# Can you win when the odds are in your favor?

Imagine if you could predict with 60% certainty whether the market will go up or down tomorrow — theoretically, this should make you a billionaire in no time.

But, in reality, most investors cannot take advantage of this edge.

Consider the coin flip experiment by Victor Haghani. You walk into a room with \$25. There is a biased coin on the table, which gives a 60% probability for heads. If you make the correct call, you double your money; otherwise, you lose the bet amount.

You can bet any amount of your total portfolio on each bet, toss the coin as many times as you want, and change your bet amount each time.

Before going forward, we highly recommend you play this simulation and see how much you can make.

Haghani conducted the experiment on finance students from top colleges, analysts, and associates from leading asset management firms.

The results were disastrous. Even with a very apparent edge,

• 28% of the participants went bust

• 33% had less capital than they started off with

• Only 22% of participants had made >\$200

The main problem you would face while playing this simulation is how much to bet.

Some of you might bet your total portfolio on one coin toss and bust out, while others might bet too little, which minimizes the total outcome but preserves your portfolio.

The right way to play this game would be to use the Kelly Criterion, which shows that you should only bet ~20% of your portfolio on every toss.

If you do this, you have a 95% chance of getting to the maximum payout of \$250.

The researchers conclude by raising an important question:

If a high fraction of quantitatively sophisticated, financially trained individuals have so much difficulty in playing a simple game with a biased coin, what should we expect when it comes to the more complex and long-term task of investing one’s savings?

Kelly Criterion Bet Calculator: Optimizing Bet Sizes

Link :

I would just add that for continuous betting the optimal bet size is mean expected return/variance. There are published corrections for fat tails with this SSRN paper as an example: A Prospect-Theory Approach to the Kelly Criterion for Fat-Tail Portfolios: The Case of the Student t-Distribution

Jim,

I want to highlight this paragraph from the concluding remarks in the paper.

Regards
James

In addition, a correspondence is made with the optimal leverage indicated by the
popular fractional Kelly formula. This fractional Kelly approach results from trying to mitigate the absence of short-term risk aversion in the traditional Kelly criterion. A corresponding linear regime, when leverage is proportional to expected return, appears naturally in the current formalism in the limit of small expected returns. The fixed fraction in the fractional Kelly approach is related to the prospect exponent and the fatness of the tails of the returns distribution. In practice, considerations beyond maximizing long-term gains play a role when determining a desired leverage, even when a non-Gaussian distribution and a subjective aversion to tail events are taken into consideration.

It started off well…
I bet about 10% each round but if I lost, I doubled my bet, and then doubled again. I lost 4 in a row…
Its a lesson to seek my thrills in places other than my portfolio.