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Unit 4: Risk and Return Analysis

or the total risk of a portfolio of securities. The historical standard deviation can be calculated Notes
for individual securities or portfolios of securities using total returns for some specified period
of time. This ex post value is useful in evaluating the total risk for a particular historical period
and in estimating the total risk that is expected to prevail over some future period.
The standard deviation, combined with the normal distribution, can provide some useful
information about the dispersion or variation in returns. In a normal distribution, the probability
that a particular outcome will be above (or below) a specified value can be determined. With
one standard deviation on either side of the arithmetic mean of the distribution, 68.3% of the
outcomes will be encompassed; that is, there is a 68.3% probability that the actual outcome will
be within one (plus or minus) standard deviation of the arithmetic mean. The probabilities are
95% and 99% that the actual outcome will be within two or three standard deviations, respectively,
of the arithmetic mean.

4.2.4 Beta

Beta is a measure of the systematic risk of a security that cannot be avoided through diversification.
Beta is a relative measure of risk – the risk of an individual stock relative to the market portfolio
of all stocks. If the security's returns move more (less) than the market's returns as the latter
changes, the security's returns have more (less) volatility (fluctuations in price) than those of the
market. It is important to note that beta measures a security's volatility, or fluctuations in price,
relative to a benchmark, the market portfolio of all stocks.

Securities with different slopes have different sensitivities to the returns of the market index. If
the slope of this relationship for a particular security is a 45-degree angle, the beta is 1.0. This
means that for every one per cent change in the market's return, on average this security's
returns change 1%. The market portfolio has a beta of 1.0. A security with a beta of 1.5 indicates
that, on average, security returns are 1.5 times as volatile as market returns, both up and down.
This would be considered an aggressive security because when the overall market return rises
or falls 10%, this security, on average, would rise or fall 15%. Stocks having a beta of less than 1.0
would be considered more conservative investments than the overall market.

Beta is useful for comparing the relative systematic risk of different stocks and, in practice, is
used by investors to judge a stock's riskiness. Stocks can be ranked by their betas. Because the
variance of the market is constant across all securities for a particular period, ranking stocks by
beta is the same as ranking them by their absolute systematic risk. Stocks with high betas are
said to be high-risk securities.
The risk of an individual security can be estimated under CAPM model. The market related risk,
which is also called ‘systematic risk,’ is unavoidable even by diversification of the portfolio. The
systematic risk of an individual security is measured in terms of its sensitivity to market
movements which is referred to as security’s beta. Investors can avoid or eliminate the
unsystematic risk by investing funds in wide range of securities and by having well diversified
portfolio. Beta coefficient is a measure of the volatility of stock price in relation to movement in
stock index of the market; therefore, beta is the index of systematic risk.

Cov   Cor   Cor
  im  i m im  i m im
I
Var m  m 2  m
Where,
 = Beta of individual security
I
Cov = Covariance of returns of individual security with market portfolio
im
3
Var = Variance of returns of market portfolio ( )
m m

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