Reward-to-Variability Ratio
Measure excess portfolio return for each unit of total risk
- Difficulty
- Easy
- Time to result
- ~days to results
- Steps
- 5
- Confidence
- 99%
Sharpe's original reward-to-variability ratio asks how much return a whole portfolio delivered above a risk-free Treasury-bill return for each unit of total variability. The numerator is the portfolio's average return minus the risk-free return; the denominator is the portfolio's standard deviation. A higher value means more reward relative to the journey's variability. Sharpe stresses that the original setting was the complete portfolio, not one fund among many. For a component such as a growth manager, the analysis should instead compare its return with a relevant growth benchmark and measure the variability of that difference. The ratio is therefore a compact decision aid with a scope rule: use total risk for the whole portfolio, benchmark-relative measures for components, and richer diagnostics when the investment has several market exposures.
Origin
Sharpe originally called the measure the reward-to-variability ratio; another person began calling it the Sharpe ratio and that name persisted.
Core principles
- 01Return is a reward only in relation to the risk taken to earn it.
- 02The risk-free return should be removed before measuring reward for risk.
- 03Total variability belongs in the denominator when evaluating a whole portfolio.
- 04A component portfolio requires a relevant benchmark and a different risk comparison.
- 05One ratio is informative but cannot replace a fuller analysis.
How to run it
- 1
Check the portfolio scope
Determine whether the investment is the evaluator's whole portfolio or only one component. Apply the classic ratio to the whole portfolio.
Pro tip Write down the portfolio's role before calculating anything.
Watch out Using the ratio on one manager among many can misrepresent that manager's contribution.
- 2
Calculate excess return
Subtract the average Treasury-bill or other risk-free return from the portfolio's average return over the same period. This is the reward earned for accepting risk.
Pro tip Align the return frequency and period for both figures.
Watch out A mismatched risk-free period distorts the numerator.
- 3
Measure total variability
Calculate the standard deviation of the complete portfolio's returns. This represents the variability experienced on the path to the average return.
Pro tip Review the underlying return distribution as well as the single statistic.
Watch out The measure treats upside and downside volatility alike.
- 4
Divide reward by variability
Divide excess return by total variability to produce the ratio. Compare ratios only when portfolios and time periods are meaningfully comparable.
Pro tip Use the ratio as one summary number, not as a complete diagnosis.
Watch out A precise-looking ratio can still rest on noisy historical data.
- 5
Adapt component analysis
For an individual manager, subtract a relevant benchmark's return and measure the variability of that return difference. Use regression or more sophisticated analysis when several market exposures remain.
Pro tip Match a growth manager with a growth benchmark rather than Treasury bills.
Watch out Most hedge funds are not truly hedged and can carry both stock and bond beta.
In the wild
An investor compares a complete diversified portfolio with a total-stock-market alternative over the same twenty years. For each, the investor subtracts the Treasury-bill return from the average return and divides by standard deviation.
→ The investor gets a consistent one-number comparison of reward relative to total variability.
A pension fund evaluates one growth manager among a hundred managers. Instead of using the classic ratio, it compares the manager's average return with a growth index and measures the variability of the return difference.
→ The evaluation reflects the manager's benchmark-relative role rather than penalising all market variability as if the manager were the entire portfolio.
Common mistakes
Applying it to every fund
The original ratio was designed for a whole portfolio, not automatically for each component in a multi-manager structure.
Ignoring hidden beta
A hedge fund with stock or bond exposure needs analysis beyond a simple excess-return-to-total-volatility ratio.
Treating one number as enough
Sharpe notes that modern computers remove the need to restrict evaluation to a single summary number.
Is it for you?
Best for
It is best for comparing complete portfolio strategies measured over consistent periods and against the same risk-free baseline.
Not ideal for
It is not ideal for ranking one manager inside a diversified multi-manager portfolio unless that investment is genuinely zero-beta.
From the transcript
“what did you get an expected return per unit of risk that you took”
“this is for a whole portfolio.”
“my average return over the treasury bill, how much did I earn over for taking risk?”
From the episode
Interview With William Sharpe: Masters in Business (Audio)
William Sharpe