Sharpe Ratio

The numerator is the mean excess return over the measurement period: average portfolio return less the risk-free rate applied over that same interval. The denominator is the standard deviation of the portfolio's returns, and the standard convention uses the standard deviation of total returns rather than of the excess series, though the two differ only slightly when the risk-free rate is stable. Both inputs must share a frequency: monthly returns require a monthly risk-free rate.

To annualize a Sharpe ratio computed from monthly data, multiply by the square root of twelve, because mean excess return scales roughly with time while standard deviation scales with the square root of time. That scaling assumes returns are independent across periods. When returns are serially correlated, as with smoothed valuations in private assets, the square-root rule understates true volatility and inflates the reported figure.

The ratio is geometrically the slope of the line connecting the risk-free asset to a risky portfolio in mean-standard-deviation space. That is why the tangency portfolio on the efficient frontier is precisely the portfolio with the highest attainable Sharpe ratio: every investor combining cash and one risky portfolio wants the steepest capital allocation line available, since a steeper slope delivers more expected return at any chosen level of volatility.

Because the denominator is total risk, systematic plus idiosyncratic, the measure is appropriate for evaluating a portfolio that represents an investor's entire risky allocation. Adding or removing leverage by borrowing or lending at the risk-free rate leaves the ratio unchanged, which makes it a clean tool for ranking strategies whose gearing differs. Treynor's measure, dividing excess return by beta, is the counterpart when the holding sits inside a broader diversified portfolio and only its market exposure matters.

Standard deviation treats upside and downside dispersion identically, so strategies that sell options, write insurance-like exposures or harvest carry post attractive ratios during calm periods while accumulating left-tail exposure that volatility never captures. Illiquid holdings marked infrequently show artificially low measured volatility, lifting the ratio without reducing economic risk. Practitioners respond with the Sortino ratio, which uses downside deviation, or by inspecting skewness, kurtosis and drawdown alongside the headline number.

Backfill and survivorship effects in hedge fund databases push reported cross-sectional averages upward. A further limitation is statistical: Sharpe ratios estimated from short samples carry wide confidence intervals, so a gap between two managers over three years rarely establishes genuine skill.

A candidate should be able to compute the ratio from raw return and volatility data, convert between frequencies, and rank portfolios by risk-adjusted performance. Expect items that pair the ratio with the capital allocation line, asking which portfolio an investor should combine with the risk-free asset, and items that add an asset to an existing portfolio, where the correct test is whether the new asset's Sharpe ratio exceeds the existing portfolio's Sharpe ratio multiplied by the correlation between the two.

Distinguish it clearly from neighbouring statistics. M-squared restates the same ranking in percentage-return terms by levering the portfolio to the benchmark's volatility. Jensen's alpha and Treynor use beta and therefore reward only systematic exposure. The information ratio replaces the risk-free rate with a benchmark and the denominator with tracking error, measuring active skill rather than total risk-adjusted return.