Seaboard Corp stock is selling for 1799.20 and pays a $15 dividend in three mont

Question

Seaboard Corp stock is selling for 1799.20 and pays a $15 dividend in three months and again in six months (a) (b) 3. (5 points) what is the no-arbitrage price of a five-month forward contract if interest rates are 11%? (5 points) Suppose the forward contract is priced at $1,885.00 Is there an arbitrage opportunity? If so, conduct an arbitrage showing all steps. What is your profit on this arbitrage? (c) (5 points) Suppose the forward market price was $1,860.94. What would be your arbitrage profit? (show all steps of the arbitrage (d) (5 points) Suppose you originally entered into a short forward position in Seaboard Corp stock at $1,870.00. In two months the spot price of the shares changes to $1,850. What is the value of your short forward position? (e) (5 points) What would be the value of your position if this were a futures contract?

Explanation / Answer

(a) We will first calculate the present value of the dividends:

PV(3 month dividend) = 15 * e-11%*3/12 = 14.59

Now the 5 month forward price = (1799.20 - 14.59) * e11% * 5/12 = 1868.31

(b) If the forward is priced at 1885, then we can profit from it as below:

(c) If the forward price is 1860.94, then we can profit as below:

(d) We will first calculate forward price after two months for which we will also calculate the present value of dividend at that time:

PV dividend = 15 * e-11% * 1/12 = 14.86

Forward price after 2 months when the spot is 1850 = (1850 - 14.86) * e11% * 3/12 = 1886.30

Now we can calculate the value of short forward with delivery price of 1870 and residual period of 3 months = (1870 - 1886.30) * e-11% * 3/12 = -15.86

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