Question

You are an analyst at a large hedge fund company. You are analyzing the arbitrage opportunity related to Spot and Futures party. Suppose that a six-month futures price on lean hog is 65 cents per pound and the spot price of lean hog is 62 cents. The risk-free rate of interest is 10% per annum.

a. is there an arbitrage opportunity?

b. if there is an arbitrage opportunity, then will you borrow money or lend money?

c. What is the arbitrage profit per pound of lean hog if there is an arbitrage opportunity in today's dollar (PV of the profit) ignoring the transaction fee?

Answer 1

Hi

Below is the relation between spot and future price

F=S*(1+r)^t

Where F = future price

S = spot price

r = interest rate

t = time

here F = 65 cents

S*(1+r)^t = 62*(1+10%)^(1/2)

=62*1.1^(1/2) = 65.026 cents

a) hence there is small arbitrage opportunity.

b) since future price is lower than spot + interest rate, I will sell spot price and lend that money at 10%.

c) arbitrage profit after 6 months = 65.026-65 = 0.026 cents

PV of arbitrage profit = 0.026/(1+10%)^(1/2)

   =0.02479 cents per pound

Thanks