Question 1
Multiple ChoiceA portfolio analyst wants to compute the coefficient of variation (CV) for a portfolio based on annual returns over the past five years. The following table shows the returns of the portfolio and the prevailing inflation rate:
Year | Return (Ri) | Ri – Mean | (Ri – Mean)² |
|---|---|---|---|
1 | 6.5 | 2.3 | 5.29 |
2 | 3.0 | -1.2 | 1.44 |
3 | -2.0 | -6.2 | 38.44 |
4 | 8.5 | 4.3 | 18.49 |
5 | 5.0 | 0.8 | 0.64 |
What is the coefficient of variation of the portfolio returns (using nominal returns, not real)?
Explanation
Step 1: Calculate the mean portfolio return:
R = \frac{6.5 + 3.0 + (-2.0) + 8.5 +5.0}{5} = \frac{21.0}{5} = 4.2%
Step 2: Compute the sample standard deviation:
s = √ \frac{1}{n -1} \sum_{i = 1}^{n} ( R _{i} - R ) ^{2}
Year | Return (Ri) | Ri – Mean | (Ri – Mean)² |
|---|---|---|---|
1 | 6.5 | 2.3 | 5.29 |
2 | 3.0 | -1.2 | 1.44 |
3 | -2.0 | -6.2 | 38.44 |
4 | 8.5 | 4.3 | 18.49 |
5 | 5.0 | 0.8 | 0.64 |
Step 3: Calculate the coefficient of variation:
CV = \frac{Standard Deviation}{Mean Return} = \frac{4.01}{4.2} = 0.9548