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NISM-Series-V-A: Mutual Fund Distributors · Mutual Fund Scheme Performance

Risk-Adjusted Returns: Sharpe, Treynor and Alpha for NISM Mutual Fund Distributors

Updated 11 October 2026 · Fact-checked

Risk-adjusted return measures show how much return a scheme earned for the risk it took. Sharpe = (Rp − Rf) ÷ standard deviation. Treynor = (Rp − Rf) ÷ beta. Alpha is the return above what beta and the market return predict. For Sharpe and Treynor, higher is better.

Understand Risk-Adjusted Returns: Sharpe, Treynor and Alpha

A scheme with a high return may simply have taken high risk. So raw returns can mislead you. Risk-adjusted measures ask: how much extra return did you earn for each unit of risk?

All three measures start with excess return. This is the scheme return minus the risk-free rate (usually the return on a government treasury bill). It is the reward for taking risk over a safe option.

The Sharpe ratio divides excess return by standard deviation, which is total risk (market risk plus scheme-specific risk). The Treynor ratio divides excess return by beta, which is market (systematic) risk only. Use Sharpe when you judge a scheme on its own. Treynor suits a scheme that is one part of a well-diversified portfolio, where scheme-specific risk is already diversified away.

Alpha (Jensen's alpha) measures return above or below what the scheme should have earned given its beta. Expected return = Rf + β × (Rm − Rf). Alpha = actual return − expected return. A positive alpha means the manager added value. A negative alpha means the scheme did worse than its risk justified.

These ratios are only useful for comparing schemes of the same category over the same period, using the same risk-free rate and benchmark. A ratio on its own has no meaning. It matters only against another scheme or a benchmark.

Key formulas to remember

Excess return
Excess return = Rp − Rf
Rp is scheme return, Rf is risk-free return. Both must be for the same period and in the same form (for example, annualised).
Sharpe ratio
Sharpe ratio = (Rp − Rf) ÷ σp
σp is the standard deviation of scheme returns. Measures return per unit of total risk. Higher is better.
Treynor ratio
Treynor ratio = (Rp − Rf) ÷ βp
βp is scheme beta. Measures return per unit of market risk. Higher is better.
Expected return (CAPM)
Expected return = Rf + β × (Rm − Rf)
Rm is the market (benchmark) return. Used to find alpha.
Jensen's alpha
Alpha = Rp − [Rf + β × (Rm − Rf)]
Positive means outperformance after adjusting for beta. Negative means underperformance. Zero means return matched the risk taken.

How to solve Risk-Adjusted Returns: Sharpe, Treynor and Alpha questions

Use this method for any question on Sharpe, Treynor or alpha.

  1. 1Identify what is asked: Sharpe, Treynor, alpha, or interpretation.
  2. 2List the given values: scheme return, risk-free rate, standard deviation, beta, market return.
  3. 3Check that all returns are for the same period and in the same units (all in %).
  4. 4Compute excess return: scheme return minus risk-free rate.
  5. 5For Sharpe divide by standard deviation. For Treynor divide by beta. For alpha compute expected return with beta first, then subtract from actual return.
  6. 6If comparing schemes, calculate the same ratio for each and pick the higher one (for alpha, the higher alpha).
  7. 7Match your result to the options and check the sign and size make sense.

Quickest way: Match the denominator to the name

When to use it: Use when a question gives numbers and four close options, and time is short.

  1. Subtract Rf from the return first. Do this every time.
  2. Sharpe means standard deviation (σ). Treynor means beta (β).
  3. Divide and compare. Round only at the end.
  4. For alpha, find expected return Rf + β(Rm − Rf) before subtracting.
  5. In comparison questions, a rough division is often enough to rank the schemes.

Common mistakes in Risk-Adjusted Returns: Sharpe, Treynor and Alpha

  • Dividing the scheme return by risk without subtracting the risk-free rate.

    Students remember the denominator but forget the numerator is excess return.

    Fix: Write Rp − Rf first, every time, before touching the denominator.

  • Mixing up Sharpe and Treynor denominators.

    Both formulas look alike and both use the same numerator.

    Fix: Sharpe uses standard deviation (total risk). Treynor uses beta (market risk).

  • Calling a scheme with higher return the better scheme.

    Raw return is the most familiar measure.

    Fix: Compare per unit of risk. A lower-return scheme can have a higher Sharpe ratio.

  • Calculating alpha as scheme return minus market return.

    Students ignore beta.

    Fix: Alpha compares the scheme to the return expected for its beta: Rp − [Rf + β(Rm − Rf)].

  • Treating a negative Sharpe ratio as better because the number is smaller or the scheme looks safe.

    Confusion with measures where lower is better, such as standard deviation.

    Fix: A negative Sharpe means the scheme earned less than the risk-free rate. Higher Sharpe is always better.

  • Comparing ratios across different categories or periods.

    The ratios look like universal scores.

    Fix: Compare only schemes of the same category, over the same period, with the same Rf.

Worked examples

Example 1

Scheme A returned 15% a year with a standard deviation of 10%. Scheme B returned 18% with a standard deviation of 16%. The risk-free rate is 6%. Which scheme has the better Sharpe ratio, and what is it?

Show the solution
  1. Scheme A excess return = 15 − 6 = 9%.
  2. Scheme A Sharpe = 9 ÷ 10 = 0.90.
  3. Scheme B excess return = 18 − 6 = 12%.
  4. Scheme B Sharpe = 12 ÷ 16 = 0.75.
  5. 0.90 is higher than 0.75, so A gave more return per unit of total risk.

Answer: Scheme A, with a Sharpe ratio of 0.90 (against 0.75 for Scheme B), even though B had the higher return.

Example 2

A scheme returned 14% with a beta of 1.2. The market returned 12% and the risk-free rate is 6%. Find the Treynor ratio and Jensen's alpha.

Show the solution
  1. Excess return = 14 − 6 = 8%.
  2. Treynor = 8 ÷ 1.2 = 6.67 (approximately).
  3. Market premium = 12 − 6 = 6%.
  4. Expected return = 6 + 1.2 × 6 = 6 + 7.2 = 13.2%.
  5. Alpha = 14 − 13.2 = 0.8%.

Answer: Treynor ratio is about 6.67 and Jensen's alpha is +0.8%, so the scheme beat the return expected for its beta.

Exam tips

  • Expect direct formula questions: which ratio uses standard deviation and which uses beta.
  • Learn the interpretation lines: higher Sharpe or Treynor is better, positive alpha means the manager added value.
  • Remember the use case: Sharpe for a standalone scheme, Treynor for a scheme inside a diversified portfolio.
  • In numerical questions, subtract the risk-free rate first and check that all figures are in the same units.
  • Read the stem for the word 'total risk' (standard deviation) versus 'market risk' (beta).

Practice questions from Mutual Fund Scheme Performance

Risk-Adjusted Returns: Sharpe, Treynor and Alpha 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 Returns: Sharpe, Treynor and Alpha: frequently asked questions

What is the Sharpe ratio formula for a mutual fund?

Sharpe ratio = (scheme return − risk-free return) ÷ standard deviation of scheme returns. It shows the excess return earned per unit of total risk. A higher value is better.

What is the difference between Sharpe and Treynor ratio?

Both use excess return as the numerator. Sharpe divides by standard deviation, which is total risk. Treynor divides by beta, which is only market risk.

What is alpha in a mutual fund?

Alpha is the return a scheme earned above or below what was expected for its beta and the market return. A positive alpha suggests the fund manager added value. A negative alpha suggests the scheme underperformed for the risk taken.

How do I interpret a Sharpe ratio?

Compare it with another scheme in the same category over the same period. The scheme with the higher ratio gave more return per unit of risk. A negative ratio means the scheme earned less than the risk-free rate.