Question

1. A corporate takeover bid is often pursued in stage as the acquiring firm seeks a controlling interest in the acquisition. A company A had identified company B as an acquisition target. B stock is currently trading at $49.50 per share. If word leak then stock price will likely be driven up increasing the cost of the acquisition. The firm therefore wants to hedge against this possibility.

1. The company wants to buy 100,000 shares on December 17. Company B stock currently has beta of 2. March contract on the S&P 500 are trading at 244.05, with multiplier of $250 time the index price. Based on this construct an optimal hedge using the March S&P contract.
2. On December 17 B stock is trading at $52.25 and the March futures price is 248.50. Calculate the additional cost of the shares as well as the gain/loss on the futures position. Was the Hedge successful? Explain

Answer 1

(a) S&P index level = 244.05 and Multiplier = $ 250, Price of One Contract = 244.05 x 250 = $ 61012.5

Purchase Price per Share = $ 49.5 and Number of Shares to be bought = 100000

Total Value of Portfolio = 49.5 x 100000 = $ 4950000

As the stock has a beta of 2, it essentially implies that a unit change in the S&P value would lead to 2x change in the stock portfolio's value. Hence, the number of contracts required to hedge the stock portfolio position is twice the number that would have been usually required.

Therefore, number of contracts required = (4950000 / 61012.5) x 2 = 162.26 ~ 163

Further, as the investor is short (does not posses) on the stocks at present, an optimal hedge would involve going long (buying) the calculated number of S&P contracts to ensure an optimal hedge of the position.

(b) Initial Stock Portfolio = $ 4950000 and Initial Futures Portfolio = 244.05 x 250 x 163 = $ 9900000

Final Stock Price = $ 52.25 and Final Stock Portfolio = 52.25 x 100000 = $ 5225000

Additional Cost of Shares = 5225000 - 4950000 = $ 275000

This additional cost is actually a loss suffered by the investor in the stock position

Final Futures Price = 248.5

Final Futures Position = 248.5 x 250 x 163 = $ 10080516.29

Gain in the futures position = 10080516.29 - 9900000 ~ $ 180516.29

Net Loss in Hedging = 275000 - 180516.29 ~ $ 94483.71

As the losses in the stock position are not entirely offset by gains in the futures position, the hedge was only partially successful.