Question

The spot price of gold today is $1,505 per ounce, and the futures price for a contract maturing in seven months is $1,548 per ounce. Suppose ACG puts on a futures hedge today and lifts the hedge after five months. What is the futures price five months from now? Assume a zero basis in your answer.

Answer 1

Future price = SPot price * e^{net cost of carry * Time}

Net cost of carry = risk free rate + continuously paid storage cost - continuously paid convenience yield

Net cost of carry = risk free rate + continuously paid storage cost - continuously paid convenience yield

F(0,7) = S * e^{net cost of carry * 7/12}

1,548 = 1,505 * e^{net cost of carry * 7/12}

Taking log on both side

Ln(1,548/ 1,505) = net cost of carry * 7/ 12

0.028171 = net cost of carry * 7/ 12

Net cost of carry = 0.028171 * 12/ 7

Net cost of carry = 0.048293

The five month future price:

F (0,5) = S * e^{net cost of carry * 5/12}

F (0,5) = 1,505 * e^{0.048293* 5/12}

F (0,5) = 1,535.59