Mathematicians like D’Alembert and Paroli have devised strategies to improve odds in gambling, which can be effectively used in money management.

Consider the following trade. An investor buys stock X at a given price. X falls in price. So the investor buys again. X falls again; the trader buys again, perhaps increasing his commitment because he is confident about X’s long–term prospects. Each time, he is lowering the average cost of the holding.

An eventual recovery in X’s price will fetch higher profits for the investor who has averaged down. The risk is, of course, that he may be throwing good money after bad if the stock never recovers. Averaging down is fairly common for long–term investors and this logic is the foundation of an SIP or systematic investment plan for a mutual fund.

Now consider another trading possibility. An investor buys X at a given price and the price moves up. The investor buys again at the enhanced price. The price increases a second time and again, the investor buys at the higher price rather than taking a profit.

This is averaging up or pyramiding. On each transaction, the average cost of the position rises. However, the investor feels that he has identified a trend and he is confident enough to commit more funds to a winning position. Actually, pyramiding is a more common trading technique than an investor’s tool. Traders use it on both long and short positions starting with a small stake and increasing their commitment as the trend intensifies.

Investors have also been known to pyramid. Warren Buffett for instance, increased his core holding in Coca–Cola several times at enhanced price over an entire decade. But he also bought Coke several times when the price dropped. It was more a question of liking the fundamentals and increasing his stake whenever he couldn’t find anything better.

Implicitly, when an investor or trader pyramids, he is expecting the chosen asset to continue beating the street. When a trader does it, he is often pulling cash out of low-return liquid assets so there is an asset allocation theme. This is also what a fund investor does if he sets up a systematic transfer plan (STP) where cash is moved from a debt fund into equity or vice versa.

Now consider a situation where you can exactly predict the risks and returns when you buy a stock. For example, let’s set the return at 100 per cent and say that the probability of a favourable return is say, 18/37. If the outcome is unfavourable, you lose 100 per cent as well. In essence you are making an even-money bet with the odds slightly against you. Can you improve your money management to offset the odds?

Various people have tried. The mathematician D’Alembert suggested a small increment in the commitment every time the price dropped while others such as Paroli suggested an increment every time the price increased. D’Alembert suggested 10 per cent increase after every price drop while Paroli suggested anything up to a doubling of stake on each price rise.

Neither was an investor. Both studied roulette where the odds and the probability are exactly as described. D’Alembert Systems don’t beat the odds (especially on American wheels with two zeros where the chance of winning drops to 18/38) but they do lose less money than a standard equal stake system.

You win at roulette (betting on colour) a little less than half the time - if the D’Alembert System is used, the wins tend to come on a slightly higher stake and balance off the slightly more frequent losses.

Paroli Systems (averaging up) suffer from an inherent mathematical flaw where roulette is concerned. On an honest wheel, every spin is an independent event and Parolis gain only where a winning run or trend is established. In the market, trends are easier to envisage because prices are benchmarked to previous prices rather than being independent “spins”.

How does a D’Alembert work with a SIP - that is, you increase the SIP by some pre-set amount every time the NAV is lower than the previous NAV? This seems to offer a small positive increment on return compared to a standard SIP. A Paroli lowers the IRR compared to a standard SIP but it could be an interesting variation on an STP if you transfer more into a rising asset.