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Formula sheet/NISM Series XV: Research Analyst/Fundamentals of Risk and Return
[ FUNDAMENTALS OF RISK AND RETURN ]

Risk-Adjusted Return Ratios: Sharpe, Treynor & Jensen's Alpha

Sharpe Ratio=(Rp−Rf)/σp(Total risk benchmarked)\text{Sharpe Ratio} = (R_{p} - R_{f}) / \sigma_{p} (\text{Total risk benchmarked})
Treynor Ratio=(Rp−Rf)/βp(Systematic risk benchmarked)\text{Treynor Ratio} = (R_{p} - R_{f}) / \beta_{p} (\text{Systematic risk benchmarked})
Jensen’s Alpha(α)=Rp−[Rf+βp×(Rm−Rf)]\text{Jensen's Alpha} (\alpha) = R_{p} - [ R_{f} + \beta_{p} \times (R_{m} - R_{f}) ]
Variables

RpR_{p}: Portfolio return; RfR_{f}: Risk-free rate; σp\sigma_{p}: Portfolio standard deviation; βp\beta_{p}: Portfolio beta.

Exam note

Sharpe is best for undiversified portfolios; Treynor & Alpha are best for well-diversified portfolios.

Worked example
Risk-Adjusted Performance: Sharpe, Treynor, and Jensen's Alpha

Mutual Fund Scheme X generated an annualized return of 18.5% with a standard deviation of 16.0% and Beta of 1.15. The benchmark market return is 13.0%, and the risk-free rate is 6.5%. Calculate the Sharpe Ratio, Treynor Ratio, and Jensen's Alpha.