What the Sharpe ratio answers
The Sharpe ratio asks: how much excess return did a portfolio earn for each unit of total risk? It compares the portfolio return with a risk-free rate, then scales the difference by the portfolio’s standard deviation.
Sharpe ratio = (Rₚ − R𝒇) / σₚ
What does the standard deviation represent?
In this formula, σₚ is the standard deviation of the portfolio’s periodic returns over the same measurement window as Rₚ and R𝒇. It measures total volatility around the portfolio’s average return. It is not the standard deviation of the risk-free rate, and it is not automatically the standard deviation of one security inside the portfolio. Keep the return frequency and the volatility frequency consistent.
A higher ratio means more excess return per unit of volatility in this comparison. It does not mean the portfolio has no risk, and it does not predict the next period’s result.
Quizara's CFA Level I 2027 course places this idea in V1 Quantitative Methods → Module 8 → Optimal Portfolio Selection. There the ratio is written as expected excess return divided by portfolio standard deviation and is the slope of a capital allocation line. A question based on realized returns can use the observed portfolio return instead; the return definition and the risk-free rate must still use the same period.
Compare two portfolios with the same starting question
Assume both portfolios are measured over the same period and use the same 2% risk-free rate.
Scroll horizontally to see every column.
Portfolio A earned the higher raw return. Portfolio B earned more excess return for each unit of total volatility under these assumptions, so it has the higher Sharpe ratio.
Change the inputs
How to interpret the sign and the comparison
- Positive ratio: return exceeded the chosen risk-free rate.
- Zero ratio: return matched the risk-free rate.
- Negative ratio: return was below the chosen risk-free rate for the period.
- Comparison rule: compare portfolios with the same return frequency, risk-free convention and measurement window.
The ratio uses total volatility. Treynor ratio instead divides excess return by beta, so it answers a different question about systematic risk. Do not swap the denominators.
Check your understanding
Portfolio C earns 9% with 7% volatility; D earns 12% with 20% volatility. The risk-free rate is 1%. Which has the higher Sharpe ratio?
Common mistakes
- Using the raw return in the numerator and forgetting the risk-free rate.
- Comparing a monthly return with an annual standard deviation.
- Treating a high Sharpe ratio as a guarantee of future performance.
- Using beta when the question asks for total volatility.
FAQ
Is a Sharpe ratio of 1 good?
It means one unit of measured volatility was associated with one unit of excess return in the sample. Whether that is attractive depends on the strategy, period and comparison set.
Does a negative Sharpe ratio mean the portfolio lost money?
Not necessarily. A positive return can still be below the risk-free rate, producing a negative excess return.
How CFA Level I can test Sharpe ratio
The 2027 Level I outline expects candidates to calculate and interpret the Sharpe ratio. A question can give a portfolio return, a risk-free rate and a standard deviation, then ask you to calculate the ratio, compare two portfolios, or explain what a negative or higher ratio means. Write down the return period and the risk-free rate before calculating.
Curriculum context and further reading
The CFA Institute refresher reading covers calculating and interpreting Sharpe, Treynor, M² and Jensen measures. Read the official Portfolio Risk and Return Part II reading for the source context.