Can someone help me solve this and explain to me what arbitrageopportunities are

Question

Can someone help me solve this and explain to me what arbitrageopportunities are as well as solving the following?

Consider a 3-month forward contract on a non-dividend payingasset. The spot price of the asset is $40, the risk-freeinterest rate is 5%, and the futures price is $40.

a. Describe the arbitrage opportunity the above scenariooffers and compute the profit you can make by using one forwardcontract.

b. Under what circumstances would the above prices be fair(i.e. arbitrage doesn’t exist even if there are notransaction costs).

Explanation / Answer

A. Sell one contract, borrow $40 and invest the proceeds in therisk free rate. At the end of the three months, you will berequired to fulfill the contract by giving $40 or delivery toindividual who you sold the asset to. You will have earnedinterest on the $40 you invested at the risk free rate whichamounts to $.50 (simple interest, no compounding). Therefore,when you liquidate the asset, you will receive $40.50 and will beobligated to pay $40, profiting $.50 risklessly. B. Spot-Futures Parity Equation: F=Se^(rt). Therefore,if the current spot price is $40, The futures price should be=40e^(.05*.25) => $40.50. These two prices are equivalentif there are no transactions costs.

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