Bruce I. Jacobs

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.

Risk Avoidance and Market Fragility

Products that promise protection from the risks of investing can contribute to market fragility. The era of “stocks for the long run” is over. Risk, dormant through much of the 1990s, has been rediscovered, and there is no shortage of experts willing to share their wisdom on how to stomp it out. But is there such a thing as being “too safe”? When products purporting to “insure” against declines in broad financial markets attract large numbers of investors, the financial institutions offering such products are exposed to significant amounts of systematic risk. They frequently control their exposure to this risk by purchasing options or by replicating options via dynamic hedging, buying the underlying asset as its price rises and selling as its price falls. The dealers from whom options are purchased control their own exposure by either buying options or replicating them. Financial institutions’ ability to “insure” themselves against the insurance products they have sold is thus dependent on the presence of counterparties willing to sell them options or, equivalently, to take the other side of their dynamic hedging trades. As more and more investors demand insurance, however, insurers may face increasing difficulty in finding counterparties. Furthermore, more insuring is likely to lead to more trend-following dynamic hedging, which can exacerbate market volatility. As volatility increases, the demand for insurance may increase, heightening the demand for options and thus the amount of option-replicating trades, leading to even greater market volatility. When market prices fall, the selling required to replicate an option on the market may overwhelm the willingness of other market participants to buy, creating a liquidity crisis. In such an event, the trades needed to replicate options will not get off at the prices required to guarantee the insured value and the trades will have to be executed (if at all) at much lower prices. The “insurance” can fail. When that insurance underlies the insurance products sold by a financial institution, those products, along with the institution itself, can fail. What is more, because of the linkages between counterparties, one institution’s failure can lead to systemic failure and broad economic disruption. Insurance products have taken financial markets to the brink before, in the 1980s with portfolio insurance and in the 1990s with the collapse of Long-Term Capital Management (LTCM). In both cases, the market could not accommodate the amount of trading required to “insure” supposedly “riskless” products. Market prices gapped discontinuously. Insured investors could not get their trades off at the prices required to guarantee the insured values. Thus, portfolio insurance failed to provide the promised protection. LTCM incurred substantial losses on trades that had been designed to be relatively riskless. Furthermore, the aftershocks of the portfolio insurance and LTCM debacles were felt globally. In both 1987 and 1998, markets effectively had to be bailed out by the U.S. Federal Reserve Board, which provided liquidity in the wake of both crises and also orchestrated the rescue of LTCM in 1998. With traditional insurance, risk of loss is essentially shared by many policyholders, with the insurance provider acting as intermediary. Those who buy “insurance” against a stock market decline, however, are really shifting this risk onto the insurance provider. But who is the risk bearer of last resort? It may be the taxpayer, if the government decides that the firms that offered these products are “too big to fail.” Often, it is investors in general who bear the risk, in the form of the substantial declines in prices that are required to entice risk bearers back into the market. Ironically, products designed to reduce financial risk can end up creating even more risk.

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.