FinanceLesson 4 of 4 in the course How to Think about Investing

Sharpe, Treynor, and Jensen’s Alpha in Portfolio Performance

5 flashcards · 5 quiz questions · 5 match pairs · 4 fill-in sentences · English

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Summary

A high investment return does not, by itself, show that a money manager performed well. Investors also need to consider the risks taken to earn that return. This lesson introduces three ways to evaluate investment performance: the Sharpe ratio, the Treynor ratio, and Jensen’s alpha.

Sharpe Ratio=RP−RfσP\text{Sharpe Ratio} = \frac{R_P - R_f}{\sigma_P}

Here, RPR_P is the portfolio return, RfR_f is the risk-free return, and σP\sigma_P is the standard deviation of the portfolio’s returns. The numerator, RP−RfR_P - R_f, is the risk premium: the return earned above the risk-free rate. The denominator, standard deviation, measures the volatility of returns and therefore represents total risk.

All flashcards

What is the Sharpe ratio?
It is the portfolio risk premium, RP−RfR_P - R_f, divided by the standard deviation of returns, σP\sigma_P. It measures excess return per unit of total risk.
What is the Treynor ratio?
It is the portfolio risk premium divided by portfolio beta. It measures excess return per unit of systematic risk.
What does portfolio beta represent in the Treynor ratio?
Beta measures systematic risk: how sensitive a portfolio is to market movements. It does not represent all the portfolio’s return variability.
How is Jensen’s alpha calculated?
Subtract the CAPM-predicted return, Rf+βP(Rm−Rf)R_f + \beta_P(R_m - R_f), from the portfolio’s actual return: αP=RP−[Rf+βP(Rm−Rf)]\alpha_P = R_P - [R_f + \beta_P(R_m - R_f)].
What do positive, zero, and negative Jensen’s alpha indicate?
Positive alpha means the portfolio outperformed its CAPM prediction; zero means it matched the prediction; negative alpha means it underperformed the prediction.

Quiz questions

  1. What does the standard deviation in the Sharpe ratio represent?Answer: Portfolio-wide volatility, capturing total investment risk.
  2. A portfolio earns 14%, the risk-free rate is 4%, and its standard deviation is 20%. What is its Sharpe ratio?Answer: 0.50
  3. Which risk measure is used in the denominator of the Treynor ratio?Answer: Portfolio beta, capturing sensitivity to market movements.
  4. A portfolio has a 20% return, beta of 1.2, a 3% risk-free rate, and a 12% market return. What is Jensen’s alpha?Answer: 6.2%
  5. How should an investor interpret a Jensen’s alpha of zero?Answer: The actual return matched the CAPM-predicted return for the portfolio’s beta.

Based on Principles of Finance by Julie Dahlquist, Rainford Knight (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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