IIJ-130-STAUB.qxp 4/17/08 4:45 PM Page 1 RENATO STAUB is a senior assest allocation and risk analyst at UBS Global Asset Management in Zurich. renato.staub@ubs.com Deploying Alpha: A Strategy to Capture and Leverage the Best Investment Ideas RENATO STAUB UBS Global Asset Management has sought to improve the efficiency of a fully invested stock portfolio 1 in the context of the Fundamental Law of Active Management (FLAM), which is a cornerstone of modern financial theory. 2 FLAM explains how a portfolio manager s success is tied to his or her level of skill and the way in which it is misapplied to investment decision-making. The relationship between these two factors is expressed as the manager s information ratio the alpha added by the manager per unit of unsystematic risk that he or she takes. By relaxing the long-only constraint and introducing short selling of overpriced securities, investors have the flexibility to pursue an additional source of alpha as part of the portfolio construction process. In developing a solution, the author had three objectives: 1. Examine the premise on which FLAM is based and how information is translated efficiently into alpha. 2. Explore the impact the restriction of information transfer can have on a portfolio s alpha. 3. Determine the effect of gradually unlocking restrictions on a portfolio. THE FUNDAMENTAL LAW OF ACTIVE MANAGEMENT AND THE INFORMATION RATIO FLAM deals with the efficiency of an active portfolio, while the active portfolio is defined as the difference between a strategy and its benchmark. Since the active portfolio is a package of long and short positions that add up to $0 under conventional circumstances, it does not necessarily deliver a positive return, not even in the long run, unless the portfolio manager has some skill. According to FLAM, the information ratio (IR) from stock selection will increase with the square root of breadth (n) available: IR=IC n (1) The IR is the measure of choice for judging the value added from the active portfolio s stock selection. Breadth is the number of independent bets available to the manager. Breadth is exploited by over- and underweighting selected stocks and hedging the resulting net market exposure with futures. The first crucial conclusion is that a benchmark universe of n stocks entails n bets as long as each stock has some unsystematic risk. It appears that if we could replicate the MAY 2008 A GUIDE TO 130/30 STRATEGIES 1
IIJ-130-STAUB.qxp 4/17/08 4:45 PM Page 2 behavior of one or more stocks with stocks in the benchmark, the number of available bets would be less than n. However, this is not the case in practice. 3 THE CORRELATION BETWEEN FORECASTING AND REALIZATION Good analysts provide return expectations for stocks that are correlated with their eventual performance. 4 The correlation between the prediction and actual results is called the information coefficient (IC). Usually, the IC is not large, even for good analysts. However, if a team of analysts covers many stocks, a small correlation will prove sufficient to translate their bets into a sizable added value. This outcome is well illustrated by the casino analogy of Grinold and Kahn, in which the odds are just slightly in favor of the house; however, repeated spins of the wheel can translate into a sizable gain, efficiently growing over the years. 5 E XHIBIT 1 Manager Skills Yield Better Results in an Enlarged Universe Information ratio as a function of the universe size and manager skill (IC). Overall, an information coefficient of 0.05 is considered good, while 0.10 is great. 6 Exhibit 1 shows the information ratio as a function of the number of securities within the underlying benchmark universe and the assumed IC. As Exhibit 1 shows, the extension of the universe improves the value a manager can add even those managers with a lesser skill set (exemplified by the IC line of 0.01). Managers with a higher information coefficient can exploit the additional opportunity set accordingly, as shown by the top line in the chart. Since signals can be normalized, we conclude that they are in their relevant form as much negative as positive, in terms of both frequency and magnitude. Normalized signals will help create an active portfolio that is balanced in terms of positive and negative positions over the long run. For example, Exhibit 2 illustrates two scenarios: 2 DEPLOYING ALPHA: A STRATEGY TO CAPTURE AND LEVERAGE THE BEST INVESTMENT IDEAS MAY 2008
IIJ-130-STAUB.qxp 4/17/08 4:45 PM Page 3 E XHIBIT 2 Two Allocations a Comparison vs. FLAM Allocation consistent and inconsistent with FLAM. The symbol t represents a discrete point in time when a portfolio is reallocated (e.g., monthly, yearly, etc.); t+1, t+2 and t+3 is that particular point in time plus one, two or three time units. The signal bar reflects the signals determined by the analysts. Allocation 1 is consistent with FLAM. That is, the positions are strictly proportional to the signal. Allocation 2 does not comply with FLAM. That is, the positions are not proportional to the signal. A long-only portfolio, where an investment manager could not act upon the negative signals with an allocation that fully reflects the signals, would adversely impact the potential information ratio of an investment manager. It is clear from this discussion that unconstrained longshort investing in the active portfolio 7 is a necessary prerequisite of FLAM. CONSTRAINING THE ALLOCATION RULE Now consider the hypothetical and, admittedly, unusual case in which a strategy portfolio must not have underweights, and thus the active portfolio cannot tolerate short positions. If the portfolio manager is prevented from underweighting, he can make only half as many bets as he could were he not constrained. 8 With the alpha potential cut in half, and all other assumptions unchanged, the tracking error resulting from the aggregated unsystematic stock risks is reduced by a factor of 2, as is the information ratio. (Tracking error is the risk of the active portfolio.) Exhibit 3 shows the information ratio as a function of the number of securities in the underlying benchmark. As you can see: The long-only curve provides investors the potential to achieve an information ratio of 0.35 for a portfolio of 100 securities and of 0.77 for a portfolio of 500 securities. The long/short curve provides investors the potential to achieve an information ratio of 0.50 for a portfolio of 100 securities and of 1.12 for a portfolio of 500 securities. MAY 2008 A GUIDE TO 130/30 STRATEGIES 3
IIJ-130-STAUB.qxp 4/17/08 4:46 PM Page 4 E XHIBIT 3 Efficiency of Long/Short and Long-Only Curves Efficiency (value added) for a long/short and a long-only portfolio, given an information coefficient of 0.05. While the inability to underweight securities is theoretical, it is in practice more relevant than one may imagine. For instance, consider the composition of the Russell 1000 Index: Only 100 stocks have a benchmark weight of more than 0.20%. 84% of the stocks have a benchmark weight of less than 0.13%. This suggests that a traditional long-only strategy cannot have any meaningful underweights for most positions; that is, an investment manager cannot fully exploit the signals. Exhibit 4 illustrates the benchmark weights for the securities in the Russell 1000 Index. Clearly, a portfolio that is not able to short overpriced securities at the usual levels of predicted tracking error combined with the strongly skewed weight distribution of the underlying benchmark (such as the Russell 1000 Index) is limited in its ability to provide alpha. Overall, the active portfolio based on the Russell 1000 Index proves to be much closer to the dark line in Exhibit 3 than to the long-short case. To illustrate, let us examine Exhibit 5, which reflects a simulation of the implementation of the signals for a portfolio benchmarked against the Russell 1000 Index. In this example, we have identified the 60 strongest positive and the 40 strongest negative signals and have translated them into active positions. The exhibit reflects the 60 strongest positive signals (medium shaded area) and the 40 strongest negative signals (darkest shaded area). The lightest shaded area reflects the remaining 900 stocks, where the investment manager took negative benchmark positions. In a long-only portfolio, none of the 40 negative positions could be implemented because the suggested positions exceed their respective benchmark weights (illustrated as the shaded area in the chart), discarding the opportunity to capitalize on the strongest negative signals. 4 DEPLOYING ALPHA: A STRATEGY TO CAPTURE AND LEVERAGE THE BEST INVESTMENT IDEAS MAY 2008
IIJ-130-STAUB.qxp 4/17/08 4:46 PM Page 5 E XHIBIT 4 Skewed Weight Distribution Makes Meaningful Underweights Difficult Benchmark positions of the Russell 1000. UNLOCKING CONSTRAINTS A SIMULATION To improve the information ratio of an equity portfolio, we recommend keeping the portfolio fully invested while unlocking the short constraint. As a result, the entire portfolio goes 100% + Δ% long; 9 and Δ% short That is, the portfolio can go 130% (140%, 150%, etc.) long and 30% (40%, 50%, etc.) short. As the following simulation demonstrates, such a portfolio is superior to a standard 100% long portfolio. Since no closed-form solution exists, we present a simulation to determine the resulting information ratios for various degrees of leverage: The simulated portfolio is benchmarked against the Russell 1000 Index, and the stock analysis covers 400 stocks. We do not invest in stocks that are not covered by our research team or in stocks with weak signals, keeping positions at zero (equal to their negative benchmark positions in the active portfolio). We simulate 400 signals (that is, one for each covered stock s unsystematic returns). The correlation between each stock and its signal its information coefficient is set to 0.05. Then we select, in line with the overall long bias of the portfolio, the 60 strongest and 40 weakest signals and translate them proportionally as laid out by FLAM into active positions. And finally, we rescale the positions in order to achieve the desired amount of short exposure. Overall, there are four possible reasons for any stock position in the active portfolio: 1. The signal is positive, thus take a positive position. 2. The signal is negative, thus take a negative position. MAY 2008 A GUIDE TO 130/30 STRATEGIES 5
IIJ-130-STAUB.qxp 4/17/08 4:46 PM Page 6 3. The stock is not covered; take a negative benchmark position. 4. The signal on the stock is too weak; take a negative benchmark position. Exhibit 5 illustrates these different positions. Exhibits 6, 7, and 8 show the resulting tracking error, alpha and information ratio for various degrees of leverage. All portfolios have a net market exposure of 100%. With rising leverage, the imbalance between the average size of the long positions and the short positions has an increasing impact on the tracking error. In other words, the tracking error grows at an increasing rate, while the portfolio s alpha increases linearly. Hence, the information ratio in the simulation levels off as we increase the number of securities held long and short (see Exhibit 8). A 100/0 portfolio offers an alpha of 2.4%, and a 130/30 portfolio has an alpha of 4%. E XHIBIT 5 Allocation Example for Russell 1000 Allocation of a selected simulation run. The fact that the tracking error is somewhat larger for the 130/30 portfolio is almost irrelevant, because the tracking error is uncorrelated with the benchmark and is therefore diversified. 10 This does not perceptibly affect the total portfolio risk. To interpret the results, consider the following examples. Assume an information coefficient of 0.05 and a breadth of 1,000, which results in IR = 0. 05 1000 = 1. 58 (1a) Again, the necessary assumption is that there is one signal for each stock. And since there is a zero chance that a signal equals zero exactly, the corresponding active portfolio has 1,000 long and short positions. i) Next, assume an information coefficient of 0.05 and a breadth of 60, which results in 6 DEPLOYING ALPHA: A STRATEGY TO CAPTURE AND LEVERAGE THE BEST INVESTMENT IDEAS MAY 2008
IIJ-130-STAUB.qxp 4/17/08 4:46 PM Page 7 E XHIBIT 6 Tracking Error Grows as Leverage of Portfolio Increases In a long-only portfolio with zero short positions, the tracking error will be just over 4.0%. However, in a 130/30 portfolio where the signals are interpreted for the manager to go 130% long and 30% short, while maintaining a net market exposure of 100% the tracking error grows to 5.5%. The tracking error rises to 9.5% once the portfolio is 200% long and 100% short. IR = 0. 05 1000 = 0. 39 (1b) ii) And finally, let us consider the resulting information ratio for the case 100/0 in Exhibit 8. It is based on 60 long bets. According to the chart, the simulation provides: IR = 0.59 (2) Why does (1b) not equal (2), although both cases are based on 60 stock positions? The reason is that, although we implement the same number of stock positions, the two scenarios are not identical. Advantages of i) over ii): ii) excludes short bets, 11 while i) allows both long and short bets. ii) is subject to noise due to the permanent negative bets for stock 401 to 1,000. Advantage of ii) over i) i) always makes long and short bets on the same 60 stocks, while ii) selects the 60 stocks with the strongest positive signal from a universe of 400 stocks. That is, the subset of the 60 selected stocks continuously changes its composition. We literally skim the cream. It turns out that the advantage of ii) over i) outweighs the advantage of i) over ii). CAPITALIZING ON ALPHA AND BETA Asset managers can more fully exploit the complete range of investment opportunities when the long-only constraint is relaxed and overpriced securities can be sold short. Once managers are free to pursue additional sources of alpha, they can improve the efficiency of a stock portfolio. The following example demonstrates the practical advantages of a long-short equity strategy. MAY 2008 A GUIDE TO 130/30 STRATEGIES 7
IIJ-130-STAUB.qxp 4/17/08 4:46 PM Page 8 E XHIBIT 7 Alpha Rises with the Implementation of Bigger short Signals Alpha rises as the manager translates the signals into bigger positions in the portfolio. In a portfolio consisting of 100% long positions and no shorts, alpha is 2.4%, but it climbs to nearly 8% when the portfolio goes 200% long and 100% short. E XHIBIT 8 Information ration vs. changing portfolio composition Leverage also has a growing effect on each portfolio s information ratio. However, the rate at which the portfolio gains additional alpha per unit of tracking error begins to level off as the long/short portfolio increases its leverage. 8 DEPLOYING ALPHA: A STRATEGY TO CAPTURE AND LEVERAGE THE BEST INVESTMENT IDEAS MAY 2008
IIJ-130-STAUB.qxp 4/17/08 4:46 PM Page 9 E XHIBIT 9 A Long/Short Strategy Can Pursue Alpha in Three Different Ways Source: UBS Global Asset Management. For illustrative purposes only. In a long-only strategy, the asset manager takes long positions in the most underpriced securities (denoted by the purple portion of the graph). In other words, the manager buys stocks that his fundamental research indicates are undervalued. This strategy s alpha potential is realized when stocks rise to their fair market values. In an absolute short strategy, the asset manager can act more effectively on the conviction that a security is overpriced. For example, his research may indicate that the stocks of homebuilders are overvalued. With the flexibility to short securities, he will be free to capture some of the opportunity represented by the orange portion of the graph. For example, the manager will improve the performance of the portfolio if he shorts Homebuilder Stock D and later unwinds the position after the stock s price has declined or appreciated less than the broad equity market. In a pairs trade strategy, the asset manager has the opportunity to extract alpha in two different ways: Pairing moderately mispriced stocks: The manager can add value by selling short a moderately overpriced stock and using the proceeds to buy a moderately underpriced stock. Both stocks are in the gray area of the graph and trade in correlated ways. The manager generates alpha as both stocks move toward their fair value, generating quite significant combined returns. For example, the manager shorts a slightly overvalued stock of an auto manufacturer, and invests into a moderately underpriced auto component company. Isolating insights: Based on a manager s strong conviction in a specific company, a positive insight is MAY 2008 A GUIDE TO 130/30 STRATEGIES 9
IIJ-130-STAUB.qxp 4/17/08 4:46 PM Page 10 juxtaposed with shorts within the same industry, where the aggregate alpha is deemed to be smaller, thus isolating the company-specific alpha of the security held long. For example, within the rail industry, the manager may think that a specific company is attractive but the rail industry fundamentals are not particularly appealing. To take advantage of this insight, he buys the attractive rail company, then shorts a basket of railroad stocks to hedge out the industry exposure. The result of this pair trade is an isolated bet on the attractive companyspecific fundamentals. CONCLUSION To achieve the portfolio efficiency implied by FLAM, we must apply a certain allocation rule. According to this rule, there is no bias for long or short bets. Meanwhile, conventional portfolios prefer long bets, as the maximum underweights are determined by the underlying benchmark position. Consequently, the allocation rule consistent with FLAM is restricted and the resulting efficiency is impaired. By loosening and unlocking the short constraint with a moderate amount of short exposure, we believe we can achieve a sizable increase in portfolio efficiency. Our simulation directly derived from FLAM s underlying theory reveals a significant increase in information ratio versus the corresponding long-only portfolio. For a 130/30 portfolio, it results in an additional alpha of 1.6% versus the corresponding long-only portfolio. The portfolio manager is now free to exploit the full range of investment opportunities. ENDNOTES 1 Fully invested means that the portfolio is 100% invested in dollar terms. However, the resulting beta may still be somewhat different from its neutral value, i.e., from 1.00, depending on the risk profile of the over- and undervalued stocks. 2 Grinold, Richard C. The Fundamental Law of Active Management, Journal of Portfolio Management, Spring 1989, pp. 30 37. 3 Assume, for example, you have a universe of three stocks in which you can perfectly replicate Stock C by a combination of Stock A and Stock B. If you replace Stock C by a combination of Stock A and B, then the universe only contains two stocks A and B. 4 Theoretically, it does not make a difference whether the correlation is positive or negative. An analyst who is consistently wrong is statistically as valuable as an analyst who is consistently right simply do the opposite. Admittedly, this looks suspect in reality. 5 Grinold, Richard C. and Ronald Kahn, Active Portfolio Management. Probus Publications, Chicago, 1999. 6 Grinold and Kahn, p. 272. 7 The active portfolio is the difference between the strategy and its benchmark. 8 For a discussion of portfolio constraints, see Staub, Renato, Are you about to handcuff your information ratio?, UBS Global Asset Management, Working paper, 2005. 9 Δ, the Greek letter delta, describes the difference between the total weight of the long portfolio and 100%. 10 According to our simulation, the tracking error is exclusively the result of unsystematic stock risk. 11 Because it is the 100/0 case, the 40 selected short positions are scaled with 0, and hence wiped out. To order reprints of this article, please contact Dewey Palmieri at dpalmieri@iijournals.com or 212-224-3675 10 DEPLOYING ALPHA: A STRATEGY TO CAPTURE AND LEVERAGE THE BEST INVESTMENT IDEAS MAY 2008