Question

A manager is holding a $1.25 million stock portfolio with a beta of 1.17. She would like to hedge the risk of the portfolio using the S&P 500 stock index futures contract. How many dollars’ worth of the index should she sell in the futures market to minimize the volatility of her position? (Enter your answer in dollar not in millions.)

Dollars worth of index to be sold?

Show your work with formulas in Excel

Answer 1

=> Beta measures the volatility of stock comparatively to the market

=> Here we have portfolio beta of 1.17, that means the portfolio is 17% more volatile than the S&P 500 index

* This means that if S&P 500 increase by 1% then the portfolio increase by 1.17% and if S&P 500 decreases by 1% then the portfolio decreases by 1.17%

=> Multiply the portfolio beta with the amount the manager is holding in his portfolio

* 1,250,000*1.17 = 1,462,500

=> Therefore the manager has to sell $ 1,462,500 worth of S&P stock index futures to hedge his position