Monday, May 11, 2009

Standard Deviation – Is it the right way of measuring risk

6.38, 6.36, 6.37
Don’t this numbers look familiar to you? If you are a cricket fan you might think this could be the fluctuation of required run rate across three overs or an avid bond trader will definitely bet these numbers to be the yield of a 20 year T-bond. But at least for me, it’s these numbers which are driving me to think and do something different in my final year of MBA to save myself. Yes, these are my GPA numbers in the first year of my MBA program. Had I been a bond, there will at least be risk adverse investors who will be ready to take me. But placement in a MBA program is a different phenomena, the corporate requirement is that they want high returns at a low standard deviation!!(Very cruel indeed) …More often than not everybody would have ended up with a question in interview like “Why have your performance not been consistent or why has it been so mediocre”…Did we ever ask them to give high returns at a low standard deviation? If that is the case no company can issue securities in the market and there cannot be scaling up of business!!…

In the heat of the moment (my third sem results were out yesterday), I’m deviating too much from what I initially thought of presenting in this article. 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: Through this article I have vented my anger towards the Standard deviation which is the defining variable for a normal curve (which in turn decides ones grade in a subject) .Contrary to stock markets where the samples near the mean are defined as safe, in a college grading system samples who are near are the mean are the most punished.

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