Portfolio Performance, Risk Metrics, and Mean-Variance Optimization
Summary
The document surveys measures for evaluating portfolio returns alongside the risks taken to earn them. It describes risk-adjusted measures such as Sharpe, Sortino, and Calmar ratios; benchmark-relative measures such as up and down capture; and risk measures including variance, maximum drawdown, correlation, beta, and value at risk. The discussion explains how these metrics illuminate different aspects of performance, downside exposure, market sensitivity, and diversification rather than relying on returns alone.
It also introduces portfolio optimization using historical returns and covariance estimates, with a mean-variance objective and Sharpe ratio, and gives an example output assigning weights to several stocks. The provided excerpt is incomplete: the value-at-risk discussion is cut off, and parts of the optimization setup are missing or inconsistent about the example assets. Historical estimates and optimized weights depend on the selected data and assumptions; the example does not demonstrate future performance or robustness. Metrics should be interpreted together and in context.
Key ideas
- Returns should be evaluated alongside the risk and variability taken to produce them.
- Sharpe uses total volatility, Sortino focuses on downside variation, and Calmar relates return to maximum drawdown.
- Capture ratios compare portfolio performance with a benchmark during rising or falling markets.
- Variance, drawdown, correlation, beta, and value at risk describe distinct dimensions of portfolio risk.
- Historical mean-variance optimization uses estimated returns and covariance to propose portfolio weights, which remain sensitive to the estimation choices.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.