Biases in Variance of Decomposed Portfolio Returns

Abstract

Significant portfolio variance biases arise when contrasting multi-period portfolio returns based on the assumption of fixed continuously rebalanced portfolio weights as opposed to buy-and-hold weights. Empirical evidence obtained using S&P500 constituents from 2003 to 2011 demonstrates that, compared with a buy-and-hold assumption, applying fixed weights led to decreased estimates of portfolio volatilities during 2003, 2005 and 2010, but caused a significant increase in volatility estimates in the more turbulent 2008 and 2011. This discrepancy distorts assessments of portfolio risk-adjusted performance when inappropriate weight assumptions are employed. Consequently, for individual investors, who in practice often employ buy-and-hold strategy, the portfolio size recommendations required to achieve the most diversification benefits are typically understated.