# CFA Level 3 – Fixed Income Session 9

## CFA Level 3 – Fixed Income, Session 9 – Reading 23

### (Notes, Practice Questions, Sample Questions)

1. If a bond portfolio manager specifies liabilities as a benchmark, she is attempting to earn a return that is:

A)equal to or higher than the return promised to the liability holders.

B)as high as possible.

C)the least risky

(Explanation): The manager that specifies liabilities as a benchmark must ensure that the rate of return earned in the portfolio satisfies the return promised to liability holders.

(This objective may be accomplished by earning equal to or higher than the promised return.)

2. Which of the following is a difference between the investment objective for a liability based benchmark and an index based benchmark? If liabilities are chosen as a benchmark:

A)a return higher than the liability has to be achieved by any means.

B)the objective is only return oriented.

C)the objective is to match the amount and timing of the liability payments.

(Explanation): The objective when managing a portfolio against a liability is to maintain sufficient portfolio value to meet the liabilities

3. Why should a pension fund manager NOT manage against a typical broad-based bond market index?

A)The manager might outperform the index.

B)The duration of a typical broad-based bond market index and the liabilities of a pension fund are not similar.

C)This indexing strategy may produce tracking error risk

(Explanation): The pension fund manager should define the benchmark in terms of the pension liabilities that must be satisfied. Most broad-based bond market indexes have shorter durations.

If the pension fund manager decides to use a bond index, then he should chose one that matches the duration of the pension plan

4. If a bond portfolio manager has specified the benchmark in terms of a bond index, she is attempting to earn a return that is:

A)less risky than the index.

B)as high as possible.

C)equal to or superior to the index.

(Explanation): The manager that uses an index as a benchmark is attempting to earn a rate of return that is equal to or superior to the index

5. Which of the following is a difference between the investment objective for a liability based benchmark and an index based benchmark? If a bond index is chosen as a benchmark the:

A)bond index has to be outperformed on a risk-adjusted basis.

B)objective is primarily return oriented.

C)objective will be less risk averse.

(Explanation): A passive bond portfolio manager’s objective is to get as close to the index return as possible by mimicking the bonds in the index and matching their duration with the understanding that due to management expenses their return will be slightly less than the index. An active bond portfolio manager would attempt to at least meet the index return and outperform it. Outperforming an index on a risk adjusted basis implies using a risk adjusted measurement such as the Sharpe ratio to compare the manager’s performance to the index which is not normally done when comparing the manager’s performance to an index. In a liabilities based benchmark the portfolio manager’s objective is to at least match the value of the liabilities when they come due

6. When the performance of an investment grade corporate bond portfolio is compared to a relevant bond index, which of the following statements about tracking error is CORRECT?

A)If the return on the bond portfolio is substantially lower than the return on the bond index the tracking error is small.

B)If the return on the bond portfolio closely matches the return of the bond index the tracking error is small.

C)Tracking error refers to how closely the return on the bond index matches traders’ expectations and is not related to the return on the bond portfolio

(Explanation): Tracking error is incurred when the return on the bond portfolio deviates from the return on the bond index. Greater deviation means higher tracking error.

7. The manager of a bond fund is assessing several choices in attempting to immunize a portfolio. To meet a predetermined liability, the manager needs a 6% return. Which of the choices below would be the best in pursuit of that goal? An immunized strategy with a target return equal to:

A)6.4% with a 95% confidence interval at +/- 40 basis points.

B)6.0% with a 95% confidence interval at +/- 10 basis points.

C)6.0% with a 99% confidence interval at +/- 20 basis points.

(Explanation): Of the three portfolios, the portfolio with a 6.4% target return and a +/-40 basis point confidence interval has the best chance of achieving the specified return. The chance of not achieving that return is (1 – 95%) / 2 = 2.5% or one out of 40. The portfolios with the 6% target return have only a 50% chance of achieving the specified return

8. The manager of a bond portfolio must immunize the portfolio to meet multiple liabilities over time. To do this the manager needs to:

A)equate the duration of the portfolio with the duration of the composite of liabilities and have the distribution of durations of the portfolio’s assets be narrower than that of the distribution of the liabilities.

B)make the duration of the portfolio higher than the duration of the composite of liabilities and have the distribution of durations of the portfolio’s assets be equal to that of the distribution of the liabilities.

C)equate the duration of the portfolio with the duration of the composite of liabilities and have the distribution of durations of the portfolio’s assets be wider than that of the distribution of the liabilities

(Explanation): Necessary conditions to meet multiple liabilities over time are for the durations to be equal and the distribution of durations of the portfolio’s assets to be wider than that of the distribution of the liabilities

9. A commercial bank takes in short-term deposits and the uses those funds to make longer term loans. As such, the duration of the bank’s assets tends to be longer than the duration of the bank’s liabilities. What will happen when interest rates rise? The bank’s:

A)assets will decrease in value by more than the bank’s liabilities causing the bank’s equity (surplus) to decrease.

B)liabilities will decrease in value by more than the bank’s assets causing the bank’s equity (surplus) to increase.

C)assets will increase in value by more than the bank’s liabilities causing the bank’s equity (surplus) to decrease

(Explanation): As interest rates rise, the long-duration assets will decrease in value by more than the short-duration liabilities. As assets decrease in value by more than liabilities, the bank’s equity (surplus) must decline (A=L+E)

10. Which of the following is a relative measure of the interest rate sensitivity of a portfolio compared to an underlying index?

A)Spread duration.

B)Value at risk.

C)Portfolio duration

(Explanation): Spread duration is a relative measure of the interest rate sensitivity of a portfolio compared to an underlying index. The other choices are both absolute measures

11. Which of the following is an absolute measure of the interest rate sensitivity of a portfolio?

A)Spread duration.

B)Value at risk.

C)Portfolio duration

(Explanation): Portfolio duration is an absolute measure of the interest rate sensitivity of a portfolio.

12. If a portfolio manager is interested in the interest rate sensitivity of her portfolio as compared to a Treasury bond index, which measure should she examine?

A)Spread duration.

B)Portfolio duration.

C)Value at risk

(Explanation): Since the portfolio manager is interested in the interest rate sensitivity of her portfolio as compared to a Treasury bond index, she should examine spread duration

13. Which of the following best describes the difference between spread duration and portfolio duration? Spread duration allows the manager to measure the sensitivity of portfolio value from changes in:

A)both convexity and yield changes.

B)the price of the underlying securities.

C)yield levels relative to a benchmark yield.

(Explanation): With duration a parallel shift in the yield curve could be caused by a change in inflation expectations which causes the yields on all bonds, including treasuries, to increase/decrease the same amount. In spread duration, the shift is in the spread only, indicating an overall increase in risk aversion (risk premium) for all bonds in a given class

14. Two portfolios have the same portfolio duration but one of them has a higher nominal spread duration. How does the higher spread duration affect the portfolio characteristics? The higher spread duration portfolio will have:

A)the same exposure to small parallel shifts in the Treasury curve but will have a higher exposure to changes in the yield difference between non-Treasury and Treasury bonds.

B)the same exposure to small parallel shifts in the Treasury curve but will have a higher exposure to changes in the yield difference between long and short-term Treasury securities.

C)a higher exposure to small parallel shifts in the Treasury curve and a higher exposure to changes in the yield difference between non-Treasury and Treasury bonds

(Explanation): Nominal spread is the spread between the nominal yield on a non-Treasury bond and a Treasury of the same maturity

15. If interest rates rise sufficiently such that the dollar safety margin is negative in a contingent immunization strategy, which of the following statements is least accurate?

A)Contingent immunization is still a viable alternative.

B)The portfolio manager can no longer use contingent immunization.

C)A switch to immunization is necessary.

(Explanation): If the dollar safety margin is negative, the present value of liabilities exceeds the present value of assets and the portfolio manager can no longer use contingent immunization. Equivalently, the portfolio manager must switch to immunization.

16. A portfolio manager has decided to pursue a contingent immunization strategy over a four-year time horizon. He just purchased at par $26 million worth of 6% semiannual coupon, 8-year bonds. Current rates of return for immunized strategies are 6% and the portfolio manager is willing to accept a return of 5%. Given that the required terminal value is $31,678,475, and if the immunized rates rise to 7% immediately, which of the following is most accurate? The dollar safety margin is:

A)positive ($370,765) and the portfolio manager can continue with contingent immunization.

B)negative (-$1,423,980) and the portfolio manager must switch to immunization.

C)positive ($6,158,602) and the portfolio manager can continue with contingent immunization

(Explanation): We are given the required terminal value of $31,678,475.

Next, we calculate the current value of the bond portfolio: PMT = ($26,000,000)(0.03) = $780,000; N = 16; I/Y = 7/2 = 3.5%; and FV = $26,000,000; CPT → PV = $24,427,765.

Next, compute the present value of the required terminal value at the new interest rate: FV = $31,678,475; PMT = 0; N = 8; I/Y = 7/2 = 3.5%; CPT → PV = $24,057,000.

Alternatively $31,678,475 / (1.035)8 = $24,057,000

The dollar safety margin is positive ($24,427,765 − $24,057,000 = $370,765) and the manager can continue to employ contingent immunization

17. A portfolio manager has decided to pursue a contingent immunization strategy over a three-year time horizon. He just purchased at par $93 million worth of 10.0% semiannual coupon, 12-year bonds. Current rates of return for immunized strategies are 10.0% and the portfolio manager is willing to accept a return of 8.5%. If interest rates rise to 11% immediately, which of the following statements is most accurate? The dollar safety margin is:

A)positive ($303,066) and the portfolio manager can continue with contingent immunization.

B)negative (-$2,489,748) and the portfolio manager must switch to immunization.

C)positive ($303,066) and the portfolio manager must switch to immunization

(Explanation): We must first compute the required terminal value: PV=$93,000,000, N=6, I/Y=8.5/2=4.25%, PMT=0, compute FV=$119,382,132. Next, we calculate the current value of the bond portfolio: PMT=($93,000,000)(.05)=$4,650,000, N=24, I/Y=11/2=5.5%, and FV=$93,000,000, CPT → PV=$86,884,460. Next, compute the present value of the required terminal value at the new interest rate: FV=$119,382,132, PMT=0, N=6, I/Y=11/2=5.5%, CPT → PV=$86,581,394.

Alternatively ($119,382,132) / (1.055)6 = $86,581,394

The dollar safety margin is positive ($86,884,460 − $86,581,394 = $303,066) and the manager can continue to employ contingent immunization

18. Which of the following is NOT a key consideration in implementing a contingent immunization strategy?

A)Identifying a suitable and immunizable safety net.

B)Decide in advance about the frequency the portfolio will be rebalanced.

C)Establishing well defined immunized initial and ongoing available target returns

(Explanation): The frequency of rebalancing is determined (among other things) by the level of the safety net. So the rebalancing frequency is not exogenous to interest rate movements

19. In a contingent immunization strategy, which of the following is a reason why the minimum target return might NOT be realized? The minimum target return might not be realized because:

A)interest rates move in a nonparallel manner.

B)there is a rapid market yield movement.

C)the yield volatility changes.

(Explanation): A rapid market yield movement might not give the manager enough time to shift from an active strategy to immunization mode to achieve the minimum target

20. A portfolio manager has decided to pursue a contingent immunization strategy over a three-year time horizon. She just purchased at par $84 million worth of 9.2% semi-annual coupon, 10-year bonds. Current rates of return for immunized strategies are 9.2% and the portfolio manager is willing to accept a return of 8.5%. Given that the required terminal value is $107,829,022, and if interest rates rise to 11% immediately, which of the following is most accurate? The dollar safety margin is:

A)negative (-$3,237,038) and the manager can continue with contingent immunization.

B)negative (-$3,237,038) and the manager must switch to immunization.

C)positive ($1,486,948) and the manager can continue with contingent immunization

(Explanation): We are given the required terminal value of $107,829,022. Next, we calculate the current value of the bond portfolio: PMT=($84,000,000)(.046)=$3,864,000, N=20, I/Y=11/2=5.5%, and FV=$84,000,000, CPT → PV=$74,965,511. Next, compute the present value of the required terminal value at the new interest rate: FV=$107,829,022, PMT=0, N=6, I/Y=11/2=5.5%, CPT → PV=$78,202,549. Alternatively ($107,829,022) / (1.055)6 = $78,202,548 The dollar safety margin is negative ($74,965,511 − $78,202,549 = -3,237,038) and the manager can no longer employ contingent immunization.

Therefore, a switch to immunization is necessary

21.1 John Gillian approaches Carl Mueller, CFA, about managing his bond portfolio. Gillian has two large bond positions. The first of these is $2.8 million face value with a coupon rate of 7.6% (paid semiannually), ten years to maturity, and is currently priced to yield 6.5%. The second position is $4.4 million face of zero coupon bonds that will mature in four years and are priced to yield 5.3%. Gillian asks about interest rate forecasts for the next four years. Mueller says that he expects yields to remain approximately the same (i.e. 6.5%) for maturities of six to 10 years. Gillian says that he needs to have at least $8 million in value at the end of four years.

After further discussion with Gillian about his goals, Mueller determines that a contingent immunization strategy would be the best approach for the coupon-bond position. Gillian asks Mueller to explain the strategy. Mueller says that it is a fairly simple strategy that has only two requirements: determining an available target return and an appropriate safety net return.

Mueller begins computing the necessary inputs for the coupon-bond position. He first calculates the required terminal value and associated target return. Given Gillian’s goal for the total portfolio value, Mueller computes the safety net return, cushion spread, and dollar safety margin.

Gillian asks how likely it is that Mueller will have to immunize the portfolio. He asks if Mueller’s immunization strategy would be required if there is a 50 basis point increase in the market yield today and the rates remain at that level for the next four years.Mueller’s description of the requirements of a contingent immunization strategy is:

A)correct.

B)incorrect because the strategy does not require an available target return although it does require an appropriate safety net return.

C)incorrect because it is incomplete

(Explanation): The strategy does require both an available target return and an appropriate safety net return. Mueller did not mention an important third step: the establishment of effective monitoring procedures to ensure adherence to the contingent immunization plan

21.2 The most likely reason that Mueller did not discuss an immunization strategy for Gillian’s zero-coupon bond position is:

A)there was no need to do so.

B)it is possible to immunize zero coupon bonds, but it is very costly.

C)it is impossible to immunize zero coupon bonds.

(Explanation): Since the maturity of the zero coupon bonds coincided with the investment horizon, there was no need to immunize that position. There is neither reinvestment nor price risk

21.3 The required terminal value for the coupon-bond position is:

A)$4.43 million.

B)$3.4 million.

C)$3.6 million.

(Explanation): Since Gillian requires a total of $8 million for his portfolio and the zero coupon bonds will mature with a value of $4.4 million, the coupon bonds have a required terminal value equal to $8 million minus $4.4 million, or $3.6 million

21.4 The cushion spread for the coupon-bond position is:

A)2.09%.

B)2.20%.

C)2.04%.

(Explanation): Cushion spread is the difference between current rates of return and the minimum required rate of return:

The current value of the coupon bond position is:

INPUTS: N= 20, I/Y = 6.5%/2 = 3.25%, PMT = 7.6%/2 = 3.8% of $2.8 million = $106,400, FV = 2,800,000, CPT PV → PV = -3,023,906 (ignore minus sign)

The minimum required return based upon the required terminal coupon-bond position value of $3.6 million and its present value is (3,023,906)(1+X)8 = 3,600,000. Solving for X we then have:

(1+X)8 = 3,600,000 / 3,023,906

(1+X)8 = 1.1905

1+X = 1.1905.125

1+X = 1.02204

X = .02204

I = 2.204% X 2 = 4.41%

Cushion spread = 6.50 – 4.41 = 2.09%

21.5 The dollar safety margin for the coupon-bond position is closest to:

A)$0.226 million.

B)$0.237 million.

C)$0.290 million.

(Explanation): This is the difference between the current value of the bond portfolio and the present value of the estimated terminal value given the current return:

Current value of the portfolio = $3.024 million as determined in the previous question.

Assets required given a terminal value of $3,600,000 and current rates of return of 6.5%:

3,600,000 / (1.0325)8 = 2,787,289

Dollar safety margin = 3,023,906 – 2,787,289 = 236,617

21.6 Given the forecast of a 50 basis point increase in market yield on the coupon bonds, Mueller will:

A)have to switch to an immunization strategy for the portfolio.

B)have to switch to a passive management strategy for the portfolio.

C)be able to continue with an active management strategy for the portfolio

(Explanation): For a 50 basis point increase in market yields to 7.0% the present value of assets will then become:N = 20, I/Y = 3.5, PMT = 106,400, FV = 2,800,000, CPT PV → PV = -2,919,384

Assets required at the new interest rate of 7.0% =

3,600,000 / (1.035)8 = 2,733,882

The present value of assets of $2.9 million > present value of assets required of $2.7 million thus a 50 basis point increase in market yields will not trigger a switch to immunization to achieve the terminal value of $3.6 million for the coupon bonds.

22. Which of the following refers to the risk that floating rate assets may have an upper bound on the interest rate whereby a maximum rate of interest on the asset is achieved?

A)Call risk.

B)Interest rate risk.

C)Cap risk.

(Explanation): Cap risk is the risk that the interest rate is capped (has a maximum) and that interest income from the asset is then capped