Question

Today (10/13/20), the prices on zero-coupon US Treasury STRIPS are as follows:

Maturity                                             Price                                                     Effective Annual

In years                           (per $1000 in face value)                                         YTM

      1                                                985.000                                                      ______________

      2                                               952.000                                                      ______________

      3                                                 917.500                                                      ______________

      4                                                 871.442                                                              .0350000

      5                                                 821.927                                                              .0400000

Questions:

a. What are the yields to maturity for each of these zeros? Fill in the banks above. (3 points, 1 point each)

b. You think that short-term interest rates will rise over the next year. In particular, you think that the 1-year and the 2-year rates will be higher than they are currently. If you invest in the two-year now and sell it in one year, will your return be higher or lower than what you could get by investing in the one-year and holding it until maturity? If it depends, what does it depend upon? (5 points)

c. What is the forward rate implied by the above zero yield curve for the 2-year zero effective annual yield two years from now (i.e., the rate for a 2-year zero on 10/08/21)? (4 points)

d. There is a 5 year corporate bond currently trading in the market that pays a 5 percent coupon, with (for simplicity) coupon payments made once a year at the end of the year (with the next coupon paid exactly one year from now). The current price of this bond is $1020.

What would be the price of this bond if the market considered this corporation to be free of default risk? (4 points)

e. At the price the corporate bond would be if it where default free (i.e., your answer to d above, if you did it correctly), its effective annual yield to maturity to be .03895 (3.895%). At its actual market value of $1020, is it’s actual yield to maturity higher, lower, or equal to 3.895%.

Circle one:                           higher                                                   lower                                     equal to

Explain why

(4 points total)

(Please only answer part E)

Answer 1

Part E

This can be solved by using 2 formula for yield to maturity

1st excel

2nd Formula

i have expalined by both.

1st method

Step1=Calculation of yield

PV=$1020

FV=$1000

Coupon =$50 (part d it is given)

NPER=5years

Calculate YTM using excel

USE RATE ON EXCEL

=RATE(NPER,PMT,-PV,FV)

= RATE(5,50,-1020,1000)

=4.54%

Step2

Therefore actual yield is higher compared to 3.895%

4.54%>3.895%

Hence Circle Higher.

2nd method: Formula Based

C+((F-P)/n)/ (F+P)/2

C=coupon payment, F=face value , n=years , p=price

50+((1000-1020)/5) / (1000+1020)/2

46/1010

=0.0455

4.55%

By both the formula you can see the answer remains same.

I hope your query is resolved and solution is clear kindly upvote if solution is helpful it helps me and feel free to ask any doubt related to the question. Good Luck