Page 79 - DCOM507_STOCK_MARKET_OPERATIONS

Stock Market Operations

Notes 4.2 Measurement of Risk

There are several ways of risk measurement, described as follows:

4.2.1 Volatility

Of all the ways to explain risk, the simplest and possibly most accurate is “the uncertainty of a
future outcome.” The probable return for some future period is known as the expected return.
The actual return over some past period is known as the realised return. The simple fact that
dominates investing is that the realised return on an asset with any risk attached to it may be
different from what was expected. Volatility may be portrayed as the range of movement (or
price fluctuation) from the expected level of return. For example, the more a stock goes up and
down in price, the more volatile that stock is. Since wide price swings create more uncertainty
of an eventual outcome, increased volatility can be equated with increased risk. Being able to
measure and determine the past volatility of a security is significant in that it provides some
insight into the riskiness of that security as an investment.

4.2.2 Standard Deviation

Investors and analysts should be at least to some extent familiar with the study of probability
distributions. Since the return an investor will earn from investing is not known, it must be
estimated. An investor may expect the TR (total return) on a particular security to be ten percent
for the coming year, but in truth this is only a “point estimate.”

4.2.3 Probability Distributions

To handle with the uncertainty of returns, investors need to think clearly about a security’s
distribution of probable TRs. In other words, investors need to keep in mind that, though they
may expect a security to return 10%, for example, this is only a one-point estimate of the entire
range of possibilities. Given that investors must deal with the uncertain future, a number of
possible returns can, and will, occur.

Probabilities symbolise the likelihood of a variety of outcomes and are normally expressed as
a decimal (sometimes fractions are used). The sum of the probabilities of all possible outcomes
must be 1.0, as they must completely describe all the (perceived) likely occurrences. How are
these probabilities and associated outcomes obtained? In the final analysis, investing for some
future period involves uncertainty, and therefore subjective estimates. Though past occurrences
(frequencies) may be relied on heavily to guess the probabilities, the past must be modified for
any changes expected in the future. With a distinct probability distribution, a probability is
assigned to each possible outcome. With a continuous probability distribution, an infinite number
of possible outcomes exist. The most well-known continuous distribution is the normal
distribution depicted by the well-known bell-shaped curve often used in statistics. It is a two-
parameter distribution in that the mean and the variance fully describe it.
To explain the single-most probable outcome from a specific probability distribution, it is
necessary to calculate its expected value. The expected value is the average of all possible return
outcomes, where each outcome is weighted by its respective probability of occurrence. For
investors, this can be explained as the expected return.

To calculate the total risk associated with the expected return, the variance or standard deviation
is used. This is a computation of the spread or dispersion in the probability distribution; that is,
a measurement of the dispersion of a random variable around its mean.

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