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NISM-Series-XV: Research Analyst · Fundamentals of Risk and Return

Risk-Return Tradeoff and Risk-Adjusted Performance Measures

Updated 11 October 2026 · Fact-checked

The risk-return tradeoff says higher expected return needs higher risk. Risk-adjusted measures compare returns after allowing for risk. Sharpe ratio = (Rp − Rf) ÷ σp uses total risk. Treynor ratio = (Rp − Rf) ÷ β uses market risk. Jensen's alpha = Rp − [Rf + β(Rm − Rf)] shows excess return over CAPM.

Understand Risk-Return Tradeoff and Risk-Adjusted Performance

The risk-return tradeoff is a basic idea in investing. If you want a higher expected return, you must accept more risk. A safe asset such as a government treasury bill pays little. Equity pays more on average, but its returns swing widely. Note that this is about *expected* return. Taking more risk does not guarantee a higher actual return.

Raw return alone is a poor way to judge a fund or portfolio. A portfolio that earned 18% with wild swings may be worse than one that earned 15% with steady returns. Risk-adjusted performance measures fix this. They ask how much return you earned for each unit of risk taken above the risk-free rate.

The Sharpe ratio divides excess return (portfolio return minus risk-free rate) by the standard deviation of the portfolio. Standard deviation is total risk, both systematic and unsystematic. Use it when the portfolio is your whole investment, or when comparing standalone portfolios.

The Treynor ratio divides the same excess return by beta. Beta measures only systematic (market) risk. Use it when the portfolio is one part of a well-diversified larger holding, because diversification removes unsystematic risk.

Jensen's alpha works differently. It gives the return in excess of what CAPM says the portfolio should have earned for its beta. Positive alpha means the manager beat the benchmark-for-risk. Negative alpha means the manager under-delivered. Sharpe and Treynor are ratios. Alpha is a percentage return difference.

Key formulas to remember

Excess return
Excess return = Rp − Rf
Rp is portfolio return, Rf is risk-free rate. Used in Sharpe and Treynor.
Sharpe ratio
Sharpe = (Rp − Rf) ÷ σp
σp is standard deviation of portfolio returns (total risk). Higher is better.
Treynor ratio
Treynor = (Rp − Rf) ÷ βp
βp is portfolio beta (systematic risk). Higher is better. Meaningful when beta is positive.
CAPM expected return
E(Rp) = Rf + β × (Rm − Rf)
Rm − Rf is the market risk premium.
Jensen's alpha
α = Rp − [Rf + β × (Rm − Rf)]
Actual return minus CAPM required return. Positive alpha means outperformance after adjusting for beta.

How to solve Risk-Return Tradeoff and Risk-Adjusted Performance questions

Use this order for any numerical or conceptual question on risk-adjusted performance.

  1. 1Read what is asked: Sharpe, Treynor or Jensen's alpha. Note whether the question asks for a value or a ranking.
  2. 2List the data given: Rp, Rf, σ, β, Rm. Check that all are in the same period (all annual, for example).
  3. 3Convert percentages carefully. Keep them in % throughout, or all in decimals. Do not mix.
  4. 4Calculate excess return Rp − Rf first. It is needed for Sharpe and Treynor.
  5. 5Divide by σ for Sharpe, or by β for Treynor. For alpha, compute the CAPM return first, then subtract it from Rp.
  6. 6For ranking questions, compute the same measure for every portfolio. Higher Sharpe or Treynor ranks better. Higher alpha ranks better.
  7. 7Check the sign and the unit. Sharpe and Treynor are ratios. Alpha is in percentage points.

Quickest way: Pick the measure from the risk word

When to use it: Use this for conceptual MCQs and when time is short.

  1. Total risk, standard deviation, or standalone portfolio: Sharpe.
  2. Beta, systematic risk, or part of a diversified portfolio: Treynor.
  3. Expected return from CAPM, outperformance, or manager skill: Jensen's alpha.
  4. For numbers, do excess return first. Then one division, or one CAPM line and one subtraction.
  5. Eliminate options that are alpha-like values (small percentages) when the question asks for a ratio, and the reverse.

Common mistakes in Risk-Return Tradeoff and Risk-Adjusted Performance

  • Forgetting to subtract the risk-free rate in Sharpe or Treynor.

    Students divide the portfolio return directly by risk, as in a simple return-per-risk idea.

    Fix: Always write Rp − Rf first. The risk-free rate is in every one of the three measures.

  • Using beta in the Sharpe ratio or standard deviation in the Treynor ratio.

    The two formulas look alike and the denominators get swapped.

    Fix: Remember: Sharpe = Standard deviation (both start with S). Treynor = beta (systematic).

  • Using the portfolio return instead of the market premium in Jensen's alpha.

    Students confuse Rm − Rf with Rp − Rf.

    Fix: Inside the CAPM bracket, use the market return Rm. Then subtract the whole bracket from Rp.

  • Saying a higher Sharpe ratio always means a better investment.

    The rule is overgeneralised.

    Fix: It means better return per unit of total risk over the period measured. It is based on past data and does not guarantee future results.

  • Treating alpha as a ratio.

    Students group it with Sharpe and Treynor.

    Fix: Alpha is a return difference in percentage points. Positive is outperformance, negative is underperformance.

Worked examples

Example 1

A portfolio earned 14% in a year with standard deviation 10% and beta 1.2. The risk-free rate is 6%. Calculate the Sharpe ratio and the Treynor ratio.

Show the solution
  1. Excess return = 14% − 6% = 8%.
  2. Sharpe = 8 ÷ 10 = 0.8.
  3. Treynor = 8 ÷ 1.2 = 6.67 (in % per unit of beta).

Answer: Sharpe ratio = 0.8; Treynor ratio ≈ 6.67%.

Example 2

A fund returned 15% with beta 1.25. The risk-free rate is 7% and the market return is 13%. Find Jensen's alpha and state what it shows.

Show the solution
  1. Market risk premium = 13% − 7% = 6%.
  2. CAPM expected return = 7% + 1.25 × 6% = 7% + 7.5% = 14.5%.
  3. Alpha = 15% − 14.5% = 0.5%.
  4. Alpha is positive.

Answer: Jensen's alpha = +0.5%. The fund beat the return required for its beta.

Exam tips

  • Know which risk each measure uses. This is the most common conceptual MCQ: Sharpe total risk, Treynor systematic risk.
  • In NISM-Series-XV, wrong answers carry 25% negative marking, so do not guess blindly if you cannot narrow the options.
  • For case-based questions, write the data down once and reuse it for each sub-question.
  • If two portfolios are part of a diversified holding, Treynor is the better comparison. If standalone, use Sharpe.
  • Check the answer options for the right unit: ratio for Sharpe and Treynor, percentage for alpha.

Practice questions from Fundamentals of Risk and Return

Risk-Return Tradeoff and Risk-Adjusted Performance in other exams

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

Risk-Return Tradeoff and Risk-Adjusted Performance: 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 systematic risk.

How do you calculate Jensen's alpha?

First find the CAPM return: Rf + β × (Rm − Rf). Then subtract it from the portfolio's actual return. A positive result means outperformance.

Can a Sharpe ratio be negative?

Yes. If the portfolio return is below the risk-free rate, excess return is negative and so is the ratio. It means the portfolio did not compensate for risk.

Does higher risk always give higher return?

No. Higher risk offers higher expected return, but actual returns can be lower. The tradeoff is about compensation expected for taking risk.