You Have Been Asked to Determine the Theoretical Bounds on a Futures

Essay

You have been asked to determine the theoretical bounds on a futures contract on gold.You are supplied with the following information: spot price of gold = $400/troy oz.; time to expiration on futures contract = 6 months; riskless rate = 10%; borrowing rate for marginal investor = 12%; lending rate for marginal investor = 8%; storage costs for gold = $20/troy oz.per year.Short sellers can hope to recover only half of the storage costs that they save by short selling.
a. What is the upper bound on the theoretical futures price?
b. (Recalculate the new bounds.)
b. What is the lower bound on the theoretical futures price?
c. Assume that investors are required to put up a 10% margin on all futures transactions and that only cash (no T-bills) can be used to meet margin requirements. Evaluate the effect this would have on the upper and lower bounds you estimated in part a and part