Question

The Chicago Board of Trade has just introduced a new futures contract on Brandex stock, a company that currently pays no dividend. Each contract calls for delivery 1,000 shares of stock in one year. The risk-free rate is 6% per year semi-annual compounding. An investor has shorted 2 futures contracts.

a. If current Brandex stock sells at $120 per share, what should the futures price be?

b. If the Brandex price drops by 3% immediately, what will be the change in the futures price and the change in the investor's margin account?

c. Assume the volatility of Brandex stock increases 20%, how does it impact its future price? How does it impact investor's margin account requirement?

Answer 1

a) Theoretical Futures price

F= S* (1+r)^t

where S is the spot price of the asset , r is the interest rate per period and t is the no, of periods

So, F = 120*(1+0.06/2)^2 = $127.31

b) The investor has shorted two contracts , ie. shorted 2000 shares

Spot price after drop of 3% = 120 * 0.97 =$116.40

The new Futures price ater 3% drop = 116.40*(1+0.06/2)^2 = $123.49

So, change in Futures price = (123.49-127.31)/127.31 = -0.03

So, Futures price will also decrease by 3%

profit on 2000 shorted shares = (127.31-123.49)*2000 = $7638.48

So, the margin account would increase by a value of $7638.48

c) The volatility makes the futures prices more volatilie. This happens because the Future prices are more or less directly related to spot price and hence when spot prices are more volatilie , the futures prices are also more volatile.

Volatility increases the requirement on margin account as now, the stock prices are more volatile and the margin account needs more money in terms of initial and maintenance margin on the futures contract of the stock.