## Saturday, April 17, 2010

### How do you limit drawdown using Kelly formula?

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 won't 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 won't lose all of the equity of this sub-account, or equivalently, you won't 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.