Investments & Securities Chapter 15 Assuming that the expectations hypothesis is valid

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Problem 15-7

The following is a list of prices for zero-coupon bonds of various maturities. Calculate the yields to

maturity of each bond and the implied sequence of forward rates. (Do not round intermediate

calculations. Round YTM answers to 2 decimal places and other answers to the nearest whole

percent.Omit the “%” sign in your response.)

Problem 15-8

Assuming that the expectations hypothesis is valid, compute the expected price path of the 4-year bond using the data given below as time passes. What is

the rate of return of the bond in each year?(Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the “%” sign in your

response.)

Data

Bond maturity ytm

interest rate 0.085141

Problem 15-9

Consider the following $1,000 par value zero-coupon bonds:

par 1000

a rate of return 0.06

Problem 15-10

The term structure for zero-coupon bonds is currently:

a.What do you expect the rate of return to be over the coming year on a 3-year zero-coupon bond?(Omit the “%” sign in your response.)

b-1.Under the expectations theory, what yields to maturity does the market expect to observe on 1- and 2-year zeros at the end of the year? (Do not round

intermediate calculations. Round your answers to 2 decimal places. Omit the “%” sign in your response.)

Data par 100

zero

zero, 1 year

2-year coupon

Problem 15-11

The yield to maturity on 1-year zero-coupon bonds is currently 7%; the YTM on 2-

year zeros is 8%. The Treasury

plans to issue a 2-year maturity coupon bond, paying coupons once per year with a coupon rate of 9%. The face

value of the bond is $100.

a.An 8.5% coupon $1,000 par bond pays an annual coupon and will mature in 3 years. What should

the yield to maturity on the bond be? (Round your answer to 2 decimal places. Omit the “%” sign in

your response.)

3-year bond

coupon 60

par 1000

c yield 0.066593528

par 1000

zero bond effect annual ytm

1 0.061

2 0.062

3 0.063

4 0.064

4 year bond 0.067005648 780.2495

par 1000

t 1 t 2 t 2

Problem 15-15

The yield to maturity (YTM) on 1-year zero-coupon bonds is 5% and the YTM on 2–

year zeros is 6%. The

yield to maturity on 2-year-maturity coupon bonds with coupon rates of 12% (paid annually) is 5.8%.

a.What arbitrage opportunity is available for an investment banking firm? (Omit the “$” sign in your

response.)

Data

t 1 t 2 t 2

zero par 100 zero par 100 coupon 0.12

par 100

Problem 15-16

Suppose that a 1-year zero-coupon bond with face value $100 currently sells at $94.34, while a 2-year zero sells at

$84.99. You are considering the purchase of a 2-year-maturity bond making annualcoupon payments. The face

value of the bond is $100, and the coupon rate is 12% per year.

b 1 892.7847 12.01%

2782.9583 13.01%

upward

Problem 15-17

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

a.What are the implied 1-year forward rates? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the “%” sign in your response.)

b.Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the pure yield curve (that is, the yields to maturity on 1-

and 2-year zero coupon bonds) next year?

c.If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? What if you purchase a 3-year zero-coupon bond? (Hint: Compute the

current and expected future prices.) Ignore taxes. (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the “%” sign in your response.)

d.What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually? If you purchased it at that price, what would your total expected rate of return be

over the next year (coupon plus price change)? Ignore taxes. (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the “$” & “%” signs in your

response.)

Data par 1000

0.0800

0.0825

0.0850

0.0875

0.0900

a 2 0.0850

Problem 15-18

Suppose that the prices of zero-coupon bonds with various maturities are given in the following table. The face value of each bo

is $1,000.

a.Calculate the forward rate of interest for each year. (Round your answers to 2 decimal places. Omit the “%” sign in your

response.)

b.How could you construct a 1-year forward loan beginning in year 3? (Round your Rate of synthetic loan answer to 1 decimal

place. Omit the “$” & “%” signs in your response.)

Data par 1000

t ytm forward

b cash flows

0 0

31000

5 -1204.49231

Problem 15-19

The prices of zero-coupon bonds with various maturities are given in the following table.

Suppose that you want to construct a 2-year maturity forward loan commencing in 3 years. The face value of each bond is $1,000.

a.Suppose that you buy today one 3-year maturity zero-coupon bond. How many 5-year maturity zeros would you have to sell to make your initial cash flow equal to

zero? (Round your answer to 4 decimal places.)

b.What are the cash flows on this strategy in each year? (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places. Omit the “$” sign in