Risk-adjusted Return

Between two portfolios, a higher Sharpe ratio indicates:

1. A.Higher feesFees do reduce the return that feeds into the numerator, so heavy fees push Sharpe down rather than up. The ratio itself contains only return, the risk-free rate, and standard deviation.
2. B.Lower returnReturn sits in the numerator, so a lower return pushes the ratio down. A higher Sharpe means more excess return was earned for each unit of volatility endured.
3. C.Higher total riskStandard deviation is the denominator, so more total risk lowers the ratio unless return rises faster. The whole point of a risk-adjusted measure is that raw risk-taking earns no credit on its own.
4. D.Better risk-adjusted returnCorrect - more return per unit of risk.

Why: A higher Sharpe ratio means better return per unit of total risk (risk-adjusted return).

The Sharpe ratio measures:

1. A.Correlation to the marketCorrelation to the market is measured by beta or by the correlation coefficient. Sharpe uses standard deviation, which captures total variability rather than the relationship to any benchmark.
2. B.Return onlyReturn appears in the numerator, but a bare return figure would tell you nothing about what was risked to earn it. The whole purpose of the ratio is to divide excess return by the volatility endured.
3. C.Return per unit of total riskCorrect - excess return divided by standard deviation.
4. D.Return per unit of systematic riskThis is the Treynor ratio, which is a genuine risk-adjusted measure built the same way. The two differ only in the denominator: Treynor divides by beta for systematic risk, while Sharpe divides by standard deviation for total risk.

Why: The Sharpe ratio is risk-adjusted return per unit of total risk (standard deviation).