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There is an inherent fuzziness to the movement of financial asset prices. Hence, investment strategies are built around convenient assumptions, rather than iron-clad rules. For example, investors often assume stock prices show mean reversion with prices tending to move around a central point.
An assumption of mean reversion can lead logically to passive index investing. At any given moment, some industries may be outperforming and some underperforming. The underperformers should improve and revert to normal performance and the outperformers should also revert to normal. By systematically buying and holding a diversified index over the longterm, the investor is assured an averaged return.
Most financial assets have semi-normal distributions. The frequency distribution of prices looks like the well-known bell curve with most prices clustered in a central area, close to the average values, with some prices scattered to the left and the right of the central "bell".
The mathematical laws of such distributions give investors a rough roadmap of where prices could go. If prices are far from the mean, they are likely to move back closer to the centre. The "semi-normal" description is because financial assets often have much longer tails and wider dispersions than "pure" normal distributions. Also, over time, prices show upwards trend in growing economies.
That second factor - the growth trend makes the central tendency of prices meaningless over very long periods. But although prices trend up over long periods, balance sheet ratios tend to be mean-reverting in much more stable fashion even over the longterm. The price-to-earning ratio and the price-book value ratios tend to be distributed in ranges, with occasional booms or busts where the ratios go to extreme values.
If we examine the Nifty over 15 years, (actually January 1999 to July 2014, which is 15 years, seven months), the index has shifted a lot in values. Prices have swung from a low of 850 to a high of above 7,800. The historic highs (of July 2014) are 9x the lows of 850 (September 2001). But in the PE ratio of the Nifty over the same 15-year period, the minimum PE value is 10.7 and the maximum value is 28.5. The spread of PE values is just 2.7x versus the spread of 9x in prices.
The frequency distribution of PEs is a bell curve. The PE average is 18.4 for the entire period, versus an average of 19.4 for the period between January 2009-July 2014. The median PE is 18.3 for the entire period, and 18.9 for the past six years. The standard deviation is 3.4 for the whole period and 2.6 since 2009. This reflects moderately rising PE valuations since 2009. There are similar periods of high average PE in the past as well.
About 65 per cent of all the PE values fall within the range of the first standard deviation (14.9-21.8). Only 0.6 per cent of values fall outside the second standard deviation (11.5-29.9). This frequency distribution is actually more "centralised" than a classic normal distribution where about five per cent would fall outside the second SD. The current value of the Nifty PE is 20.7 which is higher than its average but within the first standard deviation.
Can such data be used to develop or modify investment strategy? A passive index investor will invest systematically through most market phases. But he can make larger commitments if the Nifty drops below the lower end of the range of the first standard deviation (below 14.9) or the lower end of the second standard deviation ( below 11.5).
Conversely, the passive index investor could decrease commitments if the Nifty PE rises beyond the top end of the first standard deviation (above PE 21.76). He should consider selling some holdings if the PE approaches, or crosses the top end of the second deviation (PE 29.9) since this value has not been hit in the past 15 years.
A more active index player may also be able to use this sort of data effectively. Buying ETFs or Index funds only when the index is below the average and median PE levels is one way to increase odds on a decent return. Another possible method is to trade mean reversion by buying index puts if the index rises beyond the top end of the first standard deviation range (above 21.76). This strategy of puts could be employed by a hedger as well.
