Question

A stock currently sells for $80, and it will pay no dividends in the future.

Consider a 2-year forward contract on this stock.

The forward price is $90. The risk-free rate is 3% per annum.

Is there an arbitrage?

If so, show the arbitrage strategy using a table listing asset positions and cash flows.

Answer 1

Theoretical Futures Price = [Spot Price + PV of Cost of Carry - PV of Dividends]*Future Value Factor = [S + (C*e^-rt) + (D*e^-rt)]*e^rt

Where S = Spot Rate, e = constant (2.71828), r = Risk Free Rate, t = years to expiry

Applying the above formula,

S = 80, r = 0.03, t = 2 , C = 0, D = 0

Therefore, Theoretical Futures Price = [80 + 0 + 0]*e^(0.03*2) = 80*e^0.06 = 80*1.0618= $84.944

Actual Futures Price is $90 i.e Greater than Theoretical Futures Price

Therefore, Future is Overvalued

Therefore, There IS an Arbitrage Opportunity

To make an Arbitrage Gain, Buy Spot & Sell under Futures Contract

Steps to Arbitrage:

Now,

(1) Borrow $80 for 2 years @3%

(2) Buy Stock @ current price i.e. $80

(3) Sell Futures contract, expiring in 2 years to sell at $90

Net Asset Position = 1 Share held @$80, Future Contract to Sell 1 share in 2 years @$90

Net Cash Flow = 80-80 = 0

After 2 years,

(4) Sell under Futures Contract and receive $90

(5) Repay loan with interest 80*e^0.03*2 = 80*e^0.06= 80*1.0618 = 84.944

Net Asset Position = NIL

Net Cash Flow = 90-84.944 = $5.056 = $5.06