Risk Budgeting, Parameter Uncertainty,and Risk Realizations

Abstract

Risk budgeting is a process by which investors make asset allocation decisions subject to a portfolio-to-benchmark tracking error constraint. We use simulations of multi-asset class portfolio returns to compare risk budgeting outcomes in two contexts: a world in which the parameters of the distribution of asset returns are known (parameter certainty) and one in which those parameter values vary from evaluation period to evaluation period (parameter uncertainty). Even under parameter certainty, risk budgets are different from resource budgets in that high tracking error (active return volatility) does not imply a violation of the risk budget. Under the level of parameter uncertainty (variation in the parameters of asset return distributions) observed during the 1976–2004 period, tracking error volatility across simulations is approximately twice as large as is observed under risk certainty. Our results suggest that risk budgeting does not provide an appropriate analytical framework for measuring the realized performance of portfolios or portfolio managers relative to their benchmarks