Prop Betting and Hedging Bets
Nov 7, 2011

Prop Betting and Hedging Bets

As a poker player, talking about betting with non-poker friends often illustrates some pretty basic misconceptions with the process. Correcting some of these misconceptions also is important in understanding how things like hedge funds and other financial instruments operate.

Firstly, we have all heard somebody express their confidence in some proposition by claiming a willingness to bet a very large amount of money on it - typically with the stated or unstated assumption that it will be bet at even money so that each party is risking the same sum. This is entirely the wrong way to measure confidence in a bet. The more confident we are in the outcome of some proposition, the better odds we should be willing to lay. For instance, if we think it is 10 times more likely that outcome A happens than outcome B, then we ought to be willing to bet with 10:1 odds - for example, willing to risk $100 dollars to win $10. So if you are wanting to demonstrate how confident you are, change the odds from 50:50 to something less favorable, don't raise the stakes of the bet.

The amount we are willing to risk depends on some other factors such as the size of our total bankroll, our risk of ruin, our tolerance for variance in outcomes and the like. If we are getting a very good price on the bet (betting, say, at 50:50 when we would be willing to accept 10:1) then our tolerance for these other factors changes, but this depends on the specifics of the bet and we don't have some standalone number that represents our confidence that holds outside of the contest of a specific bet. 

A bet also does not occur standing alone. It occurs in competition with other places people could make bets such as with other friends or online in places like Intrade that allow for proposition betting. I might turn down a good bet with you because I believe I can get a better bet somewhere else. So the amount of money one risks, and the odds at which it is risked, is dependent on the larger marketplace of betting. It is often possible to hedge one's bets in ways that are profitable no matter what happens. 

Imagine, for instance, Person A believes that the chance that Obama wins reelection is 10% (a silly claim I have seen on multiple occasions).  Intrade typically has the odds of Obama winning being traded at arround 50%. Suppose I was able to get someone to agree to make the bet at the 10:1 odds where I risked $10 and stood to win $100 if Obama won. I could then go and bet, on InTrade, $55 that Obama would lose. This way, if Obama wins I get $100 from Person A and lose $55 on InTrade, thus netting $45. If Obama loses, I win $55 on InTrade and lose $10 to Person A, thus again netting $45. I am guaranteed a large profit no matter what, and thus should be willing to "risk" as much money as I can get both parties to reliably put up. If I wish, I can modify the presciently chosen $55 Intrade bet to be anything between $10 and $100 and I will still risk nothing but my winnings are tilted to prefer one option over the other. 

This is more or less how hedge funds work.  They don't actually compute the chances of a certain event happening and then bet wherever they can get a better price than their computed odds indicated. They instead look at the market of various bets available and try to find situations where by making different bets and combining them they profit regardless of the outcome. It is a competitive market places so the kinds of egregious profitability given in the example above is unheard of, and it is also often difficult to eliminate one's risk entirely by the above method, but typically the actual amount risked will be quite small compared to the nominal size of the various bets being made. Indeed, by betting very large amounts on very small differences in prices, one can make a quite reliable profit. This is part of the reason why financial companies leverage up their money so much: because the real amounts being risked are so much smaller than the nominal values, they can mulitply the nominal values through leverage a large amount to maximize real profit.
In the world of finance, people often think that decisions are largely made based on probabilities. They are not; they are largely based off of prices, such as we have seem above. Typically prices are listed and not odds (10:1, say) but this is just a matter of convention and they are functionally equivalent. A credit default swap, say, that pays $1000 if a loan is defaulted, may have a price of $100 and thus be 10:1 odds. 

Actuarial economics is the branch that actually tries to directly compute odds of events occurring and thus bet accordingly. It works best for things like life insurance where there is a lot of data out there about a repeating and testable phenomenon that one can compute the probabilities of and bet accordingly. But there is a reason such actuarial processes are limited to certain specific industries and can't be so easily applies to something like the risk of inflation or the risk of a Greek default. Even things like corporate bond prices, the alleged risk of default as calculated by bond prices is an order of magnitude greater than actuarial risk as determined by historical precedent. Anything that is suspect to financial speculation turns from an actuarial game towards a prices game. 

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