Kenneth N. Levy

Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions

This paper presents fast algorithms for calculating mean-variance efficient frontiers when the investor can sell securities short as well as buy long, and when a factor and/or scenario model of covariance is assumed. Currently, fast algorithms for factor, scenario, or mixed (factor and scenario) models exist, but (except for a special case of the results reported here) apply only to portfolios of long positions. Factor and scenario models are used widely in applied portfolio analysis, and short sales have been used increasingly as part of large institutional portfolios. Generally, the critical line algorithm (CLA) traces out mean-variance efficient sets when the investors choice is subject to any system of linear equality or inequality constraints. Versions of CLA that take advantage of factor and/or scenario models of covariance gain speed by greatly simplifying the equations for segments of the efficient set. These same algorithms can be used, unchanged, for the long-short portfolio selection problem provided a certain condition on the constraint set holds. This condition usually holds in practice.

Long-Short Portfolio Management: An Integrated Approach

With the freedom to sell short, an investor can benefit from stocks with negative expected returns as well as from those with positive expected returns. The authors explain that the benefits of combining short positions with long positions in a portfolio context, however, depend critically on the way the portfolio is constructed. Only an integrated optimization that considers the expected returns, risks, and correlations of all securities simultaneously can maximize the investors ability to trade off risk and return for the best possible performance. This holds true whether or not the long–short portfolio is managed relative to an underlying asset class benchmark. Despite the incremental costs associated with shorting, the authors argue that a long–short portfolio, with its enhanced flexibility, can be expected to perform better than a long–only portfolio based on the same set of insights.

Financial Market Simulation

When they want to see how complex systems work, scientists often turn to asynchronous-time simulation models, which allow processes to change sporadically over time, typically at irregular intervals. While rarely used in finance today, such models may turn out to be valuable tools for understanding how markets respond to changes in the participation rates of different types of investors, for example, or to changes in regulatory or investment policies. The asynchronous, discrete-event, stock market simulator described here allows users to create a model of the market, using their own inputs. Users can vary the numbers of investors, traders, portfolio analysts, and securities, as well as their own investing and trading decision rules. Such a simulation may be able to provide a more realistic picture of complex markets.

Enhanced Active Equity Strategies

Enhanced active equity investing relaxes the long-only constraint by permitting short sales, while maintaining full exposure to equity market return and risk. The enhanced active equity approach is facilitated by modern prime brokerage structures that allow investors to use the proceeds from short sales to purchase long positions. Freeing equity portfolios from the long-only constraint can enhance performance by permitting meaningful underweight positions that are simply not achievable in long-only portfolios. The investor can thus more fully exploit security valuation insights.

The Long and Short on Long-Short

By balancing long positions in equity with short positions of roughly equal dollar amount and market sensitivity, it is possible to construct a portfolio whose return is neutralized against overall market moves. Properly constructed, using an integrated optimization process, a long-short portfolio offers advantages over long-only portfolios in enhanced flexibility to pursue return, control risk, and allocate assets. Any additional costs do not outweigh the benefits of such a strategy.

The complexity of the stock market

The stock market is a complex system, somewhere between the domains of order and randomness. Ordered systems are simple and predictable, and random systems are inherently unpredictable. Simple theories do not adequately describe security pricing, nor is pricing random. Rather, the market is permeated by a web of interrelated return effects. Substantial computational power is needed to disentangle, model, and exploit these return regularities.

Enhanced Active Equity Portfolios Are Trim Equitized Long-Short Portfolios

Investors considering the new enhanced active equity strategies such as 120–20 or 130–30 often ask how these strategies differ from equitized long-short strategies (market-neutral long-short with an equity overlay). Examination of the relation between enhanced active equity and equitized long-short portfolios demonstrates that the two can be shown to be equivalent, but the enhanced portfolio has the advantage of being more compact and requiring less leverage.

Alpha Transport With Derivatives

Derivatives can be used to transport the alpha from a managers selection of securities to virtually any desired asset class benchmark. The authors demonstrate that, by liberating the security selection return from the asset class return, alpha transport allows investors to find the best opportunities in both asset allocation and security selection. They also show how long-short portfolio construction can further enhance return by allowing managers to pursue the best investments in both “winning” and “losing” securities.

Leverage Aversion and Portfolio Optimality

Portfolio volatility is the only source of risk in mean-variance optimality, but it fails to capture all the risks faced by leveraged portfolios. These risks include the possibility of margin calls and forced liquidations at adverse prices and losses beyond the capital invested. To recognize these risks, the authors incorporated leverage aversion into the optimization process and examined the effects of volatility and leverage aversion on optimal long-short portfolios.

High-Definition Style Rotation

That various “styles” of stocks perform differently suggests a strategy of rotating a portfolio’s allocations across styles — growth, value, large-cap, and small — in line with changes in the economic environment. The issue then is how to define style. A “high-definition” approach looks at many stock attributes to disentangle the effects of each. Because the approach results in a detailed map of returns to stock attributes, it offers potential to provide better returns than those of naive style rotation strategies.