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Alice is managing a diversified portfolio consisting of three independent assets: A, B, and C. The portfolio is designed to track a benchmark index, but it also has some specific risk due to the unique characteristics of the selected assets and their weights in the portfolio. The following information is provided:
| Asset | Beta | Weight in the portfolio |
|---|---|---|
| A | 1.2 | 0.5 |
| B | 0.9 | 0.2 |
| C | 0.8 | 0.3 |
Portfolio variance (σ²ₚ) = 0.0205
Benchmark index variance (σ²ₘ) = 0.0225
The specific risk of the portfolio (also known as idiosyncratic risk) is the portion of the portfolio's variance that cannot be explained by the benchmark index. What is the portfolio specific risk in variance?