Page 80 - DCOM507_STOCK_MARKET_OPERATIONS

Unit 4: Risk and Return

Notes

Notes Probability distributions can be either discrete or continuous.
Computing a standard deviation using probability distributions involves making subjective
estimates of the probabilities and the likely returns. Though, we cannot avoid such estimates as
future returns are uncertain. The prices of securities are based on investors’ expectations about
the future. The relevant standard deviation in this situation is the ex ante standard deviation and
not the ex post based on realised returns.
One significant point about the estimation of standard deviation is the differentiation between
individual securities and portfolios. Standard deviations for well-diversified portfolios are
reasonably steady across time, and thus historical calculations may be fairly reliable in projecting
the future. Moving from well- diversified portfolios to individual securities, though, makes
historical calculations much less reliable. Luckily, the number one rule of portfolio management
is to diversify and hold a portfolio of securities, and the standard deviations of well-diversified
portfolios may be more stable.

Something very crucial to remember about standard deviation is that it is a measure of the total
risk of an asset or a portfolio, including, therefore, both systematic and unsystematic risk. It
captures the total variability in the asset or portfolio return whatever the sources of that
variability. In a brief statement, the standard deviation of return measures the total risk of one
security or the total risk of a portfolio of securities. The historical standard deviation can be
calculated for individual securities or portfolios of securities using total returns for some particular
period of time. This ex post value is useful in evaluating the total risk for a specific historical
period and in estimation 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 specific 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 covered; 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.
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
significant 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 specific security is a 45-degree angle, the beta is 1.0. This
means that for every 1% 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 shows that on an average
security returns are 1.5 times as volatile as market returns, both up and down. This would be
considered an aggressive security since, 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
regarded more conservative investments than the overall market.

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