Sharpe ratio, Treynor ratio and Jensen's alpha calculator

Enter a portfolio's return and risk, and the market's, to get the standard risk-adjusted return measures. Fill in only what you have: each ratio needs different inputs.

How it works

Sharpe = (R_p − R_f) ÷ σ_p

Treynor = (R_p − R_f) ÷ β_p

Jensen's alpha = R_p − [R_f + β_p × (R_m − R_f)]

M² = (R_p − R_f) × σ_m ÷ σ_p + R_f − R_m

Sharpe and M² use total risk (standard deviation); Treynor and Jensen use systematic risk (beta).

A worked example

A portfolio returns 12% with a standard deviation of 15% and a beta of 1.1, when the risk-free rate is 2% and the market returns 9% with a standard deviation of 12%. The Sharpe ratio is (12 − 2) ÷ 15 = 0.667. The Treynor ratio is 10 ÷ 1.1 = 9.091. Jensen's alpha is 12 − [2 + 1.1 × (9 − 2)] = 2.30%.

Common mistakes on the exam

Sharpe uses total risk, Treynor uses systematic risk: use Treynor or Jensen for a portfolio that is one part of a well-diversified whole.
Jensen's alpha and M² are in percent return; Sharpe and Treynor are ratios.
A higher ratio is better, but ratios computed on different benchmarks or periods are not comparable.

The exam allows only certain calculator models, and the rules change: check CFA Institute's current calculator policy before you rely on any keystroke here.

Where this is taught

Derive a stock's alpha and beta by regressing its excess returns on those of the market CFA Level I · Quantitative Methods
Explain why, as more assets are added, covariance becomes the main driver of portfolio risk CFA Level I · Portfolio Management
Work out a required return with the capital asset pricing model CFA Level I · Portfolio Management
Work out the information ratio on both an ex post and an ex ante basis, explain what it means, and contrast it with the Sharpe ratio CFA Level II · Portfolio Construction

Practise what you read

Today's practice question One question, with every wrong option explained.
Free Level I diagnostic test Twelve questions that show which topics to start with.
Free finance calculators Check your arithmetic on the exam's core formulas.

Questions people ask

When should I use Treynor instead of Sharpe?

When the portfolio is one holding among many and only systematic risk matters to the investor. Sharpe suits a portfolio that is the investor's whole stake.

What does a positive Jensen's alpha mean?

The portfolio earned more than the capital asset pricing model says its beta justifies: it beat the security market line.

What is the information ratio?

Active return, the return above the benchmark, divided by tracking error, the standard deviation of that active return. It measures the reward per unit of active risk.

Practise this until the arithmetic is automatic: questions on every topic, with the reason each wrong option is wrong.

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