Arbitrage in a Mispriced Forward Contract Using Stock and Borrowing
Summary
The example asks how a company can exploit a forward contract offered at an unfavorable price. It assumes a non-dividend-paying stock, a continuously compounded interest rate, and a transfer of an existing long forward position for a fee before maturity. The proposed trade borrows the fee amount, takes over the original forward, and sells a new forward at the market price implied by the current spot price and financing rate.
At maturity, the company buys shares through the acquired forward, delivers them into the forward it sold, and repays the loan. The worked example reports a positive net cash result after these obligations are combined. Its logic is to offset the stock exposure and compare the contract terms with the fair forward price. The conclusion depends on stable interest rates, the ability to borrow and trade at the assumed rates, and the absence of transaction costs, credit risk, or other constraints; those practical frictions are not analyzed.
Key ideas
- A forward's fair price is linked to spot price and financing over the remaining term.
- A mispriced contract can be offset by entering an opposing forward at current fair terms.
- Borrowing the transfer payment makes its future repayment part of the arbitrage cash flows.
- The maturity payoff combines delivery under both forwards with repayment of the loan.
- The example assumes unchanged rates and frictionless access to borrowing and forward markets.
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Full text
# Constructing an arbitrage opportunity for a company involving Forwards
# Constructing an arbitrage opportunity for a company involving Forwards
Let's say an investor enters a long forward contract on 100 units of underlying assets $S$ and maturity $T$ = 4 years. The asset $S$ pays no dividends and the spot price of one asset is $S_0$ = £5. The continuously compounded interest rate is $r = 0.04%$.
i. Calculate the forward price $F$ (for 100 units) at time $T = 4$.
ii. Suppose that the investor agrees to sell the forward contract at $t$ = 1 year to a company for a price of $P_1 = $ £60, when the stock price is $S_1$ = £6. Construct an arbitrage opportunity for the company. Note that the company is only allowed to borrow money, buy Zero Coupon Bonds, buy or short-sell stocks and enter any forward contract on stocks.
So for part (i), I established the forward price was $F =$ $500e^{0.04*4}$ $= 586.76$
For part (ii) I never really know where to start on these sorts of questions. Could someone take me through the steps and logic for something like this? My exam is tomorrow so it would be much appreciated.
## Answer by AlRacoon (score 1, accepted)
https://quant.stackexchange.com/a/50716
In any "arbitrage" situation, you are trying to create a scenario where you sold a rich asset and bought a cheap asset, while keeping the overall position as flat as possible to risk.
Assuming interest rates have not changed from continuously compounded 4%, and the company can borrow at this rate and sell a forward at this rate.
The company is buying the forward from the initial investor for £60 by borrowing the £60 for 3 years (will pay back (60*e^0.04*3)). The company has taken over the obligation to buy the 100 shares for a total of £646.76 (£586.76 from the forward contract + £60 they paid for the forward. They would also sell the stock forward at £676.50 (6*100*e^(0.04*3)).
At maturity of the position, they will buy the stock for £586.76. Sell the same stock for £676.50 from the forward they sold. And repaid the £60 loan with interest for a total of £67.6 (60*e^(0.04*3)). The net profit being a total of £22.14Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.