Financial Risk Manager Part 1

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Explanation:

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.

Explanation:

$Tp = \frac{E(Rp) - RF}{\beta_p}$

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:

$Tp = \frac{9\% - 3\%}{0.3} = \frac{6\%}{0.3} = 20\%$

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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:

$\text{Treynor Ratio} = \frac{\text{Portfolio Return} - \text{Risk-Free Rate}}{\text{Portfolio Beta}}$

Given this formula, determine the Treynor ratio for the LCM portfolio.

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Last updated: July 15, 2026 at 14:11

0.08

5.3%

0.15

8.0%