Risk-Adjusted Return: Why Raw Returns Mislead

Return is the gain or loss on an investment over a period: buy at $100, sell at $110, and the return is 10%. Risk-adjusted return divides that gain by some measure of the uncertainty that came with it, so two investments can be compared on what they paid for each unit of risk, not just on what they paid. The most common version is the Sharpe ratio.

Key takeaways

A raw return, such as the S&P 500's total return of nearly 29% in 2021 or about 18% in 2020, says nothing about the swings along the way.
The Sharpe ratio is average return above a risk-free rate divided by the standard deviation of that excess return; the Sortino ratio measures return above a chosen target and divides by downside deviation, which counts only results below that target.
In the hypothetical example below, the portfolio averaging 9% has a Sharpe ratio of 0.40, against 0.95 for the one averaging 7%.
Borrowing at the 3% risk-free rate to scale up the steadier portfolio lifts its average to 9% but leaves its Sharpe ratio at 0.95; at a 6% borrowing rate the average is 7.5% and the Sharpe ratio drops to 0.71.
These ratios are built from past data, assume returns are summarized well by a mean and a spread, and change with the period chosen.

What raw return leaves out

A single return figure compresses a path into one number. The S&P 500 index returned about 28.7% with dividends in 2021 and about 18.4% in 2020, according to a table citing S&P Dow Jones Indices data; NYU Stern's historical returns dataset, which estimates dividends its own way, shows 28.5% and 18.0%. Both are large gains, yet neither tells a reader how far the index fell and recovered inside those years, or what the same figure would have cost in sleep and forced selling for someone who needed the money.

The SEC's investor education site states that all investments involve some degree of risk and that investors generally seek higher returns as risks rise. It also notes that large-company stocks as a group have lost money on average about one year in three. FINRA says an investment's level of risk typically goes with the return it might achieve, and notes that stocks do not always beat bonds. Risk-adjusted measures try to put a number on that trade, so a fund that earned its return with small swings can be told apart from one that earned the same return with large ones.

These ratios take volatility and any borrowing as given inputs; this guide does not cover those topics in depth.

The Sharpe ratio, step by step

William Sharpe's 1994 paper "The Sharpe Ratio" in the Journal of Portfolio Management describes the measure as differential return per unit of risk. The historic (ex post) version divides the average of the differences between a fund's returns and a benchmark's returns by the standard deviation of those differences. The benchmark can be a riskless asset, which is the original case, or a benchmark portfolio chosen for the strategy.

Sharpe ratio = (average return - risk-free return) / standard deviation of (return - risk-free return)

average return        mean of the periodic returns (here, annual)
risk-free return      return on a riskless asset, often a 3-month Treasury bill
standard deviation    how widely the excess returns spread around their mean

A 3-month Treasury bill is a common stand-in for the risk-free rate. The Federal Reserve's series, published through FRED as TB3MS, showed 3.94% for September 2026 on a discount basis. The example below uses a round 3% instead, so every number can be checked by hand.

Sortino, Treynor, alpha, drawdown

The Sharpe ratio treats a surprise on the upside the same as a surprise on the downside, because standard deviation does not care about direction. The Sortino ratio, as a CFA Institute article on the measure describes it, is calculated like the Sharpe ratio except that a minimum acceptable return (MAR) replaces the risk-free rate and downside deviation replaces standard deviation. The MAR can be the risk-free rate, an index return, an absolute target or zero. Gains above the target never raise the denominator, so when two portfolios have the same spread, the one whose spread comes mostly from good years ranks higher on Sortino than it does on Sharpe.

Sortino ratio = (average return - target) / downside deviation

downside deviation = square root of the average of min(return - target, 0) squared,
                     taken across all periods (periods above target count as zero)

The same CFA Institute article warns that several versions of the downside deviation calculation exist and that the choice matters a great deal. It adds that the simple method based on historical returns can understate downside risk, especially when most of the returns are positive. Two Sortino figures are comparable only if they use the same target and method.

Two further measures come from the capital asset pricing model, according to a CFA Institute article on Treynor and Jensen. The Treynor ratio divides excess return by beta, a portfolio's sensitivity to market movements, instead of by total volatility.

Jensen's alpha is the return above what the model would expect for the beta taken. Because beta ignores risk that diversification can remove, the article calls Treynor most relevant for a diversified portfolio and warns that a poorly diversified portfolio with low beta can look better than it is. CFA Institute's page on risk-adjusted performance measures lists the Sharpe, Sortino, Treynor and Jensen articles together.

Maximum drawdown is a different kind of number: the largest peak-to-trough fall over the period, as a percentage. It needs no statistical assumptions and shows the worst stretch an investor would have lived through, but it depends entirely on which dates are examined and says nothing about how often large falls occur.

Worked example: two portfolios

The figures below are hypothetical, chosen for round arithmetic, and do not describe any real fund. Both portfolios earn a stated annual return for ten years, and the risk-free rate is 3% every year. Portfolio X returns 8, 5, 11, 2, 9, 7, -1, 10, 6 and 13 percent. Portfolio Y returns 24, -14, 19, -6, 27, -9, 21, 3, 18 and 7 percent.

Measure (10 years)	Portfolio X	Portfolio Y
Average annual return	7.0%	9.0%
Standard deviation (sample)	4.22%	14.88%
Sharpe ratio (risk-free 3%)	0.95	0.40
Downside deviation (target 3%)	1.30%	7.17%
Sortino ratio	3.07	0.84
Maximum drawdown (year-end values)	-1.0%	-14.0%
$10,000 grows to	$19,533	$21,693

Portfolio Y wins on raw return: its average is two points higher and its $10,000 ends about $2,160 ahead. X wins on every risk-adjusted line. Its excess return is 4.0 points over a spread of 4.22, so the Sharpe ratio is 4.0 / 4.22 = 0.95. Y earns 6.0 points of excess return over a spread of 14.88, so 6.0 / 14.88 = 0.40. The Sortino gap is wider (3.07 against 0.84) because Y's bad years are deep, and its worst year-over-year fall was 14%. X has only two years below the 3% target, so its downside deviation rests on very little data.

The result is not "X is better" in any absolute sense. A reader who can hold through a 14% fall and wants the higher ending value may reasonably prefer Y, and ten annual observations are far too few to estimate a spread with confidence. The ratios only state how much return each portfolio produced per unit of risk, using these particular years.

What borrowing does to the ratio

Suppose a holder of X borrowed an extra half of the portfolio's value at the same 3% risk-free rate, ending at 1.5 times exposure. Each year's return becomes 1.5 times X's return minus 0.5 times 3%. The average rises to 9.0%, matching Y, and the standard deviation rises to 6.32%, still far below Y's 14.88%.

The Sharpe ratio stays 0.95 and the Sortino ratio stays 3.07, because excess return and spread both scale by 1.5. Sharpe's paper makes the same point: changing the size of a position financed by borrowing leaves the ratio unaffected.

That result depends on borrowing at the risk-free rate, which individual investors rarely can. If the extra half costs 6% a year instead, each year's return is 1.5 times X's return minus 3 points. The average falls to 7.5%, the spread stays 6.32%, and the Sharpe ratio against the 3% risk-free rate drops to 0.71. Borrowing above the risk-free rate lowers return per unit of risk. Other costs and hazards of borrowing, such as variable rates and margin calls, are outside the scope of this guide.

Where risk-adjusted numbers mislead

Normal-shape assumption. Standard deviation summarizes a spread well when returns are roughly bell-shaped. Strategies that earn small gains most months and take rare large losses can show a flattering Sharpe ratio until the loss arrives. Sortino and maximum drawdown help, but they also come from the same observed history.
The lookback period. The ratio changes with the start and end dates. A window that begins after a market fall and ends at a peak looks better than one that includes the fall. Always check how many years are behind a figure.
Negative excess returns. A 2010 CFA Institute digest of a study on refining the ratio notes that when excess return is negative, the Sharpe ratio can rank a fund with lower return and higher volatility above a fund with higher return and lower volatility, because the negative number becomes less negative as volatility grows.
Choice of benchmark and risk-free rate. Sharpe's paper notes the ratio should use returns relative to a chosen benchmark. Change the benchmark, or the T-bill rate, and the ranking can change.
Ratings are packaged versions. Morningstar's star rating for funds is based on a risk-adjusted return measure compared among funds in the same category, combining three-, five- and ten-year results where available. Funds with less than three years of history are not rated, and the rating is built only from past returns.

Frequently asked questions

What counts as a good Sharpe ratio?

No official threshold exists. The ratio is only meaningful for comparing investments measured over the same period against the same benchmark, since Sharpe defined it relative to a chosen benchmark. A value that looks high for a bond fund over one stretch may say little about a stock fund over another.

Which risk-free rate should be used?

Sharpe's original case uses a riskless asset, and a 3-month Treasury bill is the usual stand-in. The Federal Reserve series TB3MS shows monthly values, so a ten-year calculation can use the rate for each period instead of a flat number. Whatever is chosen, comparisons only hold if every investment uses the same one.

Is the Morningstar star rating the same as a Sharpe ratio?

No. Morningstar uses its own risk-adjusted return measure and ranks funds against others in the same category: the top 10% get five stars and the bottom 10% one star. The overall rating is a weighted average of the three-, five- and ten-year ratings, depending on how much history a fund has. Morningstar says the measure places more emphasis on downward variations and rewards consistent performance, which is closer in spirit to Sortino than to Sharpe.

Can a high ratio protect against losing money?

No. The SEC states that all investments involve some degree of risk, and a ratio built on past returns cannot rule out a loss ahead. FINRA's risk page notes that stock prices fell 57 percent during 2008 to 2009, a fall no earlier average or spread could have promised against.

When does alpha or Treynor matter more than Sharpe?

Treynor and alpha measure return against market sensitivity (beta), so they are most informative for a well-diversified portfolio whose risk is mostly market risk. For a concentrated portfolio they can flatter the result, because they ignore risk specific to individual holdings. Sharpe uses total volatility, so it captures that risk. Both also depend on which market index is used to estimate beta.

A checklist for reading fund data

Find the period behind any return or ratio, and whether it covers at least one market fall.
Check that the benchmark and the risk-free rate match the ones used for the investments being compared.
Read Sharpe and Sortino together with maximum drawdown, and note whether the drawdown is one a holder could stay through.
If one portfolio's return looks higher only because it uses borrowed money, compare the ratios rather than the raw gains, and check what the borrowing costs.
Test a scenario in the investment growth calculator, using a stated assumed return rather than a past figure.