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Alpha, Beta, Rho - the risk busters

A N Shanbhag

Last week we examined standard deviation - one of the ways to measure risk or, more precisely, the volatility in any investment. However, the drawback of standard deviation is that it is an absolute measure.

Though it sheds light upon the expected volatility and the probability thereof, it does not tell you much about the environment that you are investing in. For example, say the standard deviation of a scrip is extremely low. It tells you that the returns from the scrip are pretty steady.

However, if the average return of that scrip is extremely poor as compared to its peer group, (this fact the standard deviation does not reveal) it may not make much financial sense to invest in that particular scrip.

Hence, in addition to standard deviation, this time we shall look at other commonly used measures - Beta and related measures, Alpha and Rho.

Beta

Beta captures systematic risk - risk common to the entire economic system - the market. Macro-economists call this business cycle risk. Unlike standard deviation, it measures the volatility of a security relative to a benchmark index. This tells the investor how volatile the returns on his scrip are as compared to the broad market index. However, it is very important to select the appropriate benchmark.

To determine the Beta of any security, you'll need to know the returns of the security and those of the benchmark index you are using for the same period. Using a graph, plot market returns on the X-axis and the returns for the stock over the same period on the Y-axis.

Upon plotting all of the monthly returns for the selected time period (usually one year), we draw a best-fit line that comes the closest to all of the points. This line is called the regression line.

Beta is the slope of this regression line. The steeper the slope, the more the systematic risk; the shallower the slope, the less exposed is the company to the market factor. In fact, the coefficient (Beta) quantifies the expected return for the stock, depending upon the actual return of the market.

Let's understand this by means of a simple example. The table lists the performance of a stock vis-à-vis the benchmark index over a five-month period.

You may use any popular spreadsheet program to calculate the slope of the given series of numbers, which is nothing but the Beta. In the above example, the Beta works out to 1.09.

Beta is fairly easy to interpret. It measures the sensitivity of the returns of a security to market movements. The Beta of the index is always one. A Beta that is greater than one means that the stock or the fund is more volatile than the benchmark index, while a Beta of less than one means that the security is less volatile than the index.

A negative Beta indicates that the returns on the security move in an opposite direction to that of the index. In our example, we interpret our result as for every unit movement in the market index, our scrip moves by 1.09 units. In other words, our scrip is slightly more volatile than the broad market.

Stocks that rise and drop dramatically as compared to the market are those with high Betas. Typically, Betas tend to be related to the industry. Technology, for instance, is a high-Beta industry. On the other hand, FMCG or pharmaceuticals are low beta industries.

Alpha

Alpha is the point at which the regression line crosses the Y-axis. It represents the average return produced by the stock, independent of the market. Suppose Alpha is 1 per cent and Beta is 1.5 per cent.

If the market's average return for a particular month was 2 per cent, Beta will give you the value of expected return to be 3 per cent (= 2 per cent x Beta of 1.5 per cent). To this we add Alpha and we get the most likely average return on the stock that month as 4 per cent.

Rho

It is obvious that the relationship between the returns on the stock and the returns on the market are not perfectly consistent for each and every month. If they were, all the points would fall on the line of regression. But they do not.

Also, the efficacy of Beta only comes into play when calculated against a relevant benchmark. For example, if you measure the slope of returns on real estate against a bond index, you are sure to get an extremely low Beta.

Does this mean real estate is a relatively safe investment? Definitely not. The only reason we get a low Beta is because the prices of the two sets of investments have not much correlation with each other.

So, to reiterate, Beta is relevant only if the benchmark index is relevant. How do we know it is? Statisticians have developed a measure 'Rho', which is the correlation coefficient. It indicates the extent to which individual observations deviate from this line of relationship.

Rho lies between +1 and -1. A value of +1 would indicate perfect correlation, meaning thereby that our predictions are most accurate and when one parameter increases, the other also increases too and vice versa.

A value of -1 would also yield accurate predictions but when one increases, the other decreases and vice versa. A correlation value of zero means no correlation whatsoever.

Standard error

Finally, a good analyst must also know the degree of uncertainty of his estimates. We have earlier examined the possibility of measuring this risk in the case of single variable through s, the standard deviation. We know 67 per cent of the population lies within the mean and ±s, 95 per cent within ±2s and 99 per cent within ±3s. In the case of the regression line, a similar statistical measure is called standard error.

Using these tools, which are available in financial newspapers and websites, investors can definitely benefit. However, one should not lose sight of the fundamentals of a scrip before taking a decision.

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