NISM-Series-X-A: Investment Adviser (Level 1) · Portfolio Performance Measurement and Evaluation

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

Updated 11 October 2026 · Fact-checked

Risk-adjusted performance ratios compare a portfolio's return with the risk it took. Sharpe uses total risk (standard deviation), Treynor uses market risk (beta), Jensen's alpha is excess return over the CAPM-expected return, Sortino uses downside deviation, and the information ratio uses tracking error. Compute the numerator first, then divide by the right risk measure.

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

A higher return means little if it came from taking a lot of risk. Two funds can each earn 12%, but one may swing wildly while the other is steady. Risk-adjusted ratios let you compare them fairly.

All of them start with excess return: the return above something. For Sharpe, Treynor and Sortino, that something is the risk-free rate (for example, a Treasury bill yield). The ratios differ in the risk measure they divide by.

Sharpe ratio divides by standard deviation, which is total risk (market risk plus unsystematic risk). Use it to judge a whole portfolio, or when comparing funds held on a stand-alone basis. Treynor ratio divides by beta, which is only systematic risk. Use it when the portfolio is one part of a well-diversified larger holding, since diversification removes unsystematic risk.

Jensen's alpha is different: it is a return difference, not a ratio. It equals actual return minus the return CAPM says the portfolio should earn for its beta. Positive alpha means the manager added value; negative means the manager lagged what the risk justified. Sortino ratio is like Sharpe, but it divides by downside deviation, which counts only returns below a target (often the risk-free rate or zero). It does not penalise upside swings.

Information ratio compares active return (portfolio minus benchmark) with tracking error, the standard deviation of that active return. It shows how consistently a manager beats the benchmark per unit of active risk. For all ratios, higher is better, but only compare funds using the same ratio, period and benchmark or risk-free rate.

Key formulas to remember

Sharpe ratio: (Rp − Rf) ÷ σp; Rp = portfolio return, Rf = risk-free rate, σp = standard deviation of portfolio returns. Total risk.
Treynor ratio: (Rp − Rf) ÷ βp; βp = portfolio beta. Systematic risk only. Output is excess return per unit of beta.
Jensen's alpha: α = Rp − [Rf + βp × (Rm − Rf)]; Rm = market return. Result is in percentage points of return, not a ratio.
Sortino ratio: (Rp − target return) ÷ downside deviation; Target is often Rf or the minimum acceptable return. Only returns below the target enter the risk measure.
Information ratio: (Rp − Rb) ÷ tracking error; Rb = benchmark return. Tracking error = standard deviation of (Rp − Rb).
Interpretation rule: Higher ratio = better; α > 0 = outperformance; Compare only on the same period, same Rf and same benchmark.

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

Use this method for any question on risk-adjusted performance.

1Identify which measure is asked for, or which one suits the situation: total risk (Sharpe, Sortino), market risk (Treynor, alpha) or benchmark-relative (information ratio).
2List the given data: Rp, Rf, Rm, Rb, σ, β, tracking error, downside deviation.
3Check units. Keep all returns in the same period (annual with annual) and convert percentages consistently.
4Compute the numerator: excess return over Rf, over the benchmark, or over the CAPM expected return.
5Divide by the matching risk measure (not for alpha, which is a subtraction only).
6Compare with the other fund or benchmark. Higher ratio or positive alpha is better.
7If asked to choose a measure, match it to the portfolio: whole portfolio uses Sharpe; part of a diversified portfolio uses Treynor; downside concern uses Sortino.

Quickest way: Match the measure to the risk word

When to use it: Use for theory and ranking questions where time is short.

Spot the risk word: standard deviation or total risk means Sharpe; beta or systematic means Treynor or alpha; downside means Sortino; tracking error or benchmark means information ratio.
Write the numerator once: return minus Rf (or benchmark).
Divide by the risk figure and compare answers.
For alpha, compute CAPM return first: Rf + β × (Rm − Rf), then subtract it from actual return.
Eliminate options with the wrong sign or wrong risk measure before calculating anything else.

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

Using beta in the Sharpe ratio or standard deviation in the Treynor ratio.
Both ratios look the same except for the denominator.
Fix: Remember S for Sharpe and Standard deviation; T for Treynor and bTa (beta).
Calling Jensen's alpha a ratio or forgetting to compute the CAPM expected return first.
Students rush and subtract Rm or Rf directly from Rp.
Fix: Always compute Rf + β(Rm − Rf) first. Alpha is then Rp minus that figure.
Forgetting to subtract the risk-free rate in the numerator.
Return seems like the obvious thing to divide by risk.
Fix: Sharpe, Treynor and Sortino all use excess return over Rf (or target). Check the numerator before dividing.
Saying Treynor is better than Sharpe, or the reverse, in all cases.
Students look for one winner.
Fix: Sharpe suits stand-alone or total-risk comparison. Treynor suits a well-diversified portfolio where only beta matters. The two can rank funds differently.
Treating Sortino as using total standard deviation.
It is introduced as an improvement on Sharpe.
Fix: Sortino divides by downside deviation, which counts only returns below the target.
Using the information ratio with standard deviation of the portfolio instead of tracking error.
Confusing portfolio risk with active risk.
Fix: Tracking error is the standard deviation of the difference between portfolio and benchmark returns.

Worked examples

Example 1

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

Show the solution

Fund A excess return = 14 − 6 = 8%. Fund B excess return = 12 − 6 = 6%.
Sharpe A = 8 ÷ 10 = 0.80. Sharpe B = 6 ÷ 6 = 1.00.
Treynor A = 8 ÷ 1.2 = 6.67. Treynor B = 6 ÷ 0.8 = 7.50.
Fund B is higher on both measures.

Answer: Fund B has the higher Sharpe ratio (1.00 vs 0.80) and the higher Treynor ratio (7.50 vs 6.67).

Example 2

A portfolio earned 15% with beta 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%.
Zero alpha means the portfolio earned exactly what its beta justified.

Answer: Alpha = 0%. The manager neither added nor lost value after adjusting for market risk.

Exam tips

Read the denominator word carefully: standard deviation, beta, downside deviation or tracking error decides the ratio.
Expect questions on which measure suits a given case, such as a fund forming one part of a diversified portfolio (Treynor).
Remember alpha is a percentage return gap, while Sharpe, Treynor, Sortino and information ratio are ratios.
With negative marking, skip if you cannot recall which risk measure belongs to which ratio, but the memory hooks usually settle it.
Check the sign: a negative alpha or a negative ratio means underperformance relative to the reference.

Practice questions from Portfolio Performance Measurement and Evaluation

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 Sharpe ratio formula and how do I interpret it?

Sharpe ratio = (Rp − Rf) ÷ σp. It shows excess return earned per unit of total risk. A higher Sharpe ratio means better risk-adjusted performance when compared on the same period.

What is the difference between Sharpe and Treynor ratio?

Sharpe divides excess return by standard deviation, which is total risk. Treynor divides by beta, which is only systematic risk. Treynor suits well-diversified portfolios, while Sharpe suits stand-alone evaluation.

How do I calculate Jensen's alpha?

First find the CAPM expected return: Rf + β × (Rm − Rf). Then subtract it from the portfolio's actual return. A positive result shows outperformance after adjusting for market risk.

What is the information ratio?

Information ratio = (Rp − Rb) ÷ tracking error. It measures active return per unit of active risk against a benchmark. A higher value shows a manager beats the benchmark more consistently.