– The Kelly formula supports the concept of a concentrated portfolio including your best ideas
– Don’t “diworsify”
– In practice, focus on plausibility, not probabilities
Last week I reviewed the book The Dhandho Investor by Mohnish Pabrai in the post “Heads, I win; tails, I don’t lose much!” and there is a concept presented in the book, which although isn’t anything new, is worth exploring a bit further. This concept or theory is called the Kelly formula (also called the Kelly criterion, Kelly strategy or Kelly bet) and was formulated by John Larry Kelly Jr. whilst he was a researcher at Bell Labs in New Jersey in 1956. The Kelly formula is not designed solely to tackle an investment related issue. However, as we will see, it can be helpful in reflecting on the capital allocation challenge faced by investors.
The first question is: what is the Kelly formula? The formula tells you how much of your total capital you should be investing in a specific opportunity/target given predetermined outcomes and their corresponding probabilities of actually happening.
The Kelly formula is: Edge/Odds = Fraction of your capital which should be invested
Let’s consider an example provided in Pabrai’s book which was originally put together by Michael Mauboussin. Assume you’re offered a coin toss where if you get heads you get $2 and tails you lose $1. How much of your total capital should you bet if you’re offered these odds? Based on the formula, the edge is $0.50 ((0.5*$2)+(0.5*-$1)) and the odds are what you win, if you win, so in this case $2. The result would therefore be that you should invest 25% of your capital in this situation ($0.50/$2.00). Obviously, this example is extremely simple and offers only two possible outcomes. Calculating the Kelly formula can get vastly more complicated, however there are plenty of resources on the web which will make all the necessary calculations for you. Let’s now see what kind of scenarios and probabilities we can get based on an investment case.
Odds of a 200% or greater return in three years: 90%
Odds of a breakeven return in three years: 5%
Odds of a loss of up to 10% in three years: 4%
Odds of a total loss on the investment: 1%
Based on the above situation, the Kelly formula would suggest to invest 98.3% of your capital in this opportunity. However, as you might imagine, you might not want to go almost all-in on one specific target. First, the Kelly formula considers you only have two choices, you either invest your capital in the opportunity under review or you leave it in cash. However, it’s probably not the case as there are thousands of investment opportunities out there. Second, the formula doesn’t know how long it will take for your investment to reach the anticipated results – it’s basically up to you to build this assumption into your different outcomes and probabilities. In the above example, 3 years was used. If you wish to double your money within 1 year only, then the probability of that scenario happening would probably have to be decreased accordingly. Most importantly, you have to take an educated guess on 1) the possible different outcomes and 2) the probability of each outcome, on which you might be totally off track – predicting the future is no easy task. Some argue that to counter these unknowns, investors should apply fractional Kelly. Which basically means that you should only invest a fraction of the amount recommended by Kelly. Fair enough. If you do use the Kelly formula, I would also argue that you might want to impose a ceiling to whatever the Kelly formula recommends. For example, 40%, so that you don’t invest more than 40% of your portfolio in any given investment target. In my view and as mentioned in my post “Forecasting the future – a matter of plausibility”, it’s more important to spend time on thinking and analysing plausible outcomes. This will provide you with a lot more insight than randomly allocating probabilities to a set of events. There are way too many variables to consider to be able to accurately allocate probabilities. That’s mainly why investing is considered part art, part science.
What is important to remember is that the Kelly formula supports a concentrated portfolio with some level of diversification – while avoiding “diworsification”. Most successful investors, Buffett, Greenblatt, Pabrai, etc. all have concentrated portfolios. They might not use the Kelly formula directly but they clearly understand the concept. As mentioned in previous posts, it’s always a matter of opportunity cost and focusing on your best ideas (why would you want to consider your fiftieth best idea?).
In short, focus on your best ideas (say 8-12), put more emphasis on your very best ones, be patient and spend time on plausible events (not on unknown probabilities).
Featured image: Wedding Cake Rock in NSW, Australia (Dec 2017) – What’s on the horizon?!
Embedded image: John Larry Kelly Jr. – Source: Wikipedia
Next post, next week!
Keep growing your snowball!