Question

Suppose the spot price of an investment asset that provides no income is $30 and the risk-free rate for all maturities (with continuous compounding) is 10%. Suppose that the three-year futures price is quoted at $41. Assume that there is no transaction cost. How can an arbitrageur generate riskless profits from this case? Please provide as many details as possible in explaining your strategy.

Answer 1

Solution:

The spot price of the 'no income' asset is $30 and the risk free rate for all maturities is 10% continuous compounding.

The three-year futures price is quoted at $41.

The arbitrager has these investment alternatives:

1. Invest $30 at the risk free rate of 10% in which case after 3 years he receives $30 *1.10 * 1.10 * 1.10 = $39.93. Thus his profit is $39.93 - $30 = $9.93. This is riskless profit but in a single spot market.

2. Write / sell 1 three-years futures contract at $41 and invest $30 to buy the no income asset. Invest the net balance of $41 - $30 = $11 at the risk free rate of 10% to receive $11 * 1.10 * 1.10 *1.10 = $14.64. So his total profit is $41 - $30 + ($14.64 - $11) = $14.64. This is his riskless profit from an arbitraging opportunity arising from the price differences in the spot and futures market.

In alternative 2 he has made an riskless profit of $14.64 just from arbitraging the price differences in the spot and futures market.