Latest Revision: October 30, 1995 (to add Eurodollar yields)

**Note**: This problem set is to be completed separately by each student -- which means that it is not acceptable to compare solutions. In some of the questions, it will greatly
help if you use EXCEL for the calculations.
Make sure to print the calculations and explain what you are doing.

1 year 7.87

2 year 8.20

3 year 8.41

5 year 8.90

7 year 9.22

10 year 9.50

20 year 9.97

30 year 8.92

The interest is compounded semi-annually. (Hint: To find semi-annual interest rates, divide given interest rates by 2.)

(a) At these yields, what are the actual prices of all of these zero coupon bonds with maturities from 1 to 30 years?

(b) What are the durations and modified durations of these STRIPs?

(c) If interest rates moved up 2% on all of these, what would be the new set of zero coupon prices? What would the holding period return be if you bought at the above quoted price and sold after the rates moved up 2%?

(d) Answer question (c) for a drop of 2% in interest rates.

(e ) What are the predicted percentage changes using modified duration for these plus or minus 2% rate moves? Describe the errors made by the duration approximation to the gains and losses, i.e., how do the errors behave across the maturities, and can you account for the pattern in these errors.

(f) Assume that forward interest rates are constant between maturities listed in the part (a). For example, assume that the four semi-annual intervals between the 5 year and 7 year have the same forward rate. Calculate the (semi-annual) forward rates implied between the following maturities:

(i)Year 0 and 1

(ii)Year 1 and 2

(iii)Year 2 and 3

(iv)Year 3 and 5

(v)Year 5 and 7

(vi)Year 7 and 10

(vii)Year 10 and 20

(viii)Year 20 and 30

Graph these rates and the yield curve of part (a) on the same graph. Comment on them.

(b) From those prices, what modified durations would you infer for each of those maturities given the 9% market interest rate scenario. (Hint: Price elasticity is a good estimate for modified duration. Calculate two different price elasticities for each maturity, depending on the direction of the interest rates. Approximate the modified duration for each maturity by averaging these two results.)

(c) Compare the price volatilities (modified durations) of the coupon Treasuries to those of the STRIPs in question 1. Why are they different?

(a) Compute the value of the bill at delivery if the annual `discount' rates are (i) 7% and (ii) 8%. (Hint: Use the banker's discount formula to get the prices.)

(b) What is the bond price elasticity if the bond price moves (i) from 7% to 8% and (ii) from 8% to 7%.

(b) Treasury bond futures have as standard delivery an 8%, 20 year bond, such as that priced in question 2. The par amount in 1 contract is $100,000. A hedge position attempts to create (equal but opposite) gains in futures markets from those that occur in the cash market when rates move. Calculate the amount the government bond dealer would gain (or lose) on each shorted T-bond contract if the rates moved from 9% to 10%?

(c) How many T-bond futures should the dealer short so that the gain (or loss) of part (a) is offset by the loss (or gain) by the position in futures?}

(d) How does the hedge perform if the interest rate drops from 9% to 8%? Calculate the gain or loss of the cash and futures positions and show the net effect. Why would the bond dealer perform the hedge specified in part (c)?

Below is a set of Eurodollar quotations. You can these into a spread sheet. Alternatively, you can use another day's quotations.

Eurodollar Quotation for Tuesday October 24, 1995 Yield Annualized Dec95 5.8 Jan96 5.66 Mr 5.58 June 5.58 Sep 5.62 Dec 5.76 Mr97 5.79 June 5.96 Sept 5.92 Dec 6.04 Mr98 6.05 June 6.12 Sept 6.17 Dec 6.27 Mr99 6.28 June 6.34 Sep 6.36 Dec 6.47 Mr00 6.47 June 6.52 Sep 6.57 Dec 6.66 Mr01 6.66 June 6.71 Sep 6.77 Dec 6.86 Mr02 6.96 June 6.91 Sep 6.95 Dec 7.02 Mr03 7.02 June 7.07 Sep 7.12 Dec 7.221 Mr04 7.2 June 7.25 Sept 7.31 Dec 7.39 Mr05 7.39 June 7.44 Sept 7.46

*Optional. Not required for full grade.

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