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Money Management
By Lawrence G. McMillan

This article was originally published in The Option Strategist Newsletter Volume 17, No. 15 on August 15, 2008. 

Trading or investing involves several facets of operation: trade analysis, money management (including trade execution and position size), and follow-up action (including exiting the trade). Most successful and experienced traders agree that trade analysis is the least important – contrary to what a novice would expect. In fact, I have seen a successful system trader state that he could turn any reasonable system into a profit through proper money management (i.e., through proper position sizing and follow-up action).

If one is too conservative, he can ruin a successful system (by stopping himself out at the tiniest hint of a loss, for example). On the other hand, if one is too aggressive – say, leveraging position size up too aggressively when profits exist, he will also fail because one small downturn will eventually be a disastrous loss.

One well-known aggressive method for position sizing is the Kelly Criterion1. Kelly is based on one’s expectations for success in the trade. If the trade is foolproof (riskless arbitrage, for example) then invest 100% of your capital in the trade. On the other hand, if the trade has a negative expectation, then don’t invest any of your capital. There is actually a formula for sequential investments (or bets), but investors don’t just invest in one trade at a time, nor do they always use the same trading system. In short, that formula boils down to this:

% of NAV to invest = probwin – probloss

That is if you have a system that historically has shown a 55% probability of winning, then you would invest 10% of your portfolio in that trade. That’s pretty aggressive and most professional money managers would reject that large of an investment.

One way to tone it down and to use the concept of expected return with the formula is this:

If e = expected return of this trade
Then probwin = (1 + e) / (2 + e)
and, of course, probloss = 1 – probwin

Suppose you find a naked put write with a 2% expected return (not annualized), which is about the non-annualized expected return for most of the index puts that we write. You would invest this much of your account in the trade:

e = 2.0%
probwin = (1 + 0.02) / (2 + 0.02) = .505
probloss = 1 – probwin = 1 – .505 == .495

So Kelly says to invest probwin – probloss = 1.0% of your account in this put write.

Say you are trading a $500,000 account. Then you would invest $5,000 in this trade. If we state (or you determine) that the expected investment is $1,000 per put, then you would sell 5 puts for this particular trade.

Some traders feel this restriction on Kelly is too onerous – especially in an environment where it is hard to find new positions. That is, one won’t be able to get enough money to work. For example, for small accounts, or for high-priced indices, one would only be writing one put at a time. That isn’t optimal from other standpoints, such as commissions.

Some traders counter this by using annualized expected returns, but that may produce too aggressive of a result. In the above example, suppose the annualized expected return is 24%, so Kelly would instruct one to invest 10% of his capital in the trade. That’s aggressive, but not unreasonable for an index put write. However, if one is going to use annualized expected returns in conjunction with Kelly, he should probably have some limit – such as 10%, no matter what Kelly calls for.

In addition, the standard caveats, such as “having somewhere to roll to,” still apply.


This article was originally published in The Option Strategist Newsletter Volume 17, No. 15 on August 15, 2008.  

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