Hi all,

Does anybody has any experience to share on anti-martingale money management? (i.e leverage/deleveraging as ur position goes in/ out of the money)

Recently i ran a VB simulation on constant fraction bet sizing and found that i could make 130% return per annum with zero occurance of a capital wipe out ("risk of ruin"). As a start i did not model the bid/offer spreads and slippage. But still, it seems promising! Can somebody poke holes at this?

Also, i like to draw the similarity b/w antimartingale betting and portfolio insurance. In the later one rebalances a portfolio of the underlying so that the payout mimics that of a call option. That way supposedly, u get capital protection, all the potential upside and avoids paying a call premium. There was no free lunch ofcourse as the 1987 crash has proven. The (delta) rebalancing requires buying high and selling low- in a chopping environment, it hurts P&L big time. But the similarity ends there- in anti-M betting, the traders ability to call the direction determines P&L growth. For portfolio insurance, the manager's fate is subjected to the market's volatility. i think the risks are :
Probabilty(calling it wrong 10x in a row) Is there any pit falls in this line of reasoning? Will like to listen to your views v much. Thanks.

Max:

Can you explain further what exactly you mean by "anti-martingale money management?"

There is arguably an advantage to be gained by doing basically the exact opposite of portfolio insurance by keeping a constant amount of exposure to the risky market. Given most of the usual assumptions, buying and holding a market investment will yield an expected return of exp(m+0.5*s^2) with a median return of exp(m). By keeping a constant exposure to the market (i.e., moving more to fixed on upswings and more to the market on downswings), you can drive your median return to exp(m+0.5*s^2), albeit with more loss potential. (Portfolio insurance would drive your median return down, which has always made me astonished that so many grown men would have bought into it so completely.)

Martingale betting is the casino promoter’s way to lure in the fool (and his money). The carrot is that if you double your stake everytime you lose (say in a 50-50 odds game)- you will make back all your losses (breakeven) if you win just once. The flaw in such a system is it doesn’t account for losing streaks which can wipe out a finite account. Likewise most traders know that averaging on losses is the sure way to disaster. Opposite to this, in anti-martingale systems, you increase your risk when you win. Averaging on your winners could be the key to wealth(?). There’s a fair bit of research under gambling maths- try:

http://keplerweb.oeh.uni-linz.ac.at/tra ... eyMan9.htm

There are many variants such as fixed fraction, fixed ratio, optimal F, etc. It will be convincing if one can show maths/ intuitively that it works and how to implement a simple system given the constraints in the real world (slippage, etc.).
i am also interested in simulations for such a system before throwing in real money. What are the key points to model to ensure that "what you find is in fact what you will get"?
Thanks and cheers!

Martingale betting is the casino promoter’s way to lure in the fool (and his money). The carrot is that if you double your stake everytime you lose (say in a 50-50 odds game)- you will make back all your losses (breakeven) if you win just once. >>


Actually, casinos dislike martingale betting. The goal of the casino is not to bankrupt customers, but to maximize the handle, the total amount bet. The casino also likes positive skew. Ideally, most customers will lose but sometimes one will walk away a big winner. One big winner does more to encourage business than one thousand moderate gainers. Therefore, casinos encourage raising bets when you win (to increase handle and make winners rarer and bigger) and cutting bets when you lose (also to increase the handle, and to keep you playing and making the casino active). It seems counterintuitive that the handle is increased by winners raising bets and losers cutting them, the key insight is winners are limited by time (you have to sleep sometime) and losers by running out of money.

The key difference between a casino and the stock markets, of course, is the house has the edge in the former and the bettor has the edge in the latter. Therefore, in the stock market, it is the bettor who wants to maximize the handle. Most people also like positive skew. This is not to maximize the chance of becoming a billionaire, but to minimize the chance of unaffordable losses. This makes anti-martingale strategies attractive for the same reason casino owners like them.

Another advantage of sensible anti-martingale betting is they shift your money toward strategies that work. It makes sense to cut back on risk when you lose a bet, because losing should decrease your confidence in the investment picking.

It's important to remember that increasing the bet means increasing the stake, not keeping the bet in the same direction. If you buy a stock and it goes up, anti-martingale strategies say you should bet more on the stock market, but not that you should necessarily bet it long on the same stock.

Thanks Aaron,
i like your perspective about the casino- i do agree intuitively the bottom line is to have an edge then.
But my trading simulation using a 50% odds of up/down (i.e no statistical edge) showed an exponential growth in P&L over time. it seems strange that in a neutral game the betting strategy alone turned me into a winner?! Will like to hear from you.

In a fair game the expected value of wealth after any fixed number of bets is equal to initial wealth. However, the expected value of wealth can be different from initial wealth if measured at termination of a strategy. The most familiar example is the strategy of doubling your bet after each loss and stopping after the first win. This produces a profit equal to the initial bet amount, with zero risk. Of course, the difficulty is that you will not be able to execute the strategy all the time unless you have unlimited wealth or credit. If you are stopped either after a fixed number of bets or a fixed loss amount, the expected return collapses to zero. No fixed-horizon betting strategy on a fair game can have expected profits.

I don't know why your simulations are showing exponential growth, they should show a random walk with rare sharp increases and common small decreases.