Financial Risk Manager Part 1

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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.

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TTanishq

0.1

1.37

0.19

0.29

Explanation:

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

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