# Equity markets: average word does not make sense..unless you understand standard deviation

On an average the equity market gives 19% p.a. return is a statement that you may have heard often, right?

Well this piece of information is useless. Completely useless. It is like knowing the average depth of a lake!

So read on…

The best example that I have heard as a trainer regarding averages and standard deviation is the following:

If one leg of yours is in the oven, and the other in a freezer, on an average you are comfortable. This is a big learning in statistics – the word average makes no sense if the standard deviation is very high.

In cricketing language if you see Shahid Afridi and Rahul Dravid, both have an average of 22 and 58. However, Shahid Afridi has a high standard deviation and Rahul has a low standard deviation.

Which means whenever Shahid Afridi goes out to bat, the probability of his getting 22 is NOT AS HIGH as Rahul Dravid getting 58.

However, you need to remember that over the past 20 years, Rahul has an average of 58 and Shahid has an average of 22. So if you believe in regression to the mean, the average will catch up.

The stock market isn’t much different. Over very long stretches, stocks, on average, have returned around say 18% annually. But in any given year–or even over several years–the stock market can diverge markedly from its long-term average. Throughout the prosperous 1978-79 to 2000, for instance, till 2000 the Sensex rose 24% per year. No wonder Sensex was widely called a can’t-miss investments. However, from the year 1990 to the year 2000 the sensex moved from 1000 to 6000 – giving a return of 20% per annum. How has the sensex fared from the year 2000 (at 6000) to the year 2008? The answer can vary from 11% (index 13700) or 17% (index 21000).

I am sure you understand what I mean. The word average makes no sense at all when we talk equities. Equities gyrate, and gyrate like this. So please do not use the word average when talking average.

If you use the word average, it clearly shows you are mathematically challenged and you do not understand the word standard deviation.

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## pattu

This applies to the universe as well in general.

The universe is stable and we exist (quite literally exist) because the atoms in the universe behave like Afridi and Shewag!

That is the standard deviation of an atoms position is larger than the mean!

One would think they would behave like Rahul Dravid for stability!

God works in weird ways!

## Swapnil

Dear Pattu Sir, This reminds me of “Werner Heisenberg’s Uncertainty Principle “.You simply can neither predict precisely the position (displacements of atoms), momentum of atoms nor equity market returns.

## pattu

Dear Swapnil, It is precisely the uncertainty principle. Life exists because of the uncertainty and (Pauli’s) exclusion principles!

## Pravin

i think certain kind of mathematical facts,the human brain cannot even comprehend without some deep thinking.

example: the exponential curve/compounding.the technology world has been compounding exponentially since the dawn of history if one looks at bigger trends

2 million years of foraging/hunter gathering 10000 years of agriculture

330 years of industrial life

50 years of information age?

what next? the trend tells us,the changes will be rapid and incomprehensible to most of humanity

## Swapnil

Subra Sir/Pattu Sir,

The mathematical concepts are indeed very difficult to comprehend and visualise. I think our brains have evolved to understand simple things (which can be visualised) as it could solve our purpose of existence till few thousand years back. However a few complex things like understanding quantum physics, theory of relativity and our understanding of the universe, we can only try understanding it by using mathematics.

It is difficult to imagine that space and time in this universe are warped. Mathematically off course it can be proved.

Regarding equity returns, it also has something to do with understanding the power of small numbers. Many people do not realise how big the corpus can get if we keep it compounding for years.

I have placed bets with many of my colleagues in the following manner to check how people interpret the value of small numbers

“I will pay you one lakh rupees each day for the 30 days of the month (i.e.30 lakhs total) and in return you have to pay me just Re.1 for the first day, 2 for the second day, 4 for the third day, and 8 for the fourth day (doubling every day) and so on up to the 30th day of the month.” Many of them accepted and I need not say what the result was.

Maybe few hundred thousand years later, we may be able to visualise mathematical complex concepts better due to evolution.

## pattu

We will never be able to visualise anything that requires math to figure out. This is applicable for compounding or the physical world. We will need to put pen to paper and work it out. Imagining and refusing to do nothing else is the problem.

## aditya modi

@ Swapnil and Pattu sir,

“I will pay you one lakh rupees each day for the 30 days of the month (i.e.30 lakhs total) and in return you have to pay me just Re.1 for the first day, 2 for the second day, 4 for the third day, and 8 for the fourth day (doubling every day) and so on up to the 30th day of the month.” Many of them accepted and I need not say what the result was.”

People will make a ponzi or Direct marketing scheme of what you quoted above in the comment section.. Result will be catastrophic for the poor greedy masses 😀