Motif Capital Horizon Models: A robust asset allocation framework

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Horace Knight
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1 Motif Capital Horizon Models: A robust asset allocation framework Executive Summary By some estimates, over 93% of the variation in a portfolio s returns can be attributed to the allocation to broad asset classes. Therefore the selection and weights of broad asset classes are especially important drivers of both returns and risk in a portfolio. Today, many broad asset allocation portfolios are based on the Nobel Prize winning research of Harry Markowitz and Modern Portfolio Theory (MPT). While MPT lays the foundation for developing a diversified investment portfolio, we believe it falls short in three important respects: It uses unreliable forward-looking assumptions for asset class returns. MPT s choice of volatility as a measure of risk may underestimate risk as investors actually experience it. It makes simplistic assumptions about the co-movement of asset classes. The combined effect of these features can lead to undesirable outcomes for investors as MPT ignores the high correlations between asset classes during times of market turmoil. Motif Capital sought to address the weaknesses in classic MPT with the introduction of our Horizon models, a suite of nine asset allocation models, which seek to deliver diversification across asset classes. The models cover three different time horizons one, five and 15 years and each of these time horizons also comes in one of three risk tolerances conservative, moderate and aggressive. This white paper describes the underlying philosophy, methodology and implementation of Motif s Horizon models and how we believe they can improve on Modern Portfolio Theory. Modern Portfolio Theory falls short To build the appropriate weights of the different asset classes, investors have used MPT to identify the asset portfolios that offer the highest expected return for the lowest level of risk. These optimal portfolios are used to build what is called the efficient frontier. The procedure to calculating the efficient frontier uses a system called mean variance optimization (MVO). In our view, MVO has the following limitations: Expected return is almost impossible to know MPT believes that the expected returns of each asset class are known. But the task of selecting the expected returns for the model is not an easy one. There are three common approaches and each one has pros and cons: 1. Historical data on asset returns Two obvious flaws in this method are that historical data on asset returns going back 40 to 50 years cannot provide robust estimates for expected returns and correlations in this framework and that there is uncertainty about how much asset class behavior will mirror the past. 2. Implied expected returns The most widely used tool for estimating the implied expected return is the Black-Litterman model, which still requires an important piece of information: the covariance matrix of asset class returns. The covariance matrix requires even more data than the estimate of returns. 3. Factor models for forward-looking returns This involves combining market implied returns with the views of investment managers, even if these views are subjective or unfounded. Motif Capital Horizon Models: A robust asset allocation framework 1

2 Actual Returns vs Assumed Normal Distribution 14% 12% 10% 8% 6% 4% 2% 0% Market Crash (10/87) Financial Crisis (10/08) LTCM Fail (8/98) -25% -20% -15% -10% -5% 0% 5% 10% 15% Actual Returns Assumed Normal Asset class returns do not follow a normal distribution MVO assumes normal distributions for asset class returns. Consider this example: about two-thirds of the time returns may be within one standard deviation of the average return. However, a normal distribution is unable to account for extreme market events, which occur more often than this model would imply. As the above graph showing the distribution of actual market returns demonstrates, events like the Market Crash in October 1987 cannot be explained by the assumption of a normal distribution of returns. Correlations between asset class returns are not linear MVO assumes that correlation coefficients among asset class returns move in a linear fashion. In fact, they are asymmetrical. Correlations in bull markets are different from correlations in bear markets and can diverge greatly. Investors perception of risk MPT uses standard deviation commonly known as volatility as a proxy for risk. A security that rises by 10% and one that falls by 10%, are deemed to have the same risk. However, this approach does not capture that investors feel and fear loss much more than they enjoy gain. Standard deviation does not differentiate between portfolios with large upside surprises and those with large downside surprises. Moving toward optimal: The Motif Horizon approach In our approach, we seek to tackle the limitations of classical MPT by employing advances in computational techniques and statistical methods. Specifically, in building the Horizon models, these are the areas we sought to improve upon: 2 Motif Capital Horizon Models: A robust asset allocation framework

3 Expected returns cannot be known We start with the premise that the only information known with complete certainty is historical returns. While historical returns are not indicative of future returns, we can reasonably assume that certain characteristics of asset class returns will persist into the future. Our next challenge is to tease out those features that characterize the historical asset class returns and build a model for them. We selected a method called the Kernel Density Estimator, which deals with the distributional uncertainty with what form and shape the distribution of returns will take, rather than assuming these beforehand. We also looked at the parameter uncertainty to what degree of certainty the distribution parameters can be estimated. Portfolio risk and return For assessing long-term expected returns, we use geometric mean because it does not overstate cumulative portfolio return. It is also helpful in calculating realized compound return. To measure risk, the method we chose is Conditional Value-at-Risk (CVaR) because it does not treat upside and downside as the same. It assigns greater risk to negative surprises because that is how investors experience them, i.e. the impact of market declines is perceived as more of a risk than equivalent moves to the upside. Asset Class Returns Distribution Probability Density % -12% -4% 4% 12% 20% Monthly Returns Kernel Density Normal Density Motif Capital Horizon Models: A robust asset allocation framework 3

4 Large Negative Surprises 3.50% 3.00% 2.50% 2.00% 1.50% 1.00% 0.50% 0.00% -5.5% -4.5% -3.5% -2.5% -1.5% -0.5% 0.5% 1.5% 2.5% 3.5% 4.5% 5.5% Monthly Returns (%) 3.50% Large Positive Surprises 3.00% 2.50% 2.00% 1.50% 1.00% 0.50% 0.00% -5.5% -4.5% -3.5% -2.5% -1.5% -0.5% 0.5% 1.5% 2.5% 3.5% 4.5% 5.5% Monthly Returns (%) 4 Motif Capital Horizon Models: A robust asset allocation framework

5 In the illustration to the left, both distributions are approximately normal, but one has a large negative tail (top graph) and one has a large positive tail (bottom graph). The standard deviation for both is identical, but the CVaR is significantly more negative for the distribution in the top panel because it takes into account the average return for the 5% worst cases. The efficient frontier We combine the asset returns distribution with measures of risk and return to develop a set of optimal portfolios, each of which has the highest geometric returns for a given level of downside risk (in our case, CVaR) which is similar to the efficient frontier used in the traditional MVO framework. To arrive at the calculations of geometric mean and CVaR, we use extensive resampling from the kernel density, which is computationally intensive, but achievable today with a modern desktop computer. Next we use a genetic algorithm, commonly used to find computational solutions when a straightforward analytic solution is not available, that in our case is designed to maximize the geometric average returns while simultaneously minimizing the risk (CVaR). Asset class selection Allocation across multiple asset classes can help investors maximize their risk-adjusted return. Therefore, each included asset class is intended to add value either increase returns or reduce risk. The asset classes should also be investable in an efficient and cost-effective way. As a result, we include these asset classes: U.S. equities International equities U.S. bonds International bonds Commodities U.S. real estate One notable asset class exclusion is Treasury Inflation- Protected Securities (TIPS), which is intended to protect investors from inflation. However, we have chosen to omit TIPS because our research indicates that TIPS correlate better with changes in inflationary expectations than the level of inflation itself. Motif Capital Horizon Models: A robust asset allocation framework 5

6 1 Year Horizon Motifs US Bonds International Equities International Bonds Commodities US Equities US Real Estate 3.3% 4.9% 3.7% 4.2% 5.6% 5.1% 10.7% 19.4% 23.9% 39.0% 12.5% 30.0% 23.1% 25.3% 16.5% 27.2% 17.8% 27.8% Conservative Moderate Aggressive 5 Year Horizon Motifs US Bonds International Equities International Bonds Commodities US Equities US Real Estate 2.7% 5.7% 3.4% 4.4% 5.6% 8.0% 10.7% 19.5% 39.0% 13.2% 19.4% 27.6% 29.6% 23.9% 16.5% 25.4% 16.0% 28.5% Conservative Moderate Aggressive 15 Year Horizon Motifs US Bonds International Equities International Bonds Commodities US Equities US Real Estate 5.6% 7.8% 3.4% 4.4% 5.7% 8.8% 9.9% 18.1% 31.7% 13.3% 18.7% 16.3% 15.8% 27.9% 31.3% 24.0% 31.8% 25.5% Conservative Moderate Aggressive 6 Motif Capital Horizon Models: A robust asset allocation framework

7 Putting it together: The Horizon models We recognize that risk and time horizon are independent variables, so each of the time horizons (one, five and 15 years) is available in each of three risk tolerances (conservative, moderate and aggressive). We recognize that some 30-year olds can be more risk-averse than some 65-year olds, despite their longer time horizons. The illustration to the left shows how allocations to the asset classes vary in each of the nine different Horizon models. For a given investment horizon, as one moves up the risk tolerance scale, the allocation progressively moves from U.S. bonds and international bonds to historically riskier asset classes (e.g., U.S. equities, international equities, commodities and U.S. real estate). The changes in asset class weights for the different risk tolerances are not dramatic, but there is a discernible shift toward international bonds and international equities when we increase the investment horizon. While developing a distinct asset allocation model is key, implementing it in a cost effective way is equally important. Motif utilizes passive, low-cost index-based exchangetraded funds for each asset class. There are a number of reasons for this: ETFs are priced in real time and trade throughout the day. Average ETF fees are around 0.60%, much lower than mutual funds. ETFs are transparent and more liquid than mutual funds. With over 1400 ETFs in the U.S., investors can easily access all the major asset classes, sectors and industries. We select the ETFs for inclusion based on factors such as: cost, liquidity, ability to track the benchmark and credit ratings of the underlying securities. Rebalancing Once a model is selected, investors must be mindful that it continues to meet their goals, cash flow needs and risk tolerance. Market movements may also alter the asset class composition of the model. It might be necessary to rebalance from time to time. The primary goal of rebalancing is not to maximize returns but rather to minimize risk relative to the target asset allocation. Motif s Horizon models use a time and threshold-based rebalancing strategy. When asset classes hit a pre-defined threshold at the scheduled month-end date, the portfolio will automatically be rebalanced back to the target allocation. We find our time and threshold-based rebalance strategy has a number of benefits: Objective, rules-based rebalancing provides investors discipline and reduces unintended reactions due to emotions. Reduces unnecessary rebalances when portfolio allocation is consistent with investor goals. Allows investors to buy securities that have depreciated in value, while selling those that have risen. Gives investors the ability to tailor the rebalance frequency to their individual needs. Conclusion Modern Portfolio Theory is a good starting point for building a diversified asset allocation portfolio that addresses investors time horizon and risk tolerance. However, due to shortcomings in MPT and with the ability to run more robust computational models, we believe Motif s nine Horizon models can present a better reflection of risk tolerance and expected return. This methodology, coupled with broad, non-overlapping asset classes and low-cost ETFs, can deliver a robust asset class allocation solution. Motif Capital Horizon Models: A robust asset allocation framework 7

8 Contributing Authors Tuhin Ghosh, PhD, CFA Chief Investment Officer Peter Andes, CFA Director of Investment Strategies Andrew Kovalev, PhD Senior Quantitative Researcher Xin Zhang Quantitative Researcher About Motif Capital Motif Capital Management is a next-generation global equity investment manager that specializes in the management of thematic investment strategies for financial institutions such as private wealth management, investment companies, endowments, and family offices. Our unique disciplined, scientific, and transparent approach to thematic investing relies on combining data-driven insights with objective fundamental research, algorithmic portfolio design and cutting-edge technology & analytics. Our goal is to work with our institutional partners to act on the economic, socio-political, and technological forces that are shaping the global economy for the benefit of their clients portfolios. Learn more at Motif Capital Management, Inc. is an SEC registered investment advisory firm located in San Mateo, California. The company is privately held and a wholly-owned subsidiary of Motif Investing Inc., a broker-dealer registered with the SEC and member FINRA/SIPC. ETFs have unique features that you should be aware of, which can include distribution of any gains, risks related to securities within the portfolio, and tax consequences. The data quoted herein represents past performance and is not indicative of future results. The investment return and principal value of an investment will fluctuate so that your investment, when redeemed, may be worth more or less than their original value. Current performance may be lower or higher than the performance data provided. Please review the prospectus or other research tools provided on this site for more recent performance information. Contact Motif Investing at to obtain the most recent month-end performance data. Contents contained herein created for informational purposes only and does not represent a recommended investment or investment strategy you should pursue for investment purposes. Investing in securities involves risks, you should be aware of prior to making an investment decision, including the possible loss of principal. An investment in individual stocks, or a collection of stocks focused on a particular theme or idea, such as a motif, may be subject to increased risk of price fluctuation over more diversified holdings due to adverse developments which can affect a particular industry or sector. Investments in ETFs can include those with a narrow or targeted investment strategy and can be subject to similar sector risks than more broadly diversified investments. Motif makes no representation regarding the suitability of a particular investment or investment strategy. You are responsible for all investment decisions you make including understanding the risks involved with your investment strategy. Communication created for institutional audience only Motif Capital Management Inc. All rights reserved.