Investments & Securities Chapter 22 Index Was However Will Change Over Time The Fund The Aggregate Will

index was 4.05; however, it will change over time. The fund, in the aggregate, will seek to maintain

a weighted average credit rating of A- or better, based on the weighted average credit quality of

the fund’s portfolio securities.

The fund may continue to hold an investment in its core portfolio that is downgraded to below

investment grade after purchase. If such rating downgrades cause high yield exposure to exceed

Discuss in detail the strategy of this fund.

This fund is following a core strategy. With a core/satellite strategy there is a blending of an

indexed strategy (to create a low-risk core portfolio) and an active strategy (to create

a specialized higher risk tolerant satellite portfolio). Basically, this strategy involves building

a blended portfolio using an indexed and active strategy. The core component is a low-risk

portfolio constructed using one of the indexing strategies. The benchmark for the core portfolio

The core component provides broad market exposure and therefore captures systematic market

risk or what is commonly referred to as a “beta.” In contrast, an active return (commonly referred

to as “alpha”) is sought in the actively managed satellite portfolio. The advantage cited for the

core strategy is that it provides a cost-efficient means for controlling portfolio risk relative to

a benchmark. This relative risk is referred to as tracking error.

486

This satellite allocation may be implemented into 100% equity allocations and/or allocations that

blend with fixed-income or non-equity positions.

9. What are the limitations of using duration and convexity measures in active portfolio

strategies?

Recall that duration is just a first approximation of the change in price resulting from a change in

interest rates while convexity provides a second approximation. Below we discuss the limitation

involved in using the measures of duration and convexity to estimate how portfolio values will

be affected when interest rates change.

There are several limitations to achieve a change in a portfolio’s duration. First, the client may

limit the degree to which the duration of the managed portfolio is permitted to diverge from that

of the benchmark index. Second, research does not support the notion that an active strategy can

profit from the ability to forecast the direction of future interest rates. The academic literature

argues that interest rates cannot be forecasted so that risk-adjusted excess returns can be realized

consistently. It is doubtful whether betting on future interest rates will provide a consistently

superior return.

An additional limitation is that knowing duration and convexity is not always enough to insure

that an active strategy will succeed even if managers are correct in their assessment about

changes in interest rates. For example, suppose that a portfolio manager has a choice of investing

in the bullet portfolio or the barbell portfolio. Which one should be chosen if the manager knows

the following?

487

the two portfolios do not have the same dollar convexity. However, even the benefit of the

greater convexity depends on how much yields change.

In closing, the key point here is that looking at measures such as yield (yield to maturity or some

type of portfolio yield measure), duration, or convexity reveals little about performance over

some investment horizon, because performance depends on the magnitude of the change in

yields and how the yield curve shifts. Therefore, when a manager wants to position a portfolio

based on expectations as to how the yield curve will shift, it is imperative to perform total return

analysis. For example, in a steepening yield curve environment, it is often stated that a bullet

portfolio would be better than a barbell portfolio. However, it is not always the case that a bullet

portfolio would outperform a barbell portfolio. Whether the bullet portfolio outperforms the

barbell depends on how much the yield curve steepens.

10. Next are two portfolios with a market value of $1000 million. The bonds in both

portfolios are trading at par value. The dollar duration of the two portfolios is the same.

Issue

Years to

Maturity

Par Value

(in millions)

Bonds Included in Portfolio I

A

4.0

$240

B

5.0

$260

C

40.0

$300

D

41.0

$200

Bonds Included in Portfolio II

E

19.4

$400

F

20.0

$460

G

20.2

$ 140

Answer the below questions.

(a) Which portfolio can be characterized as a bullet portfolio?

(b) Which portfolio can be characterized as a barbell portfolio?

(c) Suppose the two portfolios have the same dollar duration; explain whether their

performance will be the same if interest rates change.

Even if the yield curve shifts in a parallel fashion due to changes in interest rates, two portfolios

with the same dollar duration will not give the same performance if they have differences in

(d) If they will not perform the same, how would you go about determining which would

perform best assuming that you have a six-month investment horizon?

To determine which portfolio would have the superior performance, we would want to look at

the total return for the six-month investment horizon given expectations about change in yields

and how the yield curve will shift.

11. Answer the below questions.

(a) Explain why you agree or disagree with the following statement: “It is always better to

have a portfolio with more convexity than one with less convexity.”

It is not always better to have a portfolio with more convexity than one with less convexity. This

is illustrated if one examines the portfolios associated with Exhibit 22-9. Although with all other

(b) Explain why you agree or disagree with the following statement: “A bullet portfolio will

always outperform a barbell portfolio with the same dollar duration if the yield curve

steepens.”

One would disagree with the statement that a bullet portfolio will always outperform a barbell

portfolio with the same dollar duration if the yield curve steepens.” This is because the

489

a nonparallel shift of the yield curve. Specifically, the first nonparallel shift column assumes that

if the yield on bond C (the intermediate-term bond) changes by the amount shown in the first

column, bond A (the short-term bond) will change by the same amount plus 25 basis points,

whereas bond B (the long-term bond) will change by the same amount shown in the first column

less 25 basis points. Measuring the steepness of the yield curve as the spread between the

long-term yield (yield on bond B) and the short-term yield (yield on Bond A), the spread has

decreased by 50 basis points. Such a nonparallel shift means a flattening of the yield curve.

As can be seen in Exhibit 22-9, for this assumed yield curve shift, the barbell outperforms the

bullet.

In the last column, the nonparallel shift assumes that for a change in bond C’s yield, the yield on

bond A will change by the same amount less 25 basis points, whereas that on bond B will change

by the same amount plus 25 points: Thus the spread between the long-term yield and the

short-term yield has increased by 50 basis points, and the yield curve has steepened. In this case

the bullet portfolio outperforms the barbell portfolio as long as the yield on bond C does not

rise by more than 250 basis points or fall by more than 325 basis points.

12. What is a laddered portfolio?

13. A portfolio manager owns $10 million par value of bond ABC. The bond is trading at

of 3.

Answer the below questions.

(a) What is the dollar duration of bond ABC per 100-basis-point change in yield?

490

100-basis-point change in yield, a 100-basis-point change in yield for bond ABC would change

its price by about 7%. Based on a price of 80, its price will change by about 0.07(80) = $5.6 per

$80 of market value. Thus, for bond ABC, its dollar duration for a 100-basis-point change in

yield is $5.6 per $80 of market value.

[Similarly, for bond XYZ, its dollar duration for a 100-basis-point change in yield per $90 of

market value can be determined. In this case it is 0.03 (100) = $3.00. So if bonds ABC and XYZ

are being considered as alternative investments in a strategy other than one based on anticipating

interest-rate movements, the amount of each bond in the strategy should be such that they will

both have the same dollar duration.]

(b) What is the dollar duration for the $10 million position of bond ABC?

(c) How much in market value of bond XYZ should be purchased so that the dollar

duration of bond XYZ will be approximately the same as that for bond ABC?

Mathematically, this problem can be expressed as follows: Let

$DABC = dollar duration per 100-basis-point change in yield for bond ABC for the market value

of bond ABC held;

100

Solving for MVXYZ yields:

ABC

$D

491

MVXYZ =

100

3

000,560$

= $18,666,666.6667.

Thus, the market value of bond XYZ that should be purchased (so that the dollar duration of

bond XYZ will be approximately the same as that for bond ABC) will be $18,666,667.

(d) How much in par value of bond XYZ should be purchased so that the dollar duration of

bond XYZ will be approximately the same as that for bond ABC?

The market value of bond XYZ is 90 per $100 of par value, so the price per $1 of par value is

0.9. Dividing MVXYZ (which is $$18,666,667) by 0.9 indicates that the par value of bond XYZ

that should be purchased. We have:

9.0

667,666,18$

= $20,740,740.74

14. Explain why in implementing a yield spread strategy it is necessary to keep the dollar

duration constant.

When comparing positions that have the same dollar duration, it is critical to assess yield spread

strategies. Failure to adjust a portfolio repositioning based on some expected change in yield

spread so as to hold the dollar duration the same means that the outcome of the portfolio will be

15. The excerpt that follows is taken from an article titled “Smith Plans to Shorten,” which

appeared in the January 27, 1992, issue of BondWeek, p. 6:

“When the economy begins to rebound and interest rates start to move up, Smith

Affiliated Capital will swap 30-year Treasuries for 10-year Treasuries and those with

What type of portfolio strategy is Smith Affiliated Capital pursuing?

Smith appears to be following an interest-rate expectation strategy. A manager who believes that

he or she can accurately forecast the future level of interest rates will alter the portfolio’s

sensitivity to interest-rate changes. As duration is a measure of interest-rate sensitivity, this

492

the duration of the managed portfolio is permitted to diverge from that of the benchmark index

may be limited by the client.

If we can assume the remaining maturities or the same, it appears that Smith is following a

substitution swap strategy. A swap in which a money manager exchanges one bond for another

bond that is similar in terms of coupon, maturity, and credit quality, but offers a higher yield, is

called a substitution swap. This swap depends on a capital market imperfection. Such situations

sometimes exist in the bond market owing to temporary market imbalances and the fragmented

nature of the non-Treasury bond market. The risk the money manager faces in making a

substitution swap is that the bond purchased may not be truly identical to the bond for which it is

exchanged. Moreover, typically, bonds will have similar but not identical maturities and coupon.

This could lead to differences in the convexity of the two bonds, and any yield spread may

reflect the cost of convexity.

16. The following excerpt is taken from an article titled “MERUS to Boost Corporates,”

which appeared in the January 27, 1992, issue of BondWeek, p.6:

MERUS Capital Management will increase the allocation to corporates in its $790

million long investment-grade fixed-income portfolio by $39.5 million over the next six

What types of active portfolio strategies is MERUS Capital Management pursuing?

MERUS is increasing corporates in it long investment-grade fixed-income portfolio in the next

months to one year. They are focusing upon investment-grade securities because they expect the

spread will tighten and some issues will be given higher ratings thus increasing their value.

Consequently, now is the time to lock in a higher spread as well as investing in investment-grade

securities that will be strengthened by a robust economy.

493

capacity to service their contractual debt obligations. Yield spreads between Treasury and federal

agency securities will vary depending on investor expectations about the prospects that an

implicit government guarantee will be honored.

17. This excerpt comes from an article titled “Eagle Eyes High–Coupon Callable Corporates”

in the January 20, 1992, issue of BondWeek, p. 7:

“If the bond market rallies further, Eagle Asset Management may take profits, trading $8

million of seven-to 10-year Treasuries for high-coupon single-A industrials that are

callable in two to four years according to Joseph Blanton, Senior V.P. He thinks a further

rally is unlikely, however.

What types of active portfolio strategies are being pursued by Eagle Asset Management?

Blanton may take profits by trading seven-to 10-year Treasuries for high-coupon single-A

industrials that are callable in two to four years because the market rally will fade. This means

Blanton believes the spread will stop decreasing and may even increase making these securities

less desirable. By buying callable bonds, it is implied that interest rates may increase. Blanton

has already sold some seven-to 10 year Treasuries to buy high-coupon single-A nonbank

financial credits implying that he further believes interest rates will increase. In anticipation of

Additionally, Blanton is engaged in a strategy that involves changing his portfolio’s duration.

A money manager who believes that he or she can accurately forecast the future level of interest

rates will alter the portfolio’s sensitivity to interest-rate changes. As duration is a measure of

interest-rate sensitivity, this involves increasing a portfolio’s duration if interest rates are

expected to fall and reducing duration if interest rates are expected to rise. For those managers

18. The following excerpt is taken from an article titled “W.R. Lazard Buys Triple Bs,”

which appeared in the November 18, 1991, issue of BondWeek, p. 7:

“W.R. Lazard & Co. is buying some corporate bonds rated triple B that it believes will be

upgraded and some single A’s that the market perceives as risky but Lazard does not,

What types of active portfolio strategies are being followed by W.R. Lazard & Co.?

Schultz wants to capitalize on what he believes are underpriced bonds rated triple B’s and single

A’s. Thus, Schultz appears to be using a credit spread strategy.

Credit or quality spreads change because of expected changes in economic prospects. Credit

spreads between Treasury and non-Treasury issues widen in a declining or contracting economy

19. In an article titled “Signet to Add Pass–Throughs,” which appeared in the October 14,

1991, issue of BondWeek. p. 5, it was reported that Christian Goetz, assistant vice president

of Signet Asset Management, “expects current coupons to outperform premium

pass-throughs as the Fed lowers rates because mortgage holders will refinance premium

mortgages.” If Goetz pursues a strategy based on this, what type of active strategy is it?

Goetz appears to be pursuing an active strategy that relies on forecasts of future interest-rate

levels. Future interest rates, for instance, affect the value of options embedded in callable bonds

and the value of prepayment options embedded in mortgage-backed securities. Callable

corporate and municipal bonds with coupon rates above the expected future interest rate will

20. The following excerpt comes from an article titled “Securities Counselors Eyes Cutting

Duration” in the February 17, 1992, issue of BondWeek, p. 5:

“Securities Counselors of Iowa will shorten the 5.3 year duration on its $250 million

fixed-income portfolio once it is convinced interest rates are moving up and the economy

is improving … It will shorten by holding in cash equivalents the proceeds from the sale

Answer the below questions.

(a) Why would Securities Counselors want to shorten duration if it believes that interest

rates will rise?

(b) How does the purchase of cash equivalents and short-maturity high-grade utilities

accomplish the goal of shortening the duration?

(c) What risk is Securities Counselors indicating in the last sentence of the excerpt that it is

seeking to avoid by not buying corporate bonds?

496

A hostile takeover can involve retiring holdings making the duration very short. The risk is the

unexpected nature of the takeover that would cause a portfolio manager to rearrange their

portfolio and perhaps have to invest in securities that do not pay as high a rate of return.

21. The next excerpt is taken from an article titled “Wood Struthers to Add High-Grade

Corporates,” which appeared in the February 17, 1992, issue of BondWeek, p. 5:

Wood Struthers & Winthrop is poised to add a wide range of high-grade corporates to

its $600 million fixed-income portfolio … It will increase its 25% corporate allocation

to about 30% after the economy shows signs of improving …It will sell Treasuries and

agencies of undetermined maturities to make the purchase … Its duration is 4 1/2

−

5

years and is not expected to change significantly …

Comment on this portfolio strategy.

As the economy improves, there will be less risk. This implies that corporate fixed-income

investments may be upgraded. The upgrade will increase the value of these securities. If Wood

Struthers & Winthrop (WS&W) increases its corporate allocation it will be in a position to

22. Explain how a rating transition matrix can be used as a starting point in assessing how

a manager may want to allocate funds to the different credit sectors of the corporate bond

market.

A rating transition matrix can be a starting point because it provides a framework for how the

23. What is the risk associated with the use of leverage?

A portfolio manager can create leverage by borrowing funds in order to acquire a position in the

market that is greater than if only cash were invested. The funds available to invest without

borrowing are referred to as the “equity. The basic principle in using leverage is that a manager

24. Suppose that the initial value of an unlevered portfolio of Treasury securities is $200

million and the duration is 7. Suppose further that the manager can borrow $800 million

and invest it in the identical Treasury securities so that the levered portfolio has a value of

$1 billion. What is the duration of this levered portfolio?

The portfolio has a market value of $200 million and the manager invests the proceeds in a bond

with a duration of 7. This means that the manager would expect that for a 100-basis-point change

in interest rates, the portfolio’s value would change by approximately (7 / 100)$200 = $14

million. For this unlevered fund, the duration of the portfolio is 7.

Thus, the duration for the portfolio is $70 million per $200 million or $35 per each $100

rendering a duration of 35 because a duration of 35 will change the portfolio’s equity value of

$200 million by 35% or $70 million for a 100-basis-point change in rates.

In general, the procedure for calculating the duration of a portfolio that uses leverage is as

follows:

rate change used in Step 2 in bps

To illustrate the procedure for our problem, the initial value of the unlevered portfolio is $200

million and the leveraged portfolio is $200 million equity plus $800 million borrowed =

$1 billion.

498

Step 2: Let’s use a 50 basis point change in interest rates to compute the dollar duration. If the

duration of the levered portfolio is 7, then the dollar duration for a 50-basis-point change in

interest rates is 7(0.05)($1 billion) = $350 million (7 times 0.5% = 3.5% change for a

50-basis-point move times $1 billion).

Step 3: The ratio of the dollar duration for a 50-basis-point change in interest rates to the

$200 million initial market value of the unlevered portfolio is $350 million / $200 million = 1.75.

Step 4: The duration of the unlevered portfolio is:

ratio computed in Step 3 ×

100

rate change used in Step 2 in bps

× 100 = 1.75 ×

100

50

× 100 = 350.

25. Suppose a manager wants to borrow $50 million of a Treasury security that it plans to

purchase and hold for 20 days. The manager can enter into a reverse repo agreement with

a dealer firm that would provide financing at a 4.2% repo rate and a 2% margin

requirement. What is the dollar interest cost that the manager will have to pay for the

borrowed funds?

360

26. Two trustees of a pension fund are discussing repurchase agreements. Trustee A told

Trustee B that she feels it is a safe short-term investment for the fund. Trustee B told

Trustee A that repurchase agreements are highly speculative vehicles because they are

leveraged instruments. You’ve been called in by the trustees to clarify the investment

characteristics of repurchase agreements. What would you say to the trustees?

First, one could define a repurchase agreement or repo by stating that a repo is the sale of

a security with a commitment by the seller to buy the same security back from the purchaser at

a specified price at a designated future date. One could emphasize that a repo is a collateralized

loan, where the collateral is the security sold and subsequently repurchased. From the customer’s

perspective, one could positively point out that the repo market offers an attractive yield on

a short-term secured transaction that is highly liquid.

27. Suppose that a manager buys an adjustable-rate pass-through security backed by

Freddie Mac or Fannie Mae, two government-sponsored enterprises. Suppose that the

coupon rate is reset monthly based on the following coupon formula:

one-month LIBOR + 80 basis points

with a cap of 9% (i.e., maximum coupon rate of 9%).

Suppose that the manager can use these securities in a repo transaction in which (1) a repo

margin of 5% is required, (2) the term of the repo is one month, and (3) the repo rate is

one-month LIBOR plus 10 basis points. Also assume that the manager wishes to invest $1

million of his client’s funds in these securities. The manager can purchase $20 million in

par value of these securities because only $1 million is required. The amount borrowed

would be $19 million. Thus the manager realizes a spread of 70 basis points on the $19

million borrowed because LIBOR plus 80 basis points is earned in interest each month

(coupon rate) and LIBOR plus 10 basis points is paid each month (repo rate).

What are the risks associated with this strategy?

The return earned must be commensurate with the risk undertaken to determine if the strategy is

viable. First, there is a cap on the adjustable-rate pass-through security that may cause problems

and negate the current spread of 70 basis points.

Second, there is a credit risk involved for both parties in repo transaction. For example, if the

dealer cannot repurchase the securities, the customer may keep the collateral. If interest rates on

the securities increase subsequent to the repo transaction, however, the market value of the

securities will decline, and the customer will own securities with a market value less than the

amount it lent to the dealer. If the market value of the security rises instead, the dealer will be

concerned with the return of the collateral, which then has a market value higher than the loan.

28. Why is there credit risk in a repo transaction?

Despite the fact that there may be high-quality collateral underlying a repo transaction, both

parties to the transaction are exposed to credit risk. Why does credit risk occur in a repo

transaction? To answer this question, consider the example in the text in which the dealer uses