Risk results can change for many reasons: trading activity that generates exposure to new factors, changes in exposures to existing factors, changes in risk factor volatilities, or changes in correlation among risk factors. Understanding changes in risk estimates can be key, especially in times of crisis when volatilities spike and correlations point in the same direction, eliminating the diversification that was supposed to protect a portfolio. Understanding those changes also enables us to determine whether portfolio management over the period has increased or reduced risk. Yet understanding those changes, especially for simulation-based analytics, can seem impossible.
The parametric method makes understanding these changes relatively simple. This method is valid for a large range of portfolios exhibiting small or negligible convexity. The parametric approach and the closed formula used to derive portfolio volatility lend themselves to easy mathematical calculations that can typically provide the sensitivity of the risk function to the parameters being used: exposures, factor volatilities, and correlations. The methodology proposed here decomposes the variation in risk through a simple Taylor expansion of the parametric-risk function. Using first and second order sensitivities, the methodology works in a similar fashion for performance attribution or P&L explanation. When the residual part is small, the method is effective and appealing because effects computed are additive.