Strategic Financial Management · Mutual Funds

Mutual Fund Returns and Performance Evaluation for CMA Final

Updated 11 October 2026 · Fact-checked

Mutual fund return is the total gain on a unit over a period: dividends plus capital gain (change in NAV), divided by the opening NAV. To judge performance, adjust return for risk using Sharpe (per unit of total risk), Treynor (per unit of beta) and Jensen's alpha (excess over CAPM return).

Understand Mutual Fund Returns and Performance Evaluation

A mutual fund investor earns in two ways. The fund may pay a dividend (income distribution), and the NAV of the unit may rise or fall (capital gain or loss). Total return counts both. Looking at only one of them gives a wrong answer.

The basic return is the gain over the period divided by the amount you started with. Start with the opening NAV. Add the NAV change and any distribution received. Divide by the opening NAV. If the period is not one year, you annualise the figure so you can compare funds.

A high return alone does not make a fund good. A fund may earn more simply because it took more risk. So you compare return with the risk taken. This is risk-adjusted performance.

There are three standard measures. Sharpe ratio divides excess return over the risk-free rate by the standard deviation (total risk). Treynor ratio divides the same excess return by beta (systematic risk). Jensen's alpha is the actual return minus the return CAPM says the fund should have earned for its beta. A higher Sharpe or Treynor is better. A positive alpha means the manager added value.

Use Sharpe when the fund is your whole portfolio, because total risk matters. Use Treynor when the fund is one part of a well-diversified portfolio, because only systematic risk matters. Jensen's alpha gives the answer in return percentage points, not as a ratio.

Key rules to remember

Single-period return: Return % = [(NAV₁ − NAV₀) + Dividend + Capital gain distribution] ÷ NAV₀ × 100; NAV₀ is the opening NAV. Use the distributions actually received in the period.
Return with reinvestment: Return % = [(Units after reinvestment × NAV₁) − (Units at start × NAV₀)] ÷ (Units at start × NAV₀) × 100; Use when dividends are reinvested at a given NAV and extra units are allotted.
Annualised return: Annualised return = (1 + r)^(12 ÷ months) − 1, or simple: r × (12 ÷ months); Use the method the question asks for. If not stated, say which one you used.
Sharpe ratio: Sharpe = (Rp − Rf) ÷ σp; σp is the standard deviation of fund returns. Measures excess return per unit of total risk.
Treynor ratio: Treynor = (Rp − Rf) ÷ βp; Measures excess return per unit of systematic risk.
Jensen's alpha: α = Rp − [Rf + βp × (Rm − Rf)]; Positive alpha means the fund beat the CAPM-required return.

How to solve Mutual Fund Returns and Performance Evaluation questions

Follow this order for any return or performance question on mutual funds.

1Read what is asked: simple return, annualised return, or a risk-adjusted ranking.
2List the data: opening NAV, closing NAV, dividend, capital gain distribution, period, reinvestment details.
3For return, compute total gain = NAV change + all distributions. Divide by opening NAV.
4If dividends are reinvested, work with units and closing value instead of per-unit figures.
5Annualise if the period is not one year, using the method that suits the question.
6For risk-adjusted measures, find Rp, Rf, σ, β and Rm from the data. Convert all to the same period basis.
7Compute Sharpe, Treynor or alpha as asked. Rank funds from highest to lowest.
8Write a one-line conclusion: which fund is better and why (total risk, systematic risk, or alpha).

Quickest way: Gain over opening NAV, then rank

When to use it: When several funds are given and you must rank them under time pressure.

Write each fund's excess return (Rp − Rf) in a small column first.
Divide by σ for Sharpe and by β for Treynor in the same column layout.
Compute alpha only if Rm is given: Rp − Rf − β(Rm − Rf).
Rank, then state the conclusion. Keep two decimals for ratios.

Common mistakes in Mutual Fund Returns and Performance Evaluation

Ignoring the dividend and using only the NAV change
Students focus on NAV because it is the visible price.
Fix: Always add dividends and capital gain distributions to the NAV change before dividing.
Dividing by closing NAV instead of opening NAV
The closing figure is the one just calculated.
Fix: The base for return is the amount invested at the start, the opening NAV.
Using Rp instead of Rp − Rf in Sharpe or Treynor
Students remember the denominator and forget the numerator adjustment.
Fix: Write (Rp − Rf) first, every time.
Mixing Sharpe and Treynor in the wrong denominator
Both look alike.
Fix: Sharpe uses standard deviation (total risk). Treynor uses beta (systematic risk).
Mixing monthly and annual figures
Return is given for a period but Rf is annual.
Fix: Convert everything to the same basis before computing.
Treating positive alpha as proof of skill without conclusion
Students stop at the number.
Fix: State that the fund earned more than the CAPM-required return for its beta, and compare funds.

Worked examples

Example 1

A fund unit had an NAV of ₹50 at the start of the year and ₹56 at the end. During the year it paid a dividend of ₹3 per unit and a capital gain distribution of ₹1 per unit. Compute the total return for the year.

Show the solution

NAV change = 56 − 50 = ₹6
Distributions = 3 + 1 = ₹4
Total gain = 6 + 4 = ₹10
Return = 10 ÷ 50 × 100 = 20%

Answer: The total return is 20%.

Example 2

Risk-free rate is 6% and market return is 12%. Fund A: return 15%, σ 10%, β 1.2. Fund B: return 13%, σ 5%, β 0.8. Compute Sharpe, Treynor and Jensen's alpha for each, and state which fund is better.

Show the solution

Fund A excess return = 15 − 6 = 9%. Fund B excess = 13 − 6 = 7%.
Sharpe A = 9 ÷ 10 = 0.90. Sharpe B = 7 ÷ 5 = 1.40.
Treynor A = 9 ÷ 1.2 = 7.50. Treynor B = 7 ÷ 0.8 = 8.75.
Required return A = 6 + 1.2 × (12 − 6) = 13.2%. Alpha A = 15 − 13.2 = 1.8%.
Required return B = 6 + 0.8 × 6 = 10.8%. Alpha B = 13 − 10.8 = 2.2%.
Fund B is higher on all three measures.

Answer: Sharpe: A 0.90, B 1.40. Treynor: A 7.50, B 8.75. Alpha: A 1.8%, B 2.2%. Fund B performed better on every measure despite its lower return.

Exam tips

Show the formula line before substituting. Marks are given for method even if arithmetic slips.
In MCQs, check whether the question gives standard deviation or beta. That tells you Sharpe or Treynor.
If a ranking differs between Sharpe and Treynor, explain it: the fund holds unsystematic risk that Sharpe penalises and Treynor ignores.
State the period basis and annualisation method you used when the period is not a year.

Practice questions from Mutual Funds

Mutual Fund Returns and Performance Evaluation in other exams

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

Mutual Fund Returns and Performance Evaluation: frequently asked questions

What is the formula for mutual fund return with dividend and capital gain?

Return = (closing NAV − opening NAV + dividend + capital gain distribution) ÷ opening NAV × 100. All income received during the period must be included. If distributions are reinvested, compute using units and closing value.

What is the difference between Sharpe, Treynor and Jensen measures?

Sharpe and Treynor are ratios of excess return to risk. Sharpe uses standard deviation, Treynor uses beta. Jensen's alpha is the difference between actual return and the CAPM-required return, expressed in percentage points.

When should I use Sharpe instead of Treynor?

Use Sharpe when the fund is the investor's entire portfolio, since total risk matters. Use Treynor when the fund is one part of a diversified portfolio, since only systematic risk matters.

How do I annualise a return of less than one year?

Either multiply by 12 ÷ months for a simple annual figure, or compound it with (1 + r)^(12 ÷ months) − 1. Follow the method the question specifies and say which one you used.