Question

43Use the following information to answer the questions. Suppose we see the following prices for zero coupon bonds (face value $100) with maturities ranging from one to six years:

Maturity in years Bond Price

1 $98

2 $97

3 $95

4 $92

5 $88

6 $84

a) (5 points) What is the four-year spot rate?

b) (5 points) Assuming that the expectations hypothesis holds, what do you expect the four-year spot rate to be one year from now? Please report the annually compounded APR.

c) (5 points) What is the price of a six-year coupon bond that has a face value of $1,000 and an annual coupon rate of 8%? The coupons are paid annually.

d) (5 points) What is the bond’s yield-to-maturity?

e) (5 points) What is the (Macaulay’s) duration of the bond?

f) (5 points) How much would the price of the bond change if the yield increased by 1%? Please report both the exact price change as well as the approximate price change based on your answer to part e).

Answer 1

1.
Answer:
1 year: =(100/98)^(1/1)-1=2.0408%
2 year: =(100/97)^(1/2)-1=1.5346%
3 year: =(100/95)^(1/3)-1=1.7245%
4 year: =(100/92)^(1/4)-1=2.1064%
5 year: =(100/88)^(1/5)-1=2.5896%
6 year: =(100/84)^(1/6)-1=2.9485%

2.
Answer: 2.7273%
4 year spot rate 1 year from now=((1+rate for 5 year)^5)/(1+rate for 1 year))^(1/4)-1=(((1+2.5896%)^5)/(1+2.0408%))^(1/4)-1=2.7273%

3.
Answer: 1283.201345
Price=8%*1000/(1+2.0408%)+8%*1000/(1+1.5346%)^2+8%*1000/(1+1.7245%)^3+8%*1000/(1+2.1064%)^4+8%*1000/(1+2.5896%)^5+8%*1000/(1+2.9485%)^6+1000/(1+2.9485%)^6=1283.201345

4.
1283.201345=8%*1000/ytm*(1-1/(1+ytm)^6)+1000/(1+ytm)^6
=>ytm=2.80577749710496%

P.S.: I am not allowed to answer more than 4 questions