Level 1 CFA® Exam:
Arbitrage

Arbitrage & Law of One Price

Arbitrage is a process through which an investor earns a profit without bearing any risk. The trick is to notice that the same or equivalent assets have different prices in different markets or in the same market. The basis for arbitrage is the so-called law of one price which has it that assets generating identical future cash flows should be priced at the same level.

Short Selling

Short selling is when you borrow a share, then sell it in the market and after some time you repurchase it and return it to the lender. Generally investors will engage in the short sale of shares if they expect a decrease in share prices. But in the case of arbitrage, as you you’ll see in examples below, investor’s expectations about future share prices are not important at all. It’s because, thanks to arbitrage you earn risk-free profits, so any changes in asset prices are irrelevant.

Theoretical Forward Price

Using simple compounding, the theoretical forward price, i.e. the price that eliminates the arbitrage profit in case of a forward contract, is equal to the price of the underlying stock times one plus risk-free interest rate:

$F=S\times(1+r)$

Let us see how arbitrage works if we have stocks and forward contracts on these stocks.