Question

A fund manager has a portfolio worth $50 million with a beta of 0.75. The manager is concerned about the performance of the market over the next two months and plans to use three-month futures contracts on a well-diversified index to hedge its risk. The current level of the index is 2,750, one contract is on 250 times the index, the risk-free rate is 6% per annum, and the dividend yield on the index is 2% per annum. a) What position should the fund manager take to eliminate all exposure to the market over the next two months? b) Calculate the effect of your strategy on the fund manager’s returns if the level of the market in two months is 2,700 and 2,800.

Answer 1

(a) To hedge the risk, the manager must sell index futures

No. of futures to sell = value of portfolio to be hedged / notional value of futures

value of portfolio to hedge = portfolio * portfolio beta

Futures price = spot price * (1 + risk free rate - dividend yield)

Futures price = 2750 * (1 + 0.06 - 0.02) ==> 2860

No. of futures to sell = ($50 million * 0.75) / (2860 * 250)

No. of futures to sell = 52.44, or roughly 52

(b) Futures price = spot price * (1 + risk free rate - dividend yield)

When index is 2700, futures price = 2700 * (1+ 0.06 - 0.02), ==> 2808

At this level, fall in index = (2700 - 2750) / 2750 ==> 1.82%

fall in portfolio value = fall in index * portfolio beta * beginning portfolio value

fall in portfolio value = 1.82% * 0.75 * $50 million ==> $682,500

profit from futures position = no. of futures sold * (beginning futures value - ending futures value) * lot size

profit from futures position = 52 * (2860 - 2808) * 250 ==> $676,000

Net profit = $676,000 - $682,500 => - $6,500 (loss)

When index is 2800, futures price = 2800 * (1+ 0.06 - 0.02), ==> 2912

At this level, rise in index = (2800 - 2750) / 2750 ==> 1.82%

rise in portfolio value = rise in index * portfolio beta * beginning portfolio value

rise in portfolio value = 1.82% * 0.75 * $50 million ==> $682,500

loss from futures position = no. of futures sold * (ending futures value - beginning futures value) * lot size

loss from futures position = 52 * (2912 - 2860) * 250 ==> $676,000

Net profit = $682,500 - $676,000 => $6,500