Question

An investor's portfolio with a beta of 1.25 is worth $1 million. The current S&P500 price is $1500. The current futures price on the S&P500 (each contract is on $250 times the index) is $1800. Next period, the S&P500 is priced at $1250 and the futures price on the index is $1500. What is the final value of the portfolio after the hedging process? Enter numeric value without the '$' symbol.

Answer 1

Notional value of 1 futures contract = price of 1 contract*contract multiplier

= 1800*250 = 450,000

Value at risk = protfolio value*beta = 1,000,000*1.25 = 1,250,000

Hedge ratio = value at risk/nomial value of futures contract = 1,250,000/450,000 = 2.78 contracts or 3 contracts

3 futures contracts have to be shorted for hedging the portfolio.

Loss on portfolio = (drop in S&P index/current index value)*portfolio value*beta

= ((1500-1250)/1500)*1,000,000*1.25 = 208,333.33

Gain on 3 futures contracts = number of contract*contract multiplier*drop in points = 3*250*250 = 187,500

Final portfolio value = original portfolio value - loss in portfolio + gain on futures = 1,000,000 - 208,333.33 + 187,500 = 979,166.67