Question

What is the arbitrage opportunity when 9-month forward price is out of line with spot price for asset providing dollar income (asset price =$50; forward price=$45; income of $4 occurs at 5 months; 5-month and 9-month interest rate are 4% and 6% per annum; maturity of forward contract =9 months)

Answer 1

Assumption: Interest rates given in the question are continuously compounding rates

Arbitrage Opportunity =  the risk less profit

Arbitrage is executed by buying low and selling high. Let's find out which of the two options; buying asset or selling futures is cheaper.

Let's find out the present value of both options.

PV (Buying Asset in Spot Market) = Asset price - present value of future dollar income

Discount the future cash flow at corresponding interest rate to find present value of cash flow.

PV of future asset value

PV (Buying Asset in Spot Market)

Thus, cost of buying asset at spot price taking future dollar income into consideration is $46.07

Now,

PV (Buying futures)

As can be seen from above calculation, entering into a future contract to buy the asset in 9 months is cheaper than buying the asset at spot price in the market. Thus there exists an arbitrage opportunity.

Arbitrage Opportunity: Enter into a forward contract to buy asset at $45 in future (9 months). Short Sell the asset today at spot price in the market and invest the proceeds at 6% interest rate.

Arbitrage profit is the difference between the expensive and cheaper options.

Arbitrage Profit from opportunity= $46.07 - $43.02 = $3.05.