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NISM-Series-XXI-A: Portfolio Management Services (PMS) Distributors · Investments

Performance Measurement Ratios: Sharpe, Treynor and Alpha

Updated 11 October 2026 · Fact-checked

Performance measurement ratios judge a portfolio's return after adjusting for risk. Sharpe = (Rp − Rf) ÷ σp uses total risk. Treynor = (Rp − Rf) ÷ β uses market risk. Jensen's alpha = Rp − [Rf + β(Rm − Rf)] shows excess return over CAPM. Compare results against a suitable benchmark.

Understand Performance Measurement Ratios

A high return alone does not show skill. A manager may have earned it by taking a lot of risk. Risk-adjusted ratios ask: how much return did you get for each unit of risk taken?

All three main measures start with the excess return, which is portfolio return minus the risk-free rate. The risk-free rate is usually the return on a government treasury bill. The ratios differ in what they divide by.

The Sharpe ratio divides excess return by standard deviation, which is total risk. It suits a portfolio that is your whole investment, or when you compare portfolios that are not well diversified. The Treynor ratio divides excess return by beta, which is market (systematic) risk only. It suits a well-diversified portfolio that is one part of a larger holding. Jensen's alpha does not divide. It is the actual return minus the return CAPM says the portfolio should have earned for its beta. Positive alpha means the manager added value. Negative alpha means the manager lagged.

A benchmark is a reference index or yardstick used to judge a portfolio. It should match the portfolio's style, market-cap range and asset mix. For example, a large-cap equity portfolio is compared with a large-cap index, not a small-cap one. A poor benchmark gives a misleading verdict.

Returns themselves can be measured two ways. The time-weighted return (TWRR) removes the effect of client cash inflows and outflows, so it reflects the manager's skill. The money-weighted return (MWRR, like IRR or XIRR) is affected by the timing and size of cash flows, so it reflects the client's actual experience.

Key formulas to remember

Sharpe ratio
Sharpe = (Rp − Rf) ÷ σp
σp is the standard deviation of portfolio returns (total risk). Higher is better.
Treynor ratio
Treynor = (Rp − Rf) ÷ βp
Uses beta (systematic risk). Higher is better. Works best for diversified portfolios.
Jensen's alpha
α = Rp − [Rf + βp × (Rm − Rf)]
Rm is the market (benchmark) return. Positive alpha means outperformance after adjusting for beta.
Excess return over benchmark
Excess return = Rp − Rbenchmark
Simple comparison with no risk adjustment.
Time-weighted vs money-weighted
TWRR = [(1 + r1)(1 + r2)…(1 + rn)] − 1
r1 to rn are sub-period returns between cash flows. TWRR ignores cash-flow timing; MWRR does not.

How to solve Performance Measurement Ratios questions

Use this method for any ratio or benchmark question.

  1. 1Read what is asked: Sharpe, Treynor, alpha or a conceptual comparison.
  2. 2List the given data: Rp, Rf, σ, β, Rm. Keep all in the same units (percent).
  3. 3Compute the excess return Rp − Rf first.
  4. 4Pick the divisor: σ for Sharpe, β for Treynor. For alpha, compute the CAPM expected return instead.
  5. 5Calculate and keep the sign. A negative result is meaningful.
  6. 6If comparing portfolios, rank by the same ratio. Higher is better.
  7. 7Check the choice of measure: total risk means Sharpe, market risk means Treynor, outperformance versus CAPM means alpha.

Quickest way: Match the risk word to the ratio

When to use it: Use for conceptual MCQs where numbers are not needed.

  1. See 'total risk' or 'standard deviation': answer Sharpe.
  2. See 'beta' or 'systematic risk': answer Treynor.
  3. See 'CAPM' or 'excess over expected return': answer Jensen's alpha.
  4. See 'removes effect of cash flows' or 'manager skill': answer TWRR.
  5. See 'client's actual experience' or 'timing of cash flows': answer MWRR.

Common mistakes in Performance Measurement Ratios

  • Dividing by beta in the Sharpe ratio, or by standard deviation in the Treynor ratio.

    The two formulas look alike and the names are easy to mix up.

    Fix: Remember S for Sharpe and Standard deviation. T for Treynor and beTa.

  • Forgetting to subtract the risk-free rate.

    Students use the portfolio return directly.

    Fix: Always write Rp − Rf first. Alpha also uses Rf inside the CAPM bracket.

  • Treating Jensen's alpha as a ratio.

    It is taught alongside Sharpe and Treynor.

    Fix: Alpha is a difference in return, stated in percentage points, not a per-unit-risk number.

  • Using Rm − Rf as the market return in CAPM.

    Confusing market return with market risk premium.

    Fix: In alpha, the bracket is Rf + β(Rm − Rf). Rm is the market return; Rm − Rf is the premium.

  • Saying TWRR is affected by when the client adds money.

    Mixing up TWRR and MWRR.

    Fix: TWRR neutralises cash flows. MWRR is affected by them.

  • Accepting any index as the benchmark.

    Students think a bigger index is always better.

    Fix: A benchmark must match the portfolio's strategy, market-cap and asset class.

Worked examples

Example 1

A portfolio returned 14% with standard deviation 10% and beta 1.2. The risk-free rate is 6%. Find the Sharpe and Treynor ratios.

Show the solution
  1. Excess return = 14 − 6 = 8%.
  2. Sharpe = 8 ÷ 10 = 0.80.
  3. Treynor = 8 ÷ 1.2 = 6.67 (approximately).

Answer: Sharpe ratio = 0.80; Treynor ratio ≈ 6.67.

Example 2

A PMS portfolio returned 15% with beta 1.1. The market returned 12% and the risk-free rate is 6%. Calculate Jensen's alpha.

Show the solution
  1. Market risk premium = 12 − 6 = 6%.
  2. CAPM expected return = 6 + 1.1 × 6 = 6 + 6.6 = 12.6%.
  3. Alpha = 15 − 12.6 = 2.4%.

Answer: Jensen's alpha = +2.4%, so the portfolio outperformed its risk-adjusted expectation.

Exam tips

  • Expect both conceptual MCQs (which ratio uses which risk) and short calculations. Do the excess return first.
  • Know that higher Sharpe or Treynor is better, and positive alpha is good.
  • Questions often ask which measure suits a well-diversified portfolio: Treynor. Not diversified or standalone: Sharpe.
  • For TWRR versus MWRR, link TWRR to the manager and MWRR to the client.
  • Where a calculation has negative marking, check the units and the divisor before choosing.

Practice questions from Investments

Performance Measurement Ratios in other exams

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

Performance Measurement Ratios: frequently asked questions

What is the difference between Sharpe ratio and Treynor ratio?

Both measure excess return per unit of risk. Sharpe uses standard deviation, which is total risk. Treynor uses beta, which is only market risk.

How do you calculate Jensen's alpha?

First find the CAPM expected return: Rf + β × (Rm − Rf). Then subtract it from the portfolio's actual return. A positive answer means the manager beat expectations for the risk taken.

What is a benchmark in portfolio performance?

It is a reference index or yardstick used to judge a portfolio's returns. It should match the portfolio's strategy and asset class so the comparison is fair.

What is the difference between time-weighted and money-weighted return?

Time-weighted return removes the effect of client deposits and withdrawals, so it shows the manager's skill. Money-weighted return includes the timing and size of cash flows, so it shows the investor's actual experience.