Wednesday, December 19, 2012

Don't Take Our Word For It

"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.

GMO forecast

AQR forecast

Hussman forecast

Gray forecast

Pimco forecast

BPG forecast

Monday, December 3, 2012

Tactical Alpha: The Case for Active Asset Allocation

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, AssoĆ©, 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: AssoĆ©, L'Ehr and Plant (2006)

ALP suggest that the results above reveal 3 important takeaways from the analysis. Directly from the paper:
  1. the relative importance of asset allocation and security selection is time-dependent;
  2. the asset allocation driven dispersion is more volatile than the security selection induced dispersion
  3. 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:
  1. The investment decision: invest in risky assets vs. holding cash
  2. Asset classes
  3. Geographic markets within each asset class
  4. 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:
  • 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 bonds
Source: Yahoo finance

Chart 4. Implied correlation between S&P 500 stocks
Source: 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.

Future Directions

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:
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.

Tuesday, November 20, 2012

Equity Portfolio Optimization with Factor Tilts


A variety of techniques are applied to improve upon passive capitalization weighted equity market portfolios via intelligent integration of the four equity market factors introduced by Fama, French and Carhart. In consideration of structural and regulatory constraints imposed upon most investment practitioners, long-only factor tilt portfolios are substituted for the traditional long-short factors, which facilitates simple implementation of techniques using liquid Exchange Traded Funds. Factor tilt portfolios are assembled using equal weight, equal volatility weight, risk parity and minimum variance optimizations, and simple filters are introduced to reduce turnover and commensurate trading frictions. Finally, a simple but prospective balanced portfolio framework is proposed.


There has been a cluster of papers recently about factor allocations as an addition to the traditional asset allocation framework. We believe the market cap, small cap, and value equity factors described by Fama and French (1992), as well as the momentum factor identified by Jagadeesh and Titman (1993) and eventually specified by Carhart (1997), represent mildly interesting diversifiers for portfolios in certain contexts. However, many institutions are increasingly interested in how to intelligently allocate to these factors to improve the risk-adjusted performance of their equity portfolios. This led us to explore optimal allocation methods.

Sharpe introduced the first equity factor, sometimes called ‘market beta’, in 1964 when he described the Capital Asset Pricing Model (CAPM). The CAPM model was meant to explain the degree to which market returns to stocks were a function of non-diversifiable risk; stocks with higher non-diversifiable risk were theoretically presumed to possess a possess a higher required rate of return in order to compensate for the extra risk of owning them. Fama and French extended the model in 1992 to describe the excess returns observed in small capitalization stocks, and ‘value’ stocks, the latter which was defined by stocks’ price to book ratio. 

In Fama’s and French’s initial tests it was observed that stocks with low market capitalizations delivered higher returns than their large capitalization counterparts. It was also observed that stocks with high book values relative to their market values offered higher returns than stocks with low book to market ratios. Further, these performance anomalies could not be completely explained by higher market betas associated with the factor portfolios.

In 1993 Jagadeesh and Titman published research on the momentum factor, which they defined as a stocks’ 12 month historical return, with a lag of one month. They found that stocks that delivered high returns over the past 12 months (with a 1 month lag) tended to outperform over the next month; this worked in reverse as well, such that stocks with poor performance in the recent past tended to underperform over the next month.

While the low volatility anomaly was noted in the literature as far back as 1977 (Miller, 1977), Miller first published exclusively on the low volatility anomaly in 2001. Additionally, Eric Falkenstein submitted his dissertation on the phenomenon in 1994, but it seems the academic community was not ready to accept a theoretical framework that effectively repudiated the CAPM at the time. As a result, his findings were never published. However, the seminal work on this factor seems to belong to Ang, Hodrick, Xing and Zhang (2006) with their examination of U.S. stock markets, while Baker and Haugen (2012) confirmed Ang et al.’s results in all major international equity markets earlier this year.

Robeco provided a superb summary of the observed magnitude of the above anomalies in a 2011 paper, Strategic Allocation to Premiums in the Equity Market, from which we copied the table below.

Source: Robeco

These are not inconsiderable premiums considering that they represent simple, persistent, systematic techniques that anyone can apply. This is especially true now that there are liquid ETFs that effectively capture these factors that anyone can use in portfolios:

Small-cap stocks: IWM (cap weighted) and EWRS (equal weight)

Value stocks: IVE (S&P 500), IWD (Russell 1000), PRF (FTSE RAFI)

Momentum stocks: PDP (all-cap), HMTM (large-cap), SMTM (small-cap)

Low Volatility: SPLV (volatility weighted), LVOL (volatility weighted)

In contrast to most academic factor investigations, this paper will focus on the same long-only versions of the factors described in the Robeco paper, as most practitioners encounter structural or regulatory barriers to shorting. Further, we would argue that short factors should be disaggregated from long factors, as long and short factors often 'work' at different times, and long-only factors display more persistence in practice.

This article will explore factors in a variety of asset allocation frameworks; we will introduce the factors individually and then see if we can create a better passive 'equity' basket, and extend this concept to create a better 'balanced' portfolio.

Factor Charts

To get us started, we have published below the charts and summary statistics for each of the major long-only factor tilts listed above. For all factors except the low volatility factor we sourced the data from Ken French's database. We used the S&P Low Volatility Index Total Return series for the low volatility anomaly. As the Low Vol data only goes back to 1991, the charts go back to 1992 in order to provide a year of 'priming' for the asset allocation overlays that we will introduce in later posts.

Large Cap Stocks

Source: Ken French database, 2012

Small Cap
 Source: Ken French database, 2012

Large Cap Value

Source: Ken French database, 2012

Large Cap Momentum
Source: Ken French database, 2012

Large Cap Low Volatility
Source: Standard and Poor’s, 2012

Equal Weight

The obvious next step in our exploration is to determine how well the factors work together in a portfolio. To answer, we first ran an equal weight factor tilt portfolio, rebalanced quarterly with data back to 1992:

Five Equity Factors, Equal Weight, Rabalanced Quarterly
Source: Ken French database, Standard & Poor’s, Yahoo Finance

Equal allocations to long-only factor tilts improve what is essentially a long-only beta portfolio (the Fama French Large Cap portfolio) by about 2.25% in terms of CAGR, and offer slight improvements to volatility, drawdowns, and the frequency of positive periods. Of course, these improvements come at the expense of extra trading.

Equal Volatility Weighting

We have explored volatility management techniques at length in many prior articles (see herehereherehere, and here for a few examples). Equal volatility weighted portfolios are constructed to target an equal volatility contribution by all assets in the portfolio, such that the portfolio is always fully invested. This requires that volatility be estimated for each asset going into every rebalance period; we use the 60-day observed historical volatility for all estimates in this article to be consistent with our other articles, though there is no particular significance behind using this lookback horizon.

Five Equity Factors, Equal Volatility Weight, Rebalanced Quarterly
Source: Ken French database, Standard & Poor’s, Yahoo Finance

This technique doesn't offer much improvement over simple equal weighting, in all likelihood because the factor tilts are all so highly correlated during periods of market distress.

Position Size Volatility Limits

In this variation on the theme of volatility management, factors are granted equal volatility weighting in the portfolio up to a fixed volatility contribution limit, in this case 1% daily. When any asset exhibits volatility in excess of its 1% limit, exposure to that asset is scaled back in favour of cash in order to maintain our prescribed volatility limit. In this way, total portfolio exposure is less than 100% during periods where individual positions are highly volatile.

5 Equity Factors, Equal Volatility Budgets (1% daily), Rebalanced Quarterly
Source: Ken French database, Standard & Poor’s, Yahoo Finance

Setting position level volatility limits does improve risk-adjusted performance (see Sharpe ratio), in this case exclusively due to lower realized average portfolio volatility. More notably, drawdown is reduced by 40% because allocations are scaled back during the high volatility periods that are generally characterized by large drawdowns.

This technique does improve measurably with more active rebalancing, as evidenced by the results below based on a monthly rebalance schedule:

5 Equity Factors, Equal Weight Volatility Budgets (1% daily), Rebalanced Monthly
Source: Ken French database, Standard & Poor’s, Yahoo Finance

Observe: A realized Sharpe over 0.6 with no tactical overlay at all.

While some might object to the large number of trades, in this case the number of trades is deceiving because most trades are small and nuanced in reaction to small changes in volatility. Further, by setting range-based rebalancing targets of 25% (that is, when any allocation target changes by 25% or more relative to its current allocation in the portfolio, the whole portfolio is rebalanced to new target weights), we can reduce turnover by 70% with no loss in performance.

5 Equity Factors, Equal Weight Volatility Budgets (1% daily), Rebalanced Monthly, 25% Filter
Source: Ken French database, Standard & Poor’s, Yahoo Finance

Risk Parity

The risk parity concept merges precepts from equal volatility weighting at the individual asset level, and fixed volatility budgeting at the portfolio level, with the idea that lower volatility assets can be levered up to provide a similar return contribution to the portfolio as more risky assets while better balancing risk across the portfolio.

Risk parity requires a volatility budget to be set at the portfolio level; in this case, we maintain the same 1% daily target for portfolio volatility using 60 day realized volatility as the estimate for each asset, as well as for the portfolio in aggregate.

Note from the chart below that it is not possible to reach our volatility target without the use of leverage; the realized volatility of the un-levered version is just 13%. 

5 Equity Factors, Risk Parity (1% daily), Rebalanced Monthly, 25% Filter
Source: Ken French database, Standard & Poor’s, Yahoo Finance

It is a simple thing to use traditional margin to reach our volatility target with up to 100% leverage (or a maximum portfolio exposure of 200%) when required during periods of low aggregate portfolio volatility.

Obviously this less constrained version provides better performance, adding 2% to annualized returns, with commensurately higher volatility but, perhaps surprisingly, almost no incremental boost in drawdown. The following simulation also includes a cost of margin equal to .5% above the t-bill rate, which is excruciatingly onerous, but we like to be conservative.

5 Equity Factors, Risk Parity (1% daily), Rebalanced Monthly, 25% Filter, Max 200% Exposure
Source: Ken French database, Standard & Poor’s, Yahoo Finance

Minimum Variance

Minimum variance algorithms strive to create optimal portfolios using the equations described by Modern Portfolio Theory, but with the objective of minimizing total portfolio variance rather than maximizing portfolio Sharpe. In contrast with standard mean-variance optimization therefore, minimum variance optimization does not require or use any return estimates, focusing instead exclusively on volatility and the covariance matrix.

The average correlation between momentum and value tilts over the past 20 years is 0.85; between value and low volatility, it is 0.82; and between momentum and low volatility it is 0.75. As a result, there is an opportunity to leverage the diversification between factors explicitly, a process for which minimum variance optimization is well suited.

5 Equity Factors, Minimum Variance, Rebalanced Monthly, 25% Filter
Source: Ken French database, Standard & Poor’s, Yahoo Finance

As with virtually all optimization procedures we have analyzed over the years, the minimum variance optimization is improved by overlaying a portfolio level volatility target. In this case we will use the same 1% daily target as in our risk parity example above.

5 Equity Factors, Minimum Variance, Rebalanced Monthly, 25% Filter, Portfolio Target Volatility (1%), Max 100% Exposure
Source: Ken French database, Standard & Poor’s, Yahoo Finance

This seems to be quite a powerful combination. We have achieved a Sharpe ratio of 0.84 with a pure beta portfolio. Returns increase by almost 4% per year and drawdowns are reduced by 45% while volatility drops by 40%.

Adventurous beta seekers might wish to lever up the minimum variance portfolio at opportune times in order to actually achieve the target 1% daily volatility. If we set a maximum leverage factor of 100%, we achieve the following profile:

5 Equity Factors, Minimum Variance, Rebalanced Monthly, 25% Filter, Portfolio Target Volatility (1% daily), Max 200% Exposure
Source: Ken French database, Standard & Poor’s, Yahoo Finance

A Better Balanced Fund

As a parting gift, we ran the minimum variance portfolio as the equity portion of a risk parity version of a traditional balanced portfolio, with a target volatility of 7% annualized (equal to the realized volatility of the 10 year Treasury over the same period), rebalanced quarterly.
5 Equity Factors (Minimum Variance) and 10-Year Treasuries, Risk Parity (7% annualized), Max 100% Exposure
Source: Ken French database, Standard & Poor’s, Yahoo Finance

Notice that, due to the lower volatility of the minimum variance factor tilt equity portfolio, and a low structural correlation between the factor portfolio and Treasuries, the realized volatility of this balanced fund is just 5.4% despite our 7% target. Of equal importance, the maximum drawdown for this portfolio is just 11.65% over the past 20 years!

Many prospectus mutual funds can carry up to 125% exposure under their mandates. If we raise the maximum exposure to accommodate this limit, we can get closer to our 7% target, with commensurately juicier returns.

5 Equity Factors (Minimum Variance) and 10-Year Treasuries, Risk Parity (7% annualized), Max 125% Exposure
Source: Ken French database, Standard & Poor’s, Yahoo Finance


Long-only factor tilt portfolios are very accessible by average investors using highly liquid Exchange Traded Funds. Equity factors appear to provide some diversification benefits in a portfolio context, and algorithms that explicitly account for portfolio level volatility and factor covariance can provide a very substantial boost to absolute returns while reducing portfolio risk.

Indeed, investors might wish to explore these techniques as interesting complements to existing equity allocations, especially in the context of a diversified balanced portfolio.
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.