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A trader owns a commodity that provides no income and has no storage costs as part of a long-term investment portfolio. The trader can buy the commodity for $1250 per ounce and sell it for $1249 per ounce. The trader can borrow funds at 6% per year and invest funds at 5.5% per year (both interest rates are expressed with annual compounding.) For what range of 1-year forward prices does the trader have no arbitrage opportunities?Assume there is no bid-offer spread for forward prices.

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ammary456

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There is no arbitrage opportunity if the forward price is between $1317.695 and $1325 per ounce.

Assuming that F0 is the one-year forward price of the commodity. When F0 is high, the trader can borrow $1250 at 6%, buy one ounce of the commodity and then enter into a forward contract to sell it in one year for F0.

The profit that will be made in one year is  F0 = 1250 x 1.06 = 1325

This will be profitable if F0 > 1325. The profit relative to the position the trader would be in if the commodity were held in the portfolio during the year will be  1249 x 1.055 - F0 = 1317.695 - F0

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