A man went out for a picnic with his family near a riverbank. There were some beautiful sites on the other side of the river. However, there wasn’t a bridge or any other means available, and one had no choice but to go through the water to reach the other side. The man simply did some calculations and announced that they could all actually walk across the river since the average height of the family members was 4 ft while the average depth of the river was only around 3 ft. Unfortunately, his young son started drowning by the time they reached the middle of the river.

You get the message. There is a problem with averages. This is especially true when one is looking at something where individual observations could be far from the average. In the language of statistics, this is known as values with high standard deviations.

**Not the whole picture**

While averages are good in many areas of life, they may give an inappropriate picture in certain other areas. Stock market is one such place where averages may not help beyond a point. We will take the example of mid- and small-cap segments of the market to elaborate further on this point. Of late, there have been many discussions about very high valuations in this segment of the market. If we look at the price-to-earnings (P-E) ratio (among the most common valuation indicators) of the segment, it is too high compared to: 1) historical averages, and 2) for the large-cap segment. This has happened due to a massive rally in the mid- and small-cap segment of the market.

However, here the P-E ratio being considered of the mid-cap segment is an average of the entire segment. When we refer to this ratio for an index, we are referring to an average, just the way an index is considered to be an average of all its constituents.

To make things simple, let us look at the Nifty 500 Index, which comprises the top 500 stocks listed on the National Stock Exchange (NSE). Since this index comprises top 500 stocks, it obviously has a combination of large-, mid- and small-cap stocks. Thanks to the rally in mid- and small-cap segments in the past 3 calendar years, the Nifty MidSmallcap 400 Index delivered 22.28% compounded annualised returns (CAGR) over a 3-year period ending 31 December 2017. Nifty 500 Index delivered 14.88% compounded annualised returns over the same period. This is the average or the index performance. Let us look at how the segments performed.

The index was divided into two parts—the top 250 companies and the bottom 250 companies. The segmentation was in terms of market capitalization. Going by the popular belief, the bottom 250 companies should have registered very high returns, as they represent the mid- and small-cap segments. However, the actual numbers looked very different.

Out of the bottom 250 stocks of the Nifty 500 index, 27% of the stocks (67) delivered negative returns over the same period. Another 31% (77) delivered positive returns, but less than 20% CAGR. Talk of averages.

The P-E ratio for the Nifty MidSmallcap 400 Index was 64.65 on 31 December 2017. This would be considered too high by any standard. However, on the same day, out of the bottom 250 companies we discussed earlier, the P-E ratio was:

· below 14 for 90 companies (36% of the universe),

· between 14 and 20 for 40 companies (16%), and

· between 20 and 25 for 35 companies (14%).

Only in case of 85 companies (which would form a little over one-third of the index), the P-E ratio was in excess of 25 as on 31 December 2017 (source for the analysis on P-E ratio is a presentation by L&T Mutual Fund).

Now comes the trick. For the purpose of calculating P-E ratio, we need two numbers: price per share (P) and the profit per share or earnings per share (E).

The data may be easily available for a company but in order to calculate the P-E ratio for an index, we need to add up the numbers. The important thing to remember here is that when a company is making losses, the E is taken as zero and hence the P-E ratio is not calculated. On the other hand, while calculating the ratio for the index, the profits and losses of all the companies have to be added up.

There are at least 9-10 companies in the mid- and small-cap universe that reported losses worth more than Rs2,000 crore each. Therefore, the total loss incurred by these 9-10 companies adds up to more than Rs30,000 crore. When this number is deducted from all the profits made by the mid- and small-cap companies, we might be bringing the profits down by around a third.

These numbers indicate that there could be many profit-making companies in this segment that may not be as costly as perceived.

Investors should be careful of averages. There could be a flaw in looking at only averages.

*Amit Trivedi is a trainer in financial markets*