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Q.87 Suppose a stock index has an expected return of 5.5% and volatility of 7.5%. Suppose further that Fund X, with an expected annual return of 4.5% and volatility of 6.0%, is benchmarked against the stock index. If the risk-free rate is 3.0% per annum, what is the beta of the fund? | Financial Risk Manager Part 1 Quiz - LeetQuiz

Explanation:

Under the Capital Asset Pricing Model (CAPM), the expected return of a portfolio/fund is given by: $E(R) = R_f + \beta \times (E(R_m) - R_f)$ Given:

Expected return of index (Market return, $E(R_m)$ ) = 5.5%
Risk-free rate ( $R_f$ ) = 3.0%
Expected return of Fund X ( $E(R)$ ) = 4.5%

Plugging in the values: $4.5% = 3.0% + \beta \times (5.5% - 3.0%) $`$ 1.5`% = \beta \times 2.5%\beta = 1.5% / 2.5% = 0.6$

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Q.87 Suppose a stock index has an expected return of 5.5% and volatility of 7.5%. Suppose further that Fund X, with an expected annual return of 4.5% and volatility of 6.0%, is benchmarked against the stock index. If the risk-free rate is 3.0% per annum, what is the beta of the fund?

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