A Robust Asset Allocation (RAA) Solution [ANALYSIS]

Our Robust Asset Allocation (RAA) Solution by Wesley R. Gray, Ph.D., Alpha Architect

Robustness: Strong and effective in all or most situations and conditions.

Executive Summary:

Many investors are faced with a fundamental problem: What should I do with my money?

People usually pursue one of four broad solutions to this problem–each has costs and benefits:

Hire an expensive investment advisor that offers a limited value proposition. (generally a bad idea, although quite common)
Hire an affordable advisor that delivers a strong value proposition. (reasonable idea)
Hire a cheap robo-advisor that will deliver a generic, but reasonable value proposition. (reasonable idea)
Do-it-yourself. (reasonable idea)

We think educated investors can successfully move down the “do-it-yourself” path when equipped with the tools and knowledge to move forward. There are a few critical areas to get familiar with, but once that’s complete, DIY is perfectly viable for many. For those who are not comfortable with the DIY approach, we recommend approach 2 or 3, depending on personal preferences and circumstances.

I want to be a DIY investor, so what do I do next?

Easiest solution: 50% BND; 50% VTI (or your own special weights depending on your risk tolerance, individual circumstances).

Insanely cheap; insanely easy; throw away the key. Not an unreasonable approach.

1. What is Your Portfolio’s Mission?

1.1 The Purpose-Driven Portfolio

Wealth is often built by concentrated holdings, but wealth is protected by diversification. Most people accumulate wealth by working, which is a concentrated position, as this usually requires time and effort.

Having a clear purpose is the premise of portfolio investment.

Example:

Purpose of the portfolio: Preserve and compound wealth to assure financial security.
Return objective: RF (10Yr) + 400bps, AFTER TAX.
Risk appetite: As low as practical to achieve objective.
Taxes: Can be huge drag on returns for private individuals –> minimize damage.
Human capital: Don’t confuse frenetic human activity, or a large staff, with higher risk-adjusted return potential.

1.2 Strategy Assessment: Stick to FACTS

“Get your facts first, then you can distort ‘em as you please.”
— Attributed to Mark Twain

While there is no “one-size fits all” strategy assessment and allocation model, a systematic framework for decision-making can help simplify the process and maximize returns. For every allocation contemplated, and each strategy that needs to be critically assessed, the FACTS framework (consisting of Fees, Access, Complexity, Taxes and Search) can be employed to clarify important considerations for the prospective investor.

Click to read our white paper: Stick to the FACTSA in-depth look at the FACTS framework is here.

The high level summary is as follows: Create a portfolio that minimizes fees, increases access to your own capital (e.g., liquid investments), is easy to understand (low complexity), minimizes taxes, and minimizes manager search costs. Our goal is to propose a portfolio that optimizes across all 5 key points.

2. Does Complexity Enhance Asset Allocation?

2.1 Do Fancy Models Work? Not Exactly…

“Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1/N rule…”
— DeMiguel, Garlappi and Uppal.

Victor Demiguel and his colleagues have explored many sophisticated methodologies to optimize asset allocation. They have solutions that can possibly beat an equal-weight allocation, but these alternative solutions add a high degree of complexity. Prof. DeMiguel has an outstanding outline of asset allocation research here if you’d like to explore further. We’ve discussed the empirical rational for following a simple asset allocation model in the past, here, and here. An equal-weight portfolio–also promoted by DeMiguel et al.–would seem to fly in the face of modern portfolio management, which in general has suggested that investors rely on mean-variance type allocation, or other highly engineered schemes. However, while mean-variance-analysis has reverse engineered the best historical Sharpe ratio (i.e. the tangency portfolio), this solution relies on a correlation matrix input, which is highly unstable and difficult to estimate. Indeed other approaches have this same weakness. The results below, taken from the DeMiguel et al. paper on asset allocation, highlight the incredible robustness associated with an equal-weight, or 1/N, type of asset allocation regime.

Source: DeMiguel, V., L. Garlappi, and R. Uppal, 2009, Optimal Versus Naïve Diversification: How Inefficient is the 1/N Portfolio Strategy? Review of Financial Studies 5, 1915-1953.DeMiguel et al. are not the only researchers pointing towards the 1/n solution. Even the great Harry Morkowitz, a Nobel Prize winner and the founder of portfolio management, is quoted as saying:

“I should have computed the historical covariance of the asset classes and drawn an efficient frontier…I split my contributions 50/50 between bonds and equities.”

A few quotes attributed to Einstein sum up the key lessons learned from piles of disinterested research compiled on the subject of asset allocation.

Keep it simple.
Complexity does not imply value.

2.2 Simplify the Allocation Problem: Simplify; Simplify; Simplify

“Don’t try anything fancy. Stick to a simple diversified portfolio, keep your costs down and rebalance periodically to keep your asset allocations in line with your long-term goals.”
–David Swensen, Yale Endowment CIO.

The “IVY 5” portfolio, described by Faber (2007) and then further elaborated by Faber and Richardson (2009), includes 5 asset classes:

SP500 = SP500 Total Return Index
EAFE = MSCI EAFE Total Return Index
REIT = FTSE NAREIT All Equity REITS Total Return Index
GSCI = GSCI Index
LTR = Merrill Lynch 7-10 year Government Bond Index

Click to enlarge.At a high level, one can think of the IVY 5 portfolio as a 40% equity, 40% real asset, and 20% fixed income portfolio. I consider it a goldilocks portfolio: Not too simple; not too complex; just right.

2.3 Simplify Risk-Management

In general, while efforts to time the market should be viewed with skepticism, certain systematic timing strategies that have been explored in academia appear to reduce risk, without significantly impacting long-run returns. In particular, the application of simple moving average rules has been demonstrated to protect investors from large market drawdowns, which is defined as the peak-to-trough decline experienced by an investor. Jeremy Siegel, in his book, “Stocks for the Long Run,” explores the effect on performance on the Dow Jones Industrial Average from 1886 to 2006, when applying a 200-day moving average rule. Applying the rule is straightforward. If the market is above the 200-day moving average rule, hold, otherwise go to cash. Siegel found that this simple technical rule outperforms a buy-and-hold approach, both in absolute terms and on a risk-adjusted basis.

The simple moving average trading rule can be used across asset classes and is suggested in the Faber/Richardson Ivy Portfolio book. Below I outline how this rule might look over the past few years on the S&P 500 (12-month SMA depicted).

Click to enlarge.Below is a diagram of how the IVY 5 with a moving average rule might look in practice.

Click to enlarge.The IVY 5 with moving average model sounds good in theory, but what does this portfolio look like historically?

3. Exploring a Simple IVY5 Model

3.1 Simulation Background:

Simulated Historical Performance: 1/1/1979 to 12/31/2013

Results are gross of management fee and transaction costs for illustrative purposes only. These are simulated performance results and do not reflect the returns an investor would actually achieve. All returns are total returns and include the reinvestment of distributions (e.g., dividends). Data is from Bloomberg and publicly available sources. Portfolios are annually rebalanced.

The following 5 asset classes are used in the back-test (referred to as the “IVY 5”):

SP500 = SP500 Total Return Index
EAFE = MSCI EAFE Total Return Index
REIT = FTSE NAREIT All Equity REITS Total Return Index
GSCI = GSCI Index
LTR = Merrill Lynch 7-10 year Government Bond Index (prior to 6/1982, Amit Goyal Data)

3.2 Benchmark Summary Statistics

10-Year Bonds and US Equity have performed the best over the past 30+ years. No wonder everyone is so enamored with the 60/40 S&P 500/10-year portfolio…

3.3 Strategy Summary Statistics

Below we depict the simple IVY 5 portfolio, the IVY 5 portfolio with a moving average rule applied, a 60/40 SP500/LTR portfolio, and a SP500 portfolio.

IVY5_MA: 5 assets, equal-weight, annual-rebalance, MA rule –> Tough to beat.
60/40: 60% SP500; 40% LTR, annual-rebalance –> Tough to beat.

4. The Robust Asset Allocation Solution (RAA)

Unfortunately, we can’t buy IVY5 index returns, but can only backtest them. Investment vehicles cost money in the real world, so we need to choose wisely. To replicate the IVY5 we could do the following with iShares products, which happen to have an ETF for all of the IVY 5 exposures:

IVV (7bps): iShares Core S&P 500
EFA (34bps): iShares MSCI EAFE Total Return Index
IYR (46bps): iShares US Real Estate
GSG (75bps): iShares S&P GSCI Commodity-Indexed Trust
IEF (15bps): iShares 7-10 Year Treasury Bond

In our backtests above, we looked at gross of fee performance, but we clearly can’t invest in an index for free. Using iShares, the ETF fee costs are 35.4bps, on average, plus transaction costs and RIA fees.

All that said, one could certainly implement the IVY 5 with moving average strategy with minimal brain damage. Yahoo Finance charting allows you to run a monthly 12-month moving average test for each asset class, and with a yearly rebalance across asset classes, you would be in DIY heaven.

But can we do better?

4.1 Three Simple, but Important, Improvements Over IVY5

1. We believe value and momentum can work.

How do we get access to these exposures without buying the asset manager a new yacht each year?
- Focus on affordable exposures that take active bets (not closet index) on value and momentum.

Value and Momentum strategies have been shown to outperform, historically. Since they are far and away the strongest anomalies explored in academia, they are probably worth getting exposure to, but we want to confirm this.

Here we present simulated gross of fee performances of these two strategies from 1/1/1963 to 12/31/2013, using publicly available data from Ken French’s website.

First, we examine momentum:

MOM_10 = Top Decile Momentum (Data); Momentum has worked!

VAL_10 = Top Decile Value (Data); Value has also worked!

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.The implication is that we should look at replacing our market-weight passive exposures with high-conviction value and momentum strategies–but only if we can access these exposures in an affordable, tax-efficient, and transparent way. Otherwise, much of the purported “edge” will go to the croupiers and Uncle Sam.

2. We believe we can deliver a simple and effective risk management system.

We have examined hundreds of risk-management platforms over the past 5 years. You name it–we’ve backtested it, thought about it, or implemented it.

Conclusion: Asset allocation models are 99% noise; 1% signal.

Here is a sampling of the various ideas we have tested:

Macroeconomic Fundamental Indicators

Wealth Ratio — Lettau and Ludvigson (2001) , “Consumption, Aggregate Wealth, and Expected Stock Returns”
Adaptive Macro Indexes — Bai (2010) ,”Equity Premium Predictions with Adaptive Macro Indexes”
Sum of Macro Variables — Ferreira and Santa-Clara (2011), “Forecasting Stock Market Returns: The Sum of the Parts is More than the Whole”
Industrial Mental Return — Jacobsen, Marshall and Visaltanachoti (2013), “Stock Market Predictability and Industrial Metal Returns”
Implied Cost of Capital — Li, Ng and Swaminathan (2013), “Predicting Market Returns Using Aggregate Implied Cost of Capital”
Oil Factor — Kilian and Park (2007), “The Impact of Oil Price Shocks on the U.S. Stock Market”
CAPE — Robert Shiller (2013)

Technical Indicators

Historical Data Forecast — Maheu and McCurdy (2006), “How Useful are Historical Data for Forecasting the Long-Run Equity Return Distribution?”
Time-Varying Sharpe Ratio — Tang and Whitelaw (2011), “Time-Varying Sharpe Ratios and Market Timing”
Return Dispersion — Maio (2012), “Return dispersion and the predictability of stock returns”
Mean Reversion Indicator — Huang, Jinag, Tu and Zhou (2012), “Mean Reversion, Momentum and Return Predictability”
Cross-sectional Technical Analysis–Han, Yang, Zhou, “A New Anomaly: The Cross-Sectional Profitability of Technical Analysis”
Simple MA Rule –Faber (2007), “A Quantitative Approach to Tactical Asset Allocation.”
Challenging MA rule #1 –Scholz and Walther (2011), “The trend is not your friend! Why empirical timing success is determined by the underlying’s price characteristics and market efficiency is irrelevant”
Challenging MA Rule #2–Zakamulin, “The Real-Life Performance of Market Timing with Moving Average and Time-Series Momentum Rules”
Challenging MA Rule #3–Marmi, Pacati, Risso, Reno, “A Quantitative Approach to Faber’s Tactical Asset Allocation”
Overview of Technical Analysis — Park and Irwin (2007), “What we know about the profitability of technical analysis?”

Sentiment and Variance Indicators

Investor Sentiment — Huang, Tu, Jiang and Zhou (2014), “Investor Sentiment Aligned: A Powerful Predictor of Stock Returns”
Cross-Section of Volatility — Ang, Hodrick, Xing and Zhang (2006), “The Cross-Section of Volatility and Expected Returns”
Variance Risk Premia — Bollerslev, Tauchen and Zhou (2009), “Expected Stock Returns and Variance Risk Premia”
VIX Term Structure — Johnson (2011), “Equity Risk Premia and the VIX Term Structure”
Equity Shares — Baker and Wurgler (2000), “The Equity Share in New Issues and Aggregate Stock Returns”
Broker-Dealer Leverage — Adrian, Etula and Muir (2013), “Financial Intermediaries and the Cross-Section of Asset Returns”
Implied Volatility Spread — Atilgan, Bali and Demirtas (2011),”Implied Volatility Spreads, Skewness and Expected Market Returns”

Comprehensive Summary of Different Predictors

Gupta, Modise and Uwilingiye (2012) — “Out-of-Sample Equity Premium Predictability in South Africa: Evidence from a Large Number of Predictors”
Welch and Goyal (2008) — “A Comprehensive Look at The Empirical Performance of Equity Premium Prediction”
Rapach and Zhou (2011) — “Forecasting Stock Returns”
Combo — Neely, Rapach, Tu and Zhou (2011), “Forecasting the Equity Risk Premium: The Role of Technical Indicators”

The sad conclusion is that none of these ideas stand up to intense robustness tests, except for the simplest, technical rules. You just can’t beat them. It’s kind of crazy when you think about it. We had hoped that having tested every model and approach under the sun that we would be able to triumphantly announce that we had identified a way to reliably predict the market using fancy algorithms derived from 100’s of academic researchers. But it just wasn’t the case. We’ve built these models: They aren’t reliable; they aren’t robust; and they are littered with data-mining. A large swath of the financial services industry would love to have you believe in their magic. I’m here to tell you that it doesn’t exist. Sorry.

But after all the years of research and analysis, what have we concluded?

Is market timing all for nothing? Perhaps…but…

We’ve boiled robust market-timing mechanisms down to two rules that are the best of a bad bunch:

1. Time Series Momentum Rule (MOM)

Excess return = total return over past x months less return of T-bill
- If Excess return >0, go long risky assets. Otherwise, go alternative assets (T-bills or Zero).
- Popularized by Gary Antonacci and rigorously examined by Moskowitz et al.

2. Simple Moving Average Rule (MA)

Moving Average (N) = average N month prices
- If Current Price – Moving Average (N) > 0, go long risky assets. Otherwise, go alternative assets (T-bills or Zero).

We have actually identified the mathematical relationship between MOM and MA Rules, outlined in the chart below:

Click to enlarge.As the equations highlight, MOM and MA rules are tied together: Time-series momentum rules (MOM) are a function of MA rules. And while MOM and MA triggers are highly correlated, there are circumstances where the rules have a difference of opinion.

It turns out that this “difference of opinion,” where one zigs when the other zags, adds some robustness to a comprehensive risk-management system.

3. We believe we can minimize taxes.

Annually rebalance taxable accounts.
Systematically harvest losses (book short-term losses to offset gains in other parts of the portfolio).
Tax manage risk management events (i.e., MA rule triggers a move to cash).

Uncle Sam is increasing tax rates year by year. For individual investors, taxes are extremely important–much more important than asset allocation or so-called “alpha.” This important reality is often overlooked by consumers of Wall Street products. Nobody can withstand Uncle Sam’s 50%+ carried interest program, also known as tax rates. Only the most sophisticated and intelligent proprietary traders can earn such a performance. Uncle Sam makes hedge fund fees look cheap with his 50%+ performance fee hurdle. But our goal is to minimize Uncle Sam’s fees. We can do this by minimizing capital gains, maximizing short-term capital losses, and deferring taxes as far out into the future as possible.

Click to enlarge.An example workflow for tax management is outlined in the figure below:

Click to enlarge.Taxes are everything for taxable investors. A failure to plan for taxes is to fail as an investor.

4.5 Three (3) RAA concepts (Pick your poison or create your own)

In general, thinking outside of a model is hazardous to one’s wealth. But every investor is different. The three options below are meant to suffice for a wide swath of investors whose primary goal is to protect against inflation, preserve capital, and grow their real wealth by 3-4% a year, if they’re lucky.

But perhaps you are an investor with an extremely bearish view on bonds; or perhaps you are extremely bullish on equities; or maybe you think the value anomaly is a fraud. As someone who has earned their hard-earned wealth, you also maintain the right to allocate as you see fit. Go for it. We merely present the three options below as a reasonable starting point.

Click to enlarge.How do these models perform, in theory?

4.6 Example RAA Process

Keep things as simple as possible, but no simpler.

Step 1 in the RAA process is to replace generic passive allocations to domestic and international equity with affordable high-conviction tax-efficient value and momentum alternatives.

Step 2 in the process is to calculate MA and MOM risk-management calculations on each “line” of the system (e.g., REITs, Domestic Value, etc.). If MA=MOM = 1 , 100% long; if MA=MOM = 0, 100% cash; otherwise, if MA<>MOM, go 50% long, 0% cash.

Step 3 in the process involves the implementation of tax-management techniques: harvest short-term losers; tax-manage hedging events; and annually rebalance such that one maximizes long-term capital gain and minimizes short-term capital gains. If an investor is running this system across qualified and non-qualified accounts, concentrate taxable dollars in tax-efficient equity exposures; concentrate non-taxable dollars in tax-inefficient fixed income and real asset exposures.

Click to enlarge.

4.7 Simulation Background for the Robust Asset Allocation Solution

Simulated Historical Performance: 1/1/1992 to 12/31/2013 (limited due to international momentum data limitations).

Benchmark results (4.8) are gross of management fee and transaction costs for illustrative purposes only.

Strategy results (4.9) are net of 50bps management fee and 50bps transaction costs (1% total annual costs). These are simulated performance results and do not reflect the returns an investor would actually achieve. All returns are total returns and include the reinvestment of distributions (e.g., dividends). Data is from Bloomberg and publicly available sources. Portfolios are annually rebalanced. MA and MOM risk-management rules applied on a monthly basis.

The following 5 asset classes are used in the RAA back-test:

SP500 = SP500 Total Return Index
EAFE = MSCI EAFE Total Return Index
REIT = FTSE NAREIT All Equity REITS Total Return Index
GSCI = GSCI Index
LTR = Merrill Lynch 7-10 year Government Bond Index (prior to 6/1982, Amit Goyal Data)
MOM_10 = U.S.Top Decile value-weight Momentum (Data)
VAL_10 = U.S. Top Decile value-weight Value (Data)
IMOM_5 = International Top Quintile Momentum (Average Top 3 market cap value-weight quintiles, Data)
IVAL_5 = International Top Quintile Value (Average Top 3 market cap value-weight quintiles, Data)

4.8 Benchmark Summary Statistics

Domestic value and momentum outperform the buy & hold index.
International value and momentum outperform the buy & hold index.
Bonds outperform real assets.

4.9 Strategy Summary Statistics

The results for the three perturbations of the robust asset allocation solution are presented below.

RAA_BAL = 40% Equity; 40% Real; 20% Bonds. Equity split between value and momentum. Risk-Managed.
RAA_MOD = 60% Equity; 20% Real; 20% Bonds. Equity split between value and momentum. Risk-Managed.
RAA_AGG = 80% Equity; 10% Real; 10% Bonds. Equity split between value and momentum. Risk-Managed.
IVY5_MA = 40% Equity; 40% Real; 20% Bonds. Moving average rule applied.
60/40 = 60% Equity; 40% Bonds.

RAA has historically outperformed the IVY 5 with MA system by 150-200bps–without excessive complication!

Conclusion:

Robust asset allocation solutions should be relatively simple, minimize complexity, and be robust across different market regimes. Simultaneous to these requirements, the solution must be affordable, liquid, simple, tax-efficient, and transparent, otherwise, many of the benefits of the solution will flow to the croupiers and Uncle Sam.

We recommend that investors explore our robust asset allocation framework and go for the do-it-yourself solution. You’ll be paying yourself 1%+ a year via saved RIA fees.

Is this the only solution? No. But any solution must be robust, simple, tax-manageable, and low-cost. This is our best effort to develop a simple model. Developing a complicated model is easy; simple is difficult.

We even provide some tools to facilitate (we’ll be improving these over the next few months–stay tuned).

If you are simply too overwhelmed by portfolio management, we implement our robust asset allocation for 50bps (minimum investment size is $1mm and above and we can go to 25bps for larger accounts).

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Please contact us if you are interested.

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