Question

A share of Berkshire Hathaway stock (BRK.B) is currently selling for $230. A pension fund manager is planning to purchase 1,000 shares in three months. He is concerned that the price will rise by then. To hedge this risk, he enters into a forward contract to buy 1,000 shares of BRK.B in three months. Assume that the risk-free rate is 2%(APR, continuous compounding).

•Calculate the appropriate price per share at which the pension fund manager can contract to buy BRK.B in three months.

•Assume that two months into the contract the BRK.B stock price is $225. Calculate the pension fund manager’s gain or loss from the forward contract.

•Suppose that at expiration, the price of the stock is $245. Calculate the pension fund manager’s gain or loss from the forward contract.

Answer 1

1)

Theoretical Forward Price = Spot Price*e^{rate of interest*number of years}

where, e = Exponential Value (i.e. 2.71828)

Therefore, Appropriate Forward Price = 230*e^0.02*3/12

= 230*e^0.005 = 230*1.005(from table or 2.71828^0.005) = 231.15(approx)

2)

Theoretical Forward Price after 2 months(using the same above formula) = 225*e^0.02*1/12

= 225*e^0.00167 = 225*1.001668 = 225.38(approx)

Therefore, Gain/Loss from Forward contract (before expiry) = Theoretical Forward Price - Contract Buy Price =225.38-231.15 Therefore, Loss = 5.77(approx)

3)

Gain/Loss from forward contract(on expiry) = Actual Spot Price - Contract Buy Price =245-231.15 Therefore, Profit=13.85(approx)

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