Left skewed financial bets


Most of the money invested can be traced back to people who want good return and little risk. Be it through hedge funds, pension funds, funds of funds, bank deposits, ultimately there's someone out there who wants his capital to grow, and there's a money manager with a different incentive.

Most money management involves asymmetric risk for the manager and symmetric risk for the client. This is a classical principal agent problem. The manager has an incentive to increase the risk taken to make the most money. Heads we both win, tails we both lose, but I don't really lose that much while you get the full hit. This can be mitigated by various tricks, risk management, watermarks, and countless other, but overall the asymmetry persists.

But "risk" is a crude measure of what really matters, the probabilistic distribution for the payoff of the bet. One can use for example historical standard deviation, but it vastly underestimates the risk of fat tail distribution.

The most beneficial distribution for a money manager is really a negatively skewed or left-skewed distribution. A left skewed bet will turn in a profit with high probability and a loss with low probability. However, the loss will be larger than the profit. Its historical mean is also very likely to overestimate its true mean, implying that analysis of past performance is likely to overestimate future performance. A typical left-skewed bet would be to bet that Hillary Clinton will not be elected in 2008. You can lay this on Intrade and I think you are pretty sure to make $3 dollar on this, but then you might lose $100 if it happens (most likely scenario, Obama is killed by a crazy white supremacist sniper)

Not only are left-skewed distribution good for a money manager, right-skewed distribution are really bad. You lose money most of the time, and the evaluation of your performance from your track record underestimate your true expected performance. Imagine a betting strategy that loses a dollar every month, and wins 36 every two year. It's actually a great strategy, but unless a money manager can prove it works, he's likely to lose his customer or get fired before he can even turn in a profit.

On financial markets, every product can be thought of as a bet, and every bet has its own implied distribution. Overall the price of the bets move so that supply and demand are matched. If most of the trading is done by money manager, then there should be good demand for left-skewed bets and good supply of right-skewed bits, as a result, the price of left-skewed bets fall, and the price of right-skewed bets (which are by the way just laying a left-skewed bet). This also mean that the price of financial assets does not reflect the market risk-adjusted expected return, but some other, skew-dependent value.

There are ways for a money manager to extract this value. One way to do it is to package as much negatively skewed bets as possible. The distributions should average out and produce a nice normal distribution with no skew... Well that's the central limit theorem, but in practice, if you're dealing with fat tails, it could take a lot of bets to average this out, if it's even possible. It could be infeasible for a money manager to extract this value.

However, a simple investor with symmetrical incentives can profit from this situation by making right-skewed bets. He will not "beat the market", he will be helping money managers get rid of unwanted risk profiles and get paid for that.

So what are the right-skewed bets?

Out of the money options are the obvious... a put struck very low bets that a stock will fall a lot, a call struck very high bets that a stock will rise a lot. Most of the time, the option will expire worthless, sometimes it will make money.
Generally you can bet that the distribution of return of assets will have fatter tails that assumed by the market. Nassim Taleb makes nice epistemological arguments for fat tails and how they are underestimated. This is not really the point I am making here. I am simply saying that money manager will bet that distributions have no fat tails because it's a left skewed bet. Therefore, taking the opposite side should bring profits. One of the most common skewed trade is the yen carry trade. From a trader's perspective it's a great trade: borrow yen at low low rates, invest it in New Zealand at high rates, pocket the differential as long as the yen doesn't appreciate to much. You get money every day, it's fantastic. Of course, if yen rates start to rise, the yen will appreciate, many traders will get squeezed, try to get out by buying yen, producing further appreciation and pushing more people out of the trade. If a money manager wants to bet on that scenario, he stands to make a lot of money, but how will he explain to his boss or his customers losing money every day on the trade? Even options involved regular money loss... every day that passes without the event that you're expecting happening is a day where the market value of the option diminished, out of the money option have negative carry. A call option on the yen/new Zealand dollar is a massively right-skewed trade that does not appeal to money managers.
Betting that debtors will default is also a typical right-skewed trade, which can be made by buying protection with a CDS... again it involves shedding money regularly. This works if things go wrong, if things go well a winning right-skewed trade is betting on the recovery of distressed companies.

So right-skewed trade are nice, and if economics are right they can make lot of money, what's not to like ? A good reason to hate right-skewed bets is the income tax, which really makes your incentive asymmetrical. Two month ago, I wanted to bet that oil would quickly go to $200 or $100. The way to make that bet are option on oil futures (keyword is quickly). The problem is, if by chance you actually win your bet, enjoy a 50% tax on your profit. If you lose, well you can sort of carry your losses over fiscal years, but it is very limited. You might get by if you make a lot of trades but it pretty much kills every edge you could possibly have. One (legal) way to do it is through an offshore company which does not pay corporate tax. You still get taxed when you get the money out, but it can be after a long time, after many trades, when hopefully your return isn't skewed.

Disclaimer : whatever you do don't ever blame me, this does not necessarily represent anyone's view, including my employer or even mine.

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Found this post from a google search and it ended up really helping with a homework assignment. :) Thanks a lot for the great post!

Glad I could help :) What

Glad I could help :)
What was the assignment ?