In: Finance
The following information applies to the next three questions.
A portfolio manager controls $5 million in common stock. In anticipation of a stock market decline, the decision is made to hedge the portfolio using the S&P 500 futures contract. The portfolio's beta is 1.20 and the dividend yield on this portfolio is 4% annually, and the current value of the S&P 500 futures contract with 120 days to delivery is 238.50. The S&P 500 index itself is at 220.
8. How many futures contracts should be bought or sold?
a. buy 101 contracts
b. sell 101 contracts
c. buy 91 contracts
d. sell 91 contracts
9. Suppose that when the contracts are closed out, the S&P 500 index has decreased in value by 15%. How much is the gain or loss on the combined positions? (stock portfolio and futures contracts)
a. $-834,246.58
b. $1,300,375
c. $466,128.42
d. $2,134,621.58
10. Suppose that when the contracts are closed out, the S&P 500 index has increased in value by 10%. How much is the gain or loss on the combined positions? (stock portfolio and futures contracts)
a. $665,753.42
b. $-88,375
c. $754,128.42
d. $577,378.42
Solution:
8) No. of the stock index futures contract required is given by-
X = Vp(BT - Bp) / F * m * Bf
Where,
Vp= Value of Portfolio, BT = Target Beta, Bp= Beta of portfolio, F =Future price, Bf = Beta of futures, m = multiple i.e 250
X = 50,00,000 (0 - 1.2) / 238.5 * 250 * 1
= 60,00,000 / 59625
= 100.62 i.e 101 contracts to be sold as market is expected to decline.
9) If S&P 500 index decrease in value by 15%, then the common stock will decrease by (15*1.2) = 18%,
S& P index = 220 * 0.85 = 187
Gain on futures contract = (238.5 - 187) * 101 * 250
= $ 13,00,375
Loss on common stock = 50,00,000 * 0.18 = $ 900,000
Dividen yeild for 120 days = 50,00,000 * 0.04 * (120/365) = $ 65753.42
Net Gain = 13,00,375 +65753.42- 900000
= $466,128.42
10) If S&P 500 index incresed in value by 10%, then common stock will increase by (10*1.2) = 12%,
S& P index = 220 * 1.1 = 242
Loss on futures contract = (242-238.5) * 101 * 250
= $ 88,375
Gain on common stock = 50,00,000 * 0.12 = $ 600,000
Dividen yeild for 120 days = 50,00,000 * 0.04 * (120/365) = $ 65,753.42
Net Gain = 600,000 + 65,753.42 - 88375
= $ 577,378.42