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

376 Part THREE Debt Securities

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

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

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
.0005 .00127 .127%
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)
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%
The annualized rate of return over the two-year period would then be (1.107)1/2 1 .052, or

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.
Bodie’Kane’Marcus: IV. Security Analysis Introduction © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition



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

Bodie’Kane’Marcus: IV. Security Analysis 11. Macroeconomic and © The McGraw’Hill
Essentials of Investments, Industry Analysis Companies, 2003
Fifth Edition



> 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.



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