Suppose you currently hold a security valued at R750, and the prevailing risk-free rate is 5.5%. You plan to sell this security in three months. The theoretical forward contract price is calculated at R760.12 and will be used to hedge against potential price declines. Now, if the dealer offers a tradable price to unlock the arbitrage profit of R745 on the forward contract, determine the arbitrage opportunity available to you, and subsequently, provide a calculation for the potential arbitrage profit.
The Correct Answer and Explanation is:
Arbitrage Opportunity and Profit Calculation
Given:
- Spot Price (Current Security Value) = R750
- Risk-Free Rate = 5.5% per annum
- Time = 3 months = 0.25 years
- Theoretical Forward Price = R760.12
- Dealer’s Forward Price = R745
Step 1: Understand the Arbitrage Situation
The theoretical forward price of R760.12 is calculated using the cost-of-carry model: F=S×(1+r)t=750×(1+0.055)0.25=R760.12F = S \times (1 + r)^t = 750 \times (1 + 0.055)^{0.25} = R760.12
However, the dealer is offering a forward price of R745, which is below the theoretical fair price. This creates an arbitrage opportunity because the forward is undervalued.
Step 2: Construct the Arbitrage Strategy
To exploit this:
- Short the Security Now: Sell the security at R750.
- Invest Proceeds at Risk-Free Rate: Invest R750 at 5.5% p.a. for 3 months.
- Buy Forward Contract from Dealer: Agree to buy the security in 3 months at R745.
Step 3: Calculate Arbitrage Profit
Investment Growth: 750×(1+0.055)0.25=750×1.01344=R760.12750 \times (1 + 0.055)^{0.25} = 750 \times 1.01344 = R760.12
Cost to Repurchase via Forward Contract: R745
Profit: Profit=AmountatMaturity−ForwardPurchasePrice=R760.12−R745=R15.12Profit = Amount at Maturity – Forward Purchase Price = R760.12 – R745 = R15.12
An arbitrage opportunity arises when the forward price deviates from its theoretical value, allowing investors to exploit pricing inefficiencies. In this case, the current spot price of the security is R750 and the risk-free rate is 5.5% annually. Using the cost-of-carry model, the theoretical forward price is R760.12 for a three-month period.
However, a dealer is offering the forward at R745, which is undervalued compared to the fair price. This discrepancy enables a riskless arbitrage opportunity. To capitalize on this, the investor can initiate a short sale of the security at the current market price (R750) and simultaneously invest the proceeds at the risk-free rate. Over three months, the invested amount grows to R760.12.
At the same time, the investor enters a forward contract to buy the security back at R745. When the forward contract matures, the investor uses R745 to repurchase the security and return it to the lender, thereby closing the short position. Since the invested funds have grown to R760.12, the investor earns a profit of R15.12 without exposure to market risk.
This strategy works because the arbitrage relies on predictable interest rate growth and a known forward purchase price, ensuring a locked-in profit. Such mispricings do not usually last long, as arbitrageurs act quickly to exploit and correct them, pushing prices back in line with theoretical values. Thus, this illustrates how arbitrage enforces market efficiency.
