FRM Part I · FRM Exam Part I · The Arbitrage Pricing Theory and Multifactor Models of Risk and Return
A well-diversified portfolio has a factor beta of 1.4 and the factor's volatility is 10%. Idiosyncratic risk is negligible. What is the portfolio's approximate standard deviation of return?
The standard deviation is about 14%. With idiosyncratic risk diversified away, total risk equals beta times factor volatility, so 1.4 times 10% gives 14%. Using beta squared confuses variance with standard deviation.
- A14%Correct
- B10%
- C1.96%
- D24%
Explanation
With negligible idiosyncratic risk, portfolio volatility is beta times factor volatility: 1.4 × 10% = 14%. Squaring the beta (1.96%) mixes variance with standard deviation.
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