On July 1, an investor holds 50,000 shares of a certain stock. The market price is $30 per share. The investor is interested in hedging against movements in the market over the next month and decides to use an index futures contract. The index futures price is currently 1,500 and one contract is for delivery of $50 times the index. The beta of the stock is 1.3. What strategy should the investor follow? Under what circumstances will it be profitable?

26 Contracts

Explanation:

Portfolio value= P = 50,000 * 30 = 1,500,000

The formula to calculate the number of contracts is given by:

Number of contracts N = (β∗P) / Futures Value

P is the fair value of the portfolio in the market, β is the beta of the stock which is 1.3 and Future value is can be calculated by following formula:

Futures Value = Fair Value of Assets * Fair value of unit Future / Fair value of unit share

By putting values we have:

Futures Value = (45,000) * $50 per Future / $30 per Share = 75,000

By putting values we have:

Number of contracts N = (1.3∗$1,500,000) / 75,000  = 26 contracts

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