25. A fixed-income portfolio manager is unwilling to realize a rate of return of less than

3% annually over a five-year investment period on a portfolio currently valued at

$1 million. Three years later, the interest rate is 8%. What is the trigger point of the

portfolio at this time, that is, how low can the value of the portfolio fall before the

manager will be forced to immunize to be assured of achieving the minimum

acceptable return?

26. What type of interest rate swap would be appropriate for a corporation holding long-

term assets that it funded with floating-rate bonds?

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10 Managing Bond Portfolios

27. What type of interest rate swap would be appropriate for a speculator who believes

interest rates soon will fall?

28. Several Investment Committee members have asked about interest rate swap

agreements and how they are used in the management of domestic fixed-income

portfolios.

a. Define an interest rate swap and briefly describe the obligation of each party

involved.

b. Cite and explain two examples of how interest rate swaps could be used by a fixed-

income portfolio manager to control risk or improve return.

29. A corporation has issued a $10 million issue of floating-rate bonds on which it pays

an interest rate 1% over the LIBOR rate. The bonds are selling at par value. The firm is

worried that rates are about to rise, and it would like to lock in a fixed interest rate on its

borrowings. The firm sees that dealers in the swap market are offering swaps of LIBOR

for 7%. What swap arrangement will convert the firm™s borrowings to a synthetic fixed-

rate loan? What interest rate will it pay on that synthetic fixed-rate loan?

30. A 30-year maturity bond has a 7% coupon rate, paid annually. It sells today for $867.42.

A 20-year maturity bond has a 6.5% coupon rate, also paid annually. It sells today for

$879.50. A bond market analyst forecasts that in five years, 25-year maturity bonds

will sell at yields to maturity of 8% and that 15-year maturity bonds will sell at yields of

7.5%. Because the yield curve is upward sloping, the analyst believes that coupons will

be invested in short-term securities at a rate of 6%. Which bond offers the higher

expected rate of return over the five-year period?

31. a. Use a spreadsheet to calculate the durations of the two bonds in Spreadsheet 10.1 if

the interest rate increases to 12%. Why does the duration of the coupon bond fall

while that of the zero remains unchanged? [Hint: Examine what happens to the

weights computed in column E.]

b. Use the same spreadsheet to calculate the duration of the coupon bond if the coupon

were 12% instead of 8%. Explain why the duration is lower. (Again, start by looking

at column E.)

32. a. Footnote 2 presents the formula for the convexity of a bond. Build a spreadsheet

to calculate the convexity of the 8% coupon bond in Spreadsheet 10.1 at the initial

yield to maturity of 10%.

b. What is the convexity of the zero-coupon bond?

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376 Part THREE Debt Securities

WEBMA STER

Bonds

Go to http://bonds.about.com/money/bonds/cs/calculators/index.htm. From the avail-

able calculators, select FiCalc. Once selected, choose calculator. The site will lead you

through a series of questions. Indicate that you plan to evaluate U.S. Corporate

Securities and Bond”Fixed Income. Once you have entered the above information you

can enter data for a particular bond and calculate the available statistics. Prior to

entering the data below, set the calculations to mark all available calculations.

For this problem, we will use a 10-year bond that is selling at its par value as the

base case. The data is entered as follows:

Price 100 Coupon 10 Maturity as d/m/yr (enter a full 10 years from

today™s date)

Settings Annual Coupons

Once the data is entered, calculate the statistics. The calculator has a printer

formatting option if you want a hard copy of the results. Repeat this process for a price

of 87 and 113. Then, answer the following questions:

1. What are the duration, convexity, and interest on interest calculations for the

bond at the base price of 100?

2. Do you earn more or less interest on interest when the price of the bond is 113

compared to the base case? Why?

3. Is the bond more or less price sensitive at a price of 87? Compare to the base

case. Does the bond have a higher or lower level of convexity at this price?

SOLUTIONS TO 1. Interest rate: 0.09

>

Concept

(B) (C) (D) (E)

CHECKS

Time until Payment Column (B)

Payment Discounted times

(years) Payment at 10% Weight Column (E)

A. 8% coupon bond 1 80 73.394 0.0753 0.0753

2 80 67.334 0.0691 0.1382

3 1080 833.958 0.8556 2.5668

Sum: 974.687 1.0000 2.7803

B. Zero-coupon bond 1 0 0.000 0.0000 0.0000

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2 0 0.000 0.0000 0.0000

3 1000 772.183 1.0000 3.0000

Sum: 772.183 1.0000 3.0000

The duration of the 8% coupon bond rises to 2.7803 years. Price increases to $974.687. The

duration of the zero-coupon bond is unchanged at 3 years, although its price also increases when

the interest rate falls.

2. a. If the interest rate increases from 9% to 9.05%, the bond price falls from $974.687 to $973.445.

The percentage change in price is 0.127%.

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10 Managing Bond Portfolios

b. The duration formula would predict a price change of

2.7802

.0005 .00127 .127%

1.09

which is the same answer that we obtained from direct computation in part (a).

3. The duration of a level perpetuity is (1 y)/y or 1 1/y, which clearly falls as y increases.

Tabulating duration as a function of y we get:

y D

0.01 (i.e., 1%) 101 years

0.02 51

0.05 21

0.10 11

0.20 6

0.25 5

0.40 3.5

4. The perpetuity™s duration now would be 1.08/0.08 13.5. We need to solve the following

equation for w

w 2 (1 w) 13.5 6

Therefore, w 0.6522.

5. a. The present value of the fund™s obligation is $800,000/0.08 $10 million. The duration is 13.5

years. Therefore, the fund should invest $10 million in zeros with a 13.5 year maturity. The face

value of the zeros will be $10,000,000 1.0813.5 $28,263,159.

b. When the interest rate increases to 8.1%, the present value of the fund™s obligation drops to

800,000/0.081 $9,876,543. The value of the zero-coupon bond falls by roughly the same

amount, to $28,263,159/1.08113.5 $9,875,835. The duration of the perpetual obligation falls

to 1.081/0.081 13.346 years. The fund should sell the zero it currently holds and purchase

$9,876,543 in zero-coupon bonds with maturity of 13.346 years.

6. Dedication would be more attractive. Cash flow matching eliminates the need for rebalancing and,

thus, saves transaction costs.

7. Current price $1,091.29

Forecast price $100 Annuity factor (10%, 18 years) $1,000 PV factor (10%, 18 years)

$1,000

The future value of reinvested coupons will be ($100 1.08) $100 $208

$208 ($1,000 $1,091.29)

The two-year return is 0.107, or 10.7%

$1,091.29

The annualized rate of return over the two-year period would then be (1.107)1/2 1 .052, or

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5.2%.

8. The trigger point is the present value of the minimum acceptable terminal value:

$10 million/(1.08)3 $7.94 million

9. The manager would like to hold on to the money market securities because of their attractive

relative pricing compared to other short-term assets. However, there is an expectation that rates will

fall. The manager can hold this particular portfolio of short-term assets and still benefit from the

drop in interest rates by entering a swap to pay a short-term interest rate and receive a fixed interest

rate. The resulting synthetic fixed-rate portfolio will increase in value if rates do fall.

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FOUR

PA RT

SECURITY ANALYSIS

ell your friends or relatives that you are provide to the public. You also need to have

T studying investments and they will ask mastered corporate finance, since security

you, “What stocks should I buy?” This is analysis at its core is the ability to value a firm.

the question at the heart of security analysis. In short, a good security analyst will be a gen-

How do analysts choose the stocks and other eralist, with a grasp of the widest range of fi-

securities to hold in their portfolios? nancial issues. This is where there is the

Security analysis requires a wide mix of biggest premium on “putting it all together.”

skills. You need to be a decent economist with The chapters in Part Four are an introduc-

a good grasp of both macroeconomics and mi- tion to security analysis. We will provide you with

croeconomics, the former to help you form a “top-down” approach to the subject, starting

forecasts of the general direction of the market with an overview of international, macroeco-

and the latter to help you assess the relative nomic, and industry issues, and only then pro-

position of particular industries or firms. You gressing to the analysis of particular firms. Our

need a good sense of demographic and social treatment of firm valuation is primarily focused

trends to help identify industries with bright on fundamental analysis, but we also devote a

prospects. You need to be a quick study of the chapter to technical analysis later in the text.

ins and outs of particular industries to choose After reading these chapters, you will have a

the firms that will succeed within each indus- good sense of the various techniques used to

try. You need a good accounting background to analyze stocks and the stock market.

analyze the financial statements that firms

> 11 Macroeconomic and Industry Analysis

12 Equity Valuation

13 Financial Statement Analysis

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Fifth Edition

11

MACROECONOMIC AND

INDUSTRY ANALYSIS

AFTER STUDYING THIS CHAPTER

YOU SHOULD BE ABLE TO:

> Predict the effect of monetary and fiscal policies on key

macroeconomic variables such as gross domestic product,

interest rates, and the inflation rate.

> Use leading, coincident, and lagging economic indicators to

describe and predict the economy™s path through the

business cycle.

> Predict which industries will be more or less sensitive to

business cycle fluctuations.

> Analyze the effect of industry life cycles and structure on

industry earnings prospects over time.

380