Terror in Poker and Finance Part II

[Sweet]

Forgive me if I have erred. I am not financially educated, so perhaps I misunderstand, but it seems to me that a remark in "Poker and Finance Part II" by Dan Mezick is so profoundly incorrect, that any decent poker player should be deeply offended, and it certainly should not appear in an article associatied with the fine name of "2+2".

Apparently, "Sharpe ratio is basically the net reward divided by the volatility." Mr. Mezick then later goes on to conclude, "The player with the better Sharpe Ratio is the better player." It would appear that the thumpers of the weak-tight bible finally have their day! Nitty McSupertight is at home cheering, "Yes! I knew that I was the best player in my game, I almost almost always quit while I'm still ahead! Some guys are up way more than me over the last 5000 hours or so, but their results are so volatile... sometimes they lose 30 big bets in one session! I knew all this time I was the best player in the game; I earn way less than some guys, but I don't have to go through those big swings!"

OK, admittedly I have vented some of my frustration in that last tirade, but do you see my point? To clarify, suppose two of us have $10,000,000,000 bankrolls, and we're playing $1-$2 limit HE. Who is the better player? The one with the higher Sharpe Ratio, or the one with the higher EV?

There are clearly some important and points to be made, but claiming that "the player with the better Sharpe Ratio is the better player" is wildly incorrect, and only serves to champion the cause of the weak-tight masses.

Am I wrong?

[Off Duty]

You're absolutely wrong.

P. 754 of Investments by Bodie, Kane and Marcus.

"Sharpe's measure devides average portfolio excess returns over the sample period by the standard deviation of the returns over that period. It measures the reward to (total) volatility trade-off.

Playing super tight certainly lowers your standard deviation, but at the expense of playing marginal hands in profitable situations.

Playing super loose is the opposite, increasing the standard deviation and playing marginal hands in less than profitable situations.

The object is to get your maximize your return to standard deviation ratio, thus maximizing your Sharpe ratio. Depending on the situation, that could mean a super nitty style or a super loose one. Depends on how high the variance is in the game. So once again, the right approach to the game is situational.

I knew all that crap I learned in MBA school and all those books I refused to throw away would come in handy one day.

[Sweet]

I'm sorry, I don't see it. You claim, "The object is to get your maximize your return to standard deviation ratio, thus maximizing your Sharpe ratio," but that is not correct. The object is to make the most money. As I said, I think there are valid points to be made, but it still seems to me that saying that the goal is to maximize your Sharpe Ratio is stone dead false.

[Off Duty]

With all due respect, I believe you lack a fundamental understanding of the Sharpe ratio and it's application. Further, I think you're trying to project something on the Sharpe ratio that isn't there. You're suggesting that the Sharpe ratio vindicates playing a particular style, which is patently false.

While the super nit will have low variance and a low expectation, somebody who plays correctly will likely have a slightly higher variance and a much higher expectation. A maniac may have the highest variance and no higher expectation than somebody who plays correctly.

Or, another way - increasing your standard deviation without a corresponding increase in your win rate is lunacy. Further, decreasing your standard deviation in a way that causes a greater decrease in your win rate is just as dumb.

The Sharpe ratios of many bond funds and many penny stocks are about the same. It's pretty easy to go busto with penny stocks (high standard deviation, high return) and tough to get rich with bond funds (low standard deviation and low returns). There are lots of spots in the middle that yeald better with a reasonable standard deviation, thus higher Sharpe ratios.

[Xhad]

Sweet, what you're missing is that when you have a ratio of:

N/D

Decreasing D increases the value of the fraction, but so does increasing N. Since "n" in this value would be the expected "reward" (i.e. how much money you make overall), then EV is still very important according to this model and can still trump decreased variance much of the time.

[Off Duty]

Absolutely correct.

Assuming that two plays have the same EV, you would be insane to choose the play with the higher variance.

Assuming that two plays have the same variance, you would be insane to choose the play with the lower EV.

The world does not often work like that, and one is left to contemplate a variety of choices with corresponding EV and variance. This is why Sharpe's model came around in the first place.

[Sweet]

[ QUOTE ]
Sweet, what you're missing is that when you have a ratio of:

N/D

Decreasing D increases the value of the fraction, but so does increasing N. Since "n" in this value would be the expected "reward" (i.e. how much money you make overall), then EV is still very important according to this model and can still trump decreased variance much of the time.

[/ QUOTE ]

Well, I didn't actually miss that. I didn't claim that the player with the higher Sharpe ratio cannot be the best player. I did observe that there are ways for your EV to decrease while your Sharpe index increases, which, from my position, means that claiming the player with the higher Sharpe ratio is "the better player" is digustingly false. I gave a $10,000,000,000 example that I thought made this pretty clear. No?

[Sweet]

[ QUOTE ]
I believe you lack a fundamental understanding of the Sharpe ratio and it's application.......
While the super nit will have low variance and a low expectation, somebody who plays correctly will likely have a slightly higher variance and a much higher expectation.

[/ QUOTE ]

You may be right about my understanding. For example, I might've guessed that playing "correctly" would give a slightly higher expectation but a much higher variance. Usually the low-earn high-variance hands are exactly the ones that nits don't play, right? These are relative terms though, so maybe I don't understand the units in the numerator and denominator.

In any case, I think my $10,000,000,000 example clearly demonstates that the player with the higher Sharpe ratio need not be the best player.

[Off Duty]

You can do a lot to lowering your personal sharpe ratio by playing poorly.

[King Yao]

[ QUOTE ]
To clarify, suppose two of us have $10,000,000,000 bankrolls, and we're playing $1-$2 limit HE. Who is the better player? The one with the higher Sharpe Ratio, or the one with the higher EV?

[/ QUOTE ]

In your question, you should add:
One of the players has a higher standard deviation, but also a higher EV such that the Sharpe's Ratio is lower.

So:

Player 1 EV > Player 2 EV
Player 1 Sharpes Ratio < Player 2 Sharpes Ratio
Player 1 SD > Player 2 SD

(Unless I missed something, I think the combination shown above is possible and not an impossible situation)

Who would you rather be if you had 10mil, and you are playing $1/$2?

I'd rather be Player 1.