Question

Problem 5 ():

Below is a table of the prices of a set of Treasury STRIPS (per $1000 in face value). Recall that Treasury STRIPS are zero-coupon bonds with no risk of default.

Maturity (in years)                          Price (per $1000 in face)                             

1. $980.39
2. $951.81

3                                                          $915.14

4                                                          $871.44

5                                                          $821.93

6                                                          $767.90

1. There is a 5-year 5% coupon corporate bond with a face value of $1000 that pays its coupon once a year. If the price of this bond is valued off of the STRIPS yield curve (i.e., under the assumption that there is no risk of default for this corporate bond), then what is its price? (4 points)

2. Given your answer to a above, what is the yield to maturity on the corporate bond?   You may use a spreadsheet. (4 points)

3. It turns out the that market price of the corporate bond in the market is $1010. If so, what is the YTM on this bond? You may use a spreadsheet. (4 points)

4. Does the market think there is any risk of default? If so, what is an estimate of the likelihood of default if the recovery rate is 75 percent? (6 points)

Answer 1

a.First, we shall find the yield to maturity of the 5 year treasury STRIP for the given price of $ 821.93

which is required to discount the coupon cash flows of the 5 year corporate bond

ie.

821.93=1000/(1+r)^5

(1+r)^5=(1000/821.93)

r=(1000/821.93)^(1/5)-1

4.00%

So, the price of the 5 yr. corporate bond=

821.93+((1000*5%)*(1-1.04^-5)/0.04)=

1044.52

b. Given the price of the 5 yr. corporate bond as in a. , ie. 1044 52,

YTM on the bond is

1044.52=((1000*5%)*(1-(1+r)^-5)/r)+(1000/(1+r)^5)

Solving for r, we get the same

4%

c. Now, if the market price of the above bond is $ 1010

then the supposed YTM on the bond is

1010=((1000*5%)*(1-(1+r)^-5)/r)+(1000/(1+r)^5)

Solving for r, we get that YTM as

4.78%

d. YES.The market thinks that there is risk of default ---as it is evident from the price, that they require a higher yield, ie. 4.78% > 4%

Likelihood of default=(1-Recovery Rate)

ie. (1-75%)=25%

(Answer)

In money terms,

the difference between the prices as per a & c

ie.(1044.52-1010)/1044.52=

3.30%

(difference between should-be price & current market price)