We show that the probability of risk parity beating any other portfolio is more than 50 percent. We also prove that if portfolio performance is measured by Sharpe ratio, risk parity is the only maximin portfolio when (1) all assets' future Sharpe ratios are greater than an unknown constant and...

This paper offers theoretical, empirical, and simulated evidence that momentum regularities in asset prices are not anomalies. Within a general, frictionless, rational expectations, risk-based asset pricing framework, riskier assets tend to be in the loser portfolios after (large) increases in...

We take a deeper look at the robustness of evidence presented by Pastor, Stambaugh, and Taylor (2015) and Zhu (2018), who find that an actively managed mutual fund's returns relate negatively to both fund size and the size of the active mutual fund industry. When we apply robust regression...

We propose an improved formulation for the widely used active share metric. The new definition is derived analytically and then tested by empirical analysis. We explain why the active share metric, in its current form, gives ambiguous results. The improved formulation is consistent across...

This paper identifies a clear tradeoff between tracking error — performance differences relative to a targeted asset allocation — and turnover—a proxy for rebalancing costs — that can help guide investors’ rebalancing choices. We find that calendar-based approaches, while convenient,...

Three concepts: stochastic discount factors, multi-beta pricing and mean-variance efficiency, are at the core of modern empirical asset pricing. This chapter reviews these paradigms and the relations among them, concentrating on conditional asset-pricing models where lagged variables serve as...

This chapter provides a perspective on the rapidly developing literature on investment performance evaluation. I use the stochastic discount factor approach to present and critique current performance measurement techniques in a unified setting. I offer a number of suggestions to improve...