If one project has a higher standard deviation than another
a it has a higher expected value
b it has more possible outcomes
c it has a greater risk
d it may be riskker, but this can only be determined by the coefficient of variation
The correct answer and explanation is :
The correct answer is **d) it may be riskier, but this can only be determined by the coefficient of variation.**
Explanation:
In project evaluation, standard deviation measures the absolute variability of a project’s returns or outcomes around its expected value (mean). A higher standard deviation indicates that the project’s returns are more spread out, suggesting greater uncertainty or risk. However, standard deviation alone doesn’t provide a complete picture of risk, especially when comparing projects with different expected values.
To assess and compare the relative risk of projects, the coefficient of variation (CV) is used. The CV is calculated by dividing the standard deviation by the expected value (mean):
**Coefficient of Variation (CV) = (Standard Deviation / Expected Value) × 100%**
The CV expresses risk as a percentage of the expected value, allowing for a standardized comparison between projects with varying scales of expected returns. A higher CV indicates a higher level of risk relative to the expected return.
Example:
Consider two projects:
- Project A: Expected return = $100, Standard deviation = $20
- Project B: Expected return = $200, Standard deviation = $50
Calculating the CV for each:
- Project A: CV = ($20 / $100) × 100% = 20%
- Project B: CV = ($50 / $200) × 100% = 25%
Despite Project B having a higher standard deviation, Project A has a lower CV, indicating that Project A’s risk is smaller relative to its expected return compared to Project B.
Therefore, while a higher standard deviation suggests greater variability and potential risk, the coefficient of variation provides a more accurate measure to determine which project is riskier relative to its expected return.