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(EV) Expected Value

May 28, 2010

There was one computation that every serious poker player knows because it is crucial to making decisions,  and that is the EV or expected value. The applications to trading are quite obvious (though the elements of fat tails in financial markets preclude true estimation of EV):

EV= W% x amount you stand to win +L% x amount you stand to lose

where w% is the winning percentage and l% is the losing percentage or (1-w%)

There were several principles concerning EV that are relevant:

1) The outcome of any hand was considered irrelevant since a pro tries to maximize their long-term expected EV over time. You can have a 90% chance of winning with the odds being known with complete certainty and still lose multiple times in a row due to bad luck. This is something that you learn to deal with as a necessary part of winning. The best way to handle this is not to change your strategy to micro-manage your current equity, but rather to focus on maximizing long-term EV and not worrying about outcomes. The same applies to traders– there is no point worrying about any one trade, you focus on making the right decision and then you have to execute from start to finish. You have zero control beyond that point.

2) EV will converge to fair value as a consequence of the law of large numbers–however this may take 30-50 situations even with a fixed 52-card deck. In contrast, the population mean of a trading strategy is not truly known with a high degree of certainty, so you require a larger sample to converge upon fair value assuming you have correctly estimated the mean. This requires that you do random sampling and track new samples versus the sampling distribution to ensure that you have the right EV estimate as well as the standard deviation of EV.

3)  The best players estimate EV as being conditional upon a wide variety of contingencies–sort of like what Rob Hanna does at Quantifiable Edges http://quantifiableedges.blogspot.com/. This conditional estimate is as much an art as a science, which is why Rob also tends to assess things on a case by case basis. The essence of  a good EV estimate is that you in most cases take the baseline/base case estimate and only adjust it based on very strong mitigating factors–perhaps you are  drawing to hit a flush or a straight, and are offered slightly negative EV to see the last card. In most cases this would be a fold, but against a very bad player in No-Limit holdem, this is a high EV situation because you will probably get paid a large sum if you are fortunate enough to complete the hand. Thus this is sort of like a situation where you have “option value.”

Suggested EV applications: EV can be used in conjunction with Monte Carlo simulation to create out of sample equity curves that are more realistic than backtests.  This is because a data history is just a consummation of one possible outcome among many, and tommorow’s market will only echo the past. The order with which trades occurred, and the degree to which there were lucky trades or unlucky trades shapes the unique pattern exhibited in the past. EV can also be computed more accurately by adjusting the base case EV for the type of regime/environment that tends to affect the value the most. As such you can create simulations of what you can expect depending on the market environment.   Since EV is still ephemeral given the nature of financial markets distributions there are many possible avenues to pursue a more robust approach.    This is a formula from quantum physics called the relativistic Breit- Wigner distribution which is  a more appropriate version of the Cauchy distribution which is normally used to handle “fat tails.” There are some interesting properties/applications for the serious nerds out there to explore.       f(E) \sim \frac{1}{\left(E^2-M^2\right)^2+M^2\Gamma^2}. \!

One Comment leave one →
  1. May 29, 2010 7:37 pm

    Enjoy your blog. I just posted a recent topic dealing with same issues on my blog/site under probability win %. Sklanksy bucks or Galfondo bucks also factor in to this.

    Yes, many times it is possible to lose with such odds in poker. But, my take was that from a trading perspective, one could use those odds as confidence based test for the probability the system had quit working. Whereas in poker, I looked at it like you are suggestion. In other words, if one has a 8% probability of 5 losses in a row based on their “believed” win % then can look at that and say there is ONLY an 8% probability this occurred due to chance, right thus so maybe something quit working.

    The difference in my perspective, I guess, comes from fact in poker the odds are fixed and known (after the fact) whereas in the market they are unknown.

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