CIMA P1 Syllabus D. Dealing With Risk And Uncertainty - Standard Deviations - Notes 4 / 5
Using Standard Deviation To Measure Risk
Co-Efficient of Variation
Standard deviation / expected value (mean)
Illustration 1
Alpha Co is considering investing in one of the following projects:
| Project | Expected value $000 | Standard deviation $000 |
|---|---|---|
| A | 950 | 600 |
| B | 1,400 | 580 |
| C | 250 | 300 |
| D | 760 | 740 |
Required
If Alpha Co wishes to select the project with the lowest risk factor (coefficient of variation) it will select project:
SOLUTION
Coefficient of variation = Standard deviation / expected value (mean)
A = 600 / 950 = 0.63
B = 580 / 1,400 = 0.41
C = 300 / 250 = 1.2
D = 740 / 760 = 0.97Lowest risk factor (coefficient of variation) = project B
Illustration 2
Beta Co is considering investing in one of two mutually exclusive projects.
Information about the projects is shown below:
| Project A | Project B | |
|---|---|---|
| Expected value of profit | $165,000 | $199,000 |
| Standard deviation | $51,533 | $133,389 |
Required
If the management of Beta Co are risk averse, which project would they be most likely to invest in?
SOLUTION
On the basis of EVs alone, project B is marginally preferable to project A, by $34,000. ($199,000-$165,000 = $34,000).
However, if the management are risk averse, they would be more likely to choose project A because, although it has a smaller EV, the possible profits are subject to less variation.
This is demonstrated through a smaller standard deviation.