1.A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.5. The company would like to use the CME December futures contract on the S&P 500 to protect the value of its portfolio. The index is currently 1,000 and each contract is on $250 times the index.

(a) What position should the company take?*

(b) Suppose that the company changes its mind and decides to decrease the beta of the portfolio from 1.5 to 0.5. What position in futures contracts should it take?*

* By position, I mean the number of contracts, and whether long or short

2. ) It is now Feb 1. NoRisk Inc. expects to buy 100 million ounces of silver at the beginning of May. Assume that Silver futures contracts have delivery months in April, June, and August (Assume delivery on the first day of the delivery month). Each contract is for the delivery of 25 million ounces. Assume that the futures price on CME for silver equals its theoretical price. Storage costs will be continuously incurred at a rate of 2% per annum. The continuously compounded risk-free rate is 10% per annum. Spot price of silver on Feb 1 is $10/oz. Spot prices at the future dates will be as follows (we do not obviously know these prices today):

April 1: $10.30/oz

May 1: $10.50/oz

June 1: $10.40/oz

July 1: $10.20/oz

Aug 1: $10.10/oz

(a) Should NoRisk Inc. go short or long on silver futures? How many contracts? Which delivery month?

(b) Calculate the basis risk (per contract).

(c) Calculate the gain or loss on the futures position (per contract).

(d) Calculate the effective price received by the company (per contract) at the beginning of May.

3. The following table provides the prices of bonds:

Bond principal Time-to-maturity Annual coupon* Bond price

($) (years) ($) ($)

100 0.50 0.0 98

100 1.00 0.0 95

100 1.50 6.2 101

100 2.00 8.0 104

* Half the stated coupon is assumed to be paid every six months.

(a) Calculate the (continuously compounded) annual rates for maturities of 6 months, 12 months, 18 months, and 24 months based on the above data.

(b) What are the forward rates for the periods: 6 months to 12 months, 12 months to 18 months, 18 months to 24 months?