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Answer: 0.20
The Treynor measure, also known as the Treynor Ratio, is a performance metric used to assess the risk-adjusted excess return of a portfolio relative to the risk-free rate. It is calculated by dividing the portfolio's excess return over the risk-free rate by its beta coefficient. The formula for the Treynor measure is: \[ Tp = \frac{E(Rp) - RF}{\beta_p} \] In the context of the question, the Treynor measure for portfolio LCM is calculated using the given values: - Expected return of the portfolio (E(Rp)) is 9%. - Risk-free rate (RF) is 3%. - Beta of the portfolio (βp) is 0.3. Plugging these values into the formula gives: \[ Tp = \frac{9\% - 3\%}{0.3} = \frac{6\%}{0.3} = 20\% \] Thus, the Treynor measure for portfolio LCM is 20%, which corresponds to option C in the multiple-choice question. This indicates that for every unit of risk taken on by the portfolio (as measured by its beta), it is expected to generate a 20% excess return over the risk-free rate. The Treynor measure is particularly useful for comparing the performance of different portfolios with varying levels of risk, as it normalizes the excess return by the portfolio's risk.
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A financial analyst is currently evaluating several performance metrics for a specific investment portfolio known as the LCM portfolio. This portfolio is characterized by an expected return of 9%, indicating the anticipated percentage gain based on historical or estimated financial data. Additionally, the portfolio features a volatility level, also referred to as standard deviation, of 21%, which measures the degree of variation or risk associated with its returns. The portfolio's systematic risk in relation to the overall market is represented by a beta coefficient of 0.3, indicating lower sensitivity to market movements.
In the context of evaluating the risk-adjusted performance of the LCM portfolio, consider that the risk-free rate, which is the theoretical return on an investment with zero risk, is currently 3%. Utilizing this information, calculate the Treynor ratio for the LCM portfolio. The Treynor ratio is a performance metric that assesses how much excess return is earned per unit of systematic risk, measured as:
Given this formula, determine the Treynor ratio for the LCM portfolio.
A
0.08
B
0.15
C
0.20
D
0.40