Sunday, July 27, 2008

Std deviation vs Beta

The difference between Standard deviation vs Beta of a stock can be understood by starting asking few basic questions.

Let us say you have 2 choices, one to pick investment A and other B.
A is positioned such a way that the expected return, which is the probability of different expected returns due to various factors, is calculated as

E(A) = p(x) * E(x) + p(y) * E(y) + p(z) * E(z)
Note that sum of the above probabilities is 1.
A similar calculation can be done for E(B).

Any average person would pick either A or B, whichever is higher. An educated investor would like to find the risk he/she is taking.

Risk can be measured by calculating standard deviation. Mathematically, std dev is the square root of variance. If an investment's return varies like a roller-coster to provide the return calculated above, it more sounds like a gamble. On the other hand, if the investment has a smaller variance, it is a relatively stable investment where one can lay back and not worry too much on the odds.

How to calculate Std Dev/Risk?
Std dev = sqrt(Variance)
where
Variance = (p(x) * (E(x) - E(A))^2) + (p(y) * (E(y) - E(A))^2) + ( p(z) * (E(z) - E(A))^2

Okay, now that we have a better sense of what the risk is and what the corresponding return is, it makes life easy since the investment with higher return and lower risk wins. No Brainer !!

Let us assume that the return and risk for Investment A than those of B. Now it is logical that A being risky will yield higher return, but is that the best that one can choose. Since we have been comparing oranges and apples, its time to calculate risk for an unit of return. This is called Coefficient of variance.
Calculation is simple .. Just divide Std Dev (A) / E(A). Lets call it C(A).
The investor would pick C(A) or C(B), whichever is lower since the risk to earn an unit of return needs to be lower.

With the above detailed explanation of the basics, one should recall the standard deviation as the risk of a particular investment.

Shifting gears to Beta.

Beta of a stock/investment is the risk of the stock relative to its market risk. While standard deviation measures the standalone risk, Beta measures the relative risk to the market. Eg: Std dev of investment A could be lower than std Dev of B, however B's Beta could be better. To understand this better, let us explore the Beta concept further.

If the entire market in which you trade stock consist of only 1 stock. Then the Beta of the stock will be same as the market risk, meaning when the stock return is of the same proportion and direction as the market return. In contrast, let us assume you have 5 stocks forming a market. When the market return goes up, let us say one of the stock goes down, then the stock is negatively correlated with the market.
Ideally if you have an equal weightage of all stocks forming the market, the unsystematic or stock risk can be nullified. The systematic risk, which is the market risk due to economy and non-company related factors affecting returns cannot be controlled by diversification or effective asset allocation of investments within a portfolio.

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