The term structure is flat at a rate of 6%

The term structure is flat at a rate of 6%

Subject: Business    / Finance   
Question
1.    The term structure is flat at a rate of 6%. You are currently managing the portfolio of bonds listed below:

long 500 of 6.5% coupon bonds t = 4 (maturity date)
long 1,000 of 8.0% coupon bonds t = 3
short 800 of 8.5% coupon bonds t=5

a.    If interest rates rise by .5%, what is the estimated effect of that change on the value of your portfolio?
b.    You wish to reconfigure the relative positions in the 6.5% and 8.0% bonds to make your portfolio insensitive to small rate changes. How would you accomplish this goal?

2.    The term structure of interest rates is currently flat r = 10%. You own a portfolio of bonds as follows:
500 bonds, each with a 9.5% coupon maturing in 7 years
1200 bonds, each with a 6% coupon, maturing in 4 years
a.    You wish to hedge against losses due to interest rate changes by taking a position in 7 year discount bonds. What must the value of your position be?

b.    After 4 years (when the 6% bonds have matured), how would you expect this position to have changed assuming rates remain constant up to and including that time period?

3.    Portfolio X consists of a 1-year zero-coupon bond with a face value of $2,000, and a 10¬year zero-coupon bond with a face value of $5000. Portfolio Y consists of a 5.63 year zero-coupon with a face-value of $5000. The current yield on all the bonds considered is 10% per annum.

a.    What is the duration of the two portfolios?
b.    Use duration to estimate the impact of a .5% decrease in the interest rate on the present values of the two portfolios.

4.    You currently hold a portfolio consisting of 100 of 1-year T-bill selling for $960 and 150 3-year 5% coupon bonds. (Coupons are paid annually.) You want to immunize your portfolio against small changes in interest rates by using futures contract, written on 3-monts T-bill. How many futures contracts do you need to achieve this goal? Is it a long a short position? The term structure is currently flat. Assume that one futures contract calls for the delivery of $100,000 face value of T-bills.

5.    (a) You observe the following anticipated floating rate swap payments, each based on a notional $ 100 M. Assume semi-annual compounding.

Floating Payments

t=0 0.5 1 1.5
1 year swap 1M 1.1M
1.5 year swap 1M 1.1M 1.12M

a.    Construct the implied term structure of LIBOR rates. What are the corresponding swap rates?

b.    You plan to sign a 1.5 year Eurodollar loan today (t = 0) for $l,000,000 for 1% over LIBOR. What is the “no arbitrage” forecast of the interest payments you will make at the end of each 6 month period?

c.    Rates may go up and your floating rate payments increase. Conceptually, how would you hedge this possibility?