Risk Management and Investment Management
Performance and risk-adjusted measures
Sharpe ratio uses total volatility and suits fully diversified portfolios; Treynor uses beta and suits a sleeve inside a larger portfolio. Jensen's alpha is the CAPM intercept. The information ratio is active return divided by tracking error (the standard deviation of active returns), and the Sortino ratio replaces volatility with downside deviation. M-squared rescales a portfolio's return to the volatility of the benchmark so Sharpe comparisons become return differences.
Factor models and risk decomposition
CAPM, Fama-French three- and five-factor models, and multi-factor risk models decompose return into factor exposures and specific return. VaR decomposition gives marginal VaR (sensitivity of portfolio VaR to a small position change), incremental VaR (effect of adding or removing a position), and component VaR. Component VaRs sum exactly to diversified portfolio VaR, and the gap between that and the sum of standalone VaRs is the diversification benefit.
Risk budgeting and alternatives
Risk budgeting allocates risk, not capital. Risk parity weights by inverse volatility or risk contribution rather than by expected return. Hedge fund and private equity analysis must correct for survivorship bias, backfill bias, and infrequent or smoothed pricing, which induces serial correlation and understates volatility - inflating Sharpe ratios. Returns-based style analysis regresses fund returns on asset-class indices to infer exposures; holdings-based analysis uses actual positions.
Traps
The most common errors are using Sharpe for a portfolio that is one piece of a larger one, dividing by total risk instead of tracking error in an information ratio, and comparing smoothed private-asset indices to public benchmarks without adjustment.
Worked example
A portfolio with standalone component VaRs of 60, 50 and 40 has a summed standalone VaR of 150. If diversified VaR is 120, the diversification benefit is 30, and the component VaRs (which sum to 120) will each be lower than their standalone values.