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.











Wednesday, May 22, 2019

Bubbles - The shining new thing

One of the popular statements heard when there is a bubble is "This time it is different".

It is fashionable to look back at these statements and think how foolish these statements were. But what if it is true?

During the Bitcoin boom, I actually said it afew times, when talking about Bitcoin. "This is a different asset".

A bitcoin is not a stock. It had not been seen before. How would I value something that has only existed for a few years, that was made up of complex software and that kept coming up in the news everyday?

I think back to previous bubbles that I have lived through and remember vividly - the housing bubble in the US, the dotcom boom, and a real estate bubble in India, etc. I realize it is true that every bubble has a novelty effect. During the start of every bubble, there is something new and shiny.

A shiny new thing is hard to quantify and evaluate in terms of risk. If there is an entirely new phenomenon, there is limited data to predict its risk. Our in-built optimism will make us focus on the upside and not focus too much on (as yet) invisible downside.

Here are some bubbles and the shiny new things that were so new that most people had no idea of how to value them.

(Note: There are many factors at play during a bubble. I am only thinking about the "new and shiny" aspect of bubbles).

  1. The internet - While it seems normal and ubiquitous today, the internet was terrifying and awe inspiring during the 1990s. There were daily articles of what the internet could do, and how it will change the world. In my opinion the Internet in 1998 was equally as complex as Bitcoin was in 2017.
  2. US housing boom around 2004 - There was financial "innovation" that bewildered people. Buying homes "easily" was the new thing. The speed of loan processing and the packaging of loans into mortgage backed securities.
  3. Bitcoins - it is the shiniest thing I have ever heard of so far.
  4. Historically, the South Sea bubble is also similar. In 12th century England, the new unexplored colonies would have been a shiny new thing, that cannot be reasonably valued and risk profiled.

Another aspect on a shiny new thing causing a bubble is that people focus excessively on the "shiny new thing" from the past. The reasoning is - "Didn't tech stocks cause the collapse in 2000? So maybe the tech stocks of today - FAANG - may cause the next bubble burst?". Or something like, "The Great Financial Crisis of 2008 was because of the collapse in housing prices. So housing prices going up now is a sign of a bubble".

I believe the next bubble will be something we haven't seen before and something that makes us say "We know the past risks....But this this is different".


Book reading - Factfulness

This is my review and notes after reading the book "Factfulness" by dr. Hans Rosling. https://www.amazon.com/Factfulness-Reason...