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Are you playing Russian Roulette with your finances?

05th September, 2022

Published in The Sunday Times on September 4th 2022

I’ve always liked Warren Buffett’s quote, "Time is the friend of the wonderful company, the enemy of the mediocre". Wonderful companies (those with a greater chance of survival) will end up doing better over time whereas the mediocre ones will fade away. The quote captures the essence of the term ‘ergodicity’ which I’ve heard of, but largely ignored, until recently reading Nassim Taleb’s book, ‘Skin in the game’. Ergodicity is an atrocious word, but if you are an investor, it’s one you cannot afford to ignore.

What is ergodicity?

In the book, Taleb recounts the example of 100 people going to the casino to gamble a certain set amount each. Some will lose, some will win, and we can infer at the end of the day what the casino’s ‘edge’ is, by counting the money left with the people who return. This provides you with an expected value for gambling at the casino. You calculate from your sample that about 1% of the gamblers go bust. Suppose that unlucky player 28 goes bust. Does this affect gambler 29? No. The 1% chance that unlucky punter 28 will go bust is already reflected in the expected value. This is called ensemble probability.

What happens if instead of 100 people, we have a single player who goes to the casino for 100 consecutive days? If they go bust on day 28, there is no day 29. In this case, a 1 per cent chance of going bust on any given day means that a repeat player has close to a 100 per cent chance of going bust. This is called time probability.

The ensemble probability is concerned with a group of people and time probability with a single person through time. Ergodicity is where the outcome for the group and the individual through time are the same. Rolling a dice is an example of an ergodic system. If 100 people roll a dice once, the expected value is the same as if one individual rolls a dice 100 times. In the casino, the probabilities of success from the collection of people does not apply to the individual. The casino is considered to be non-ergodic. 

How does this relate to financial markets and investment decision making?

In financial markets expected value calculations are used as the basis for decision making, and deviations from these are considered to be ‘irrational’. What if much of what classical finance says about decision making is based on the average outcome of a group; when my ‘rationality’ is best judged by considering my individual experience through time?

So-called ‘cognitive biases’ may be individuals realising that a system is non-ergodic and not optimising for expected value. For example, the loss aversion (i.e., most investors prefer to avoid a loss rather than make a profit) displayed by stock market investors doesn’t make sense if we use ensemble probability – after all markets generally go up over time. But it might make sense for a long-term investor that repeatedly samples from a distribution where 50 per cent plus drawdowns occur (as we have seen twice so far in this century). 

Taleb’s Russian roulette example

In his book, Taleb considers a more extreme example than the casino. Imagine a game of Russian roulette – one bullet and six chambers – and if you choose to play the game you win $1m. How do we evaluate this gamble?

Say that you run an experiment where 6 people play this identical game, but only once each. If I ran the experiment a large number of times, what I would find is that 83% of those who played become millionaires, and 17% ended up in the cemetery. 

Then you run another experiment, where the same person plays the game 6 times. Suddenly the game looks less enticing. As Taleb says, “Your expected return is… not computable.”

Russian roulette is non-ergodic. The expected value of the group differs sharply to the average of an individual carrying out the action through time.  In a non-ergodic system, the group expected value is deeply misleading as it pertains to the experience of the individual.

There’s one group of investors for whom this is particularly relevant – retirees – as they have finite resources and can’t recover catastrophic losses. 

In retirement this is particularly pertinent

Retirees cannot get the returns of the market because they do not have infinite pockets. Even though the return averages out at close to 10% for US equities over the long term, the implications vary dramatically based on what order they come in. 

This isn’t an argument for avoiding risk. It is an argument for avoiding ruin by following a couple of rules, which may seem obvious.  

In the casino example, the participants are betting everything each time. When making investment decisions, position sizing and diversification are important. You shouldn’t be betting your entire net worth on the outcome of a single event. The approach to making yourself more ergodic in different scenarios is through diversification. Diversification is collecting as many unrelated, positive expected return investments as possible. 

The alternative is in finding Buffett’s wonderful companies and concentrating your bets in those. Most of us aren’t equipped to pick these needles from the haystack. So as Jack Bogle, founder of Vanguard, once quipped – “Buy the haystack, not the needle.”

 Market Data: Calendar year returns

Total return (%) 2017 2018 2019 2020 2021
S&P500 21.8 -4.4 31.5 18.4 28.7

Source: Bloomberg. Equities in USD. 

Gary Connolly is Investment Director at Davy. He can be contacted at gary.connolly@davy.ie or on twitter @gconno1.

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