Historical Volatility and Risk-Adjusted Return Measures
Summary
The document introduces volatility as a measure of return dispersion and distinguishes historical volatility, calculated from past prices, from implied volatility inferred from option prices. Its historical-volatility example uses logarithmic returns and a rolling standard deviation over a 252-trading-day window, annualized to assess changing volatility in an index. It then surveys risk-adjusted performance measures: Sharpe, information, Modigliani, Treynor, Jensen’s alpha, R-squared, and Sortino ratios, describing the types of risk or benchmark each incorporates.
The measures offer different comparisons: Sharpe uses total volatility, Sortino focuses on downside variation, information ratio compares with a benchmark, and Treynor adjusts for systematic risk. The document notes that historical results can be misleading, market conditions change, and risk-adjusted ratios do not reveal future returns. The examples and formulas are introductory; the appropriate measure depends on the strategy, benchmark, and risk definition, and no evidence here establishes predictive performance.
Key ideas
- Historical volatility can be estimated from past returns with a rolling standard deviation and annualization.
- Implied volatility reflects expected movement embedded in option prices but does not indicate direction.
- Sharpe and Sortino ratios differ in whether they account for total volatility or downside volatility.
- Benchmark-relative measures include the information ratio, Modigliani ratio, Treynor ratio, and Jensen’s alpha.
- Risk-adjusted measures summarize historical performance and do not guarantee future returns.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.