NISM-Series-XXI-A: Portfolio Management Services (PMS) Distributors · Performance Measurement and Evaluation of Portfolio Managers

Risk-Adjusted Performance: Sharpe, Treynor, Alpha and Sortino Ratios

Updated 11 October 2026 · Fact-checked

Risk-adjusted performance ratios show how much return a portfolio manager earned for each unit of risk taken. Sharpe uses total risk (standard deviation), Treynor uses market risk (beta), Jensen's alpha shows excess return over CAPM, Sortino uses downside risk. Compute the excess return, divide by the right risk measure, and prefer the higher value.

Understand Risk-Adjusted Performance: Sharpe, Treynor, Alpha, Sortino

Raw return does not tell you whether a manager was good. A manager who earned 18% by taking very high risk may be worse than one who earned 15% with much less risk. Risk-adjusted ratios fix this by comparing return with the risk taken to earn it.

All of them start with excess return: the portfolio return minus the risk-free rate (for example, a Treasury bill yield). This is the reward for taking risk at all.

The Sharpe ratio divides excess return by the standard deviation of the portfolio. Standard deviation is total risk, so Sharpe suits a portfolio that is your whole investment, or when you compare portfolios on total risk. The Treynor ratio divides excess return by beta, which is market (systematic) risk only. It suits a well-diversified portfolio that is one part of a bigger holding, because diversification has already removed specific risk.

Jensen's alpha is different. It first works out the return the portfolio should have earned given its beta, using CAPM. Alpha is actual return minus that expected return. Positive alpha means the manager added value beyond what market risk explains. The Sortino ratio is like Sharpe, but it divides by downside deviation, which counts only returns below a target. It does not punish upside volatility.

The information ratio compares the portfolio with a benchmark. It divides the active return (portfolio return minus benchmark return) by tracking error, the standard deviation of that active return. It shows how consistently a manager beats the benchmark per unit of active risk.

For Sharpe, Treynor, Sortino and information ratio, a higher value is better. For alpha, positive is good. Ratios are only meaningful when compared across portfolios over the same period, with the same risk-free rate or benchmark.

Key formulas to remember

Sharpe ratio: Sharpe = (Rp − Rf) ÷ σp; σp is the standard deviation of portfolio returns. Uses total risk.
Treynor ratio: Treynor = (Rp − Rf) ÷ βp; Uses beta, so only market risk. Assumes a diversified portfolio.
CAPM expected return: E(Rp) = Rf + βp × (Rm − Rf); Rm is the market return. Used inside Jensen's alpha.
Jensen's alpha: α = Rp − [Rf + βp × (Rm − Rf)]; Positive means outperformance after adjusting for beta. Zero means fair return for the risk.
Sortino ratio: Sortino = (Rp − Target) ÷ Downside deviation; The target is often the risk-free rate or a minimum acceptable return. Only returns below target enter the denominator.
Information ratio: IR = (Rp − Rb) ÷ Tracking error; Rb is the benchmark return. Tracking error is the standard deviation of (Rp − Rb).

How to solve Risk-Adjusted Performance: Sharpe, Treynor, Alpha, Sortino questions

Use the same routine for any question on these ratios. Most errors come from picking the wrong risk measure or forgetting to subtract the risk-free rate.

1Identify which measure the question asks for, or which fits the situation (total risk, market risk, downside risk, benchmark-relative).
2List the data given: portfolio return, risk-free rate, standard deviation, beta, market or benchmark return, tracking error.
3Compute the numerator: excess return (Rp − Rf), or active return (Rp − Rb) for the information ratio.
4Pick the matching denominator: σ for Sharpe, β for Treynor, downside deviation for Sortino, tracking error for information ratio.
5For alpha, first compute CAPM expected return, then subtract it from the actual return.
6Divide and check the units. Returns and risk should both be in percent.
7To compare portfolios, rank by the same measure. Higher is better; positive alpha is better than negative.
8Check the answer against the options for any trap, such as a ratio computed without subtracting Rf.

Quickest way: Match the measure to the risk, then divide

When to use it: Use this when the question gives clean numbers and you have about a minute.

Subtract Rf from Rp first. Write the result down.
Look at the risk number given. Standard deviation means Sharpe. Beta means Treynor.
Divide. Round only at the end.
For alpha, compute Rf + β × (Rm − Rf) and subtract from Rp.
If a question asks which portfolio is best, compare the ratios directly. Do not compare raw returns.

Common mistakes in Risk-Adjusted Performance: Sharpe, Treynor, Alpha, Sortino

Using total return instead of excess return in Sharpe or Treynor.
Students remember 'return divided by risk' and skip the risk-free rate.
Fix: Always subtract Rf in the numerator. Only the information ratio uses the benchmark instead.
Mixing up standard deviation and beta in Sharpe and Treynor.
Both are risk measures and both ratios look alike.
Fix: Remember: Sharpe = Standard deviation (both start with S). Treynor = beta (T for 'the market's beta').
Calling alpha a ratio, or treating a higher alpha as meaningful without checking beta.
Alpha sits with the ratios in the syllabus.
Fix: Alpha is a return difference in percent, not a ratio. It already adjusts for beta through CAPM.
Using Treynor for a portfolio that is not diversified.
Students ignore the assumption behind ignoring specific risk.
Fix: If the question stresses a concentrated or standalone portfolio, Sharpe is the better measure.
Treating all volatility as bad in the Sortino ratio.
Sortino is confused with Sharpe.
Fix: Sortino counts only downside deviation, meaning returns below the target. Upside swings are not penalised.
Using standard deviation instead of tracking error in the information ratio.
Both are measures of dispersion.
Fix: Tracking error is the standard deviation of the difference between portfolio and benchmark returns.

Worked examples

Example 1

Portfolio A returned 14% with a standard deviation of 10% and a beta of 1.2. Portfolio B returned 12% with a standard deviation of 6% and a beta of 0.8. The risk-free rate is 6%. Which has the higher Sharpe ratio, and what is the Treynor ratio of Portfolio A?

Show the solution

Excess return of A = 14% − 6% = 8%.
Excess return of B = 12% − 6% = 6%.
Sharpe of A = 8 ÷ 10 = 0.80.
Sharpe of B = 6 ÷ 6 = 1.00.
B has the higher Sharpe ratio.
Treynor of A = 8 ÷ 1.2 = 6.67 (in percent per unit of beta).

Answer: Portfolio B has the higher Sharpe ratio (1.00 versus 0.80). The Treynor ratio of Portfolio A is about 6.67.

Example 2

A portfolio returned 15% with a beta of 1.5. The market returned 12% and the risk-free rate is 6%. Calculate Jensen's alpha and interpret it.

Show the solution

Market risk premium = 12% − 6% = 6%.
CAPM expected return = 6% + 1.5 × 6% = 6% + 9% = 15%.
Alpha = actual return − expected return = 15% − 15% = 0%.
Alpha is zero, so the manager earned exactly what the beta risk required.

Answer: Jensen's alpha is 0%. The higher return than the market came entirely from taking more market risk, so the manager added no value beyond it.

Exam tips

Read which risk number is given. Standard deviation points to Sharpe, beta to Treynor, tracking error to information ratio.
Expect interpretation questions: higher ratio is better, positive alpha means outperformance, and Sortino ignores upside volatility.
Watch for options that skip the risk-free rate. They are usually the trap.
Compare portfolios only on the same measure and the same period. A better Sharpe does not guarantee a better Treynor.
Do the arithmetic on paper carefully. Read the exam rules for your series: PMS Distributors (XXI-A) carries negative marking of 10% of the marks for a question, so avoid blind guesses on calculations you can finish.

Practice questions from Performance Measurement and Evaluation of Portfolio Managers

Risk-Adjusted Performance: Sharpe, Treynor, Alpha, Sortino in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Risk-Adjusted Performance: Sharpe, Treynor, Alpha, Sortino: frequently asked questions

What is the difference between the Sharpe ratio and the Treynor ratio?

Both divide excess return by a risk measure. Sharpe uses standard deviation, which is total risk. Treynor uses beta, which is only market risk. Use Sharpe for standalone portfolios and Treynor for diversified portfolios held as part of a larger portfolio.

How do you calculate the Sharpe ratio for a portfolio?

Subtract the risk-free rate from the portfolio return, then divide by the portfolio's standard deviation. For example, (14% − 6%) ÷ 10% = 0.80. A higher value means more return per unit of total risk.

What does Jensen's alpha tell you?

It shows the return above or below what CAPM predicts for the portfolio's beta. Positive alpha means the manager outperformed after adjusting for market risk. Negative alpha means the manager underperformed.

What is the information ratio and what does it mean?

It is active return over the benchmark divided by tracking error. It shows how much extra return a manager earned for each unit of active risk taken against the benchmark. A higher value suggests more consistent outperformance.