Thursday, May 30, 2019

Kelly criterion

I recently read the book The Dhandho Investor. It is a classic and I was always wanting to read it.

Here is a link to the book.

The book was good, but the most important thing I learnt from this book was the Kelly criterion.

In short, Kelly Criterion is a formula for bet sizing. The operative word here is sizing.

We all think of risks in terms of a Yes/No decision. When I analyze a company's stock, my thinking is usually in terms will this company perform well or not in the future.

This thinking is incomplete.

Evaluating probabilities of risk alone is not enough. We need to evaluate the impact or magnitude of loss/gain due to the risk.

If I have $10,000 in cash and I plan to invest $100 in a stock, the company's extreme performance, even if the stock doubles in a year or goes bankrupt and stock goes to zero, will have very limited impact on my overall portfolio.

However if I invest $1000 in this new investment,the impact on my overall wealth is much higher.

Thus we can see:

Actual Risk = Impact of risk  *  chances of risk.

Lets assume that there is a bond that gives an interest rate of 2% with a minimum investment of $10000. There is a 1% chance of the bond issuer defaulting. Is the impact on my wealth small, if I buy this bond?

No. Because even though the risk is low, the impact of the loss is higher for me since I invest the whole $10000 in this bond.

Position sizing has been a weak spot in my approach to investing. I have always invested very small amounts, to minimize the loss. However, this has limited the upside, and my overall performance has been

I have also invested a large amount in some low-risk cases, and the losses have been high.

So the first thing an investor should do is to realistically calculate the odds of an investment in its extreme cases (good and bad). Then using that he should find out the position size based on the Kelly Criterion.

Assuming that the payoff is limited by the investor, i.e, the investor has a stop loss at -X% and books profits at +X%, the simplified formula to find the fraction of the cash to invest ("bet", "risk") on an investment is 
2p -1, (where p = probability of profit).

For example, if I feel that a stick has a 60% (0.6) probability to increase in price, I should limit my investment to:

Fraction of cash= (2 * 0.6)  - 1 = 1.2 - 1 = 0.2 (20%).

The key metric here is not the probability of success, but the limit of portfolio to invest. The investor should ideally see the upper limit (20%) with a margin of safety and can invest about 10%, or 5%, to feel more safer.

There are many online calculators for applying the Kelly Criterion to find a position size for gambling & sports betting. I have not yet found a good calculator for

This blog covers this topic in much better detail.

Thanks for reading.

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