Portfolio Analytics — Sharpe, CAPM & Frontier
The core quantitative toolkit of CFA and CAIA portfolio management. Score a portfolio on every risk-adjusted ratio — Sharpe, Sortino, Treynor, Jensen alpha and M² — run a full CAPM decomposition, or build a two-asset efficient frontier with the minimum-variance and tangency portfolios and the Capital Market Line.
How it works
This tool wraps two of the most tested ideas in modern portfolio theory: risk-adjusted performance measurement and the mean–variance efficient frontier. Everything below is computed in closed form, instantly, from the inputs you enter — no data leaves your browser.
Risk-adjusted ratios
All four ratios reward a portfolio for the excess return it earns above the risk-free rate, Rp − Rf, but they each divide that excess by a different definition of risk:
Sortino = (Rp − Rf) / σdown — penalises only downside volatility.
Treynor = (Rp − Rf) / β — excess return per unit of systematic (market) risk.
M² = Rf + Sharpe × σm — the return the portfolio would earn if levered to the benchmark's risk, directly comparable in percent.
CAPM and Jensen's alpha
The Capital Asset Pricing Model says an asset's required return rises with its beta — its exposure to undiversifiable market risk:
Jensen's α = Rp − [ Rf + β(Rm − Rf) ]
A positive alpha means the manager delivered more than the market premium their beta entitled them to — genuine skill or luck. A negative alpha means the portfolio underperformed the risk it carried.
The two-asset efficient frontier
Mix two assets at weight w in A and 1−w in B. The combined return is linear but the risk is not, thanks to the correlation term:
σp = √[ w²σa² + (1−w)²σb² + 2w(1−w)ρσaσb ]
The minimum-variance weight has a clean closed form:
The tangency portfolio is the mix with the highest Sharpe ratio — we find it by scanning every weight from 0% to 100%. A line from the risk-free rate through that point is the Capital Market Line, and its slope is the best risk-adjusted return any combination of these two assets can offer. The lower the correlation, the more the frontier bows leftward and the bigger the diversification benefit.
These are ex-ante estimates built from the return, volatility and correlation assumptions you supply. They are a teaching and planning tool, not investment advice or a forecast of realised returns.