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Answer: 0.29
## Explanation The Treynor ratio measures the risk-adjusted return of a portfolio relative to systematic risk (beta). The formula is: $$\text{Treynor Ratio} = \frac{E(R_p) - R_f}{\beta_p}$$ Where: - $E(R_p)$ = Expected portfolio return = 31% = 0.31 - $R_f$ = Risk-free rate = 5% = 0.05 - $\beta_p$ = Portfolio beta = 0.9 Substituting the values: $$\text{Treynor Ratio} = \frac{0.31 - 0.05}{0.9} = \frac{0.26}{0.9} = 0.288 \approx 0.29$$ **Key points:** - The Treynor ratio uses systematic risk (beta) as the risk measure, unlike the Sharpe ratio which uses total risk (standard deviation) - The portfolio composition details (12 stocks, automotive industry breakdown) are not needed for this calculation - Market return and standard deviation are also not required for the Treynor ratio calculation - A higher Treynor ratio indicates better risk-adjusted performance relative to systematic risk
Author: Tanishq Prabhu
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As an analyst, you are analyzing the portfolio that focuses on the automotive industry. The portfolio contains 12 stocks in total with 6 stocks from the automotive industry, 3 stocks from car financing firms, and 3 stocks from car lubricant manufacturers. The expected return of the 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, compute the Treynor ratio of the portfolio.
A
0.1
B
1.37
C
0.19
D
0.29