Question

A forward contract on a non-dividend paying stock trades at 1,200. This forward contract matures 1 month from now. A second forward contract on the same stock trades at 1,220 and expires 3 months from now. Suppose perfect market and a continuously compounding interest rate which will remain same over the next 6 months.

1. What is the spot price of the underlying asset today?

2. Now, suppose there is a third forward contract, expiring in 4 months and trading at 1,250. Is there an arbitrage opportunity? If so, how could you exploit this opportunity?

Answer 1

Price of one month forward contract is 1200

Price of three months forward contract is 1220

Rate of change = 1220 - 1200 / 1200

                          = 20/1200

                          = 0.01666 two months basis

Effective ROI per month = ( 1 + r)^1.2 - 1

                            = ( 1 +0.0166)^1/2 - 1

                            = ( 1.01666)^1/2 - 1

                             = 1.008296 - 1

                             = 0.008296

Spot price of underlying security =

= FV/( 1 +r)^n

= 1200/ (1.0008296)^1

= 1190.12

2. Now, suppose there is a third forward contract, expiring in 4 months and trading at 1,250. Is there an arbitrage opportunity? If so, how could you exploit this opportunity?

FV of forward contract after four months

FV = 1190.12 * ( 1 +r)^4

      = 1190.12( 1.008296)^4

      = 1230.11

Intrinsic value of forwar contract after four months is 1230.11. However, One forward contract is exists at rate of 1250 with same time period.

Arbitrage process

= Investor shall buy underlying security with spot rate 1190.12 and book foroward contract for selling such security at 1250.

= For buying underlying security, He will borrow funds 1190.12 from bank. Bank will charge rate of interest @ 0.8296% p.m. basis. carrying cost will be = 39.99 ( 0.8296% * 4 months * 1190.12)

= Total cost for the Investor = Purchase price + carrying cost

                                            = 1190.12 + 39.99

                                             1230.11

Arbitrage Gain = Selling Price - total cost  

                          1250 - 1230.11

                         = 19.89