On January 1, an investor hold 10,000 shares of an electric vehicle company stock with a market price of $500 per share. They are concerned that the market will decline over the next month and decide to use a March eMini Nasdaq 100 futures to hedge. The index futures price is 12,000 and one contract for delivery is $20 times the index.

A monthly regression of the stock on the index reveals that the beta of the stock is 2.1. a. How many contracts should the investor sell to best hedge the risk?

b. If the total variance of the stock before hedging was 0.1789 and the variance remaining after the position is hedged is 0.0625, then what percentage reduction in the variance of your rate of return is achieved by your hedge?