Abstract
It is often said that the most dangerous words an investor can utter are: “This time it’s different.” Yet, in this article, the author argues exactly that–the tried-and-true quantitative stock-selection strategies, such as value and momentum (or at least the simple versions of these strategies), which have been very successful for many years, are unlikely to add much value going forward after adjusting for risks, fees, and trading costs. Before the article culminates with this conclusion, however, the author presents both sides of the argument, analyzes the data from new angles, and provides several reasons why it really might be different going forward before concluding with several suggestions for how managers can help add alpha in the future.
It is often said that the most dangerous words an investor can utter are: “This time it’s different.” Yet in this article I will argue exactly that—the tried-and-true quantitative stock-selection strategies that have been very successful for many years, value and momentum (or at least the simple versions of these strategies), are unlikely to add much value going forward after adjusting for risks, fees, and trading costs. Before the article arrives at this conclusion, however, I will present both sides of the argument, analyze the data from new angles, and provide several reasons why it really might be different going forward. Finally, I will offer several suggestions for how managers can help add alpha in the future.
A WATERSHED: AUGUST 2007
In August 2007, many common quant factors experienced simultaneous declines (and later rebounds) of an extraordinary magnitude relative to their prior volatilities. These synchronized moves occurred within factors and regions that had historically been uncorrelated.
Exhibit 1 shows the results for four well-known factors (value, momentum, accruals, and revisions) in four major regions—the U.S., the U.K., Japan, and Europe. Long-term correlations between these factors show that these strategies have historically shown very little correlation. During a two-week period in August 2007, however, they all moved in sync and by huge magnitudes relative to their prior volatilities. As a result, many leveraged quant funds experienced huge losses, some had margin calls, and more than a few closed down.
Exhibit 1
Popular Quant Factors Declined and Rebounded in Sync, August 2007
This type of sharp decline and subsequent snapback is characteristic of a liquidity event. The consensus explanation (with which I agree) is that quant selling pressure—possibly driven by margin calls, redemptions, and a “prisoner’s dilemma”1—led to sharp declines early in August 2007 with prices rebounding to fair value once the artificial selling pressure ended.2 Further, the liquidity pressure hit quants in many markets at virtually the same time, perhaps driven by quants who managed assets globally and who were forced to simultaneously liquidate their positions in multiple markets. The net result was that quant strategies proved to be much more volatile and highly correlated than they had ever been in the past.
THE STICKERS VERSUS THE ADAPTERS
The key question, of course, is what does this bode for the future? One group, who we can call the Stickers, believes that this was a unique event that should have little impact on their investment process. The other group, who we can call the Adapters, believes that August 2007 was the manifestation of a problem that had been growing for years, namely, quant crowding, or quantcentration. According to the Adapters, successful quants will need to revamp their processes, perhaps drastically, or be subject to lower returns and higher volatilities going forward. In the next subsections, I will present the arguments made by both sides, although I fall firmly in the Adapters’ camp.
The Stickers’ Case
Although the August 2007 crisis period was clearly harrowing, the net result was rather tame. After the liquidity pressure abated and prices snapped back, results for the month as a whole were hardly notable; there was no real, permanent economic impact. Thus, true long-term investors should not be concerned by nonfundamental price swings. Instead, long-term investors should view any liquidity-driven pressure as a buying opportunity. Stickers believe investors who stick to their guns will be amply rewarded, as they have historically been.
Stickers also often argue that quant strategies and market anomalies are based on pervasive human behavioral biases (e.g., overconfidence or over- and underreaction) that change only at the glacial pace of human evolution. Thus, these behaviors and biases, and the investment strategies and anomalies they drive, are likely to persist for the foreseeable future.
Finally, Stickers often point to the long-term results shown in Panel A of Exhibit 2 (value) and Panel B of Exhibit 2 (momentum) that show the cumulative returns to value (HML) and momentum (WML) over time. HML represents the return on a high-minus-low book-to-price (value) portfolio; WML represents the return on a winners-minus-losers (momentum) portfolio based on prior year returns. The portfolios are constructed to be independent of each other and of market capitalization. For the exact calculation methodology, see the Kenneth French Data Library at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french.
Based on these results, both strategies provide long-term information ratios (IRs) that exceed those of stocks, bonds, real estate, or just about any other asset class. In addition, neither strategy seems to show any significant recent deviation from the long-term trend. In the case of value (HML), as illustrated in Panel A of Exhibit 2, the recent dip is notable, but certainly no worse than during the Internet bubble of 1998–2000 or numerous other dips. In all of the other episodes, the strategy rebounded and continued its long-term positive trend, so there is no reason to expect the same will not happen again. In the case of momentum (WML), as illustrated in Panel B of Exhibit 2, recent results actually look better than the long-term trend, with no indication that the graph is flattening out. In fact, there is only one instance, in 1932, when the graph takes more than a year or two to recover from a decline, but after 1932, it took almost 20 years to recover!
Exhibit 2
Cumulative Returns of Value and Momentum, July 1926–December 2008
The Adapters’ Case
The Adapters argue that, although prices recovered after the liquidity crunch in August 2007, the liquidity pressure itself is evidence of crowding. If a greater percentage of investment dollars is being devoted to quant strategies, the expected returns on those strategies are likely to decline, regardless of how pervasive behavioral biases may be in the remaining investor population. That is, as more and more money chases the same anomalies, prices will adjust and the returns on those strategies will decline. Further, to the extent that quant investors follow similar strategies in each region, the correlations and volatilities of those strategies should increase, both within and across regions. Thus, the expected IRs for those strategies should be much lower than they historically have been. Smart investors will, therefore, reduce the amount of risk they allocate to these common strategies, perhaps to zero.
Exhibit 3 shows the U.S. assets under management (AUM) for select quant managers as a percentage of the value of the Russell 3000 Index; note that the graph’s trend is more important than its levels. Clearly, quants became an increasing percentage of the market over the past decade. In addition, since quants usually pursue higher-turnover strategies, their impact on pricing may have been even greater than the graph indicates. Quant crowding has become an increasing problem in recent years. In addition, even though the trend has been down since late 2006, the level still remains well above where it was earlier in the decade. Thus, Adapters would argue that investors ought to continue to monitor quant crowding to assess its impact on pricing.
Exhibit 3
Quants Have Increased as a Percentage of the Market over the Past Decade, March 1999–December 2008
A CLOSER LOOK AT THE DATA
In this section, I will examine the data from several new angles.
Value and Momentum for Large-Cap Stocks
Adapters would also argue that many long-term graphs, such as Exhibit 2, are misleading because they exclude transaction costs, even though the strategies may have rather large positions in relatively illiquid securities. Because the poor performance of many popular quant strategies in August 2007 was the result of a liquidity crunch in quant stocks, excluding trading costs can seriously overstate the likely returns to these strategies, especially in periods of acute distress. In this subsection, I will explore the performance of these strategies in the more liquid U.S. large-cap universe.
Exhibit 4 compares the performance of value (HML) and momentum (WML) strategies for U.S. large-cap stocks to the performance of the full universe. Panel A of Exhibit 4 shows the results for value (HML). As highlighted by the dashed lines, value has been in a cyclical pattern among large-cap stocks, with no secular uptrend, since 1981. Such a pattern is indicative of a risk factor rather than an anomalous alpha source. Over the last 30 years, to add value with a value strategy, even gross of trading costs (t-costs), investors would have had to focus primarily on smaller, illiquid stocks, exactly the types of names for which t-cost adjustments are likely to prove fatal, at least at institutional (high) levels of AUM.
Exhibit 4
Cumulative Returns of Value and Momentum Strategies for U.S. Large-Cap Universe and Full Universe, July 1926–December 2008
Panel B of Exhibit 4 shows a similar graph for momentum (WML). In this case, results have been trending up among large-cap stocks in recent years, but with a flattening slope. In addition, because momentum involves higher turnover than value, when adjusted for t-costs, this modest uptrend could easily disappear.
Finally, it is interesting to note that the flattening trend (at least among large-cap stocks) coincides with the advent of cheap computing power and increasing electronic data availability in the late 1970s and early 1980s. This provides indirect evidence that the discovery and exploitation of these anomalies by large groups of investors can lead to their demise.
Explicit Adjustments for Trading Costs
Although confining our backtests to liquid stocks gives us a better sense for how these strategies might work in real portfolios, it would be even better to actually estimate the relevant trading costs and deduct them from portfolio returns. The Fama–French data for HML and WML, which go back to 1926, do not provide sufficient data on portfolio holdings and characteristics to perform this type of analysis. A good indication is available, however, using Goldman Sachs Asset Management (GSAM) data, which have daily frequency going back to 1987. Of course, the impact of trading costs will depend on the size of the portfolio, as well as the liquidity of the underlying stocks, the strategy turnover, and so on. Panels A and B of Exhibit 5 compare the performance of the value and momentum strategies both gross and net of t-costs.3
In order to determine the results net of t-costs, I assumed two different portfolio values: 1) a low-AUM portfolio that starts at $10 million and ends at roughly $50 million (gross), and 2) a high-AUM portfolio that starts at $2 billion and ends at roughly $10 billion (also gross). To begin, I excluded t-costs from these “optimal” portfolios. Thus, except for their asset values, the portfolios are identical long–short portfolios that maximize exposure to either value or momentum subject to an annual volatility target of 5%. Next, I deducted estimated t-costs from gross returns using a standard t-cost model, in which assumed trading costs are a function of the stock’s liquidity (as measured by volatility and bid–ask spread) and of the trade size relative to the stock’s actual trading volume on the trade date. The average annual turnover was 235% for the optimal value portfolio and 393% for the optimal momentum portfolio.
Exhibit 5
Backtested Cumulative Daily Returns to Optimal Portfolio, February 1987–December 2008
As shown in Panel A of Exhibit 5, the value factor does quite well on a gross basis, but barely covers t-costs in a low-AUM portfolio and is devoured by t-costs in a high-AUM portfolio.4 Panel B of Exhibit 5 shows similar results for momentum. The low-AUM portfolio does slightly better than the low-AUM value portfolio, but results are just as dismal, if not more so, for the high-AUM momentum portfolio. Thus, the stellar long-term results disappear once t-costs are deducted at an institutional level of AUM.
Including T-Costs in the Optimization Process
Hold on, the Stickers might say; the portfolios created in Exhibit 5 did not include t-costs in the optimization process. Thus, the optimizer did not worry about the costs of trading these names, but simply tried to maximize the gross exposure to value or momentum subject to a risk budget. If estimated t-costs were included, the optimizer would make smarter choices, likely producing a portfolio that had lower turnover and contained more liquid names. In addition, the high-AUM portfolio should have lower turnover and contain more liquid stocks than the low-AUM portfolio.
Exhibit 6, Panel A, shows the t-cost–optimized results for value, both gross and net of t-costs, for low and high levels of AUM. The average annual turnover for the low-AUM portfolio was 140% and for the high-AUM portfolio was 89%. The net results look more promising than Exhibit 5, Panel A (and how could they not?), but are still roughly flat for the high-AUM portfolio over the 21-year period with an IR of 0.08, net of assumed t-costs, but gross of fees. Value did have some nice runs in 1991–1995 and 2001–2006 that convinced many quants the strategy continued to “work” despite its popularity in many quant models. In retrospect, however, this graph looks a lot like the liquid-stocks version of value in Exhibit 5, Panel A; that is, more like a cyclical risk factor than a secular alpha anomaly.
Exhibit 6, Panel B, shows the t-cost–optimized results for momentum. Annual turnover for the low-AUM portfolio was 254% and for the high-AUM portfolio was 174%. In this case, the net results are a bit more promising, producing a net IR of 0.42 over the period (net of assumed t-costs and gross of fees), even at high AUM. A closer look, however, reveals that results have been roughly flat (at high or low AUM) since the mid 1990s, with an IR of 0.08 post-1996. Interestingly, this flattening occurred shortly after momentum was “discovered” in the academic literature.5 Could it be that discovery and exploitation lead to diminished alphas, even if the majority of investors remain irrational and predictably biased? The Adapters would answer with a resounding yes.
Exhibit 6
Adding T-Costs to the Optimization Process Detracts from Long-Term Results, February 1987–December 2008
Exposure Decay in T-Cost Optimized Portfolios
The ideal factor portfolio (IFP) is the portfolio an investor would hold at any given time in the absence of trading costs. It is the minimum-risk long–short portfolio that has unit exposure to the most current factor values. Once t-costs are added to the objective function, the t-cost–optimized portfolio will no longer equal the IFP or solely reflect the most up-to-date factor values. Including t-costs in the objective function improves the portfolio’s expected net IR, but also prevents the optimal portfolio from immediately reflecting the latest factor realizations. Thus, an optimal portfolio that considers t-costs will have exposure to both the current IFP and “lagged” IFPs (i.e., those created using factor values when the stock originally entered the portfolio and, due to t-costs and risk, may still be in the portfolio). When t-costs are small, as in a low-AUM portfolio, the portfolio will have relatively more exposure to the current factor values compared to lagged factor values. Conversely, when t-costs are large, as in a high-AUM portfolio, the portfolio will have relatively more exposure to lagged factor values compared to current factor values.
Exhibit 7, Panel A (value) and Panel B (momentum), show partial correlations between optimized portfolios and various lagged IFPs for 1) an optimized portfolio that does not consider t-costs (i.e., the current IFP), 2) a low-AUM t-cost–optimized portfolio, and 3) a high-AUM t-cost–optimized portfolio. These results are averaged across time, starting 120 trading days after the backtest start date in February 1987.
As shown in Exhibit 7, the portfolios optimized without considering t-costs have 100% exposure to the current IFP (latest factor values) and no exposure to lagged IFPs and factor values. Once t-costs are added, however, declining exposures to current IFPs and factor values and increasing exposures to lagged IFPs and factor values are detected. These results are more acute for high-AUM portfolios and for higher-turnover strategies (i.e., for momentum relative to value). Note that the graphs in Exhibit 7 stop when the lag reaches 120 days, but the portfolios have exposures to IFPs and factor values with even longer lags. Thus, in a realistic portfolio setting (i.e., one that considers t-costs), it is necessary to examine the performance not only of our most current IFPs, but also of lagged IFPs, which still impact t-cost–optimized portfolios.
Return Decay for Lagged Factor Portfolios
Panel A of Exhibit 8 shows a return-decay graph for value. The graph charts the information ratio for IFPs created at different lags, illustrating the impact on performance of holding portfolios with various lagged exposures to value. I divided the full period in half to determine if any changes were apparent in the decay patterns in the later period when quant investing was more popular.
Exhibit 7
Partial Correlations of T-Cost–Optimized Portfolios to Lagged U.S. IFPs for Value and Momentum, February 1987–December 2008
Exhibit 8
Value and Momentum Factor Decay Can Significantly Impact Performance
Exhibit 8, Panel A, shows that if an investor had implemented a value strategy without t-costs in the first half of the test period with no delay (Lag 1, the day after optimization), the portfolio would have generated a gross IR of about 1.75. If the investor had waited 5 days to implement, however, the IR would have dropped to 1.25, with continued decay at longer lags. In addition, the IRs at all lags are smaller in the more recent period and drop to almost zero at a six-month lag (120 trading days). The value strategy thus became less effective in the recent period, while the benefit of timely implementation also declined (i.e., prices respond more quickly to changing factor values); that is, the market has become more efficient with respect to value.
Exhibit 8, Panel B, shows similar results for momentum. In this case, the results are stronger in both periods, but recall that these results are gross of trading costs and momentum is a higher-turnover strategy than value. In addition, the deterioration in performance between the first and second periods is more pronounced. Further, because both value and momentum are less effective in the second period, the recent declines are unlikely to be due to normal cyclical variation in the effectiveness of these factors.
Exhibit 9 shows return-decay graphs for other popular quant factors, such as earnings surprise, estimate revision, accrual, and return reversal. In all cases, and for virtually all lags, the recent period shows diminished results. In some cases, these results are still respectable, but again results are gross of fees and t-costs, and many of these are very-high-turnover strategies. The market has become more efficient (or the opportunities for investors have diminished) with respect to these popular quant factors.
Navigating a Different World
At this point, the Stickers might argue that, although gross IRs have diminished recently, IRs are still competitive with those for equities, commodities, real estate, or bonds. In addition, when diversifying across multiple, uncorrelated factors and regions, the combined IR is likely to be even higher, especially if less-liquid stocks and markets are included. Finally, because most quants use multiple factors, it is unfair to assess an individual factor on an individual, net-of-t-cost basis, because turnover from one factor may be offset by opposing turnover from other factors. Thus, t-cost adjustments should only be applied to net trades in a multifactor setting.
I agree. Although many of these factors will likely be much less effective in the future, they can still add value net of t-costs in a multifactor setting, especially if applied at a low level of AUM and/or with a focus on less-liquid stocks or less-developed markets. But even for managers who focus on developed markets and larger, more-liquid stocks, some popular factors may still play a reduced role. Going forward, however, it will be increasingly difficult for the Stickers to justify full active management fees when all they do is apply static tilts based on well-known and widely used factors. Instead, successful quant managers will need to build more sophisticated models that incorporate less widely known signals, data sources, and implementation techniques, as well as to develop dynamic, factor-timing strategies that take advantage of the heightened volatility of these popular factors.
Exhibit 9
Impact of Decay Rates on Performance of Popular Quant Factors
Now, I must note a few caveats. I am not saying that value and momentum, as concepts, will not work going forward. Instead, I believe that the common definitions of these and other popular factors have lost much of their efficacy. But models that use other, more-proprietary signals or techniques to identify cheap stocks with favorable business momentum should do quite well. Nor am I saying that the common definitions of these popular factors will not have a great run over the next few years. Instead, I believe that investors who look back 10 years from now will not have experienced an acceptable IR (net of fees and t-costs) from a strategy that takes static bets on the most widely known quant signals, at least not in developed liquid markets.
Developing Proprietary Factors
So, if quant investors can no longer rely on well-known factors, such as 12-month price momentum and B/P, to generate alpha, where will they find alpha in the future? Alpha opportunities can only exist when prices do not fully reflect public information. This can only occur when investors over- or underreact to information. In essence, I believe that the value effect is actually an overreaction effect, but that the market no longer systemically overreacts to the information in B/P. Similarly, the momentum effect is due to investor underreaction, but the market no longer systemically underreacts (as much) to the information in 12-month returns.
Quants have made the market more efficient with respect to the information in these simple factors, but they have not eliminated the tendency for investors, in general, to over- or underreact. Investors overreact to information that confirms their prior beliefs and underreact to information that contradicts those beliefs. Thus, the underlying behavioral bias is overconfidence in prior beliefs, which is unlikely to disappear anytime soon. In searching for new alpha sources, the goal is to find relevant information to which investors typically systematically over- or underreact.
A few areas to which investors might look include 1) new, nonelectronic, or less widely known data sources; 2) textual analysis that systematically interprets text-based sources of information; 3) industry-specific data and signals; and 4) information from related companies, such as competitors, clients, and suppliers.
Timing Popular Factors: HML Example
Although I do not expect investors to earn a significant alpha from static tilts on popular factors, it may be possible to time the ups and down of those factors. If so, the heightened volatility of popular factors may actually improve prospects for this alpha source. In fact, if investors can predict the ebb and flow of a strategy’s popularity, they can likely predict the near-term return and risk of that strategy. For instance, as a strategy becomes more popular, the returns to that strategy are likely to be strong, even as the crowding risk increases and the expected return declines.
Using HML as an example, as the value strategy grows more popular and investors buy high-B/P stocks and sell low-B/P stocks, the spread between high- and low-B/P stocks should shrink. Thus, even as the returns to HML improve, the outlook for the strategy worsens as the narrowing spread leaves less room for further shrinkage and more risk that spreads become “too low” and need to widen. Exhibit 10 shows the cumulative returns to HML along with the value (B/P) spread going back to 1926.6 When the spread is wider than average, the subsequent average annualized return to HML is 6.00%, and when it is below average, the subsequent return is 4.11%.
Of course, B/P spreads depend on more than the popularity of value investing. For example, they can be affected by market valuation levels, the relative prospects of high- and low-B/P stocks, changing accounting rules, and technological innovation. Thus, a more sophisticated model would compare actual B/P spreads to “normal” spreads given these other variables. In addition, the popularity of value investing depends on more than just quant crowding; traditional investors pursue a variety of value strategies that can impact relative B/P ratios. Nonetheless, investors can use metrics, such as relative B/P spreads, to help them gauge the outlook for value investing or other popular strategies. Further, by adroitly adjusting exposure to B/P, investors can add timing alpha to their returns.
Exhibit 10
Valuation Spreads and Cumulative Performance of a U.S. Value Strategy, January 1928–December 2008
Finally, note that a timing strategy incurs high turnover (moving in and out of factors), but can often be implemented with more-liquid stocks. In any case, adjusting for t-costs is critical in evaluating any strategy, especially a timing strategy.
ANOTHER SOLUTION: LEVERAGING HUMAN JUDGMENT
Since 1980, when I became a quant, clients have asked, “Once everyone starts using these strategies, won’t their excess returns disappear?” My response has always been, “Yes, but the vast majority of investors still use flawed human judgment to select stocks.” Some time during this decade, however, investors reached a tipping point where quant investing became too popular. I believe that excess returns—properly adjusted for risk, fees, and trading costs—have indeed been diminished for many popular quant strategies. The proper response for a “pure” quant is to develop proprietary factors and/or attempt to time the ups and downs of these popular strategies. An alternative solution is to try to overcome the underlying biases in human judgment.
For example, regardless of whether various behavioral biases are baked into our genes, if, as investors, we are aware of them, we may be able to overcome them. Studies in cognitive psychology show that people have a difficult time simultaneously considering more than two or three factors when making decisions. To overcome this, one approach might be for the portfolio manager to ask analysts to express their opinions or views on a variety of critical investment criteria, such as valuation, business momentum, earnings quality, profitability, financial strength, management, and business risk, and then combine these views into an overall rating using an objective, actuarial approach. Presumably, these “judgmental” factor values could complement purely quantitative factor values by assessing nonquantitative data, overriding misleading data, and accounting for conditional effects and other nonlinearities. These judgmental factor values should also be less crowded. The portfolio manager could use various controls, such as correlation analysis, to make sure analysts are not simply expressing the same views in different guises. Similarly, the portfolio manager could use Bayesian techniques to combine analysts’ judgments with quantitative inputs, seeking to short-circuit any overconfidence imbedded in the analysts’ views. The point is that, going forward, successful investors will need to look beyond simple metrics to find alpha, and human judgment, if properly channeled and chastened, might be one area to explore.
The events of August 2007 made it abundantly clear that quantitative managers are now so pervasive that they can have a profound impact on pricing and returns. Since then, it has been difficult to add value using simple tilts on widely known quant factors. In fact, some of these factors have not added value net of t-costs for quite some time. Even if investors remain biased decision makers, the history of markets is one of ever-increasing efficiency. In this article, I have presented compelling evidence that developed liquid markets are now much more efficient with respect to the information in many simple quant factors. In the future, I believe successful quant managers will need to develop proprietary factors and techniques, such as factor timing or blended quant/judgmental views, to add value in quant strategies.
ENDNOTES
An important group of colleagues in Quantitative Investment Strategies at GSAM have meaningfully contributed to the formation and writing of this article. I would particularly like to thank Katinka Domotorffy, Kent Daniel, Gary Chropuvka, Surbhi Mehta, and Sam Shikiar for their insights on the quantitative landscape of yesterday, today, and tomorrow. Mehmet Bayraktar and Stanislav Radchenko were important contributors with their help in the research process of the article, which included many backtests. Suzanne Escousse, Alyssa Noto, and the marketing team suggested important improvements to the language and layout of the text. The quality of the article and the discussion benefited greatly from the input of this entire group.
↵ 1In a prisoner’s dilemma, all parties would be better off following a common course (not selling), but each individual might be better off following their own course (selling before everyone else does). This led some quants to pile onto the selling pressure even if they had no immediate liquidity needs.
↵ 2See the Goldman Sachs publication “The Quant Liquidity Crunch” for additional details.
↵ 3The value factor is industry-adjusted B/P. The momentum factor is the stock’s 12-month return lagged 1 month and is also industry adjusted. The results assume daily rebalancing, but are qualitatively similar if we assume monthly rebalancing.
↵ 4The net results can be below–100% because in these graphs we sum the daily excess returns, rather than compound them. This approach gives a better visualization of the impact over time (slope), which can be misleading when using compound results (unless graphed on a log scale).
↵ 5We believe that the first widely cited academic article on momentum was Jagadeesh and Titman [1993].
↵ 6The QIS value spread is a metric formulated by the Quantitative Investment Strategies (QIS) team at GSAN to capture the industry-adjusted dispersion in company over- and undervaluations. This strategy was formed based on industry-adjusted B/P metrics. The value strategy is a portfolio that overweights equities with a high B/P (undervalued firms) and underweights equities with a low B/P. We then calculated the return to the portfolio and repeated the process on a monthly frequency. Simulated performance results do not reflect actual trading and have inherent limitations.
Disclaimer This material is provided for educational purposes only and should not be construed as investment advice or an offer or solicitation to buy or sell securities.
The portfolio risk management process includes an effort to monitor and manage risk, but does not imply low risk.
Tracking Error (TE) is one possible measurement of the dispersion of a portfolio’s returns from its stated benchmark. More specifically, it is the standard deviation of such excess returns. TE figures are representations of statistical expectations falling within “normal” distributions of return patterns. Normal statistical distributions of returns suggests that approximately two thirds of the time the annual gross returns of the accounts will lie in a range equal to the benchmark return plus or minus the TE if the market behaves in a manner suggested by historical returns. Targeted TE therefore applies statistical probabilities (and the language of uncertainty) and so cannot be predictive of actual results. In addition, past tracking error is not indicative of future TE and there can be no assurance that the TE actually reflected in your accounts will be at levels either specified in the investment objectives or suggested by our forecasts.
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