101 Concepts for the Level I Exam

Essential Concept 98: Decomposition of Value Added

A common way of decomposing value added is between value added due to asset allocation and value added due to security selection.

Let us consider a portfolio of stocks and bonds where the weights allocated to stocks and bonds differ from the benchmark and each asset class is actively managed by selecting individual securities. The total value added due to asset allocation and security allocation is given by:

$\mathrm{R}}_{\mathrm{A}}\mathrm{=(}\mathrm{\Delta }{\mathrm{w}}_{\mathrm{stocks}}{\mathrm{R}}_{\mathrm{B}},_{\mathrm{stocks}}\mathrm{+}\mathrm{\Delta }{\mathrm{w}}_{\mathrm{bonds}}{\mathrm{R}}_{\mathrm{B}},_{\mathrm{bonds}}\mathrm{)+(}{\mathrm{w}}_{\mathrm{P}},_{\mathrm{stocks}}{\mathrm{R}}_{\mathrm{A}},_{\mathrm{stocks}}\mathrm{+}{\mathrm{w}}_{\mathrm{P}},_{\mathrm{bonds}}{\mathrm{R}}_{\mathrm{A}},_{\mathrm{bonds}}\mathrm{)}$