Re: Kelly Criterion - Math Problem
- From: ime@xxxxxxxxx (Randy Hudson)
- Date: Mon, 28 Aug 2006 07:21:34 +0000 (UTC)
In article <1156010032.611665.291590@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<fsk2006@xxxxxxxxx> wrote:
The Kelly Criterion only applies to bets on a win/lose proposition,
such as a horserace or sporting event. I'm looking for a discussion
where payoffs ranging from -100% to +500% (or more) are possible.
The Kelly criterion is equivalent to maximizing the expected value of the
log of your wealth.
That restatement can be used to derive "Kelly" betting strategies for
continuous distributions of outcomes, either directly or via simulations,
depending on the outcome distribution.
I am trying to apply the Kelly Criterion to a stock market trading
strategy (specifically, options trading). My system has some weird
properties. I'm pretty sure it's +EV, but it also has a 70-80% chance
of showing a 100% loss. (It is still +EV, which means that it will
sometimes show a gain of 500% or more.)
A call option strategy will depend on the rare huge win, 1000% or more, when
there is a shift in perception of the underlying stock such that both the
(perceived) mean and the (perceived) variance of the distribution of the
underlying secirity increase.
Because of that dependence, and the implicit high variance of a call-option
program, the amount that would be invested in each option purchase, relative
to the overall bankroll, tends to be small. Thus, the growth rate of the
overall bankroll will be small, even though the expected gain from each
particular trade, as a percent of the amount traded, seems large.
I don't know exactly how much +EV it is, even though I'm confident it
is.
That's a big red flag.
I am picking multiple stocks at the same time, but they are correlated
(as the market tends to overall increase or decrease). So, instead of
hedging with independent bets, I'm making partially correlated bets
(again, I don't know how much correlated, except that they are
correlated).
Of course they're correlated. But if you don't know how correlated, you
can't figure covariance, and can't estimate the "Kelly"-optimal position to
take.
In case you are wondering what I'm doing, I'm buying out-of-the money
call options, and expecting the stocks to go up, figuring I can pick
stocks that will outperform the market. (I already have a good record
of making regular stock picks, so I figure that will continue to be
true.)
Because of variance, the "leverage" that makes option trading of good stocks
look so good is partly dissipated in a Kelly-optimal allocation.
Summarizing, the math problem I am trying to solve is:
- I am making several correlated +EV bets. (and I'm not sure how
correlated they are)
- It is +EV, but I'm not sure by how much.
- Each bet has a high probability of a 100% loss, even though it is
still +EV overall. (The distribution of returns on a given bet is not
normal.) The return will sometimes be +500% or more.
- What % of my "bankroll" should I be willing to risk at any given time?
There's too much you don't know, to be able to answer this.
But, you aren't alone in this. Read Taleb, and Lowenstein, to learn about
pros who didn't know their underlying distributions; you'll also learn how
that caused them to go broke or worse.
--
Randy Hudson
.
- References:
- Kelly Criterion - Math Problem
- From: fsk2006
- Kelly Criterion - Math Problem
- Prev by Date: Re: My first weekend playing WSEX Poker
- Next by Date: Re: My first weekend playing WSEX Poker
- Previous by thread: Re: Kelly Criterion - Math Problem
- Next by thread: Re: Kelly Criterion - Math Problem
- Index(es):
Relevant Pages
|
