First we must determine whether the futures contracts are mispriced, by multiplying the commodity price by (1 + the risk-free rate), or 1.0375. The basic equation uses the risk-free rate, but we have the actual borrowing rate, and for real-world purposes the actual borrowing rate provides a more accurate price estimate. For practical purposes, we should probably use the borrowing rate, but both rates provide the same answer to the question above. For illustration purposes, we use the risk-free rate in the discussion below.
It turns out that all three contracts are mispriced. Copper futures are overpriced, and silver and molybdenum futures are underpriced. However, transaction costs muddy the water. Assuming a 3% commission on futures trades, the price differential on molybdenum is not sufficient to justify an arbitrage trade. Thus, the traders should buy copper, for which the futures contract is overpriced, and sell silver, for which the futures contract is underpriced, and make no trades in molybdenum despite the fact that the futures contract is underpriced.
|
Copper (per pound) |
Silver (per ounce) |
Molybdenum (per pound) |
Spot price |
G3.15 |
G12.75 |
G34.45 |
Futures price |
G3.54 |
G12.82 |
G35.23 |
No-arbitrage futures price |
G3.27 |
G13.23 |
G35.74 |
Potential arbitrage profits |
G0.27 |
G0.41 |
G0.51 |
Transaction costs |
G0.11 |
G0.38 |
G1.06 |
Arbitrage opportunity |
Yes |
Yes |
No |