Wednesday, December 19, 2012
"It is difficult to get a man to understand something, when his salary depends upon his not understanding it!" Upton Sinclair
Long-time readers will know that we periodically publish a statistical forecast for U.S. stock market returns over horizons from 5 to 30 years, which we generate from a variety of long-term valuation metrics. We were motivated to conduct this analysis because we observed an enormous amount of misunderstanding and misinformation in estimates quoted in various media sources, which largely serve to protect the interests of equity managers and investment firms whose livelihood relies on equity enthusiasm.
A handful of trustworthy buy-side firms consistently publish similar forecasts based on their own analyses, and there has been a flurry of reports lately, so we thought we would summarize the findings of others who have investigated this topic so that readers don't have to just take our word for it.
Chart 1. below summarizes the forecasts of several firms or independent analysts based on papers published in the last month or so. Since few investors invest purely in stocks, we used large cap stock market forecasts as well as the current yield on the Barclays U.S. Aggregate Bond Index, and the most recent inflation expectations reading from the Cleveland Fed's model to create a real forecast for a U.S. 60/40 balanced portfolio. AQR actually published a balanced fund forecast independent of its stock market forecast, so we used their estimate directly.
Chart 1. Forecast total real returns to a U.S. 60/40 balanced portfolio over the next 7-10 years, annualized
Sorry folks, but good stock picking won't meaningfully alter this conclusion. But don't lose hope - we may have an answer.
The following reports were sources for Chart 1, and we would encourage you to read them all.
Monday, December 3, 2012
Patients with certain brain injuries often do not recognize their own limbs on one side of their body; they often wake up alarmed at the presence of an arm or leg in the bed next to them on one side of their body, which they do not recognize as their own. The name of this condition is hemispatial neglect, and it pertains to a person's awareness about one half of their field of view. Sufferers also often ignore words on one side of a page, eat the food only on one side of their plate, or render incomplete drawings of objects or faces.
The human brain is an incredible puzzle, but conditions like this may offer clues to the mystery of why investors systematically ignore over half of the opportunity to earn excess returns in markets. Despite countless studies showcasing the absence of persistent alpha in the security selection domain, and the overwhelming improbability of identifying alpha generators in advance, the vast majority of active investors continue to flock to traditional active management in pursuit of elusive excess returns.
Meanwhile, most investors remain inconceivably blind to the opportunity to generate excess returns through the other half of the active investment space - active asset allocation - despite a growing body of research suggesting this approach may be a source of substantial untapped 'tactical alpha'.
Many investors perceive that the opportunity to generate incremental excess returns is much higher in the security selection space than the asset allocation space because there are vastly more securities (i.e. stocks and bonds) than there are asset classes (i.e. stock markets and bond markets). This perception influences the relative priority placed on the pursuit of alpha from active security selection, relative to active asset allocation. This article will address this imbalance and provide compelling evidence that equal priority (at least) should be placed on generating excess returns from asset allocation, even at the expense of sacrificing active security selection.
For most institutions, the asset allocation decision and the security selection decision embody a tradeoff. This is due to the structural frictions embedded in the use of external managers employed in an attempt to 'beat the benchmark' through active security selection in a specific market.
Unfortunately, institutional investors' ability to move dynamically in and out of asset classes is constrained by the allocation and redemption policies of these traditional investment managers, such that agile rotation among and between markets and asset classes is difficult on shorter term horizons of, say, less than one year. For this reason, institutions that embrace the ability of managers to deliver alpha through security selection will necessarily sacrifice their ability to extract value from a more dynamic asset allocation process.
Market inefficiencies exist for a variety of reasons, such as asymmetric information, tax frictions, and emotional biases, but perhaps the most economically significant inefficiencies stem from structural constraints imposed on a large segment of investors. We view the structural bias in favour of security selection alpha vs. tactical alpha as an important example of this type of constraint. As a result, we assert that tactical alpha - active asset allocation - represents one of the most economically important sources of excess returns available to investors in public markets.
The next sections will review salient research contributions in the field of performance attribution related to active asset allocation versus active security selection. Our objective is to demonstrate the importance of active asset allocation as a source of potential excess returns, and persuade progressive investors to allocate more capital and resources to this objective, even if that means scaling back their commitment to the pursuit of traditional sources of alpha.
We will also add to the existing research with a novel examination of the unconstrained potential to extract excess returns from asset allocation vs. security selection using a normative quantitative approach.
Shoulders of Giants
Most studies in this area focus on analysis of pension funds and mutual funds, and explore the degree to which total portfolio return is explained by deviations from an institutions' policy asset class weights. Portfolio returns are the aggregation of the returns to the policy portfolio and 'active returns', which in most studies is defined as the residual not accounted for by the policy portfolio.
For example, Brinson regressed monthly portfolio total returns for pension funds against the monthly returns to each funds' policy portfolio, and determined that the policy portfolio explains 90% of the monthly variability in total returns. While this analysis is helpful, as it illustrates the impact of asset allocation on long-term portfolio performance, it does not allow us to determine the underlying factors that drive the unexplained 10% of returns. Further, it was highlighted by future studies, including the Kaplan study we describe below, that in fact the majority of monthly pension fund performance can be explained by the fund's decision to invest in capital markets at all, vs. holding cash.
Kaplan and Ibbotson added a second dimension to the analysis by exploring the degree to which fund policy weights explained the cross-sectional differences in total returns across a basket of funds over a ten year investment period. The purpose of the cross sectional analysis was to analyze the degree to which differences in policy weights explained the difference in the total return between funds. They discovered that asset allocation policy explained 40% of the difference in the total return across funds over the full period, and asserted that the residual difference was some combination of, "asset class timing, style within asset classes, security selection, and fees", and that for pension funds it was also attributable to manager selection.
Many people thought that the Brinson studies analyzed the proportion of fund total performance that was attributable to each funds' policy portfolio weights, rather than analyzing the proportion of fund variance. Kaplan and Ibbotson answered this question too, using the original Brinson data as well as the data from their own later studies. Table 1 summarizes their results.
Table 1. Percentage of Total Return Level Explained by Policy Return
Source: Kaplan and Ibbotson (2000)
The average across all studies is 104%. Some readers may find this measure confusing. How can asset allocation explain greater than 100% of total returns?
Remember that the total return to the funds in the studies was equal to the sum of the total return to the funds' policy portfolio using asset class benchmarks, plus the active return, minus trading frictions. So the results of this study demonstrate that, over the periods studied in the analyses, the average institutional investor lost 4% of total return to fees, ineffective active management, or poor manager selection. Given the asset allocation constraints on most institutions, the vast majority of this return decay was a result of poor security selection.
This begs the questions:
- Why do investors continue to seek excess returns from active security selection?
- Is there another source of active returns
Free from Constraints
Unfortunately, neither the Brinson nor the Kaplan/Ibbotson studies explored the degree to which the variability of returns was due to active asset allocation bets versus active security selection bets. Fortunately, Assoé, L'Ehr and Plant [ALP] (2006) performed an analysis, modeled after Kritzman and Page (2003), that applied a creative approach to answer this exact question. ALP used a normative framework rather than an empirical framework like that embraced by Brinson, Ibbotson and Kaplan, in which the potential returns in each quarterly period from 1985 - 2005 were explored for a large set of constrained, randomly generated asset class portfolios and security portfolios.
In the ALP analysis, benchmark weights were assigned for a theoretical fund that included cash (5%), bonds (30%), stocks (40%), real estate (10%), private equity (10%), and commodities (5%). At the start of each annual period, 100 draws were made from the asset pool according to the above proportions, with each draw representing 1% of the final portfolio for that year. The returns to the random portfolio are then computed for each quarter of the subsequent year, after which a new random portfolio is constructed in the same way for each year from 1985 through 2005. Then this process is repeated 10,000 times, with each repetition representing one sample portfolio.
The purpose of this procedure is to generate a large sample of possible portfolios generated exclusively from small changes to the asset allocation around prescribed weights. To this end the dispersion of portfolio returns is due exclusively to changes in the asset allocation, as opposed to the other variables cited in the Kaplan and Ibbotson study.
A similar procedure is used to generate stock portfolios from a long-term S&P 500 stock dataset. In this case stock portfolios are created at the start of each year by randomly selecting 100 stocks, where any given stocks' probability of inclusion at each random draw is equal to the stocks' current weight in the index. This procedure is also repeated 10,000 times over the entire 20 year investment period.
Chart 1. describes the dispersion between the 95th and 5th percentile portfolios in each quarter over the investment horizon for the asset allocation portfolios and the stock selection portfolios. Note that the paper asserts that the average annualized dispersion between 95th and 5th percentile portfolios over the entire sample is equivalent for asset allocation and security selection, suggesting that in aggregate asset allocation and security selection provide equal opportunities to add value in an active portfolio management process.
Chart 1. Relative importance of asset allocation and security selection: difference between the 5th and 95th percentile quarterly performance
Source: Assoé, L'Ehr and Plant (2006)
ALP suggest that the results above reveal 3 important takeaways from the analysis. Directly from the paper:
- the relative importance of asset allocation and security selection is time-dependent;
- the asset allocation driven dispersion is more volatile than the security selection induced dispersion
- the security selection activity generates as much dispersion in active return as asset allocation so that it cannot be unequivocally declared that one activity is structurally more or less important than the other
We would add a few other observations from this analysis. First, the paper deliberately constrains the allocations to the six asset classes by weighting them in the asset 'pool' according to a typical institutional weighting scheme. While this assumption is consistent with the decision-making latitude of traditional institutions, which are dominated by traditional consulting relationships, it does not allow the analysis to account for the full opportunity set offered by an unconstrained asset allocation decision, such as the opportunity set available to CTAs or unconstrained asset allocators seeking tactical alpha.
Second, the equity weights are constrained by weighting them in the equity 'pool' according to the market cap weighting in the S&P500. True active managers, especially outside the traditional mutual fund space, would take considerably more latitude in selecting stocks, and even traditional managers are beginning to accept the large amount of research demonstrating the long-term superiority of an equal weight basket over the typical market capitalization weighted approach.
Third - and this is the major focus of the rest of this article - the authors do not seek to explore the cause of the time-varying nature of the relative value of asset allocation vs. security selection. From Chart 1 we can see that at times the asset allocation contribution dominates the contribution of security selection, while at other times the reverse is true. What are the driving forces behind these time-varying shifts?
Asset Allocation or Security Selection: An Answer
Initially, our curiosity was peaked by This field has been plowed thoroughly over the years, first by Brinson et al., and later by Ibbotson and Kaplan, among others, but these pioneers left several important unanswered questions that the Staub and Singer article addressed.
This question is addressed by Staub and Singer in a paper entitled, 'Asset Allocation vs. Security Selection: Their Relative Importance', published in the CFA Journal (2011). The following is from the abstract:
Various researchers have investigated the importance of asset allocation versus security selection. Although we think this question is conceptually weak—because asset allocation and security selection have different missions—we address it to ensure appropriate quantitative treatment. We focus on feasibility rather than on what managers actually do. Hence, our approach is free of benchmark thinking and makes no assumptions regarding portfolio positions or potential constraints.
We have emphasized the final sentence because it addresses the issues we raised above regarding the constraints applied in the ALP paper.
At core, Staub and Singer assert that the only information required to determine the contribution of any asset class to standardized portfolio returns is the correlation matrix. This is because the magnitude of contribution is purely a function of leverage; an asset with a low ambient volatility can be scaled up and down at will. As such, the authors examine a correlation matrix composed of the following levels of grouping:
- The investment decision: invest in risky assets vs. holding cash
- Asset classes
- Geographic markets within each asset class
- Securities within each geographic market
Note that the decision to invest in risk assets vs. cash invokes the basket of risky assets, which in turn consists of different geographic markets within each asset class. Finally, each market contains individual securities. In this way, each layer of portfolio decision has a cascading impact on more granular sets of assets down the chain.
Further, the authors assume the following:
Further, the authors assume the following:
- There are 20 independent stock markets and 20 independent bond markets
- Each independent market is composed of 100 securities
Broadly, this decision tree describes the opportunity set for most large institutions, at least among the portion of their portfolios that is allocated to traditional asset classes (stocks and bonds).
Finally, the paper establishes stable correlation estimates between each security category and market, which quantify the impact of decisions in one layer on the constituents of other layers of the investment process.
• stocks in a national market have a correlation of 0.50,
• bonds in a national market have a correlation of 0.80,
• stocks of different national markets have a correlation of 0.40,
• bonds of different national markets have a correlation of 0.60,
• stocks and bonds of the same national market have a correlation of 0.30, and
• stocks and bonds of different national markets have a correlation of 0.20.
With these assumptions in place, the authors use a powerful statistical technique (Principal Component Analysis) to identify the explanatory power of each dimension of standardized portfolio returns, with the following results:
Chart 2. Cumulative eigenvalues for 'layers' of investment decisions
Source: Staub and Singer, 2011
You can see that, with the authors' correlation assumptions, 65% of potential portfolio standardized returns are explained in aggregate by the investment vs. cash decision; the asset allocation decision; and the market selection decision. The remaining 35% is derived from individual security selection decisions.
The Impact of Changing Correlations
The Staub and Singer paper offers a clue about what drives the time varying nature of the relative importance of asset allocation and security selection observed in the ALP paper: the relative correlation between assets, markets, and securities. But of course correlations are not static, as implied in Staub and Singer.
Our contribution to this discussion then, is an analysis of how changes in the correlations between asset classes (stock and bond markets), and between individual securities, affects their relative contribution to portfolio returns.
To perform this analysis, we used exactly the same procedure as laid out in Staub and Singer, except that we repeated the analysis for a variety of different estimates of correlation. We focused specifically on how the standardized portfolio return attribution changed as we changed the correlation between stock and bond markets, and varied the correlation between individual stocks, on a domestic market.
In contrast with ALP, and consistent with Staub and Singer, we applied no constraints to the analysis. An unconstrained analysis more effectively reveals the true opportunity set available to managers who pursue tactical alpha as well as traditional alpha.
We varied the correlation between domestic stocks and bonds from -1 to 1 to reflect the fact that stocks and bonds are sometimes highly correlated, sometimes highly negatively correlated, and sometimes exhibit no correlation at all, as evidenced by Chart 3. In contrast, domestic stocks do not in practice ever exhibit average correlations less than 0 (see Chart 4.), so we varied this coefficient between 0 and 1.
Chart 3. 60-day rolling correlation between stocks and bondsSource: Yahoo finance
Chart 4. Implied correlation between S&P 500 stocksSource: CBOE
Matrix 1. below reproduces the Straub and Singer analysis for each stock/bond and stock/stock correlation combination along the spectrum for each described above. For clarity, the number in each cell equates to the total amount of standardized portfolio variance that is cumulatively attributable to the invest/cash, asset class, and market choice opportunities. The balance (1 - the percentage in the cell) is attributable to the security selection opportunity.
Matrix 1. Sensitivity of potential standardized return attribution from active asset allocation vs. active security selection to changes in correlation estimates
Source: Butler|Philbrick|Gordillo & Associates, JP Belanger (Quantum Financier)
We highlighted two values in circles: the green circle highlights the value that corresponds with current measures for stock/bond and stock/stock correlations per Charts 3. and 4. Note that at current estimates for intra- and inter-market correlations, about 73% of potential portfolio variance is explained by asset allocation. The red circle corresponds to the long-term average measures for the same correlations over the 2004-2012 period, again per Charts 3 and 4., suggesting that on average asset allocation accounts for 69% of potential alpha, while security selection offers just 31%.
From Charts 3. and 4. above, and corresponding cells in Matrix 1. below, it would therefore appear that we are currently entrenched in a period where the asset allocation decision is of measurably greater importance than it has proven to be historically.
As discussed in the opening paragraph of this article, the question of whether to seek value from active asset allocation or traditional security selection is not a trivial one. This is because the decision to seek value through security selection is usually carried out through allocation to external managers with specialization in certain markets or assets. In order to carry out their active investment management process, these managers require that capital be committed for meaningful periods.
Unfortunately, this runs counter to the need for agility in asset allocation required to derive value from tactical asset allocation efforts.
This survey of asset allocation / security selection studies, and our group's own contribution to this important domain, serves to illustrate the relative importance of asset allocation in the pursuit of incremental risk-adjusted returns. Further, most institutions face structural, inertial and regulatory impediments to the implementation of meaningful asset allocation program. This means that there is a very large and economically significant opportunity for open-minded institutions that are willing to deviate from the status quo.
Investors who are interested in exploring active asset allocation strategies are invited to explore the following articles and papers:
- Adaptive Asset Allocation: A Primer - Butler, Philbrick, Gordillo & Varadi
- Using Factor Momentum to Optimize GTAA Portfolios - QUSMA
- Relative Strength Strategies for Investing - Faber
- Applying Value and Momentum Across Asset Classes in a Quant TAA Framework - Wang
- Value and Momentum Everywhere – Asness, Moskowitz, & Pedersen
- Modern Tactical Asset Allocation – de Silva
- A Factor Approach to Asset Allocation – de Silva
- Global Tactical Asset Allocation: Exploiting the opportunity of relative movements across asset classes and financial markets – Potjer & Gould
- Global Tactical Cross-Asset Allocation: Applying Value and Momentum Across Asset Classes - Blitz & Van Vliet
- Advanced Theory and Methodology of TAA – Lee
Links to other websites or references to products, services or publications other than those of Macquarie Private Wealth Inc.(MPW) on this website do not imply the endorsement or approval of such websites’ products, services or publications by MPW. MPW makes no representations or warranties with respect to, and is not responsible or liable for, these websites’ products, services or publications. Macquarie Private Wealth Inc. is a member of Canadian Investor Protection Fund and IIROC.