Sharpe ratio
Return earned above the risk-free rate divided by standard deviation — how much reward an investment produced for each unit of total risk its holder had to live with.
In plain language
A fund that returned 22% is not automatically better than one that returned 15%. The question an analyst has to answer is what was risked to get there.
The Sharpe ratio does that in one line: strip out the return available for taking no risk at all, then divide what is left by how much the returns bounced around. Higher is better.
How it works
The numerator is the excess return — the return over and above a government security, because no one deserves credit for earning what a treasury bill pays.
The denominator is standard deviation, which is total risk. That choice matters: the ratio judges a portfolio including its diversifiable risk, which is exactly right for an investor whose entire savings sit in it, and slightly harsh for one holding it as a small slice of a larger book. The Treynor ratio makes the other choice and divides by beta instead.
The formula
Sharpe ratio = (Rp − Rf) ÷ σp
where Rp is the portfolio return, Rf the risk-free rate and σp the portfolio's standard deviation.
A worked example
Two funds over the same five years, with the risk-free rate at 7%:
| Fund X | Fund Y | |
|---|---|---|
| Return | 22% | 15% |
| Standard deviation | 26% | 9% |
| Excess return | 15% | 8% |
| Sharpe ratio | 0.58 | 0.89 |
Fund X returned seven percentage points more each year and is the worse investment on a risk-adjusted basis. It took nearly three times the volatility to earn less than twice the excess return.
The practical meaning shows up in a bad year. One standard deviation below the mean, Fund X returns 22 − 26 = −4%, while Fund Y returns 15 − 9 = +6%. On Rs 10 lakh that is a loss of Rs 40,000 against a gain of Rs 60,000 — and the investor in Fund Y slept better to get it.
Why NISM asks about it
Chapter 12 (Fundamentals of Risk and Return) covers the risk-adjusted performance measures. Questions are usually a direct computation, or a pair of funds with the higher raw return attached to the lower Sharpe ratio — and the answer is never the higher raw return.
Common exam traps
- Subtract the risk-free rate first. Dividing raw return by standard deviation is the most common error in the paper, and it is always among the options.
- The denominator is standard deviation, not beta. Dividing excess return by beta gives the Treynor ratio, a different measure with a different use.
- A negative Sharpe ratio cannot be ranked sensibly — with returns below the risk-free rate, more volatility makes the number look better.
- The ratio assumes returns are roughly normal; it flatters strategies whose losses are rare but severe.
- Two Sharpe ratios are comparable only over the same period and the same risk-free rate.
Where this is taught
- Series XIX-B · Chapter 6: Fees Structure, Fund Performance and Benchmarkingintroduced here
- Series V-A · Chapter 11: Mutual Fund Scheme Performanceintroduced here
- Series XXI-B · Chapter 20: Performance Measurement and Evaluation of Portfolio Managersintroduced here
- Series XV · Chapter 12: Fundamentals of Risk and Returnintroduced here
- Series V-D · Chapter 11: Mutual Fund Scheme Performanceintroduced here
- Series XIX-C · Chapter 9: Fee Structure and Fund Performanceintroduced here
- Series XVII · Chapter 5: Evaluating Fund Performance & Fund Selectionintroduced here
- Series V-B · Chapter 7: Performance of Mutual Fundsintroduced here
- Series XIX-E · Chapter 7: Fee Structure and Fund Performanceintroduced here
- Series XXI-A · Chapter 10: Performance Measurement and Evaluation of Portfolio Managersintroduced here
- Series X-A · Chapter 16: Portfolio Performance Measurement and Evaluationintroduced here
Related terms
- BetaHow sharply a share moves relative to the market index — beta 1 moves with the index, above 1 amplifies it, below 1 dampens it. The standard measure of systematic risk.
- Standard deviationA measure of how far returns typically stray from their own average — the standard statistic for total risk, counting company-specific and market-wide causes alike.
- Systematic riskThe part of an investment's risk that comes from economy-wide forces moving every asset at once — it cannot be diversified away, and it is the only risk the market pays you to carry.
- Treynor ratioRisk premium per unit of market risk — the return a scheme earned above the risk-free rate, divided by its beta rather than by its standard deviation.
- AlphaThe return a fund earned above what its beta and the benchmark say it should have earned — the slice of performance left over once the market has been given credit for its share.
- Maximum DrawdownThe largest peak-to-trough fall in a Category III AIF's AUM over a reporting period, quoted as a percentage of the peak — the worst loss an investor could have suffered in that window.
- SkewnessA measure of how far a fund's return distribution departs from symmetry around its mean. Zero is symmetrical; positive has a long right tail; negative has a long left tail and is riskier.
- Long-only Equity StrategyA Category III AIF strategy that takes only buy positions in selected stocks when investing, aiming at absolute returns over the medium to long term with a strong emphasis on capital preservation.
- VarianceA measure of how widely a scheme's periodic returns fluctuate around its own average return — the square of standard deviation, and a risk measure relevant to both debt and equity schemes.
- Utility scoreA single number that scores an investment for one particular investor: expected return minus a penalty for risk, scaled by that investor's own risk aversion.
- M² measureA portfolio's return re-scaled to the market's level of risk, so it can be compared with the market return directly, in percentage points.
- Sortino RatioExcess return over the risk-free rate divided by semi-standard deviation — a Sharpe-style ratio that counts only downside volatility as risk.
- Information RatioActive return over the benchmark divided by tracking error — how much outperformance a manager delivers for each unit of risk taken by deviating from the index.
- Risk averse investorAn investor who accepts risk only when paid a positive expected risk premium for it, and who demands a larger premium the greater the risk.
- Risk Aversion IndexThe 'A' in the Markowitz utility formula U = E(r) − 0.5 × A × σ² — a number capturing how heavily an individual investor's utility is penalised for taking on variance.
- CAGRThe single smoothed annual rate at which a starting value would have to grow, compounding each year, to reach the ending value over a given period.
- Fund factsheetThe monthly scheme summary an AMC publishes voluntarily — portfolio, performance, risk measures and investment details in one document. It is an AMFI best practice, not a statutory requirement.
- Net selectivityFama's absolute performance measure: the fund's return above the risk-free rate, less the market premium the portfolio's own total risk would have earned on its own.
- Downside riskThe probability of a loss on account of falling asset prices in changing market conditions — the half of volatility investors actually mind, measured by maximum drawdown and value at risk.
- Portfolio betaThe weighted average of the betas of the holdings in a portfolio — the measure of its systematic, non-diversifiable risk used in CAPM, the Treynor ratio and market-neutral strategies.
- Unsystematic riskThe part of an investment's risk that belongs to one company or one issuer — a strike, a fraud, a downgrade — and which diversification can remove, unlike market-wide systematic risk.
- Risk adjusted returnThe return an investment earns for each unit of risk it takes on, rather than the return looked at on its own — in this paper, measured through the Sharpe ratio.
- Peer group comparisonJudging a fund against other similar actively managed funds rather than against an index — popular, but only sound if the funds follow comparable strategies and their risk is compared alongside their return.
- Due diligenceA client's own investigation of a portfolio manager before appointing them — checking process, people and past performance against a benchmark, not just the headline return.