Volatility, the square root of the variance of returns of an asset, has become the de fact measure of risk for the investment community over the last 40 years. Volatility is the standard deviation of the returns and is a statistical measure. Standard Deviation indicates the variability around an average and penalizes volatility - movement away and towards the mean - above and below this average (mean) equally.

In the world of mathematics and physical sciences, or even some branches of social sciences, this is a very useful measure of variability and is underpinned by the notion of Normal (Gaussian) distribution. If the probability distribution of a variable is Normal, and perfectly Normal, then volatility symmetrically displays the deviation away from the mean of the distribution on both sides.

However, unlike in the physical and the natural world, in the financial markets the asset return distributions are not perfectly Normal or Gaussian. A lot of investors are happy to assume that the asset returns are normal but we know otherwise. Option traders and quantitative analysts have been grappling with the issue of skew (not to mention fat tails and kurtosis) in the normal distribution for a long time now. Skew is the distortion in the normal distribution. This means that without exception, no matter whichever asset class we are trading, the positive and the negative returns will not be equidistant from the average (mean) of the distribution. This is the reason why skewness (a measure of the skew), the third moment of the Normal distribution assumes importance in estimating the risk of a particular asset return. Also, this is the reason why the standard deviation, the second moment of the normal distribution loses its appeal as the all encompassing measure of an asset's variability around the mean.

But more importantly, in physical and the natural world this measure of standard deviation is not equated with any notion of "risk", or more appropriately, any "loss" of wealth, like it is done in the world of finance. This is perhaps a crucial issue from an investor's point of view.

In finance and investment theory any variability is defined as risk per se. In calculating the risk of an asset return, information about positive and negative returns from the mean return of the asset are equally material. But in an investor's mind risk always means "losing money". If there is variability of the asset return on the positive side of the return distribution - i.e. he makes money because the asset has moved favourably - he doesn't take this as risk. Every investor or trader makes money in the financial markets because of volatility, but no one thinks that as a part of risk. Therefore, though the calculation of volatility, i.e. standard deviation, takes into account both the positive and the negative variation around the mean to an investor volatility signifies loss from investment.

Risk, to an investor, means a loss of wealth in an absolute or a relative sense. And, whether absolute or relative, a loss is always benchmarked or initialized to something. If you have $1000 to play with then the loss of your wealth is benchmarked to $1000. If you buy a stock for $100 then the loss of wealth for you would be effected for all values of the stock below $100. Therefore, risk, from an investor's point of view is always a sort of downside risk subject to some benchmark.

In the world of statistics, especially hedge fund statistics, there is another measure called the Downside Risk which perhaps captures the true risk of an investment in a risky asset.

In the following article we shall discuss the concept and calculation of the Downside Risk in greater detail with examples.

............. to be continued in Part II

Any comments and queries can be sent through our web-based form.

More Volatility Today >>

back to top