Consider a portfolio manager with a $20,500,000 equity portfolio under management. The manager wishes to hedge against a decline in share values using stock index futures. Currently a stock index future is priced at 1250 and has a multiplier of 250. The portfolio beta is 1.25. Calculate the number of contracts required to hedge the risk exposure and indicate whether the manager should be short or long.

Assume that a month later the equity portfolio has a market value of $20,000,000 and the stock index future is priced at 1150 with a multiplier of 250. Calculate the profit on the equity position.

Calculate the overall profit.

$1,550,000

Explanation:

Assume that a month later the equity portfolio has a market value of $20,000,000 and the stock index future is priced at 1150 with a multiplier of 250. Calculate the profit on the equity position.

Calculate the overall profit.

The manager should be short on the stock index futures because the position on the equity portfolio is long.

Number of contracts required to hedge

= [$20,500,000 / (1250*250) ] * 1.25 = 82 contracts

Profit on the equity portfolio

= $20,000,000 - $20,500,000 = - $500,000

Profit on the stock index future

= [ (1250) (250) - (1150) (250) ] x 82 = $2,050,000

Overall profit

= $2,050,000 - $500,000

= $1,550,000

therefore, the overall profit is $1,550,000