Again, suppose silver is currently selling at $4.23 per ounce in the spot market

Question

Again, suppose silver is currently selling at $4.23 per ounce in the spot market. Assume as well that the current risk-free rate (implied repo rate) is 3.75% and that silver contracts involve 5000 ounces each. Also, now assume that carrying costs (storage and insurance) for silver are accessed at .31% (0.0031) per ounce price.

a. Including carrying costs, what should the 6 month (180 days) silver futures contract be selling for according to the cost-of-carry model?

b. If the 6 month (180 day) futures contract for silver is selling for $4.18 per ounce, what should you, as an investor, do?

c. What arbitrage profit will you realize if you decide to work with two (2) silver contracts?

Explanation / Answer

Part A

We have following formula for futures price using cost of carry model

Futures price = So x e^(rt)

                           = 4.23 x e^(0.0375 + 0.0031)x0.50

                           = 4.23 x e^0.0203

                           = 4.3167

Part B

We can see the futures contract is going to go up as per the cost of carry model. But as per the data from the exchange it is going to go down to 4.18. Therefore, as an investor, I would short on the futures price.

Part C

Profit = (theoretical futures price – actual futures price) x size of contract

                = (4.3167 - 4.18) x 5,000

                = 683.50

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