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Q-10-40I

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Essentials Of Investments
Found in: Page 332
Essentials Of Investments

Essentials Of Investments

Book edition 9th
Author(s) Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus
Pages 748 pages
ISBN 9780078034695

Short Answer

Question: The current yield curve for default-free zero-coupon bonds is as follows:

Maturity (Years)

YTM

1

10%

2

11%

3

12%

a. What are the implied one-year forward rates?

b. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will the pure yield curve (that is, the yields to maturity on one- and two-year zero-coupon bonds) be next year?

c. If you purchase a two-year zero-coupon bond now, what is the expected total rate of return over the next year? What if you purchase a three-year zero-coupon bond?

(Hint: Compute the current and expected future prices.) Ignore taxes.

Answer

a. 12.01%, 14.03%

b. 13.02%

c. Two year zero coupon bond = 10.00% and three year zero coupon bond = 10.00%

See the step by step solution

Step by Step Solution

Step 1: Calculation of forward rates

Price for year 1 = 1000/ (1 + 10%) = $909.09

Price for year 2 = 1000/ (1 + 11%)2 = $811.62

Forward rate for year 2 = (1 + 11%)2 / (1 + 10%) – 1 = 0.1201 = 12.01%

Price for year 3 = 1000/ (1 + 12%)3 = $711.78

Forward rate for year 3 = (1 + 12%)3 / (1 + 11%)2 – 1 = 0.1403 = 14.03%

Therefore,

Maturity Years

YTM

Forward rates

Price

1

10.00%

$909.09

2

11.00%

12.01%

$811.62

3

12.00%

14.03%

$711.78

Step 2: Calculation of pure yield curve for the next year

For this, we discount each zero’s face value at the forward rates derived in the previous part, as below:

Maturity Years

Price

Forward rates

YTM

1

$892.78

1000/1.1201

12.01%

2

$782.93

1000/1.1201x1.1403

13.02%

According to the expectation hypothesis, this year’s upward sloping curve implies a shift upward in next year’s curve

Step 3: Calculation of total rate of return

Next year, the two-year zero will be a one-year zero, and it will therefore sell at: $1000/1.1201 = $892.78

Similarly, the current three-year zero will be a two-year zero, and it will sell for: $782.93

Expected total rate of return:

Two year bond = $892.78/$811.62 – 1 = 0.1000 = 10.00%

Three year bond = $782.93 / $711.78 – 1 = 0.1000 = 10.00%

Most popular questions for Business-studies Textbooks

You are the manager of the bond portfolio of a pension fund. The policies of the fund allow for the use of active strategies in managing the bond portfolio. It appears that the economic cycle is beginning to mature, inflation is expected to accelerate, and, in an effort to contain the economic expansion, central bank policy is moving toward constraint. For each of the situations below, state which one of the two bonds you would prefer. Briefly justify your answer in each case.

a. Government of Canada (Canadian pay), 4% due in 2017, and priced at 101.25 to yield 3.50% to maturity;

or

Government of Canada (Canadian pay), 4% due in 2027, and priced at 95.75 to yield 4.19% to maturity.

b. Texas Power and Light Co., 5½% due in 2022, rated AAA, and priced at 85 to yield 8.1% to maturity;

or

Arizona Public Service Co., 5.45% due in 2022, rated A 2 , and priced at 80 to yield 9.1% to maturity.

c. Commonwealth Edison, 2¾% due in 2021, rated Baa, and priced at 81 to yield 7.2% to maturity;

or

Commonwealth Edison, 9⅜% due in 2021, rated Baa, and priced at 114 to yield 7.2% to maturity.

d. Shell Oil Co., 6¾% sinking fund debentures due in 2026, rated AAA (sinking fund begins in 2015 at par), and priced at 89 to yield 7.1% to maturity;

or

Warner-Lambert, 6⅞% sinking fund debentures due in 2026, rated AAA (sinking fund begins in 2016 at par), and priced at 95 to yield 7% to maturity.

e. Bank of Montreal (Canadian pay), 4% certificates of deposit due in 2014, rated AAA, and priced at 100 to yield 4% to maturity;

or

Bank of Montreal (Canadian pay), floating-rate notes due in 2018, rated AAA.

Coupon currently set at 3.7% and priced at 100 (coupon adjusted semiannually to .5% above the three-month Government of Canada Treasury bill rate).

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