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# futures2 - An Example Suppose that a stock is currently...

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An Example Suppose that a stock is currently priced at \$100. The stock is expected to provide a dividend of \$3 payable at the end of the year. The one year risk-free rate of interest is 5%. The futures price on a one-year futures contract on the stock is \$110. Does this set of prices represents an arbitrage opportunity? If so, design a strategy to exploit the opportunity.

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Notice that since the dividend yield is 3%, the theoretical futures price should be: F 0 = 100 (1 + 0.05 - 0.03) 1 = \$102 The actual futures price is \$110, hence there is an arbitrage opportunity. In order to exploit the opportunity, consider the following strategy. Action at t=0 CF at t=0 CF at t=1 Buy a share of stock - \$100 \$(S T + 3) Take a short position in futures contract \$0 \$(110 - S T ) Borrow \$100 at the risk-free rate \$100 - \$105 Net Cash flow \$0 \$8.00
Note that the strategy is "costless" and is risk-free (the final payoff does not involve S T ). Yet it has a positive payoff at time t=1. This is an example of risk-less arbitrage! The exploitation of such opportunities would lead to a realignment

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futures2 - An Example Suppose that a stock is currently...

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