Advanced Financial Management · Mutual Funds

Mutual Fund Performance Evaluation and Risk-Adjusted Measures (CA Final AFM)

Updated 5 October 2026 · Fact-checked

Performance evaluation compares a fund's return with the risk it took. Sharpe = (Rp − Rf) ÷ σp uses total risk. Treynor = (Rp − Rf) ÷ βp uses market risk. Jensen alpha = Rp − [Rf + β(Rm − Rf)] shows excess return over CAPM. Compute each, then rank: higher is better.

Understand Performance Evaluation and Risk-Adjusted Measures

A fund that earned 18% is not necessarily better than one that earned 14%. The first may have taken far more risk. Risk-adjusted measures fix this by asking: how much extra return did you get for each unit of risk?

The starting point is the risk premium, which is the fund return minus the risk-free rate (Rp − Rf). All three main measures begin here. They differ in how they treat risk or what benchmark they use.

Sharpe ratio divides the premium by the standard deviation (σ), which is total risk. Use it when the fund is your whole portfolio, or when comparing funds that are not well diversified. Treynor ratio divides the premium by beta (β), which is only market (systematic) risk. Use it when the fund is one part of a well-diversified portfolio. Both give a premium per unit of risk, so a higher value is better.

Jensen alpha works differently. First find the return CAPM says the fund should have earned, given its beta: Rf + β(Rm − Rf). Alpha is actual return minus this required return. Positive alpha means the manager added value. Negative alpha means the fund under-performed for its risk. Zero means it earned just what its beta justified.

Rankings by Sharpe and Treynor can differ. If a fund holds a lot of unsystematic risk, its σ is high but its β may be low. Sharpe penalises it, Treynor does not. That is the usual exam interpretation point. Related measures you may meet are the Fama net selectivity, which uses total risk to set the benchmark, and the information ratio, which is active return divided by tracking error.

Key rules to remember

Sharpe ratio: Sharpe = (Rp − Rf) ÷ σp; σp is the standard deviation of the fund's returns. Higher is better. Measures reward per unit of total risk.
Treynor ratio: Treynor = (Rp − Rf) ÷ βp; Uses beta. Reward per unit of systematic risk. Higher is better. Needs a positive beta to rank sensibly.
Jensen alpha: α = Rp − [Rf + βp × (Rm − Rf)]; Positive alpha means superior performance after adjusting for beta. It is in percentage points, not a ratio.
Required return (CAPM): Required return = Rf + β × (Rm − Rf); The benchmark return used inside Jensen alpha.
Fama net selectivity: Net selectivity = Rp − [Rf + (σp ÷ σm) × (Rm − Rf)]; Like Jensen alpha but the benchmark uses total risk (σp ÷ σm) instead of beta.
Information ratio: IR = (Rp − Rb) ÷ Tracking error; Rb is the benchmark return. Tracking error is the standard deviation of (Rp − Rb).
Fund return for a period: Rp = (NAV end − NAV start + Distributions) ÷ NAV start; Add dividends or distributions paid in the period. Use the same period for Rf and Rm.

How to solve Performance Evaluation and Risk-Adjusted Measures questions

Use this order for any question that asks you to evaluate or rank funds.

1Write down Rp, Rf, Rm, σ and β for each fund. If Rp is not given, compute it from NAV and distributions.
2Check that all returns are on the same basis, such as annual. Do not mix monthly and annual figures.
3Compute the risk premium (Rp − Rf) for each fund once. Reuse it in every measure.
4Calculate the measure asked: Sharpe with σ, Treynor with β, Jensen alpha with the CAPM required return.
5Rank the funds. Higher is better for all three measures.
6If the question gives market data, compute the market's own Sharpe or Treynor as a benchmark. A fund beating it has done better than the index.
7Write the interpretation: which fund is best, and why rankings differ if they do (total risk versus systematic risk).
8Add a one-line conclusion for the investor, such as which fund to prefer and in what context.

Quickest way: Premium-first table method

When to use it: Use this when the question gives three or more funds and asks you to rank them on more than one measure.

Draw a table with one row per fund and columns for Rp, Rf, premium, σ, β.
Fill the premium column first.
Divide the premium column by σ to get Sharpe, then by β to get Treynor.
Compute the CAPM required return once per fund and subtract it to get alpha.
Rank each column with 1 as best, and write the ranks beside the values.
Mark the benchmark row (market) the same way so you can compare in one glance.

Common mistakes in Performance Evaluation and Risk-Adjusted Measures

Dividing Rp by σ or β without subtracting Rf.
Students remember 'return divided by risk' and forget the numerator is the premium.
Fix: Always write (Rp − Rf) first as its own column before dividing.
Using beta in Sharpe or standard deviation in Treynor.
The two formulas look alike and the names are easy to swap.
Fix: Remember: Sharpe goes with total risk (σ); Treynor goes with Treynor's T for the 'Trend' of the market, that is beta.
Treating Jensen alpha as a ratio and ranking by it as if it were per unit of risk.
It is grouped with Sharpe and Treynor, so students assume it is also a ratio.
Fix: Alpha is a difference in return, already adjusted for beta. Compare alphas directly, and state that it is in percentage points.
Forgetting distributions when computing fund return from NAV.
Students look only at the NAV change.
Fix: Add dividends or income distributions to the numerator, then divide by opening NAV.
Giving a ranking with no explanation when Sharpe and Treynor disagree.
Students stop after the calculation.
Fix: State that the funds differ in unsystematic risk. A poorly diversified fund ranks lower on Sharpe than on Treynor.
Mixing return periods, such as a monthly σ with an annual return.
Data in the question is given in different units.
Fix: Convert everything to the same period before computing anything.

Worked examples

Example 1

The risk-free rate is 6% and the market return is 12%. Fund A returned 15% with σ = 10% and β = 1.2. Fund B returned 13% with σ = 6% and β = 0.8. Compute Sharpe, Treynor and Jensen alpha for both funds and say which is better.

Show the solution

Premium A = 15 − 6 = 9%. Premium B = 13 − 6 = 7%.
Sharpe A = 9 ÷ 10 = 0.90. Sharpe B = 7 ÷ 6 = 1.1667.
Treynor A = 9 ÷ 1.2 = 7.50. Treynor B = 7 ÷ 0.8 = 8.75.
Required return A = 6 + 1.2 × (12 − 6) = 6 + 7.2 = 13.2%. Alpha A = 15 − 13.2 = +1.8%.
Required return B = 6 + 0.8 × 6 = 6 + 4.8 = 10.8%. Alpha B = 13 − 10.8 = +2.2%.
B ranks higher on all three measures.

Answer: Fund A: Sharpe 0.90, Treynor 7.50, alpha +1.8%. Fund B: Sharpe 1.17, Treynor 8.75, alpha +2.2%. Fund B is better on every measure, even though its raw return is lower, because it took much less risk.

Example 2

Rf = 7%, market return = 13%, market σ = 8%. Fund X returned 14% with σ = 9% and β = 0.7. Fund Y returned 16% with σ = 14% and β = 1.1. Rank the funds on Sharpe and Treynor, compare with the market, and explain any difference in ranking.

Show the solution

Market premium = 13 − 7 = 6%. Market Sharpe = 6 ÷ 8 = 0.75. Market Treynor = 6 ÷ 1 = 6.00.
Premium X = 14 − 7 = 7%. Premium Y = 16 − 7 = 9%.
Sharpe X = 7 ÷ 9 = 0.778. Sharpe Y = 9 ÷ 14 = 0.643.
Treynor X = 7 ÷ 0.7 = 10.00. Treynor Y = 9 ÷ 1.1 = 8.18.
Both measures rank X first. X beats the market on Sharpe (0.778 against 0.75) and on Treynor (10.00 against 6.00).
Y beats the market on Treynor (8.18 against 6.00) but falls below it on Sharpe (0.643 against 0.75).
Y's gap between the two results shows that a large part of its total risk is unsystematic, so it is not well diversified.

Answer: Fund X is ranked first on both measures: Sharpe 0.778, Treynor 10.00. Fund Y: Sharpe 0.643, Treynor 8.18. Y beats the market on Treynor but not on Sharpe, which signals high diversifiable risk. Prefer X.

Exam tips

Show the premium (Rp − Rf) as a separate line. Marks are often given for it even if the final figure is off.
Always add an interpretation line. Many questions say 'evaluate' or 'comment', and the numbers alone will not earn full marks.
Compute the market's own Sharpe and Treynor when market data is given. It gives a benchmark to compare against.
State which measure suits which investor: Sharpe for a stand-alone fund, Treynor for a fund inside a diversified portfolio.
In case-scenario MCQs, check the period of returns and whether distributions are included before you calculate.

Practice questions from Mutual Funds

Performance Evaluation and Risk-Adjusted Measures in other exams

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

Performance Evaluation and Risk-Adjusted Measures: frequently asked questions

What is the difference between Sharpe and Treynor measure?

Both measure excess return per unit of risk. Sharpe uses standard deviation, which is total risk. Treynor uses beta, which is only systematic risk. Treynor suits a diversified portfolio; Sharpe suits a stand-alone investment.

What does a positive Jensen alpha mean?

It means the fund earned more than CAPM predicts for its beta. The manager has added value through selection or timing. A negative alpha means the fund under-performed for the risk it carried.

Can Sharpe and Treynor give different rankings?

Yes. If a fund holds a lot of unsystematic risk, its standard deviation is high compared with its beta. Sharpe will rank it lower than Treynor does. Mention this in your answer.

Do I need to add dividends when computing fund return?

Yes. Fund return is the change in NAV plus any distributions, divided by the opening NAV. Leaving out distributions understates the return.