The Sharpe ratio for investors — did you actually get paid for your risk?
The answer
The Sharpe ratio is the return you earned above the risk-free rate, divided by how much your returns moved around. It answers one question: were you paid for the risk you took, or did you just take the risk?
A higher number is better. But the number is only as honest as the returns that went into it, and some of the worst investments in history reported excellent Sharpe ratios right up to the day they failed.
Why this costs you money
Two people compare portfolios at the end of a year. Both made 15%. They conclude they did equally well.
They did not. Here is what the year looked like from inside.
The first portfolio drifted up in most months, fell 6% at the worst point, and finished at 15%. Its owner checked it occasionally and did nothing.
The second portfolio rose 40%, fell 30%, rose again, and finished at 15%. Its owner did not sleep in March, sold a third of it near the low in April, and bought back higher in June. The reported return was 15%. The return that person actually received was much lower, because they acted during the fall.
The cost of ignoring risk-adjusted return is not theoretical. It is paid in the decisions volatility forces you to make. Almost nobody holds through a 40% fall in a portfolio they do not understand. The Sharpe ratio is the simplest available way to see, in advance, how much movement you have bought.
The second cost is the more common one. Every year, money moves into whichever fund or strategy had the highest return last year. High return with high volatility is often a temporary reward for a risk that has not yet been paid for. A strategy that borrows, or concentrates, or sells insurance against rare events will show a superb return in most years. The years it does not show one are the years it takes everything back.
How it works
Three quantities go into it.
Your return. The return of your portfolio over a period, usually a year.
The risk-free rate. What you could have earned with no risk over the same period, which means a short government security in your own currency. Subtract it, because a return you could have had for free is not a reward for anything. What is left is your excess return.
The standard deviation of your returns. A measure of how much your monthly or yearly returns moved around their own average. Small standard deviation means a steady series. Large standard deviation means a series that jumps.
Sharpe ratio = (Portfolio return − Risk-free rate) ÷ Standard deviation of the portfolio's returns
William Sharpe published the measure in 1966 and called it the reward-to-variability ratio. Other people attached his name to it. He revised the definition in 1994 to use the standard deviation of the excess return rather than of the raw return, which is the form used today.
What it is for. Comparing 2 investments that are not otherwise comparable — a fund against another fund, your portfolio against an index, this year's approach against last year's. It converts "how much did I make" into "how much did I make for each unit of movement I endured".
Where it stops being true. In 4 places, and each one has caused real losses.
It assumes returns follow a normal distribution. They do not. Real returns have what statisticians call fat tails, which means extreme events happen far more often than the normal distribution predicts. Standard deviation, which is built for the bell curve, systematically understates the chance of the events that ruin people.
It treats upside movement as risk. A portfolio that jumps up 20% in a month is penalised exactly as much as one that falls 20%. No investor feels that way. The Sortino ratio was created to fix this by using only downside movement in the denominator.
It can be inflated by assets that are not priced often. If a holding is illiquid and valued by a model rather than a market, its recorded returns are smooth. Smooth returns produce a small standard deviation and therefore a large Sharpe ratio. The risk is unchanged. Only the measurement changed.
It can be gamed by selling insurance. A strategy that collects a small premium every month and pays out rarely produces a long run of small positive returns with tiny variation. Its Sharpe ratio looks extraordinary. The distribution of outcomes is: many small gains, then one loss larger than all of them. Sharpe's own commentators have long noted that Ponzi schemes and put-selling strategies score highly on this measure until the moment they do not.
Annualising, and the mistake in it
Sharpe ratios are quoted per year. Calculating from monthly returns, the convention multiplies the monthly standard deviation by the square root of 12 and the monthly excess return by 12. That adjustment assumes each month is independent of the last, which markets are not. The annualised figure is therefore slightly optimistic. Use it, and never treat 2 Sharpe ratios that differ by 0.1 as different.
What it tells you, and what it does not
It tells you how much reward each unit of movement bought, over the period measured, using the risk-free rate chosen.
Every one of those conditions can be changed to produce a different answer, and that is why 2 published Sharpe ratios for the same fund can differ.
It does not tell you whether the strategy can survive an event it has not yet met. It does not tell you whether you can get your money out. It does not tell you whether the manager was skilled or lucky, and 3 years of data cannot distinguish those.
Most importantly, it does not tell you the size of the worst case. A portfolio and a lottery ticket can have similar averages and similar standard deviations while having entirely different shapes.
The decision rule
A Sharpe ratio is a question, not an answer. The question is: over what period, against what risk-free rate, and were all the prices in the series real?
If the ratio was measured over fewer than 3 years, treat it as noise. Short periods are dominated by luck.
If the holdings are liquid and priced daily by a market, the ratio is reasonably honest and comparisons between funds are fair.
If the holdings are illiquid, unlisted, or valued by a model, a high Sharpe ratio may be a measurement artefact. Look instead at whether investors were ever prevented from withdrawing.
If the strategy earns small, regular gains and has never had a large loss, ask what it is being paid for. A steady income with no visible risk is usually an insurance premium, and the claim has not been made yet.
Try this now
Ten minutes, your own account. This uses drawdown instead of standard deviation, because drawdown is something you can get from your own statement and it is the number you actually experienced.
- Open your portfolio's value history for the last 3 years. Most brokers show a portfolio value chart; if not, your annual statements have year-end values.
- Write down your total return over 3 years, as a percentage. If your app shows an annual figure, use the 3-year annualised return.
- Find the worst drawdown: the largest fall from a peak value to a later low value in those 3 years. In value terms, the highest your portfolio reached, and the lowest it fell to after that peak. Express the fall as a percentage of the peak.
- Divide. Return ÷ worst drawdown. Write the answer down. This is your return per unit of pain.
- Do exactly the same for the index — Nifty 50 or S&P 500 — over the same 3 years. The 3-year return is published everywhere, and the worst drawdown can be read off a 3-year chart.
- Compare the 2 numbers.
What you should see. Most people find one of 3 things, and all 3 are worth knowing.
You beat the index on return but not on return per drawdown. This is the most common outcome for a concentrated portfolio. It means the extra return was paid for with larger falls, and you should decide honestly whether you would hold through a repeat.
You matched the index on return with a much larger drawdown. This is the outcome nobody wants to find and the most useful one to find. You took more risk and were not paid for it.
You have no idea what your worst drawdown was. Also common, and it is the real finding. If you cannot state the worst fall your portfolio has had, you have been measuring only half of your results for 3 years.
Write the number on the first page of whatever you keep your records in. Next year, do it again. Two data points is not statistics, but it is 2 more than most investors have.
Three real cases
1. Long-Term Capital Management, September 1998 (United States) — a superb ratio, then insolvency LTCM was a hedge fund whose partners included 2 Nobel laureates in economics. It ran strategies designed to profit from small, reliable price relationships, and for its first years it produced high returns with remarkably little variation — exactly the profile that produces an outstanding Sharpe ratio. It achieved this with very large borrowings against a comparatively small capital base. In 1998, following Russia's default, those small reliable relationships moved together and against the fund. It lost most of its capital within weeks, and in September 1998 the Federal Reserve Bank of New York organised a group of banks to recapitalise it in an orderly wind-down. The measured risk had been small because the events that mattered had not happened yet.
2. Bernard Madoff, arrested 11 December 2008 (United States) — smooth returns that were not returns For years Madoff's investment business reported steady positive monthly returns with very small variation. That combination produced a Sharpe ratio far beyond what any real strategy sustains, and the impossibility of it was pointed out publicly before the collapse — most persistently by Harry Markopolos, who wrote to the Securities and Exchange Commission repeatedly from 2000 onward. The returns were fabricated. The lesson is not that a high Sharpe ratio means fraud. It is that a Sharpe ratio far above what the strategy could plausibly produce is information, and the correct response is to ask how, not to invest.
3. Franklin Templeton India, 23 April 2020 (India) — liquidity is not in the number Franklin Templeton's Indian arm announced the winding up of 6 debt mutual fund schemes, freezing investor withdrawals across roughly ₹25,000 crore of investor money. The schemes held lower-rated corporate bonds, which trade rarely. Because those bonds were priced infrequently, the reported daily returns of the schemes had been smooth, and their measured volatility was low relative to the credit risk being carried. SEBI subsequently found violations and ordered disgorgement and a ban on launching new debt schemes for a period. No volatility-based measure could have shown the risk, because the risk was that the assets could not be sold at all. Standard deviation measures how prices move. It cannot measure a price that does not exist.
The question that resolves it
A novice compares 2 funds and asks: which one returned more?
An expert compares the same 2 funds and asks: which one returned more for each unit of movement, over the same period, and were all of its prices real?
The second question takes 5 minutes longer and removes most bad choices.
What would make this wrong
If the Sharpe ratio identified good investments reliably, then choosing last year's highest-Sharpe fund would work consistently. It does not. Sharpe ratios measured over 1 to 3 years have weak power to predict the next 3 years, because short samples are dominated by which environment happened to occur.
The honest limits are these.
The ratio penalises the wrong thing for a long-term investor. If you are investing for 20 years and adding money monthly, price movement is not the risk. Permanent loss of capital is the risk. Volatility is what you pay to earn equity returns, and a measure that treats it as a cost can push you toward safer assets that will not meet your goal.
It rewards leverage in calm conditions. Borrowing multiplies both the excess return and the standard deviation, roughly preserving the ratio while raising the chance of ruin.
And a low Sharpe ratio is not automatically a failure. A portfolio built for a specific outcome — a single-sector holding, a founder's stake — will show a poor ratio and may still be the right thing to own.
In India
Indian mutual funds publish a Sharpe ratio in their monthly factsheets, with standard deviation and beta. The risk-free rate used is stated there, usually a short government security or an overnight rate, and it varies between fund houses. Two Indian funds' Sharpe ratios are comparable only if both used the same risk-free rate and the same period, and the factsheet tells you.
SEBI's product labelling system, the riskometer, is a category-level judgement rather than a calculation. It is not a substitute for looking at the return series.
Two features of the Indian market matter more here than elsewhere.
Small and mid-sized company shares can be genuinely hard to sell in a falling market. Trading volume concentrates in the largest companies. A fund holding smaller companies may report low volatility in calm periods and be unable to exit near the quoted price in a stressed one. SEBI began requiring mutual funds to publish stress-test results for small and mid cap schemes, showing how many days it would take to liquidate part of the portfolio. That disclosure tells you something a standard deviation cannot.
Corporate bond markets are thin. Indian corporate bonds trade far less often than government securities, so debt fund returns can be smoother than the credit risk deserves.
In the United States
The risk-free rate used in US calculations is normally the yield on 3-month Treasury bills, and the convention is consistent enough that published Sharpe ratios are broadly comparable across providers. Morningstar and similar services publish 3-year, 5-year and 10-year figures for almost every fund, free.
The depth of American data is a genuine advantage. You can look at a fund's returns for 20 years, see how it behaved in 2008 and in March 2020, and form a view about the manager rather than about a 3-year window.
Hedge funds and private assets report monthly or quarterly, and often value holdings using models. That produces smoothed return series and inflates Sharpe ratios across the private asset industry. The direction of the bias is not disputed.
Retirement accounts encourage long holding periods. Money in a 401(k) plan is not easily withdrawn before retirement, so American investors are partly protected from their own reactions to volatility. That makes the practical cost of a rough ride smaller there than for an investor who can sell everything on a phone in 30 seconds.
Where they differ, and what that tells you
The hurdle is higher in India, and this changes what a good return is.
The Sharpe ratio subtracts the risk-free rate before dividing. Indian government bond yields have generally been well above US Treasury yields, because Indian inflation has been higher. So the same headline return produces a smaller excess return in India than in the United States.
A 12% rupee return when short government securities yield 6.5% is an excess of 5.5 percentage points. A 12% dollar return when Treasury bills yield 4% is an excess of 8 points. The Indian portfolio looks identical on the headline and is doing considerably less well against its own alternative.
What that tells you is to stop comparing your rupee return with an American number you read online. Compare it with what an Indian fixed deposit or a short government security paid over the same period. That is your real alternative, and it is what the Sharpe ratio is built around.
The second difference is data. American investors can evaluate a fund across 20 years and 3 crises. Indian investors often cannot, because the fund or the category is younger. Where the history is short, weight the structure of the strategy more and the measured ratio less.
Carry this
- Return alone is half a result. Return per unit of movement is the result.
- Standard deviation cannot see risks that do not show up in prices, including the risk of not being able to sell.
- Know your own worst drawdown. If you cannot state it, you have not measured your results.