Question

1. You own a stock portfolio with market value of $600,000, with a weighted average beta of 0.87. You want to hedge this portfolio from price volatility using the E-mini S&P500 index future (ES) with a price of 50xIndex value.

1. How many contracts do you need to fully hedge your portfolio if the 1-mo S&P500 Index is currently priced at 3,477? (round to the nearest whole number)
2. If you shorted 2 ES contracts and the index moves to 3,440 in a month, what will be your net gain (+) or loss (-) (must state gain or loss) for your entire position (i.e., your portfolio + the hedge)? [Hint: first compute the % change in index and portfolio values]

Answer 1

1. How many contracts do you need to fully hedge your portfolio if the 1-mo S&P500 Index is currently priced at 3,477? (round to the nearest whole number)

# of Contracts = Market value of Stock portfolio * Beta / 50 * Index value

# of Contracts = 600000 * 0.87 / (50 * 3477)

# of Contracts = 3 Contracts

2. % change in index = - [(New Index / Current Index) - 1]= - [3440 / 3477 - 1] = 1.064%

% change in Portfolio value = Beta * (% change in index) = 0.87 * 1.064% = 0.926%

Net Loss = Change in index position - Change in Market value

Net Loss = 2 * 50 * 3477 * 1.064% - 600000 * 0.926%

Net Loss = $1854.79 or Net Gain = -$1854.79