28 bps, or −0.28% + (2 × 0.55%) − 1.10%).

If the manager has a positive butterfly view on Australian government yields-to-maturity, the best portfolio position strategy to pursue is to:

Solution

A is correct. A positive butterfly view indicates an expected decrease in the butterfly spread due to an expected rise in short- and long-term yields-to-maturity combined with a lower medium-term yield-to-maturity. The investor therefore benefits from a long medium-term (bullet) position and a short short-term and long-term (barbell) portfolio. The portfolio in answer B represents the opposite exposure and benefits from a negative butterfly view, while in C, combining short barbell and long equally weighted portfolios leaves the investor with bullet portfolio exposure.

ChatGPT (Totally Correct)

So positive butterfly is -_- -> so Medium term drops -> Price increase;

so ST & LT yields rise -> price decreases -> short bond

MT yield drops -> Price increases -> long bond

A US-based fixed-income portfolio manager is examining unhedged investments in Thai baht (THB) zero-coupon government bonds issued in Thailand and is considering two investment strategies:

Buy-and-hold: Purchase a 1-year, THB zero-coupon bond with a current yield-to-maturity of 1.00%
Roll down the THB yield curve: Purchase a 2-ear zero-coupon note with a current yield-to-maturity of 2.00% and sell it in a year.

THB proceeds under each strategy will be converted into USD at the end of the 1-year investment horizon. The manager expects a stable THB yield curve and that THB will appreciate by 1.5% relative to USD. The following information is used to analyze these two investment strategies:

Statistic

Buy and Hold

Yield Curve Rolldown

Investment horizon (years)

1.0

Bond maturity at purchase (years)

1.0

2.0

Yield-to-maturity (today)

1.00%

2.00%

Average portfolio bond price (today)

99.0090

96.1169

Expected average portfolio bond price (in 1 year)

100.00

99.0090

Expected currency gains (in 1 year)

1.5%

QuestionQ.

The rolldown returns over the 1-year investment horizon for the Buy-and-Hold and Yield Curve Rolldown portfolios are closest to:

Solution

A is correct. Since both strategies use zero-coupon bonds, the rolldown return is calculated from expected bond price changes from “rolling down” the THB yield curve, which is assumed to be static.

Buy and Hold: 1.00% = (100.00 − 99.009)/99.009
Yield Curve Rolldown: 3.01% = (99.009 − 96.1169)/96.1169

ChatGPT (Absolutely correct)

The total expected return over the 1-year investment horizon for the Buy-and-Hold and Yield Curve Rolldown portfolios are closest to:

Solution

A is correct. Under a static yield curve assumption, expected returns are equal to rolldown return plus changes in currency over the investment horizon. Using Equation 12, we solved for RFC for both portfolios in Question 18, and RFX is 1.5%. Expected returns are:

Buy and Hold: E(R) = 2.515%, or (1.01 × 1.015) − 1
Yield Curve Rolldown: E(R) = 4.555%, or (1.0301 × 1.015) − 1

Note - use multiplication of return, not addition

ChatGPT got wrong on ^

A US-based fixed-income portfolio manager is examining unhedged investments in Thai baht (THB) zero-coupon government bonds issued in Thailand and is considering two investment strategies:
Buy-and-hold: Purchase a 1-year, THB zero-coupon bond with a current yield-to-maturity of 1.00%
Roll down the THB yield curve: Purchase a 2-ear zero-coupon note with a current yield-to-maturity of 2.00% and sell it in a year.
THB proceeds under each strategy will be converted into USD at the end of the 1-year investment horizon. The manager expects a stable THB yield curve and that THB will appreciate by 1.5% relative to USD.

QuestionQ.

Which of the following statements best describes how the expected total return results would change if THB yields were to rise significantly over the investment horizon?

A.Both the Buy-and-Hold and Yield Curve Rolldown expected portfolio returns would increase due to higher THB yields.
B.Both the Buy-and-Hold and Yield Curve Rolldown expected portfolio returns would decrease due to higher THB yields.
C.The Buy-and-Hold expected portfolio returns would be unchanged and the Yield Curve Rolldown expected portfolio returns would decrease due to the rise in yields.

Solution

C is correct. In a higher THB yield scenario in one year, the Yield Curve Rolldown expected return would fall since a higher THB yield-to-maturity in one year would reduce the price at which the investor could sell the 1-year zero in one year. The Buy-and-Hold portfolio return will be unaffected since the 1-year bond matures at the end of the investment horizon.

ChatGPT (Absolutely Correct)

Thai yields == Thai interest rates

if hold to maturity, i doesn't affecy total return

if not, then i falls -> price rises -> higher returns

i rises -> price falls -> lower returns

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