Question

(a) The spot price of an asset is $135.00. The forward price for delivery in one year is $143.00. The risk-free rate is 5.4% per annum compounded continuously. Describe an arbitrage opportunity involving one asset (assume it has no storage cost and yields no dividend).

a. Go long one asset, take short position in one forward contract

b. Go short one asset, take short position in one forward contract

c. Go short one asset, take long position in one forward contract

d. Go long one asset, take long position in one forward contract

(b) Compute the profit after one year.

Answer 1

a) Risk free rate compounded continuously = r = 5.4% per year, Spot price = S = $135, Time to maturity = t = 1 year

Current Forward price = $143

Now we know that

No arbitrage Forward price = S. e^rt = 135 x e^(5.4%)(1) = 135 x e^0.054 = 135 x 1.055484 = 142.4903

It is know that we always buy(long) under priced security and sell(short) over priced security.

As current forward price is more than no arbitrage forward price, hence forward contract is overpriced, therefore we should take short position (sell) forward contract.

Simultaneously we need to take long position in Asset as asset is under priced with respect to current forward price.of $143. This is so if we take current forward price to be true, the current spot price should be = 143 x e^-rt = 143 x e^(-5.4%)(1) = 143 x 0.94743 = 135.4824. Hence Asset is under priced at $135 for current forward price.

Answer a. Go long one asset, take short position in one forward contract

b. Steps to carry out arbitrage and calculating profit

i) Borrow $135 at risk free rate to buy(long) asset and sell(short) forward contract with forward price = $143

ii) Amount owed on loan after 1 year = Loan x e^rt = 135 x e^(5.4%)(1) = 135 x e^0.054 = 135 x 1.055484 = 142.4903

iii) After 1 year settle short position by delivering the asset and receiving $143

iv) After 1 year, Profit = Proceeds from settlement of short position - Amount owed = 143 - 142.4903 = 0.5097 = 0.51 (rounded to two decimal places)

Hence profit from arbitrage = $0.51