Question

You are given: The current stock price is $85. The continuous rate of interest is 5%, ? = 0.5, and the annualizes forward premium is 2%.

(a) Find the prepaid forward price.

(b) Tom observes a 6-month forward price of $86.5 in the market. He constructs a portfolio by taking a short position in a forward contract to sell one unit of the stock and buying one unit of the stock. Determine whether Tom’s portfolio is an arbitrage portfolio or not.

Answer 1

(a) We have been given that:-

Spot Rate (SR) = $85, Rate bof interest(r) = 5%, Time = 0.5 i.e. 6 months i.e. 180 days, annualized forward premium = 2%

Now, Annualized forward premium= (Forward Rate- Spot Rate)/Spot Rate * 360days/number of days of contract

i.e. .02= (FR-85)/85*360/180

.02 = 2(FR-85)/85

1.7= 2FR- 170

FR= (170+1.7)/2 = $85.85

Thus, Prepaid Forward Price = $85.85

(b) Now.

Fair Forward Rate = Spot rate * er*t

where, r = 5% and t = 6 months = 0.5years

Fair Forward Rate = $85* e.05*0.5

Fair Forward Rate = $85 * 1.0253 = $87.15

Now Forward rate is $86.5 , whereas Fair Forward Rate = $87.15

Now, Because Tom wants to choose short position in forward contract, his portfolio is an arbitrage portfolio.

Now, Current Forward Rate is determined at $86.5, but we expect the Fair rate to be $87.15, thus we expect an increase.

Now, short position is taken when the investor planes to sell in future.Thus, Tom plans to buy in present and sell in future.

So, Tom shall buy at the rate of $86.5 and create a short forward position to sell at $87.15 in future.

Thus, his portfolio is an arbitrage portfolio giving an arbitrage profit of $87.15-$86.5 = $.65