Standard Deviation and Beta of a Portfolio, SAPM Notes

Standard Deviation and Beta of a Portfolio
Portfolio Performance Evaluation

Standard Deviation and Beta of a Portfolio

Modern portfolio statistics attempt to show how an investment's volatility and return measure against a given benchmark, such as BSE Index, NSE Index. Beta and standard deviation are measures by which a portfolio or fund's level of risk is calculated. Beta compares the volatility of an investment to a relevant benchmark while standard deviation compares an investment's volatility to the average return over a period of time. Standard deviation tells an investor a more general story about the security's tendency to move up and down abruptly, while beta tells the investor how much higher or lower a security will likely trade in relation to an index.

Standard deviation:

Standard deviation is a statistical measurement that looks at historical volatility, indicating the tendency of the returns to rise or fall considerably in a short period of time. A volatile investment has a higher risk because its performance may change rapidly in either direction at any moment. A higher standard deviation means an investment is highly volatile, more risky and tends to yield higher returns. A lower standard deviation means the investment is more consistent and moves less choppily. It tends to yield more modest returns and presents a lower risk.

A volatile security or fund will have a high standard deviation compared to that of a stable blue chip stock or a conservative fund investment allocation. A large spread between deviations shows how much the return on the security or fund differs from the expected "normal" returns. However, the steady past performance of a fund does not guarantee a similar future performance. Because unexpected market conditions can increase volatility, a security that at one period had a standard deviation close or equal to zero may perform otherwise during a different period.


Beta attempts to measure an investment's sensitivity to market movements. A high beta means that an investment is highly volatile and that it will likely outperform its benchmark in up markets, thus exceeding the benchmark's return, and underperform it in down markets. A lower beta means an investment is likely to underperform its benchmark in up markets, but is likely to do better when the markets fall.

The first step in beta is measuring the volatility of a benchmark's returns in excess of a risk-free asset's return, such as the Treasury bill. The benchmark's beta is always 1.0. So a security with a beta of 0.83 is expected to gain 17 percent less, on average, than the benchmark in up markets and expected to lose, on average, 17 percent less in down markets. By contrast, a security with a beta of 1.13, is expected to gain, on average, 13 percent more than the benchmark in up markets, and lose, on average, 13 percent more in down markets. However, beta does not calculate the odds of macroeconomic changes nor does it take into consideration the herd-like behavior of investors and its effect on the securities market.

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