CFA Level II Exam · Analysis of Active Portfolio Management

Sharpe Ratio and Information Ratio for Active Portfolio Management

Updated 7 October 2026 · Fact-checked

The Sharpe ratio is excess return over the risk-free rate divided by total standard deviation. The information ratio is active return (portfolio minus benchmark) divided by active risk, the standard deviation of that difference. Calculate each from the vignette data, then use IR to judge skill and SR to judge the whole portfolio.

Understand Sharpe Ratio and Information Ratio

Raw return tells you little. A manager who earns 11% by taking large risks is not necessarily better than one who earns 10% with less risk. Risk-adjusted ratios put return per unit of risk on one scale so you can compare.

The Sharpe ratio (SR) measures reward per unit of total risk. The reward is the return above the risk-free rate. The risk is the standard deviation of the portfolio's return. It suits the question: how good is this portfolio as the investor's whole investment?

The information ratio (IR) measures reward per unit of active risk. The reward is active return, the portfolio return minus the benchmark return. The risk is active risk (also called tracking risk or tracking error), the standard deviation of the active return. It suits the question: does this manager add value over the benchmark for the extra risk taken away from it? A higher IR means more skill per unit of benchmark deviation.

The two are linked in the active management framework. The benchmark has its own Sharpe ratio. Active management adds an information ratio. If the active return is uncorrelated with the benchmark, the Sharpe ratio of the best combined portfolio is √(SR_B² + IR²). So a manager with a higher IR raises the best achievable Sharpe ratio.

The same framework gives the optimal amount of active risk. It rises with the manager's IR and falls with the benchmark's Sharpe ratio. Vignettes often ask you to compute it, then find the expected active return as IR × active risk.

Key formulas to remember

Sharpe ratio: SR_P = (R_P − R_F) ÷ σ_P; Uses total risk. R_F is the risk-free rate. Use the benchmark's own return and standard deviation for SR_B.
Active return: R_A = R_P − R_B; Portfolio return minus benchmark return. Can be negative.
Active risk (tracking risk): σ_A = standard deviation of (R_P − R_B); Not the difference between the two standard deviations. It is the standard deviation of the return differences.
Information ratio: IR = (R_P − R_B) ÷ σ_A; For expected values, IR = E(R_A) ÷ σ_A.
Expected active return: E(R_A) = IR × σ_A; Rearranged IR. Useful once you have the optimal active risk.
Optimal active risk: σ_A* = (IR ÷ SR_B) × σ_B; Gives the active risk that maximises the Sharpe ratio, assuming active return is uncorrelated with the benchmark.
Sharpe ratio of optimal portfolio: SR_P* = √(SR_B² + IR²); Square both ratios, add, then take the square root.
Fundamental law link: IR = TC × IC × √BR; TC is the transfer coefficient, IC the information coefficient, BR the breadth. With full transfer (TC = 1), IR = IC × √BR.

How to solve Sharpe Ratio and Information Ratio questions

Use this order for any Sharpe or information ratio question in an item set.

1Read the question and decide which ratio it needs: total risk and risk-free rate point to Sharpe; benchmark and tracking error point to information ratio.
2Find the data in the vignette or exhibit: portfolio return, benchmark return, risk-free rate, standard deviations, tracking error.
3Check what the standard deviation figure refers to. Tracking error or active risk goes in the IR denominator. Portfolio standard deviation goes in the SR denominator.
4Compute the numerator first: R_P − R_F for Sharpe, R_P − R_B for IR. Keep signs.
5Divide and keep at least two decimals. Compare managers on the same ratio only.
6If asked for optimal active risk or optimal Sharpe, compute SR_B from the benchmark data, then apply σ_A* = (IR ÷ SR_B) × σ_B or √(SR_B² + IR²).
7Check the answer: a Sharpe ratio is usually below 1, and a negative IR means the manager lagged the benchmark.

Quickest way: Label, subtract, divide

When to use it: Use when the vignette gives returns and risk numbers directly and the choices are close in value.

Write the numerator and denominator labels next to each other: (R_P − R_F) ÷ σ_P or (R_P − R_B) ÷ tracking error.
Do the subtraction in your head in percentage points, then divide.
For optimal-portfolio questions, compute SR_B and IR first, then plug into the two formulas.
Eliminate options with the wrong sign or an impossible size before doing the full calculation.

Common mistakes in Sharpe Ratio and Information Ratio

Using portfolio standard deviation in the information ratio denominator.
Both ratios are 'return over risk', so the denominators blur together.
Fix: IR always divides by active risk, the standard deviation of R_P − R_B. Sharpe divides by total standard deviation.
Subtracting the benchmark's standard deviation from the portfolio's to get active risk.
Students treat risk as additive like returns.
Fix: Active risk is the standard deviation of the return differences. Use the tracking error given, or compute it from the difference series.
Subtracting the risk-free rate in the information ratio.
The Sharpe habit carries over.
Fix: For IR, subtract the benchmark return. The risk-free rate cancels out of the active return anyway.
Using the portfolio's Sharpe ratio in the optimal active risk formula instead of the benchmark's.
The vignette lists several Sharpe ratios and the symbols look alike.
Fix: σ_A* uses SR_B, the benchmark's Sharpe ratio, and σ_B, the benchmark's standard deviation.
Adding SR_B and IR directly to get the optimal Sharpe ratio.
It seems natural that skill adds to the base.
Fix: Square each, add, then take the square root: √(SR_B² + IR²).
Concluding that the manager with the higher Sharpe ratio has more skill.
Sharpe includes the market's contribution and is not a measure of value added versus the benchmark.
Fix: Judge skill relative to a benchmark with IR. Use Sharpe to judge the portfolio as a whole investment.

Worked examples

Example 1

A fund returned 11% last year. Its benchmark returned 9% and the risk-free rate was 4%. The fund's standard deviation was 16% and its tracking error was 4%. (1) Calculate the fund's Sharpe ratio. (2) Calculate its information ratio. (3) Which ratio shows the manager's value added relative to the benchmark?

Show the solution

Sharpe numerator: 11% − 4% = 7%.
Sharpe ratio: 7 ÷ 16 = 0.4375, about 0.44.
Active return: 11% − 9% = 2%.
Information ratio: 2 ÷ 4 = 0.50.
The information ratio compares active return with the risk taken away from the benchmark, so it measures relative value added.

Answer: (1) Sharpe ratio ≈ 0.44. (2) Information ratio = 0.50. (3) The information ratio.

Example 2

A benchmark has an expected return of 8%, a standard deviation of 12% and the risk-free rate is 3.2%. A manager has an expected information ratio of 0.30. Assume active return is uncorrelated with the benchmark. (1) Calculate the benchmark Sharpe ratio. (2) Calculate the optimal active risk. (3) Calculate the expected active return at that risk and the Sharpe ratio of the optimal portfolio.

Show the solution

Benchmark Sharpe ratio: (8 − 3.2) ÷ 12 = 4.8 ÷ 12 = 0.40.
Optimal active risk: (IR ÷ SR_B) × σ_B = (0.30 ÷ 0.40) × 12% = 0.75 × 12% = 9%.
Expected active return: IR × σ_A* = 0.30 × 9% = 2.7%.
Optimal Sharpe ratio: √(0.40² + 0.30²) = √(0.16 + 0.09) = √0.25 = 0.50.

Answer: (1) SR_B = 0.40. (2) Optimal active risk = 9%. (3) Expected active return = 2.7%, and the optimal portfolio Sharpe ratio = 0.50.

Exam tips

Read what the standard deviation in the exhibit is labelled. Tracking error, active risk and tracking risk all mean the IR denominator.
Expect a vignette to give several Sharpe ratios. Pick the benchmark's for σ_A* and the combination formula.
Do the numerator carefully with signs. A manager can have a positive Sharpe ratio and a negative IR.
Memorise the optimal Sharpe formula √(SR_B² + IR²). It appears often and takes seconds to apply.
For conceptual questions, state the link: IR measures skill versus a benchmark, SR measures reward per unit of total risk.

Sharpe Ratio and Information Ratio in other exams

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

Sharpe Ratio and Information Ratio: frequently asked questions

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

The Sharpe ratio uses return above the risk-free rate over total standard deviation. The information ratio uses return above the benchmark over active risk. Sharpe judges the portfolio on its own, while IR judges the manager against a benchmark.

How do I calculate the information ratio from active return and active risk?

Subtract the benchmark return from the portfolio return to get active return. Divide that by the standard deviation of the active returns, which is the tracking error. For example, 2% active return with 4% tracking error gives an IR of 0.50.

Is a higher information ratio always better?

For a given benchmark and risk measure, a higher IR means more active return per unit of active risk, which is better. It is only reliable if the benchmark is appropriate and the figures come from a long enough period. Compare managers using the same benchmark where you can.

How does the Sharpe ratio relate to the optimal active portfolio?

The best combination of a benchmark and an active strategy has a Sharpe ratio of √(SR_B² + IR²), assuming active return is uncorrelated with the benchmark. The optimal active risk is (IR ÷ SR_B) × σ_B. A higher IR therefore increases both the optimal active risk and the achievable Sharpe ratio.