The previous article The balancing act part I: Risk v/s Return familiarized the reader with the concept of different kinds of risks inherent in investments, whether debt or equity. . This time lets see how we can try and quantify this otherwise seemingly non-quantifiable idea of ‘Risk’.

Just to reiterate, return, risk, liquidity and tax efficiency are the four factors that you would consider before making any investment. The problem is that three of these, namely return, liquidity and tax efficiency are measurable in terms of numbers. In other words, you know what the return of an investment has been in the past, how liquid is it and if any amount of tax can be saved if you invest. However, risk is one factor, which is subjective, and you cannot immediately allocate a number to it.

And why is this important? Well, it is an understatement to say that the equity markets have become extremely volatile. Some time ago, the market was at an all time peak. And expected to go up further. And just when investors were thanking their lucky stars, the much-feared correction started taking place. Going ahead, would the sensex go up or will the correction continue? This is the future and no one has seen it. At best, people are taking educated guesses.

In other words, is the market too risky to enter at this stage or is the risk in line with the expected return? What are you as an investor to do in such a situation?

Well, the best thing to do is not to listen to others and take your own decisions after doing your homework.

So with the markets as they are poised, let us try and understand how to measure risk. Once you know this, then you don’t have to depend upon others to predict the future - you can take a decision depending upon your risk profile.

Modern Portfolio Theory

'Modern Portfolio Theory' helps us in measuring risk. The first parameter to measure risk is known as the standard deviation. Don’t worry about how to calculate it. These figures are given, you just have to know how to read and interpret them.

For any given expected rate of returns, (=mean of probability distribution) the investors would like to have a minimum deviation around the mean. This risk is the uncertainty of variability of returns, best measured by the standard deviation of expected returns about the mean.

If we assume that a particular security will return the average of say, its last 5 years, the standard deviation tells us the probability and extent to which the actual return would vary from the mean. In other words, it measures how risky is the investment by calculating, how much the actual return may deviate from the mean return.

What does Standard Deviation signify?

Standard deviation (SD) is probably used more than any other measure to quantify the risk of a security or that of a portfolio of securities. It is a scientifically proven fact that 67% of the population lies within the range ± 1s  (the symbol for SD being s) around the mean, 95% lies within ±2s and 99% within ±3s. Therefore, once s of a portfolio is known, the investor has a very good idea of the risk of his earning a rate of return that differs from the expectation and the probability associated with it.

Standard Deviation quantifies risk by focusing attention on the time horizon. The expectation for a 1-year period is not necessarily the same for a 5-year period. This is the most welcome aspect since the investors do have different short, medium or long-term horizons. With this concept of risk and aversion to risk the investor should strive to build a portfolio that has the expected rate of returns with minimum expected deviations by diversifying his security selection, choosing either different kind of securities of different companies.

The long and the short of it is that the higher the standard deviation, higher is the risk and vice versa. So, next time you intend to buy an equity mutual fund scheme or a share, determine the SD from the broker or the agent. If he doesn’t know, ask him to find out. Most of the websites and databases like Reuters and Bloomberg have these figures.

However, standard deviation, in a stand-alone mode has a severe drawback. It is an absolute measure and it suffers from not having a benchmark reference point. A low standard deviation may be attractive but not sufficient to make the investment decision. Common sense dictates that as an investor you need to know how your chosen security has performed vis a vis all the other securities, say the Sensex or the Sectoral Index.

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 that he operates in. 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 the company is to the market factor. In fact, the coefficient (Beta) quantifies the expected return for the stock, depending upon the actual return of the market.

Beta is fairly easy to interpret. It measures the sensitivity of the returns of a security to the market movements. The beta of the index is always 1. A beta that is greater than 1 means that the stock or the fund is more volatile than the benchmark index, while a beta of less than 1 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. For example, say the beta of a particular scrip is 1.08. We interpret the result as for every unit movement in the market index, our scrip moves by 1.08 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 is a low beta industry.

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

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

To Conclude

Use these tools do arrive at an educated decision before investing. Don’t invest merely based on tips. Even if intend to act on a tip, take time to ascertain the values of the abovementioned parameters because they throw light upon how the scrip has moved historically. You will see, over time, your investment mistakes would have reduced considerably.
 

The author, Sandeep Shanbhag, is an investment advisor. He can be reached sandeep.shanbhag@moneycontrol.com.