CIMA P2 Syllabus D. Risk and Control - Standard Deviations - Notes 10 / 13
Using Standard Deviation To Measure Risk
So SDs looks at the risk of the actual outcome deviating away from the expected outcome
The decision maker can then weigh up the EV of a project against the risk (the standard deviation) that is associated with it.
Illustration 1
The management of Cow Co is considering 2 projects...
| PROJECT A | PROJECT B | ||
|---|---|---|---|
| Probability | Profit | Probability | Profit |
| $'000 | $'000 | ||
| 0.3 | 100 | 0.1 | -150 |
| 0.3 | 150 | 0.6 | 200 |
| 0.4 | 200 | 0.3 | 300 |
Required
Determine which project seems preferable, A or B.
| PROJECT A | PROJECT B | ||||
|---|---|---|---|---|---|
| Probability | Profit | EV | Probability | Profit | EV |
| $'000 | $'000 | $'000 | $'000 | ||
| 0.3 | 100 | 30 | 0.1 | -150 | -15 |
| 0.3 | 150 | 45 | 0.6 | 200 | 120 |
| 0.4 | 200 | 80 | 0.3 | 300 | 90 |
| EV of Profit | 155 | EV of Profit | 195 |
Solution
On the basis of EVs alone, B is marginally preferable to A, by $40,000.
(195,000 - 155,000 = 40,000)
But look closer and you'll see that Project B could also make you a whopping 150 loss!
So to measure this risk - we need to look at Standard Deviations
| Probability | Profit | ||
|---|---|---|---|
| p | x | x-x̄ | p(x-x̄)² |
| $'000 | |||
| 0.3 | 100 | 100 - 155 = -55 | 0.3 x (-55)^2 = 907.5 |
| 0.3 | 150 | -5 | 7.5 |
| 0.4 | 200 | 45 | 810.0 |
| Variance | 1,725.0 |
| Probability | Profit | ||
|---|---|---|---|
| p | x | x-x̄ | p(x-x̄)² |
| $'000 | |||
| 0.1 | -150 | -195 -150 = -345 | 11,902.5 |
| 0.6 | 200 | 200 - 195 = 5 | 15 |
| 0.3 | 300 | 105 | 3,307.5 |
| Variance | 15,225 |
If the management are risk averse, they might therefore prefer project A because, although it has a smaller EV of project, the possible profits are subject to less variation.