Question

1. Suppose that you are tasked with managing a liability of $5,000 worth of 6% 4-year, annual coupon bonds when the interest rate is 4.5%. You want to minimize the interest rate risk by immunizing this position through value and duration matching. If you have 2-year and 10-year zero-coupon bonds available to create the hedge, how many dollars should you invest in each bond? Explain at least three reasons this hedge will not be perfect one year after you set it up.

2. Assume that you sell short 350 shares of a stock when the market price is 32.10–32.15. Your broker demands a 20% haircut for collateral and pays a short rebate of 3%. You borrow all needed cash for the transaction above the short proceeds at an interest rate of 4.8%. One year later, the price is 29.50– 29.55, and you close the position. What is the net profit (in $)?

3. Assume that you sell short a 3.5% semi-annual coupon bond with 7 years to maturity when the market interest rate is 4% (and you buy on a coupon payment date so that the price is clean). You deposit the short proceeds plus a 15% haircut that you pay out of your own capital. 18 months later, interests rates have risen to 4.3%, and you close the position by buying back the bond. If the repo rate is 2%, what is the net profit from these trades? What is the percent return, based on your out-ofpocket capital investment only? What is the effective annual rate for this investment?

4. If a non-dividend paying stock is trading today at $52 when the interest rate is 3%, what is the 8- month forward price? If the forward contract is available at a price of $51, what three transactions should you make in order to earn the available arbitrage profit? How much money could you make 8 months from now, and what is the present value of that profit today?

5. A stock is trading today at $90, and the company is expected to pay quarterly dividends of $0.45. (Assume that the stock is bought on an ex-dividend date, so the first dividend is to be paid three months after the purchase.) The continuously compounded interest rate is 4.2%. What is the 10-month forward price? What is the price of a prepaid 10-month forward? If the price of the stock in 10 months is $95, what is the profit or loss from the forward contract?

6. If the exchange rate is currently $2.10/₤ when the pound interest rate is 3% and the dollar interest rate is 1.5%, what is the correct price for a 1-year forward contract? (All rates are continuously compounded.)

7. Assume that you have a well-diversified portfolio valued at $3 million with a beta of 1.8, but you have a negative outlook on the short-term prospects of the market and want to reduce your market risk using index futures. In particular, you want to reposition your portfolio to have a beta to 0.7. Assume that the S&P 500 is trading at a price of 2,800, the futures multiplier is $250, and the futures price is currently 2,770. How many futures contracts would you need to trade long or short in order to alter the beta?

Question 6 and 7 are the ones I'm having trouble with.

Answer 1

Answer to Q No. 6

Given data

1₤=$2.10

We know that as per Interest Rate Parity theory, Investment Opportunity in two different countries will always be same.

Therefore we can calulate the forward rate by using the interest rate.

Forward rate($/₤)= (Spot rate *(1+ $ Interest Rate))/1+₤ Interest Rate

=(2.10*(1+0.015))/1+0.02

=(2.10*1.015)/1.02

=2.0897

Therefore correct price for 1 year forward contract is 1₤=$2.0897

Answer to Q No. 7

We have taken long position hence hedging must be taken by taking short psition.

our objective is to reduce the risk i.e we want to reduce beta of portfolio 1.8 to 0.7 by using Index future.

Hence value of Index short position= current value of portfolio *(Existing Beta- desired beta)

Now putting figures on above formula,

=$3,000,000(1.8-0.7)

=$3,300,000

No. of contract to be short= value of Index short position/(future price*future multiplier)

=$3,300,000/(2,770*250)

=$3,300,000/692500

=4.765 or 5 contract.