## ACTUAL MEASUREMENT OF RISK

A number of basic statistical devices may be employed to measure the extent of Risk Inherent in any given situation.  Two important measures are:

(a)    Standard deviation of cashflows
(b)    Coefficient of variation
(c)    The Beta (ß) can also be used and is dealt with under Portfolio Analysis

To illustrate the first two methods, let us assume that we are examining an investment with the possible outcomes and probability of outcomes as shown below:

Note: the outcome could either be cashflow or NPV.

Assumptions (states of nature)            Outcome Sh`000'            Probability
Pessimistic                        300                    0.2
Moderately successful                600                    0.6
Optimistic                        900                    0.2

The expected value which is a weighted average of the outcomes times their probabilities can be computed as follows:

Expected value (D)    =    ΣDP

Where  D is the outcome
P is the probability
D is the expected outcome

Figures in `000'
D        P        DP
300        0.2        60
600        0.6        360
900        0.2        180
ΣDP    600

The expected value is therefore Sh 600,000.  We can therefore compute the standard deviation, which is given by the following formula.

Computation of standard deviation
300    0.2    -300    90,000    18,000
600    0.6    0    0    0
900    0.2    300    90,000    18,000
36,000

=    36,000

=    SH 190,000

The standard deviation of Sh 190,000 gives a rough average measure of how far each of the three outcomes falls away from the expected value.  Generally, the larger the standard deviation, the greater the risk.

However, to compare projects of unequal size, we need a different measure since standard deviation would not do.  Consider, for example two projects with the following expected outcome and standard deviation.

Project Expected value Standard deviation

A Sh 6,000 600

B Sh 600 190

To decide which of the two projects, is a more risky project we need to compute the coefficient of variation (C.V)

The coefficient of variation is a relative measure and is given by the following formula.

7

For investments Projects A and B discussed earlier, the coefficient of variation can be computed as follows:-

Project A

CV = 600 = 0.100

6,000

Project B

CV = 190 = 0.317

600

Generally, the larger the coefficient of variation, the greater the risk. Therefore, Project B carries a greater risk than Project A.

Another risk measure, the beta (ß) is widely used with portfolios of common stock. Beta measures the volatility of returns, on an individual stock relative to a stock market index of returns.

(Note: Beta will be discussed under portfolio analysis).