Question

9. A portfolio manager has an equity portfolio that is valued at $75 million. The Portfolio has a current beta of .9 and a dividend yield of 1%. It is currently August 15 and the manager is concerned that markets are volatile and the portfolio could lose value, so they decide to hedge.

a. The manager will use the S&P 500 index contracts to hedge. The contract is settled n cash at $250 times the contract price. The current S&P index value is 1484.43 and a December S&P 500 index contract has a price of 1517.20?

b. Based on these expectations, should they take a short or long future position and why?

c. An optimal number of contract is N*=( Dollar value of the portfolio/dollar value of one future contract)X Portfolio beta?

d. Based on ( c ) Above compute N* and set up the appropriate hedge ?

e. On December 15 the position will be closed. The current S&P 500 Index is 1410.20 and the current contract matures, so convergence takes place. Compute the percentage loss in the S&P index and the percentage loss in the portfolio which will be ( % loss in market X Portfolio beta) ?

f. Compute the dollar loss on the portfolio the dollar change in the future position and they dividend earned on the portfolio ( 3 Months). Add these up to get the total hedge portfolio value?

g. How good was the hedge? Answer this by comparing the change in the market value of the portfolio to the change in the futures position?

Answer 1

(a) Current Index value = 1484.83 and Multiplier = $ 250
Current price of one contract = 1484.83 x 250 = $ 371207.5

December Contract Price = 1517.2 x 250 = $ 379300

(b) As the investor is long on the portfolio, he/she needs to take an opposite position in the S&P futures to hedge the portfolio position. Therefore, the investor must take a short future position.

(c) Optimal Number of Contracts = (75000000 / 371207.5) x 0.9 = 181.839 ~ 182

(d) In order to hedge the portfolio in which the investor is long, one needs to go short on 182 S&P future contracts, each worth $ 371207.5 Any gain(loss) in the futures position will offset a corresponding loss(gain) in the portfolio value.

NOTE: Please raise another query for solutions to the remaining sub-parts, as one query is restricted to the solution of a maximum of four sub-parts.