Portfolio A averages 12% a year. Portfolio B averages 8%. A looks better until you learn its returns vary twice as much, while cash earns 3%.
How much extra return did each portfolio earn for the uncertainty you took on?
That is the idea behind risk-adjusted return: judging the reward alongside the risk taken to earn it. The Sharpe ratio measures this trade-off using the ups and downs in returns.
Return above cash
The Sharpe ratio measures average excess return per unit of variability. Excess return over cash is the portfolio's return minus the chosen cash return for the same period.
Cash gets subtracted because you could have earned that return without owning the risky portfolio. At 12% against 3% cash, the extra return is 9 percentage points.
The cash benchmark is a risk-free proxy: a low-default-risk investment used for comparison. A short US Treasury bill, a short-term government loan, is a common choice for dollar returns. Its low default risk does not protect your buying power from inflation.
Use standard deviation to measure variability here. Sharpe uses the arithmetic mean and standard deviation of the same series of periodic excess returns.
Work the two portfolios
For this new example, give A and B the following three-year record. All examples use total returns in US dollars, with income reinvested, after ongoing investment costs and before personal tax or inflation.
- A's annual returns: −8%, 12%, 32%.
- B's annual returns: −2%, 8%, 18%.
A's mean is (−8% + 12% + 32%) ÷ 3 = 12%. B's is (−2% + 8% + 18%) ÷ 3 = 8%. Use these arithmetic means for Sharpe; CAGR measures compound growth from starting to ending wealth.
Cash earns a constant 3% each year; volatility is the sample standard deviation.
| Portfolio | Mean return | Volatility | Sharpe |
|---|---|---|---|
| A | 12% | 20% | 0.45 |
| B | 8% | 10% | 0.50 |
Subtracting the same cash return from every observation shifts the average without changing the spread. That lets us use portfolio volatility in the denominator:
- A: (12% − 3%) ÷ 20% = 0.45.
- B: (8% − 3%) ÷ 10% = 0.50.
B earned less, but delivered more excess return for each unit of variability. Its 0.50 means half a unit of excess return per unit of volatility, not a 50% return or a probability.
B's lead describes these three observations. Your choice also depends on what the portfolio must fund and how it moves alongside your other holdings. A holding with a lower Sharpe can still help the combined portfolio by offsetting some of its swings.
What counts as high or low
A zero Sharpe means the portfolio's average return matched cash. A negative Sharpe means it fell short. A portfolio can make money and still trail cash.
For a positive ratio, more excess return at the same volatility raises the score. So does the same excess return with less volatility. There is no universal grade where every strategy becomes good.
The inputs matter more than the second decimal place. A ratio measured during calm markets and one measured through a crash answer different questions. A newly quoted cash yield also cannot replace the cash returns earned during the period being measured.
Check how monthly results were converted to annual terms. The usual conversion assumes excess returns are uncorrelated across periods. Stale prices pose another problem: an asset can appear steady simply because its reported value has not caught up with the market.
A smooth sample can miss a bad tail
Consider a separate monthly history. Eleven months earn between 0.6% and 1.3%. The twelfth loses 20%.
The line barely moves for eleven months, then plunges. A calculation ending at month eleven has never seen that loss.
Tail risk is the possibility of rare, severe outcomes that a short history may miss. Sharpe compresses returns into an average and a measure of spread. Two portfolios with the same Sharpe can have very different exposure to sudden losses.
A longer history offers more evidence, but it is still a sample. The next loss can be worse than any in the record.
The Sortino ratio divides average return above a target, called the minimum acceptable return, by downside deviation: a measure of shortfalls below that target. It leaves upside variation out of the risk measure. A positive month can still fall short of a positive target. Sortino also depends on the target, sample and calculation; missing severe losses can make it look flattering too.
Read it in three passes
- Verify the inputs. Match dates, currency, return frequency, costs and cash benchmark. The average and volatility must use the same excess-return series.
- Compare like strategies. A higher positive Sharpe is useful alongside similar investments. Beating cash and beating a suitable market benchmark answer different questions.
- Inspect the losses. Look at drawdowns, the falls from earlier peaks. Then ask what could cause a sudden loss: a borrower failing to pay, buyers disappearing, or borrowing that forces the portfolio to sell during a decline.
Sharpe can help fill the performance section of your investment policy. The policy still decides what job the money has to do.
These examples stop before personal tax. The next optional US lesson, capital-gains taxes, follows an investment result through to the tax bill.
In short
- Sharpe measures average return above cash per unit of excess-return volatility.
- A higher positive ratio earns its meaning from comparable inputs and strategies.
- More volatility can make a negative Sharpe look better without improving returns.
- A smooth history can miss a severe loss. Read Sharpe alongside drawdowns and what could go wrong next.