Kelly formula revisited - forex trading systems free download

Kelly formula revisited ~ forex trading systems free download

Some discussions on Kellys formula with a reader Steven L:

Q:

"I am more than half way through your book and am stuck at a concept that I cant seem to find an answer in any other forum.

I have read Ralph Vinces "Portfolio Management Formulas," which uses Kellys formula to calculate an optimal "fraction" of the bankroll to bet on each trial. So a trader can calculate a fraction of his total trading account value to risk on each trade. What I am referring to is the so-called "fixed-fractional" trading. There exists an optimal fraction that will maximize the geometric growth rate of the trading equity, in theory anyway.

However, in the money management chapter of your book, you use Kellys formula to derive an optimal "leverage." This seems to be in conflict with what I learned from Ralph Vince, since leverage is usually great than unity and fraction is usually less than unity. I cant seem to make a connection between these two concepts. I have also seen the same optimal leverage formula in Lars Kestners Quantitative Trading Strategies and asked the same question on some forums, but no one was able to give me a clear satisfactory answer. It would be greatly helpful if you can help me sort out the confusion."

A:

I dont have Ralph Vinces book with me, but if I recall correctly, his formulation is based on discrete bets (win or lose, no intermediate outcome), much like horse-betting or in a casino game. My approach, or rather, Professor Ed Thorps approach, is based on continuous finance, assuming that every second, your P&L could fluctuatate in a Gaussian ("log-normal") fashion.

For discrete bets where you could have lost all of your equity in one bet, surely one should only bet a fraction of your total equity. For continuous finance, there is very little chance one could have lost all of the equity in one time period, due to the assumed log-normal distribution of prices. Hence one should bet more than your equity, i.e. use leverage.

Q:

In example 6.2 in your book, the portfolio consists of only long SPY, which has little chance of going to zero. So I can see how it is reasonable that you use the continuous finance approach and apply the optimal leverage to scale up the return.

But lets assume that the portfolio consists of a single strategy that buys options. Suppose this strategy will lose most of the time due to time decay but will make profit once in a while due to black-swan events. I dont think its a good idea to bet the entire portfolio equity on each trade for this strategy. Can you still apply the continuous finance approach in this case, since in reality trading is like making discreet bets? Should we expect the mean and variance of this strategy automatically result in an Optimal Leverage that is less than one? So that we actually need to risk a fraction of the account equity per trade?

A:

The formula I depicted in the book is valid only if the P&L distributions are Gaussian. If one expects a fat-tailed distribution due to black-swan events, a different mathematical model needs to be used, though it can still be within the continuous finance framework. However, for simplicitys sake, if the distribution looks multinomial (e.g. high probability of "Win a lot" v "Lose a lot"), then you may model it with fractional betting just like a casino game.
More info for Kelly formula revisited ~ forex trading systems free download:

Read More..

How do you limit drawdown using Kelly formula - forex trading techniques strategies

How do you limit drawdown using Kelly formula ~ forex trading techniques strategies

As many of you know, I am a fan of Kelly formula because it allows us to maximize long-term growth of equity while minimizing the probability of ruin. However, what Kelly formula wont prevent is a deep drawdown, though we are assured that the drawdown wont be as much as 100%! This is unsatisfactory to many traders and especially fund managers, since a deep drawdown is psychologically painful and may cause you to panic and shut down a strategy prematurely.

There is an easy way, though, that you can use Kelly formula to limit your drawdown to be much less than 100%. Suppose the optimal Kelly leverage of your strategy is determined to be K. And suppose you only allow a maximum drawdown (measured from the high watermark, as usual) to be D%. Then you can simply set aside D% of your initial total account equity for trading, and apply a leverage of K to this sub-account to determine your portfolio market value. The other 1-D% of the account will be sitting in cash. You can then be assured that you wont lose all of the equity of this sub-account, or equivalently, you wont suffer a drawdown of more than D% in your total account. If your trading strategy is profitable and the total account equity reaches a new high watermark, then you can reset your sub-account equity so that it is again D% of the total equity, moving some cash back to the "cash" account. Otherwise, you continue to keep the equity in the cash account separate from the equity of the trading sub-account.

Notice that because of this separation of accounts, this scheme is not equivalent to just using a leverage of L=K*D% on your total account equity. Indeed, some of you may be too nervous to use the full K as leverage, and prefer to use a leverage L smaller than K. (In fact, the common wisdom is that, due to estimation errors, it is never advisable to set L to be more than K/2, i.e. half-Kelly.) The problem with using a L that is too small is that, besides not achieving maximum growth, the portfolio market value will be unresponsive to gains or losses and will remain relatively constant. Using the scheme I suggested above will cure this problem as well, because you can apply a higher leverage L_sub to the sub-account (e.g. use L_sub = L/D%) as long as L_sub < K, so that the portfolio market value is much more sensitive to your P&L while still ensuring the drawdown will not exceed D%.

Has anyone tried this scheme in their actual trading? If so, I would be interested in hearing your experience and see if practice is as good as theory.
More info for How do you limit drawdown using Kelly formula ~ forex trading techniques strategies:

Read More..