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Risk-adjusted performance measures evaluate whether a portfolio's returns are commensurate with the risk taken. The Sharpe ratio = (rp − rₓ) / σp measures return per unit of total risk and is appropriate when the portfolio represents an investor's entire wealth. Jensen's alpha = actual return − CAPM-predicted return measures excess return above what the portfolio's beta predicts — positive alpha is the goal of active management. The Treynor ratio uses beta rather than total volatility in the denominator, appropriate when the portfolio is a component of a larger diversified position. These measures are used to identify genuine manager skill, to attribute performance to factor exposures vs. true alpha, and to determine whether active management fees are justified.
Calculate Sharpe ratio and Jensen's alpha for a real actively managed mutual fund over a 10-year period and compare to a passive index. Understand why a fund can have positive alpha on a CAPM basis but negative alpha once Fama-French factors are added. Note that any strategy with optionlike features (selling volatility) can artificially inflate its Sharpe ratio.
From your study of the efficient frontier, you know that investors care about both return and risk — that a higher return is not automatically better if it comes with proportionally higher risk. From CAPM, you know that the only risk that earns a premium is systematic risk, measured by beta. Risk-adjusted performance measures translate these ideas into tools for evaluating whether a portfolio — or a manager — has actually earned its returns relative to the risk taken.
The Sharpe ratio is the most widely used measure: (r_p − r_f) / σ_p. It asks how much excess return (above the risk-free rate) you received per unit of total volatility. A Sharpe ratio of 0.8 means the portfolio earned 0.8 percentage points of excess return for each 1% of standard deviation. When comparing two portfolios of similar asset classes, the one with the higher Sharpe ratio delivered better risk-adjusted performance. Crucially, the Sharpe ratio uses total risk (σ_p), making it appropriate when the portfolio under evaluation represents the investor's entire wealth — there is no larger portfolio absorbing its idiosyncratic risk.
Jensen's alpha takes a different approach rooted in CAPM. CAPM predicts what a portfolio *should* return given its beta: E(r_p) = r_f + β_p(r_m − r_f). Alpha is the actual return minus this CAPM-predicted return. Positive alpha means the manager generated return above what compensation for systematic risk alone would predict — which is the goal of every active manager. If a fund has β = 1.2 and the market earned 10%, the fund should have earned roughly r_f + 1.2(10% − r_f). If it actually earned more than that, the difference is alpha. Alpha is the right metric when you want to isolate genuine skill from leverage or systematic factor exposure — a fund that simply buys high-beta stocks in a rising market earns no alpha even with stellar raw returns.
The Treynor ratio = (r_p − r_f) / β_p uses beta in the denominator instead of total volatility. This is appropriate when the portfolio is one component of a larger diversified holding — the idiosyncratic risk of this sub-portfolio diversifies away in context, so only systematic risk matters. A manager running a tech sleeve within a diversified pension fund should be evaluated on Treynor, not Sharpe.
All three measures share a critical vulnerability: they are only as good as the risk model used to define "expected return." Jensen's alpha against CAPM looks very different from alpha against a Fama-French five-factor model. Many strategies that appear to generate alpha versus a simple market-beta benchmark are simply loading on well-known priced factors — size, value, momentum, profitability — that the benchmark missed. This is why professional performance attribution increasingly decomposes returns into factor exposures versus true residual alpha. A positive Sharpe ratio or Jensen's alpha invites the follow-up question: *what risk is this strategy actually exposed to that I am not measuring?*