Question

The current spot price of silver is $32/oz, the interest rate on three‐month loans or deposits is 0.75%, and a three‐month futures contract on silver is currently traded at $32.50/oz. The size of the contract is 100 oz.

a. Assuming that there is no storage or transaction cost, determine the theoretical price of the three‐month silver futures

b. Determine whether an arbitrage opportunity is present in the market. If so, suggest a trading strategy that would take advantage of such an opportunity, and calculate the net profit from the strategy (per contract). Make sure to clearly identify  what position you would take in the futures  whether you would buy or sell the asset  whether you would borrow or invest cash and for how long

c. Assume now that in addition to all of the conditions given above, the purchase and sale of the physical asset involves a transaction cost of 1.5% from the amount of the transaction. Calculate the no‐arbitrage bounds on the futures prices, determine whether an arbitrage opportunity still exists, and determine whether the arbitrage strategy constructed in part b would still result in an arbitrage profit.

Answer 1

(a). the formula for theoretical price of future is:

Spot price * er*t

= 32*e0.0075

=$32.24

(b). Since TFP < AFP, the future are overvalued and hence arbitrage opportunity exists. the correct action to take would be to buy in spot market and sell in future market.

Step 1: Borrow to buy in spot market amount of $32 for 3 months

Step 2: interest cost after 3 months on $32 wil be $0.24

Step 3: Sell in the future market @ $32.50

Step 4: Gain= 32.50 - 32.24

=$0.26