Thursday, August 27, 2009

Standard Deviation – Is it the right way of measuring risk

Is standard deviation the best way of measuring an inherent risk? Look at the performance of the Sensex and bonds across the last ten years. The equity market has garnered a premium of over 6-7% over the bonds in the past because of their inherent risk.

But risk is measured by the factor called standard deviation which is given by
Sqrt (Summation ((x-x bar) ^2)/n)

Now just like all other statistical measures, this measure also sees the performance/returns over a period. Say in the last ten years markets have a standard deviation of 20%. If you go on to observe carefully this 20% would have been largely driven the fact that markets collapsed in a given year or markets raised heavily in a year. These outliers have a huge effect on the market. Wonder if I could remove these outliers and calculate the standard deviation, then the numbers will be all the more comfortable for a risk adverse investor.

Now the problem with such outliers is that they push up the expectations in the market and portray a less risky security to be more risky. Now for example the long term standard deviation of the equity markets would have gone up by the fact that the markets plummeted by about 65% in the last one year . Now this will make the expected return on the market to be so risky (Now for example an investor in the market would claim that he will expect a return of 10% with a S.D of 20%-which is not true). Now this definitely misleads us because observing historically the markets have not gone down continuously in two years. Or to make myself sound more professional, the probability that the market will go down continuously in two years is negligible. Hence this essentially makes the security risk free for the investor who is currently holding. But just the fact that the standard deviation is high makes the cost of equity paid to be high and hence the companies have to look for projects with high pay off. This generally drives up the prices all round, when it could have been easily done away with if the investors had been rationale. On similar lines investor who is holding on to the stock after two or three years of nominal rise is at a heavy risk because he can claim the same returns as the investor who was holding it currently (after a big fall), but faces tremendous amount of risk because it might be more or less certain that the markets will fall.

My argument will not be valid if the same investor holds on to the stock for a prolonged period and sees in terms of the real economic growth and hence sets rational expectation. But how many of us really hold on to a stock for more than for a period of say 2 -3 years. So the person who really has a risk (holding it 4-5 after a fall) loses money and person who doesn’t have the risk (holding the stock during the first year after fall) will definetly gain money.
So contrary to the beliefs of financial pundits, is risk really bad? Or is there a better way of measuring risk?

PS: This was a post which I wrote about 4 months back and posting it after a long time . So I found the answer to my own question!! ..There are models like GARCH , EWMA which forecasts the risk based upon the past risk patterns and also factoring in some estimates of future outcomes . In fact Value at risk has been considered to be one of the best measures of quantifying risk(which again is derived from Standard deviation and mean estimates)

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