# The Betterment Portfolio Strategy

The portfolio strategy aims to achieve global diversification using Modern Portfolio Theory as a basis for asset allocation.

Our portfolio optimization includes tilts toward size and value, two drivers of performance identified by the landmark research of Fama & French.

Betterment's tax management strategy starts at the level of the portfolio strategy via inclusion of municipal bonds for taxable accounts.

Two prerequisites for the Betterment Portfolio Strategy are that it must enable personalized planning and built-in discipline.

Betterment has a singular objective: to help you make the most of your money, so that you can live better. Our investment philosophy forms the basis for how we pursue that objective: **Betterment uses real-world evidence and systematic decision-making to help increase our customers’ wealth.**

In building our platform and offering individualized advice, Betterment’s philosophy is actualized by our five investing principles. Regardless of one’s assets or specific situation, Betterment believes all investors should:

- Make a personalized plan.
- Build in discipline.
- Maintain diversification.
- Balance cost and value.
- Manage taxes.

In this in-depth guide to the Betterment Portfolio Strategy, our goal is to demonstrate how the Betterment Portfolio Strategy, in both its application and development, contributes to how Betterment carries out its investing principles. How we select funds to implement the Strategy is also guided by our investing principles, and is covered separately in our Investment Selection Methodology paper.

Within this paper, you will find that our portfolio construction process strives to define a strategy that is diversified, increases value by managing costs, and enables good tax management—three key investing principles.

Of these, portfolio strategy construction is most particularly concerned with diversification.

And that’s where most investment managers stop—diversifying a portfolio across asset classes. We don’t. As you’ll see in this paper, our prerequisites and iterative portfolio optimization process enable us to construct the portfolio strategy as one piece of a larger holistic investing approach where personalized planning, cost management, tax optimization, and discipline each are achieved through different methodologies. At the end of this paper, we will touch on the complementary processes we use in our investment process and how they work together to help our customers maximize their wealth.

## I. Prerequisites for a Betterment Portfolio Strategy

When developing a portfolio strategy, any investment manager faces two main tasks: **asset class selection** and **portfolio optimization**.

We’ll provide a guided tour of how we pursue each of Betterment’s investing principles and, in effect, accomplish each task along the way in crafting the Betterment Portfolio Strategy.

### Laying a Foundation for Personalized Planning & Discipline

To align with Betterment’s investing principles, a portfolio strategy must enable personalized planning and built-in discipline for investors. If the Betterment Portfolio Strategy—when standing alone—cannot reasonably be applied to an investor’s specific goal and situation, then it fails to help Betterment achieve its principle of helping customers formulate a personalized plan. If a portfolio strategy seems unintuitive or causes poor investor behavior, then we have failed to build in discipline.

The Betterment Portfolio Strategy is comprised of 101 individualized portfolios, in part, because that level of granularity in allocation management provides the flexibility to align to multiple goals with different timelines and risk tolerances. This helps to lay a foundation for the principles of personalized planning and built-in discipline. While Betterment solves for these principles in other ways as well, their manifestation starts with portfolio strategy itself.

## II. Achieving Global Diversification with a Nobel Prize-Winning Approach to Asset Allocation

An optimal asset allocation is one that lies on the efficient frontier, which is a set of portfolios that can achieve the maximum objective for the lowest amount of risk. The objective of most long-term portfolio strategies is to maximize return, while the associated risk is measured in terms of volatility—the dispersion of those returns. In line with our investment philosophy of making systematic decisions backed by research, Betterment’s asset allocation is based on a theory by economist Harry Markowitz called Modern Portfolio Theory, as well as subsequent advancements based on that theory.^{1}

Introduced in 1952, Markowitz’ work was awarded the Nobel Prize in 1990 after his theoretical framework and mathematical modeling informed decades of improvements in portfolio strategy construction. While there remains enormous debate (and entire sectors of financial services) devoted to portfolio construction and optimization, many practitioners rely on Markowitz’ theoretical framework to evaluate returns and measure risk for asset allocation. It’s also a very intuitive framework for constructing a portfolio strategy.

The major insight posited by Markowitz is that any asset included in a portfolio should not be assessed by itself, but rather, its potential risk and return should be analyzed as a contribution to the whole portfolio. This is mathematically expressed as an optimization of maximizing expected returns while penalizing those returns for risk. Using this insight as the objective of portfolio construction is just one way of building portfolios; other forms of portfolio construction may legitimately pursue other objectives, such as optimizing for income, minimizing loss of principal, or social responsibility.

However, our portfolio construction goes beyond traditional Modern Portfolio Theory in five important ways:

- Estimating forward looking returns
- Estimating covariance
- Tilting specific factors in the portfolio
- Accounting for estimation error in the inputs
- Accounting for taxes in taxable accounts

Each of these additions to basic Modern Portfolio Theory will be explained in full later in this paper.

### Asset Classes Selected for the Betterment Portfolio Strategy

Any asset allocation strategy starts with the universe of investable assets. Leaning on the work of Black-Litterman, the universe of investable assets for us is the global market portfolio.^{2} However, the global market portfolio is, in some sense, not well-defined, and, often, definitions depend on the context of the application. Below we describe the assets that compose our global market portfolio and, hence, the Betterment Portfolio Strategy.

To capture the exposures of the asset classes for the global market portfolio, we rely on the exchange-traded funds (ETFs) available that represent each class in the theoretical market portfolio. We base our asset class selection on ETFs because this aligns the portfolio construction with our subsequent process, our investment selection methodology, which currently evaluates and selects ETFs due to their low expense ratio compared to expected performance.

#### Equities

#### Developed Market Equities

We select U.S. and international developed market equities as a core part of the portfolio. Historically, equities exhibit a high degree of volatility, but provide some degree of inflation protection.^{3} Even though significant historical drawdowns, such as the global financial crisis of 2008, demonstrate the possible risk of investing in equities, longer-term historical data and our forward expected returns calculations suggests that developed market equities remain a core part of any asset allocation aimed at achieving total positive returns.^{4} This is because, over the long term, developed market equities have outperformed bonds on a risk-adjusted basis.

Within developed market equities, the following sub-asset classes are included in the Betterment Portfolio Strategy:

- Equities representing the total market of the United States
- Equities representing the total international developed market

#### Emerging Market Equities

To achieve a global market portfolio, we also include equities from less developed economies, called emerging markets. Generally, consistent with the research of others, our analysis shows that emerging market equities tend to be more volatile than U.S. and international developed equities. And while our research shows high correlation between this asset class and developed market equities, their inclusion on a risk-adjusted basis is important for global diversification.

Note that we exclude frontier markets, which are even smaller than emerging markets, due to their widely varying definition, extreme volatility, small contribution to global market capitalization, and cost to access.

#### Bonds

Bonds have a low correlation with equities historically. Because of this, they remain an important way to dial down the overall risk of a portfolio. To leverage various risk and reward tradeoffs associated with different kinds of bonds, we include the following sub-asset classes of bonds in the Betterment Portfolio Strategy.

- Short-term treasury bonds
- Inflation protected bonds
- Investment grade bonds
- International bonds
- Municipal bonds – read more here
- Emerging market bonds

### Figure 1. Correlation between Asset Classes in the Betterment Portfolio Strategy

**Figure 1. ***This figure demonstrates the correlation of each asset class relative to each other, using historical data from April 2007 to December 2016. A sample covariance matrix was calculated and then modified by the shrinkage method explained in this paper. The source of data for each asset class is Yahoo! Finance (a specific ETF represents each asset class).*

### Asset Classes Excluded from the Betterment Portfolio Strategy

While Modern Portfolio Theory would have us craft the Betterment Portfolio Strategy to represent the total market, including all available asset classes, we exclude some asset classes whose cost and/or lack of data outweighs the potential return gained from their inclusion in the portfolio strategy.

For this reason, we have excluded private equity, commodities, and natural resources, since estimates of their market capitalization are unreliable, and there is a lack of data to support their historical performance. Our chosen model for assessing the rate of return for a given asset also suggests that asset classes such as these may not show sensitivity to total portfolio returns.^{5}

While commodities represent an investable asset class in the global financial market, we have excluded the class of ETFs from the Betterment Portfolio Strategy for several reasons—most importantly, their low contribution to a global stock/bond portfolio’s risk-adjusted return. Read more about the case against including commodities in the portfolio strategy.

In addition, real estate investment trusts (REITs), which tend to be well marketed as a separate asset class, are not explicitly included in the portfolio strategy. We include exposure to real estate, but as a sector within equities. Adding additional real estate exposure by including a REIT asset class would overweight the portfolio strategy’s exposure to real estate relative to the overall market.

## III. Increasing Value with Evidence-based Portfolio Optimization

While asset selection sets the stage for a globally diversified portfolio strategy, to increase performance value at a reasonable cost (without sacrificing diversification) we must further optimize the portfolio strategy. This process requires tilting the portfolio strategy in ways that our analysis shows could lead to higher returns.

While most asset managers offer a limited set of model portfolios at a defined risk scale, the Betterment Portfolio Strategy is designed to give customers more granularity and control over how much risk they want to take on. Instead of offering a conventional set of three portfolio choices—aggressive, moderate, and conservative—our portfolio optimization methods enable the Betterment Portfolio Strategy to contain 101 different portfolios.

### Optimizing Portfolios to Help Increase Returns

Modern Portfolio Theory requires estimating returns and covariances to optimize for portfolios that sit along an efficient frontier. While we could use historical averages to estimate future returns, this is inherently unreliable because historical returns do not necessarily represent future expectations. A better way is to utilize the Capital Asset Pricing Model along with a utility function which allows us to optimize for the portfolio with the greatest return for the risk that the investor is willing to accept.

#### Computing Forward-Looking Return Inputs

To compute forward-looking returns for the Betterment Portfolio, we instead turn to the Capital Asset Pricing Model (CAPM), which assumes all investors aim to maximize their expected return and minimize volatility while holding the same information.^{6} Under CAPM assumptions, the global market portfolio is the optimal portfolio. Since we know the weights of the global market portfolio and can reasonably estimate the covariance of those assets, we can recover the returns implied by the market.^{7} This relationship gives rise to the equation for reverse optimization:

μ = λ Σ ω_{market}

Where μ **is the return vector**, λ **is the risk aversion parameter**, Σ **is the covariance matrix**, ω_{market}**is the weights of the assets in the global market portfolio**.^{8} By using CAPM, the expected return is essentially determined to be proportional to the asset’s contribution to the overall portfolio risk.

It’s called a reverse optimization because the weights are taken as a given and this implies the returns that investors are expecting. While CAPM is an elegant theory, it does rely on a number of limiting assumptions: e.g., a one period model, a frictionless and efficient market, and the assumption that all investors are rational mean-variance optimizers.^{9}

In order to complete the equation above and compute the expected returns using reverse optimization, we need the covariance matrix as an input. Let’s walk through how we arrive at an estimated covariance matrix.

The covariance matrix mathematically describes the relationships of every asset with each other as well as the volatility risk of the asset themselves. Our process for estimating the covariance matrix aims to avoid skewed analysis of the conventional historical sample covariance matrix and instead employs Ledoit and Wolf’s shrinkage methodology, which uses a linear combination of a target matrix with the sample covariance to pull the most extreme coefficients toward the center, which helps reduce estimation error.^{10}

#### Tilting the Betterment Portfolios based on the Fama-French Model

Decades of academic research have pointed to certain persistent drivers of returns that the market portfolio doesn’t fully capture.[9] A framework known as the Fama-French Model demonstrated how the returns of equity security are driven by three factors: market, value, and size.^{11}

The underlying asset allocation of the Betterment Portfolio Strategy ensures the market factor is incorporated, but to gain higher returns from value and size, we must tilt the portfolios. For the actual mechanism of tilting, we turn to the Black-Litterman model.

Black-Litterman starts with our global market portfolio as the asset allocation that an investor should take in the absence of views on the underlying assets. Then, using the Idzorek implementation of Black-Litterman, the Betterment Portfolio Strategy is tilted based on the level of confidence we have for our views on size and value.^{12} These views are computed from historical data analysis, and our confidence level is a free parameter of the implementation.

However, in both cases, the tilts are additionally expressed, taking into account the constraints imposed by the liquidity of the underlying funds.

#### Using Monte Carlo to Add Robustness to Our Tilted Asset Class Weights

Despite using reverse optimization to estimate the forward expected returns of our assets, we know that no one can predict the future.

Therefore, we use Monte Carlo simulations to predict alternative market scenarios. By doing an optimization of the portfolio strategy under these simulated market scenarios, we can then average the weights of asset classes in each scenario, which leads to a more robust estimate of the optimal weights. This secondary optimization analysis alleviates the portfolio construction’s sensitivity to returns estimates and leads to more diversification and expected performance over a broader range of potential market outcomes.

Thus, through our method of portfolio optimization, the Betterment Portfolio Strategy is weighted based on the tilted market portfolio, based on Fama-French, averaged by the weights produced by our Monte Carlo simulations. This highly methodical process gives us a robust portfolio strategy designed to be optimal at any risk level for not just diversification and expected future value, but also ideal for good financial planning and for managing investor behavior.

### Figure 2. Portfolio Allocations in the Betterment Portfolio Strategy

**Figure 2.*** This figure shows the Betterment Portfolio Strategy’s various weighted asset allocations for each stock allocation level.*

An easy way to see the value-add of our portfolio strategies is to look at the difference between our efficient frontier and that of a so-called “naïve” portfolio, one that is made up of only a U.S. equity index (SPY) and a U.S. bonds index (AGG). The expected returns of Betterment’s portfolio significantly outperform a basic two-fund portfolio for every level of risk (see Figure 4).

### Figure 3. Optimizing the Portfolio Strategy to Align to the Efficient Frontier

**Figure 3.** *The expected excess return hypothetical illustrated in this figure was calculated by reverse optimization using two inputs: market capitalization weight and asset covariance. The grey line can be considered a naïve portfolio of just two asset classes—U.S. Stocks (represented by SPY) and U.S. Bonds (represented by AGG). The blue line represents the the Betterment Portfolio Strategy across the entire risk spectrum. At each level of risk, the Betterment Portfolio Strategy has a higher expected excess return. This analysis is theoretical and it does not represent actual or hypothetical performance of a Betterment portfolio.*

## IV. Manage Taxes Using Municipal Bonds

For investors with taxable accounts, portfolio returns can be further improved on an after-tax basis by utilizing municipal bonds. This is because the interest from municipal bonds is exempt from federal income tax. To take advantage of this, the Betterment Portfolio Strategy in taxable accounts is tilted toward municipal bonds. Other types of bonds remain for diversification reasons, but the overall bond tax profile is improved. For investors in states with the highest tax rates—New York and California—Betterment can optionally replace the municipal bond allocation with a more narrow set of bonds for that specific state, further saving the investor on state taxes.

* Betterment customers who live in NY or CA can contact customer support to take advantage of state specific municipal bonds.*

## Conclusion

With every element of Betterment’s investing strategy, we hold to the same investment philosophy and the fundamental principles we believe lead to investing success. Our philosophy is simple: We use real-world evidence and systematic decision-making to help increase the value of our customers’ assets.

As explained throughout this paper, our portfolio construction process is built on years of research that point to three main areas of focus: diversification through asset allocation, improved value through portfolio optimization, and managing taxes. In the grander scheme of Betterment’s offering, these steps are just the beginning.

After setting the strategic weight of assets in the Betterment Portfolio Strategy, the next step in implementing the strategy is Betterment’s investment selection process, which selects the appropriate ETFs for the respective asset exposure in a low-cost, tax-efficient way. In keeping with our philosophy, that process, like the portfolio construction process, is executed in an systematic, rules-based way, taking into account the cost of the fund and the liquidity of the fund.

Beyond ticker selection is our established process for allocation management—how we advise downgrading risk over time—and our methodology for automatic asset location, which we call a Tax-Coordinated Portfolio™. Finally, our overlay strategies of automated rebalancing and tax-loss harvesting can be used to help further maximize individualized, after-tax returns.

Together these processes put our principles into action, helping each and every Betterment customer maximize the value while invested at Betterment and when they take their money home.

#### Citations

^{1} |
Markowitz, H., “Portfolio Selection”.The Journal of Finance, Vol. 7, No. 1. (Mar., 1952), pp. 77-91. |

^{2} |
Black F. and Litterman R., Asset Allocation Combining Investor Views with Market Equilibrium, Journal of Fixed Income, Vol. 1, No. 2. (Sep., 1991), pp. 7-18.Black F. and Litterman R., Global Portfolio Optimization, Financial Analysts Journal, Vol. 48, No. 5 (Sep. – Oct., 1992), pp. 28-43. |

^{3} |
Boudoukh, J and Matthew R., “Stock Returns and Inflation: A Long-Horizon Perspective.” The American Economic Review, (Dec., 1993). |

^{4} |
Siegel J., Stocks for the Long Run: The Definitive Guide to Financial Market Returns and Long-Term Investment Strategies. |

^{5} |
Stambaugh, Robert, “On the exclusion of assets from tests of the two-parameter model: A sensitivity analysis.” (1982) Accessible here. |

^{6} |
Sharpe, W. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19 (3), 425–442,Treynor, J. (1961). Market Value, Time, and Risk.Treynor, J. (1962). Toward a Theory of Market Value of Risky Assets.Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, 47 (1), 13–37.Mossin, Jan. (1966). Equilibrium in a Capital Asset Market, Econometrica, Vol. 34, No. 4, pp. 768–783. |

^{7} |
Litterman, B. (2004) Modern Investment Management: An Equilibrium Approach. |

^{8} |
Note that that the risk aversion parameter is a essentially a free parameter. |

^{9} |
Ilmnen, A., Expected Returns. |

^{10} |
Ledoit, O. and Wolf, M., Honey, I Shrunk the Sample Covariance Matrix, Olivier Ledoit & Michael Wolf. Accessible here. |

^{11} |
Fama, E. and French, K., (1992). “The Cross-Section of Expected Stock Returns”. The Journal of Finance.47 (2): 427. |

^{12} |
Idzorek, T., A step-by-step guide to the Black-Litterman Model. |

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