The Sharpe ratio is one of R02's favourite risk-adjusted return measures. The formula is short, the maths is easy, and the examiner can build half a dozen variations out of it, which is exactly why it shows up so often.
The Sharpe ratio formula
Sharpe = (R_p − R_f) ÷ σ_p
In plain English:
Sharpe = excess return ÷ total risk
| Symbol | Meaning |
|---|---|
| R_p | Portfolio (or fund) return |
| R_f | Risk-free rate (usually the 10-year UK gilt yield) |
| R_p − R_f | Excess return over the risk-free rate |
| σ_p | Standard deviation of the portfolio's returns, total risk |
Worked example
Assume:
- Portfolio return (R_p) = 9%
- Risk-free rate (R_f) = 3%
- Portfolio standard deviation (σ_p) = 12%
Step 1, Excess return: 9% − 3% = 6%. Step 2, Divide by total risk: 6% ÷ 12% = 0.50.
Sharpe ratio = 0.50.
That means the portfolio delivered 0.5 units of excess return for every 1 unit of risk taken.
How to interpret the result
R02 will rarely give you a fixed pass/fail Sharpe number. It almost always asks you to compare two portfolios. Higher is better.
| Sharpe ratio | What it suggests |
|---|---|
| Above 1.0 | Strong risk-adjusted performance |
| 0.5 to 1.0 | Reasonable risk-adjusted performance |
| 0 to 0.5 | Weak, earning little excess return for the risk |
| Negative | Underperformed the risk-free rate. The investor would have been better off in cash |
What R02 actually tests
The exam usually does one of three things:
- Compute the ratio from R_p, R_f and σ given in the question.
- Compare two funds with different Sharpe ratios and pick the better risk-adjusted performer.
- Rearrange the formula, for example, "if Fund X has a Sharpe of 0.6 and an excess return of 4.8%, what is its standard deviation?" (4.8 ÷ 0.6 = 8%).
Common R02 traps
- Forgetting to subtract R_f first. Dividing raw portfolio return by σ gives the wrong number every time.
- Using the wrong R_f. Unless told otherwise, use the gilt yield, not Bank Rate.
- Comparing Sharpe ratios across very different asset classes. Sharpe assumes normally distributed returns, which is a poor fit for hedge funds, illiquid assets, or anything with significant tail risk. A frequent R02 critique question.
- Confusing Sharpe with Treynor. Treynor uses beta in the denominator, not standard deviation. Sharpe uses total risk; Treynor uses systematic risk only.
How it relates to the other R02 ratios
- Treynor ratio = (R_p − R_f) ÷ β, uses systematic risk instead of total risk.
- Information ratio = (R_p − R_b) ÷ tracking error, compares to a benchmark, not the risk-free rate.
- Jensen's alpha measures excess return over CAPM's expected return.
All four are different ways of asking the same question: was the return worth the risk?
Bottom line
Sharpe ratio questions are some of the most reliable marks in R02. Learn the formula, practise rearranging it for σ and for excess return, and remember its key weakness. It assumes normally distributed returns. Get those three things right and you'll bank every Sharpe question the exam can throw at you.