Laws of Price: The Law of One Price

I think it's a useful exercise to try clearly to state as many requirements as possible that apply to efficient free market prices. So from time to time I'll devote a post to one or more of these, which I will call "Laws of Price."

The first that I'll look at is a very widely known law with many implementations: the Law of One Price.

Very simply, the Law of One Price states that if two different portfolios of securities have exactly the same payoff at a future date under all possible outcomes, then they must have the same price. Stated differently, there can be only one price for a given pattern of future cash flows, regardless of how the pattern is achieved.

So, a bet that pays $1 if the Steelers beat the Redskins this coming Sunday, plus a bet that pays $1 if the Redskins beat the Steelers in the same game, plus a bet that pays $1 in the event of a tie in the game, should have the same price as $1 paid after the game Sunday with certainty.* If they don't, then a guaranteed profit can be made by selling the more expensive position and buying the less expensive one: simple arbitrage. (The Law of One Price is sometimes referred to with the qualification "no arbitrage," or "arbitrage free.")

* -- These bets will not in fact add up to the value of $1 paid with certainty, but this is because the sports betting market is not efficient: the bookies and the odds-makers arrange to take a percentage of each bet as their compensation, so making all of these bets will cost more than $1 paid with certainty. Also, the "frictional costs" -- costs associated with transaction fees or expenses from acquiring or disposing of positions -- of attempting arbitrage will allow some deviation of prices away from a singular price. But the prices cannot stray too far apart.