Compounding is the 8th wonder of the world” is an oft-quoted investment statement. To give credence to this, many a time, it is attributed to Albert Einstein (though there is no proof of the same). Regardless of the attribution, there is a lot of merit in allocating to an asset class early to get the benefit of decades of compounding. However, many a time, this argument is stretched a bit too far. For example – post in various investment platforms goes as follows:
Sensex in last 40 years has compounded Rs 1 lakh to 2.81 crores in 40 years (CAGR of 16%). If person ‘A’ invest 1lakh today, for 40 year horizon, even at a conservative 12% equity return, one will net 74 lakh by year 40. However, even if another person ‘B’ invests double the amount 2 lakh after 10 years, the value in year 40 will only be 60 lakh. Hence, the best time to invest was 10 years ago, next best time is today.”
On the face of it, this seems such a factual statement, that one can hardly find any issues (other than some jabs at the long tenure of 40 years). And no, there is no excel trick involved – the data of Sensex is right, and if one ran this on excel – at 12%, one will always get this response.
So, if there were 2 fixed deposits (guaranteed to honour their commitments, 40 years down the line) – every year, the moves in wealth will be a straight upward line, the above assertion will always hold true. So what is the catch? The catch is probabilities in real world and importance of looking at the return distribution not only from prism of returns, but from other moments of distribution – volatility, skewness and kurtosis.
To do this, let’s try a simple exercise – take the daily returns of Nifty over the last 20+ years, then out of random, generate 100,000 different sequences of daily returns over 40 years. In essence, a daily return of Nifty is picked at random and over 30 and 40 years (ie. Daily sequences are jumbled randomly and some can get picked up multiple times), the terminal value of each simulation is observed.
So out of 100,000 simulations, what percent of outcomes is person ‘B’, who put in 2 lakh after year 10, better than person ‘A’, who put in 1 lakh today – after 40 years? The answer is non-trivial 32%!
Almost a third of outcomes, person ‘B’ who started 10 years later can potentially match or do better than person ‘A’. Yes, the averages still imply that it is better to be person ‘A’ – who starts early and uses the benefit of time to compound wealth. But, it is wrong to think that choosing to defer investing will always be the inferior choice
So, if for a FD type instrument (which has no volatility) has 100% chance that person “B” outcome will be inferior to person “A”, and randomised simulation taken from Nifty daily returns drops the probability to 68% (that person “B” will end up having an inferior outcome to person “A”). Is there a way to map how these odds change with different return and volatility curves?
To do this, we use Geometric Brownian Motion (GBM) so that we can simulate characteristics similar to equity markets. Over the last 20+ years, the daily returns of Nifty TR (annualised) is at 13.8% and daily volatility (annualised) is 22%. Using these 2 inputs variable for GBM, and running similar simulations (100,000) over 40 years, we can estimate the odds of person “B” having a better outcome than person “A” after 40 years at 38%.
We can vary return and volatility profiles to get probability of person “B” better than person “A”.
Odds of beating 40 year returns in 30 years with two times the capital.
If one looks at the graph from bottom left, for returns (daily, annualised) of distributions which are close to 24% and volatility (daily, annualised) at 12% , chances of person “B” having a better outcome are very slim at less than 10%. As returns keep reducing for the same volatility, we see probabilities increase significantly, so much so that for distribution with 12% returns and 12% volatility, the probabilities move to 30-40%.
Odds of beating 40 year returns in 30 years with two times the capital.
More importantly, in real world – allocators have a slightly better grasp of range of returns (either basis starting valuations or rolling returns of past or other such heuristics). So, if we believe equity returns are in range of 12-14% – over the next 30-40 years), for very low volatility (of say 12%), probability of person “B” having a better outcome than “A” is 30-40%, but as volatility moves to 20%+, odds move to 40-50%.
Investment is a probabilistic endeavour, the last decade, Indian equities have seen significant re-rating as well as lower volatility compared to earlier decade. Volatility has trended lower in last 5 years (barring the brief episode of Covid), and therefore, when drawing out investment outcomes over multiple decades, it is important for allocators to not use recent experience as the sole guiding path.
In summary, all things said and done, starting early has significant advantages. Time (t) does do all the heavy lifting, when we look at formula of compounding (i.e Terminal Value = Starting Principal *(1+r)^t)). However, just because you didn’t start 10 years ago or even now, it is not the end of world. Maybe current circumstances entail one to be spending on some other activity or investing in oneself (skills/education etc). However, whenever one does decide to invest, invest for the long term with no regrets as to how counter-factual may have been!
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