An Integrated Risk-Budgeting Approach for Multi-Strategy Equity Portfolios (Digest Summary)

The authors outline a process for constructing constrained multistrategy alpha capture portfolios. They show how their process can facilitate systematic factor strategies being combined with judgmental strategies and bottom-up stock-picking strategies being combined with top-down sector or country strategies. The authors back test their proposed process by combining multiple alpha capture strategies and demonstrate that constrained portfolios retain many of the same exposures to systematic risk factors as the unconstrained portfolio. Portfolio constraints appear to affect only nonsystematic risk exposures.

Investors who are able to decide their own risk budget allocations to alpha strategies may find the authors’ integrated portfolio framework useful. The framework also can be applied to multi-asset and fixed-income portfolios.

Active portfolio managers may find the advice of the authors noteworthy. They suggest that alphas be captured using constraint-free strategies and that portfolio constraints be dealt with at the level of portfolio construction.

The authors begin by noting that alpha is not equally available to investors because of various portfolio constraints. Common constraints include the investor’s portfolio size and the inability or unwillingness of the investor to take short positions, take positions in relatively illiquid stocks, or take positions in non-socially responsible stocks. Thus, the authors argue that an optimal alpha capture strategy should consider an individual’s portfolio size and constraints. They suggest that investor-level constraints can lead to suboptimal alpha capture strategies if investors simply invest in a portfolio of passively managed index funds (smart beta funds) that implement “off-the-shelf” active strategies.

To address this concern, the authors propose an integrated approach to constructing a single portfolio that combines different alpha capture strategies and investor constraints. The first step in constructing the portfolio begins by allocating a risk budget to each alpha strategy in the portfolio, which defines how alpha strategies are combined to form an optimal unconstrained target portfolio allocation. Then, a constrained optimal portfolio can be derived from the unconstrained optimal allocation by estimating its implied stock returns and using them as inputs in a constrained mean–variance optimization. The implied returns, calculated as the product of the variance–covariance matrix and the active weights, are the stock returns that render the underlying allocation optimal in the absence of constraints.

The authors back test their process using two years of historical weekly returns on all the stocks in the EURO STOXX 50 Index. They create an active portfolio by overlaying three active strategies (value, momentum, and size) and an arbitrary judgmental strategy (long all stocks that begin with the letter A, short all other index stocks) on the EURO STOXX 50 stocks. A comparison of the unconstrained optimal portfolio with three different constrained portfolios reveals that the systematic risk exposures in the constrained portfolios are relatively close to those in the unconstrained optimal portfolio. That is, portfolio constraints serve to affect nonsystematic risk exposures but minimally affect systematic risk exposures. A second backtest that overlays four active strategies (value, momentum, low risk, and size) on the MSCI World Index over a longer time period yields similar findings.

The point made by the authors that investor-level constraints can often lead to suboptimal alpha capture strategies used by passively managed index funds is interesting. The authors’ portfolio construction process may be appealing to sophisticated institutional investors, but it may prove too challenging for active retail investors to implement.