# Money Management Formulas, from Jim Sogi

September 19, 2007 |

Ralph Vince, in Portfolio Management Formulas, says money management analysis is as important as trade system selection. Daily Spec's own Dr. Phil McDonnell improved Vince's management ideas by using return rather than drawdown in his soon to be published book Optimal Portfolio Modeling, which I look forward to buying.

Vince mentions a number of staking schemes. Vince and Bachelier refer to the basic martingale. The martingale word is derived from an equestrian device attached to the horse's bridle to prevent the horse's head from rearing back, but allowing it to lower forward. A martingale staking scheme doubles down on every loss and takes profit on the first win. The problem with the martingale is that when there are too many random consecutive losses, capital exhaustion, or casino or exchange limits, may stop it. The small martingale adds bets down per a predetermined list. Stopping is another staking system in itself. The anti-martingale is known as pyramiding. Fixed fractional system is a small anti-martingale. The reserve strategy trades base plus a reserve of the winnings. A fixed stake is another system. Vince says a proportional fixed fraction is the best. The method to determine the fraction or multiple is the question. Taking money out of trading is another staking method. Adding down and selling a portion of gains, lowering basis but keeping stake constant, is another staking system.

Some years ago Dr. McDonnell proposed the following management formula, and has further explained it to me:

Maximize: C = Sum( f * ln r(i) ) / n

maximized over all f.

where:

n - the number of outcomes in the backtesting
f - the maximum fraction of your capital to invest
r(i) - relative profit outcome for backtest case i,
note a 1% profit means r(i) = 1.01, a 2% loss
means r(i) = .98
ln is the natural log

Determining the stake on an additinoal forward expectations factor would improve return as well. The goal is maximum captial appreciation and looking at computations and equity growth is as important as trade selection as long as the expectation is positive. A losing system is always a loser and no money management scheme can turn it positive.

Vince bases his calculations on a single trading system where the consecutive losses are independent. He says the calculations are harder for multiple systems, however expectations for multiple winning systems and the equity curve should be better and smoother, which should affect staking.