Recently while speaking of a portfolio bet, I was quizzed on position sizing within the portfolio. By letting a winner run, without trimming its wings, have I let the position become too ‘big’ within the portfolio? Have I in turn made the portfolio too volatile? Too risky?

There are two parts to answering this- one involves defining risk for an investor. The second part involves answering the question posed in view of this definition of risk.

## Investment Objective Defines Risk

Risk for an investor is defined by their investment objective. Mine is absolute wealth creation over a long period of time. For the purpose I have set out to serve through my investments, volatility is hardly a risk. The real risk lies in permanent loss of capital. Volatility only helps me get favourable purchase prices for assets I would like to own (and perhaps for conversation material with friends at dinner). Instead, I worry about going wrong in my bets in a way that it erodes my capital forever.

With such a definition of risk brought about by my investment objective, is a position becoming too big a part of my portfolio really a risk factor? The short answer is – no.

## Bayes Theorem and Position Trimming

In our hubris, we investors assume that we can keep finding great managements with exceptional execution ability, at a price we are willing to pay for them; time after time. Anyone who has tried to hire good talent for their firm knows this to be far from the reality. It is not just mere experiential gut feel that I base this on. This assertion is founded in thinking of conditional probabilities as set forth by the mathematician Thomas Bayes.

Bayes Theorem is a mathematical model for determining conditional probability. Simply put it is a formula for establishing the chances of ‘x’ occurring given that ‘y’ has already taken place. In case of trimming a position that has become too ‘big’ a part of the portfolio we need to determine the probability of deploying the gains from the winner into another winner. Let’s call event ‘y’ getting the first winner and event ‘x’ getting the second bet, made from the gains of the first winner, right.

The most under-estimated factor in getting an investment call correct is getting a management’s execution ability right. It involves judging the ‘human’ element correctly and humans are not easy to predict. There are over 12 lakh registered companies in India with just under 2% of them having a turnover of greater than 100 crore. In the listed universe, only 1800 companies (approximately 30% of the listed universe) have revenues greater than 100 crores. I am by no means tagging revenues to be the only measure of success, but rather to illustrate that it isn’t to grow businesses at a scale. Let’s assume we are able to apply filters in assessing the past execution via some standard screeners and double our success ratio in finding good managements to 60%.

The probability of therefore finding our first winner (event ‘y’) is 60%. In a post-facto world where we have seen this management’s execution to be superior resulting in this being a big winner in our portfolio, this winner has become a larger % of our portfolio vs. the allocation at cost.

Assuming I have imbibed better learnings with time, let’s say the chances of me judging the management’s execution correctly now have improved to 70%. So the chances of ‘x’ and ‘y’ both occurring are 70% x 60% = 42%. This implies the conditional probability to get the second call correct, given the first was correct is 42%/ 60% = 70%.

There is therefore still a 30% chance I get it wrong. Now posit this- a 5% allocation at cost has become 20% of the portfolio. If I trim the position to even 10%, I am likely to allocate it among two ideas and not one new idea. So the odds of being correct reduce to 70% x 70% = 49%. In the scenario I trim my 20% position to 10% and reallocate the remainder 10% to two other positions, there is a 51% chance of being wrong. Compare that to choosing to bear the volatility (which is not a risk to my investment objective) with chances of me being wrong are close to 0% since I have witnessed continued execution superiority by the management. The math speaks for itself.

I am in no way asserting that management execution is the sole deciding factor but simply saying that *ceteris paribus* (all other things being held constant), trimming a position just because it has become too big a part of our portfolio, is doing disservice to our goal of long term absolute wealth creation. The short answer is- do not get in the way of compounding.

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