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# Why downside matters and some basic arithmetic

## The most important thing about investment returns is that they are multiplicative and not additive

Here is a quick arithmetic test. What is the average of the following two series of numbers:

A) 40%, 50%, -60% and 65% (Answer: 23.75%)

B) 20%, 15%, 17% and 20% (Answer: 18%)

This would be the normal average that one would calculate. It’s also called the arithmetic mean.

Let us say you are told that the numbers represented the annual returns from two different investments, A and B, over the past four years. You may be tempted to think that despite the somewhat volatile nature of returns from A, that’s the one which gave higher investment returns over the past four years.

However, the most important thing about investment returns is that they are multiplicative and not additive. Hence, arithmetic mean will give an absolutely wrong answer in returns calculations.

In the case of investment A, 100 invested at the beginning of four years would have values of 140, 210, 84 and 138.60 at the end of years 1, 2, 3 and 4, respectively. In other words, for investment A, 100 has grown to 138.60 at the end of four years.

On the other hand, investment B will have values of 120, 138, 161.46 and 193.75 at the end of years 1, 2, 3 and 4, respectively. So, for investment B, 100 has increased to 193.75 at the end of those four years.

This high school mathematics has important lessons for investors.

A positive return of 90% and a negative return of 90% are not the same numbers with a positive and negative sign before. If you have made a 15% return instead of 90%, you would take 4.6 years to grow your money by 90% instead of one year. This may not be such a bad thing. However, if you lost 90% of the money in the first year, you would take many years just to break even. If you started out with 100, you would be left with 10 after a 90% loss and getting back to 100 would require you to grow your money ten fold.

This lesson should be kept in mind while chasing the latest fads such as buying ‘hot’ stocks or sectoral funds or buying funds focused on particular market capitalization criteria. Very high annual returns may be followed by a year or two of high negative returns, and this would be severely damaging to the long-term compounding of investor wealth.

Every bull market brings forth ‘gurus’ who espouse one or more of the following. The names of these ‘gurus’ may be different, the strategies recommended may seem to be different but at the heart of the matter they essentially say:

1) Employ leverage to get rich quickly (this may be direct leverage or use of derivatives or in the form of structured products or mutual fund schemes using call options to leverage).

2) Have a very concentrated portfolio of winners.

3) Traditional valuation metrics do not count and this time it is different. This may take various forms, such as the replacement cost theory in 1992 or eyeballs valuations at the time of dotcoms in 1999 or the land bank valuation in 2007. The current fad seems to be the India consumption story. It is being assumed that local companies have a long runway and sales by companies selling to the Indian consumers will grow exponentially, and that the current valuations, such as price-to-sales or price-to-earnings, do not matter.

In fact, valuations of many companies that have had difficulty growing sales and profits have also sustained at high levels. It seems that the only requirement to have high valuations is a ‘story’ that can be told about the huge growth down the road.

The peril of buying these stories at current valuations would be that in case these end up being false, one could see large declines in portfolio valuations. Moreover, since the starting valuations would already be quite high, even if the ‘story’ unfolds as planned, not much upside will be left thereon.

Slow and steady wins the race holds true in compounding investment. And clearly Warren Buffett was on to something when he said, “Rule No.1 is never lose money. Rule No.2 is never forget Rule No.1."

Another of his favourites is: “Be fearful when others are greedy, and be greedy when others are fearful."

At present, I would be circumspect about piling on to small- and mid-cap scrips which are in a grip of momentum, and sectors such as fast-moving consumer goods ( the Indian consumption story) or defence-related stocks (on the back of Make in India/defence offsets). And if the future turns out anything less than perfect, investors could see big declines in portfolio values in overhyped stocks and sectors.

Rajeev Thakkar is chief investment officer and director, PPFAS Asset Management Pvt. Ltd.

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