Financial Risk Manager Part 1
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The expected return of an investor's portfolio is 31% with a standard deviation of 19% while the expected return of the market is 22% with a standard deviation of 16%. Given that the risk-free rate is 5% and the portfolio's beta is 0.9, determine the difference between the Sharpe ratio of the portfolio and the Sharpe ratio of the market.
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TTanishq
A
0.31
B
0.5
C
1.06
D
0.12
Explanation:
Calculation Explanation
Sharpe Ratio Formula
Sharpe Ratio = (Expected Return - Risk-Free Rate) / Standard Deviation
Portfolio Sharpe Ratio
- Expected Return (Rp) = 31% = 0.31
- Risk-Free Rate (Rf) = 5% = 0.05
- Standard Deviation (σp) = 19% = 0.19
- Sharpe Ratio (Portfolio) = (0.31 - 0.05) / 0.19 = 0.26 / 0.19 = 1.3684 ≈ 1.37
Market Sharpe Ratio
- Expected Return (Rm) = 22% = 0.22
- Risk-Free Rate (Rf) = 5% = 0.05
- Standard Deviation (σm) = 16% = 0.16
- Sharpe Ratio (Market) = (0.22 - 0.05) / 0.16 = 0.17 / 0.16 = 1.0625 ≈ 1.06
Difference
Difference = Sharpe Ratio (Portfolio) - Sharpe Ratio (Market) = 1.37 - 1.06 = 0.31
Note: The portfolio's beta of 0.9 is not needed for Sharpe ratio calculations, as Sharpe ratio uses total risk (standard deviation) rather than systematic risk (beta).
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