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Portfolio Performance Evaluation: Sharpe, Treynor, M2, and Jensen’s Alpha

By KeyPoint Learning 8-minute read
CFA CFA Level I

Updated for the 2026-2027 CFA® Level I curriculum.

Portfolio performance evaluation compares the return a portfolio earned to the risk it took to earn that return. A high return means little if it came with excessive risk.

CFA Level I tests four specific measures of risk-adjusted performance: the Sharpe ratio, the Treynor ratio, M2, and Jensen's alpha. Each one answers the same basic question in a different way, and exam questions often test whether you know which measure fits a given situation.

Quick Answer

Portfolio performance evaluation uses four risk-adjusted measures to judge whether a portfolio's return justified its risk:

  • the Sharpe ratio

  • Treynor ratio

  • M2

  • and Jensen's alpha.

Sharpe and M2 use total risk (standard deviation); Treynor and Jensen's alpha use systematic risk (beta). The right measure depends on whether the portfolio is the investor's entire holding or one piece of a diversified portfolio.

Key Takeaways About Portfolio Performance Evaluation: Sharpe, Treynor, M2, and Jensen’s Alpha

  • Sharpe ratio and M2 both use total risk in the denominator, so they always rank portfolios the same way.

  • Treynor ratio and Jensen's alpha both use beta, so they also rank portfolios consistently with each other.

  • Use Sharpe or M2 when a portfolio is the investor's only holding, because total risk matters in that case.

  • Use Treynor or Jensen's alpha when a portfolio is one part of a larger diversified portfolio, because only systematic risk is priced.

  • M2 expresses the result as a percentage return, not a ratio, which makes it easier to compare directly against the market's return.

  • Jensen's alpha only produces fair comparisons when every portfolio is measured against the same risk-free rate and market return.

What You Need to Know for CFA Level I

  • Calculate the Sharpe ratio as excess return divided by standard deviation.

  • Calculate the Treynor ratio as excess return divided by beta.

  • Calculate M2 by scaling the portfolio's Sharpe ratio to the market's volatility, then compare the result to the market return.

  • Calculate Jensen's alpha as actual return minus the CAPM-required return for that portfolio's beta.

  • Identify which risk measure, standard deviation or beta, belongs in each formula.

  • Explain why the same two portfolios can rank differently under Sharpe versus Treynor.

  • Recognize when a measure is the wrong tool because it ignores diversification.

Where This Fits in Portfolio Risk and Return

This topic builds directly on CAPM and the security market line. Once you can calculate a portfolio's beta and its expected return under CAPM, performance evaluation asks a follow-up question: did the portfolio actually deliver enough return for the risk it carried? The four measures here are the standard toolkit for answering that question on the exam.

Sharpe Ratio: Reward for Total Risk

The Sharpe ratio divides a portfolio's excess return (return above the risk-free rate) by its standard deviation. Standard deviation captures total risk, both systematic and unsystematic. A higher Sharpe ratio means more return earned per unit of total risk.

where:

= portfolio return

= risk-free rate

= standard deviation of portfolio returns

The Sharpe ratio makes the most sense when a portfolio represents an investor's entire wealth. In that case, there is no other diversification to rely on, so total risk is the risk that matters. A limitation: the Sharpe ratio penalizes a portfolio for unsystematic risk even if that risk would disappear once the portfolio is combined with other holdings.

Treynor Ratio: Reward for Systematic Risk

The Treynor ratio divides excess return by beta instead of standard deviation. Beta measures only systematic risk, the risk that cannot be diversified away. The Treynor ratio assumes the portfolio being evaluated is already well diversified, so unsystematic risk is not a concern.

where:

  • = portfolio return

  • = risk-free rate

  • = portfolio beta

This measure fits best when judging a portfolio that is one piece of a larger investment picture, such as a fund evaluated as part of an investor's broader diversified holdings. A high Treynor ratio means the portfolio earned strong compensation for the market risk it carried.

M-Squared (M2): Sharpe Ratio Restated as a Return

M2 takes the same information as the Sharpe ratio and converts it into a percentage return. It answers this question: what would the portfolio have earned if its volatility were adjusted to exactly match the market's volatility? Because M2 is built from the Sharpe ratio, it always produces the same ranking as Sharpe. Its advantage is interpretation. A Sharpe ratio of 0.60 is hard to compare intuitively, but an M2 of 1.2% versus a market return of 9% is immediately clear.

where:

  • = portfolio return

  •  = risk-free rate

  • = market return

  •   = standard deviation of portfolio returns

  •   = standard deviation of market returns

Jensen's Alpha: Excess Return Over CAPM

Jensen's alpha compares a portfolio's actual return to the return CAPM says it should have earned, given its beta. If the portfolio earned more than its CAPM-required return, alpha is positive, which is generally read as a sign of outperformance relative to systematic risk taken. If alpha is negative, the portfolio underperformed what its beta justified.

Formula

where:

= portfolio return

= risk-free rate

= market return

= portfolio beta

Jensen's alpha uses the same risk input as the Treynor ratio, so both measures rank portfolios the same way. The catch is that every portfolio compared must use the same risk-free rate and market return assumptions. Mixing benchmarks makes the comparison meaningless.

Choosing the Right Measure: Diversification Matters

The decision between these four measures comes down to one question: is unsystematic risk still present, or has it been diversified away?

Measure

Risk Input

Benchmark

Units

Best Used When

Sharpe ratio

Total risk

Risk-free rate

Ratio

Portfolio is the investor's entire investment

Treynor ratio

Systematic risk

Risk-free rate

Ratio

Portfolio is well diversified or part of a larger whole

M2

Total risk , scaled to

Market return

Percentage

Same cases as Sharpe, but return-style output is easier to compare

Jensen's alpha

Systematic risk

CAPM expected return

Percentage

Comparing manager skill against a consistent CAPM benchmark

Worked Example

Two portfolio managers, Ana and Ben, report one-year results. The risk-free rate is 3%, the market return is 9%, and market standard deviation is 12%.

Input

Portfolio (Ana)

Portfolio (Ben)

Return

12%

11%

Standard deviation

15%

10%

Beta

1.10

1.30

Step 1: Sharpe ratio

Step 2: Treynor ratio

Step 3: M2

Step 4: Jensen's alpha

Interpretation

Sharpe and M2 both favor Portfolio . Treynor and Jensen's alpha both favor Portfolio . This is not a contradiction. Portfolio carries more total risk relative to its systematic risk than Portfolio does, meaning holds more unsystematic risk. If Ana's and Ben's portfolios are each an investor's entire holding, total risk matters, and is the better choice on a risk-adjusted basis. If instead each portfolio is one holding inside a larger diversified account, only systematic risk matters, and delivered more return per unit of that risk. The correct answer depends on the investor's situation, not just the numbers.

Common Exam Traps

Using beta in the Sharpe ratio. The Sharpe ratio denominator is standard deviation, not beta. Candidates who default to beta because it "sounds like risk" get the wrong ratio entirely.

Using standard deviation in the Treynor ratio. The Treynor ratio denominator is beta. Standard deviation includes unsystematic risk, which the Treynor ratio deliberately excludes.

Treating M2 as a ratio. M2 is a percentage return, comparable directly to . Candidates who report it as a decimal ratio, like a Sharpe ratio, are misreading the output.

Comparing Jensen's alpha across different benchmarks. Alpha is only meaningful when every portfolio in the comparison uses the same risk-free rate and market return. A portfolio evaluated against a 9% market return cannot be fairly ranked against one evaluated against a 7% market return.

Ignoring diversification before choosing a measure. Picking Sharpe for a portfolio that is only one piece of a larger investment, or picking Treynor for an investor's entire wealth, produces a technically correct calculation that answers the wrong question.

Practice Questions

Portfolio Q earned a 10% return over the past year. The risk-free rate was 2%, the market return was 8%, and Portfolio Q's beta was 0.9. Calculate Jensen's alpha for Portfolio Q.

  1. 4.6%

  2. 2.0%

  3. 2.6%

  • Correct Answer: C. 2.6%

  • Option A: 4.6% results from leaving the risk-free rate out of the CAPM-required return, calculating it as only , and subtracting that from return without adding back into the benchmark.

  • Option B: 2.0% results from treating beta as 1.0 instead of 0.9, which ignores the portfolio's actual systematic risk and defaults to the market's own expected return.

Continue Your CFA Level I Prep With KeyPoint

Use structured lessons, practice questions, mock exams, and progress tracking to focus on the time you have left

FAQs About Portfolio Performance Evaluation: Sharpe, Treynor, M2, and Jensen’s Alpha

Yes, a higher Sharpe ratio means more excess return per unit of total risk. But it only tells you about total risk, so it can rank a portfolio poorly if that portfolio would be well diversified inside a larger account.

M2 is built from the Sharpe ratio and always produces the same ranking. The difference is presentation. M2 is a percentage return, while the Sharpe ratio is a unitless number.

A negative alpha means the portfolio earned less than CAPM predicted for its level of systematic risk. It suggests underperformance relative to the risk taken, not necessarily a loss in absolute terms.

Use the Treynor ratio when the portfolio being judged is already diversified or represents only part of an investor's total holdings. In that setting, unsystematic risk is not relevant, so beta is the appropriate risk measure.

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