# How We Estimate the Added Value of Using Betterment

The estimated incremental value of Betterment’s offering to a representative customer already investing in low-cost ETFs on their own is 0.90% per year.

When we include the evidence that Betterment’s portfolio recommendations are lower cost than what the typical investor may often choose, that value increases to an estimated 1.48%.

#### Table of Contents

*Our original estimates of Betterment’s incremental value (published on April 12, 2019) were impacted by an error in the simulation code. On May 22, 2019, we corrected that error for the simulation involving a half-liquidation and moderate tax bracket scenario. On May 23, 2019, we corrected that error for all other scenarios.*

“Measure what is measurable, and make measurable what is not so”. While there is some doubt about the origin of this quote—perhaps Galileo—the message is something that all of us at Betterment strive towards in our journey to make finance—and the financial well-being of our customers—better. Our research projects often begin with the question “How will we measure the success of this proposal?” By deciding how we’ll measure, we can then readily interpret the results and later improve on that measure.

Our focus on measurement is how we improve Betterment for our customers. An investor’s chief concern is to grow the value of her money in measurable ways, and, as a fiduciary, one of the most important questions we ask ourselves is “how do we continually measure the value we bring to our customers in our services and recommendations?

Here in this methodology, we attempt to answer that question. We’ll show you how we assign a quantitative estimate of the added value you gain by following Betterment’s investing recommendations for retirement using our optional tax-smart strategies.

To understand how we arrive at an estimate on this valuation of using Betterment, you need to know the three steps of our approach:

- We take into account many possible scenarios for the future.
- We then identify which attributes reflect the typical investor’s investment choices and situation.
- Finally, we simulate how those attributes could shape future possible scenarios.

We’ll describe how we arrive at our description of Betterment’s added value by guiding you through all three steps of this process below.

## I. Measuring What Matters: We Simulate Many Possible Futures, Instead of a Naïve Forecast.

Our recommended investments are based on research looking at which investment strategies have historically outperformed, but one of the first lessons taught in finance is that what has worked in the past may not work as well in the future.

How do we know that our investment methodology will hold up in a wide set of potential market scenarios?

As the second part of that question implies, the answer won’t necessarily be one single metric.

By measuring our value with historical returns for a single customer, we would find the answer for that one situation, but it would tell us very little about future prospects. We also know that there are different variables that influence our performance, and those are also dependent on their own set of assumptions. For example, tax-loss harvesting has its greatest potential impact when funds are concentrated in a taxable account and the customer has a high tax-bracket, whereas our Tax Coordination works best for customers who spread their investments over a mix of taxable and tax-deferred accounts.

When faced with problems such as these that are highly path-dependent and sensitive to inputs, one of the most powerful tools in the quantitative analyst’s arsenal is the Monte-Carlo simulation. Named after the world-famous Monegasque casino, a Monte-Carlo simulation is a framework that takes in uncertain inputs and a formula for what to do with those inputs, and applies the formula to our inputs several hundred or thousands of times. We can then measure the outcomes in order to produce a forecast of likely future outcomes.

As an example, let’s say I flip 10 coins and want to measure how many of them land as heads. We have 10 uncertain inputs (coins) and a concrete formula for aggregating the results (summing the number of heads). If we perform this experiment once, we could get any value between 0 and 10 heads, and we won’t learn very much at all. If we run this experiment 100,000 times, however, we should get much closer to the actual distribution of probabilities:

Of course, for something as simple as coin-flips, we can calculate the probabilities analytically, and we see that our simulation (blue bar) and analytical solution (gray line) match up almost exactly. Our “naive” solution of just flipping the coins hundreds-of-thousands of times got us the same result. We now know that the chance of getting 5 heads when flipping 10 coins is a bit less than 25%, and we didn’t even have to mention binomial distributions or deeper statistical calculations.

How do we translate this into measuring our investment value? Let’s recap the two things we need: a set of uncertain inputs, and a formula to translate those inputs into a distribution of outcomes:

Both of the components in this equation are crucial if we want to get a realistic answer to our question.

### The Cloud Ferrari: Our Investment Testing Framework

Starting with the second part of our Monte-Carlo equation, let’s explore the investment testing framework we use at Betterment. Our goal here is to test our strategies in a way that simulates how the investments of our customers who follow Betterment’s investing recommendations for retirement would perform.. This means the framework must be able to simulate trading decisions down to specific moves we make based on tax lot accounting, while still optimizing decisions over the period a person is investing, which we assume here to be multiple decades (i.e. investing for retirement). The simulation must be quick, robust, and handle any historical data we give it, while also generating hypothetical market data for any scenario we can imagine so we can stress-test our algorithms at the limit.

The result is what we’ve lovingly dubbed our “Cloud Ferrari”, a replica of our real-life trading process that runs on the cloud, pulling in scenarios from a message queue and then aggregating the results. With this framework, we can see what trades our algorithms would execute in thousands of different scenarios, the reason that the algorithm decided to engage in that trade, and exactly which tax-lots the algorithm chose to buy or sell. This setup allows us to run thousands of simulations in just a few hours, while retaining a full history of the strategies’ performance.

Our Monte-Carlo engine allows us to vary several hundreds of inputs depending on what we want to test, including (but certainly not limited to) the following inputs:

- Patterns of how investors make deposits
- Account type combinations (e.g. IRAs, Roth IRAs, taxable investing accounts)
- Lot-sort algorithms
- Rebalancing algorithms
- Tax bracket assumptions
- Portfolio allocation glidepath assumptions
- Tax-loss harvesting algorithms
- Deposits into tax-coordinated accounts

## II. Describing Typical Investors and How They Invest with Betterment

Even the best testing framework will give incorrect results if given wrong assumptions. Even realistic assumptions can lead to incorrect inferences if the assumptions do not line up with the type of questions asked. In this paper, we seek to ask a very specific question: “What is the added value for the typical retail investor of switching to Betterment?” There are two implicit assumptions here that we should make explicit:

- What do we mean by “added value”?
- What do we mean by “typical investor”?

To answer these questions and more, let’s go through our assumptions in turn. For each area of assumptions, we’ll describe a typical investor elsewhere (the “benchmark” investor) and at Betterment (i.e. a Betterment user).

### 1. A Typical Investor’s Portfolio Strategy

Since Betterment is only available for U.S. residents, we assume that a typical investor that doesn’t use Betterment—hereafter the “benchmark” investor—would invest in hypothetical U.S. equity and fixed income funds. Our simulated returns for these funds incorporate expected asset class returns from our Black-Litterman-based model.

The portfolio set for Betterment’s typical investor will be the Betterment Portfolio Strategy.

### 2. Sources of Potential Underperformance

Investors may underperform their investment benchmarks for several reasons. They may underperform based on the overall construction of their portfolios. Separately, many investors end up choosing high-cost funds that have fees far higher than the low-cost funds in which Betterment invests. Some funds may also underperform based on the way they are managed, including certain less effective “active” strategies.

A great source for estimating such underperformance is S&P’s bi-annual SPIVA reports. In each report, S&P reports the model returns of its benchmarks for 18 different asset classes, as well as the average total return of funds that track the same benchmarks. More often than not, the funds significantly underperform their benchmark. To find the typical deviation in performance between the hypothetical benchmark funds in our simulations and the ex-ante expected returns, we look at the 15-year annualized numbers for each relevant asset class from SPIVA’s 2018 mid-year report. We use this deviation as an estimate of the underperformance (“SPIVA costs”) associated with investing in funds that have higher expense ratios or otherwise lag their benchmark relative to the funds in Betterment’s portfolio. Because underperformance can be attributed both to portfolio construction at the asset-class level and to fund-specific expenses and returns, we decided to view the benchmark typical investor in two ways (leading to two sets of simulations in the following section):

- In the first set of assumptions, we use the asset-class level expected returns associated with the hypothetical benchmark funds and funds in Betterment’s portfolios, such that we are measuring any differences attributable to asset allocation.
- In the second set of assumptions, we look at performance net of expenses, using the SPIVA costs provided by S&P in the mid-year report for 2018 and adding the expenses associated with the Betterment portfolio. This set of assumptions will help us measure the added benefit of Betterment’s fund selections, which typically have lower expenses and more closely track the relevant benchmark.

### 3. Asset Allocation at Start and Over Time

Given the above portfolio strategies, the question is what is the typical investor’s weighting of stocks to bonds? At Betterment, since allocation advice is based on what kind of goal you set, we chose the most common long-term goal type: a retirement goal. The goal determines both a beginning target allocation and a glidepath of allocation changes as retirement nears.

So, a typical Betterment investor (who we assume begins investing in Betterment at age 35) is considered to start with a portfolio allocation of 90% stocks, 10% bonds, and over time, the allocation adjusts automatically until the investor’s portfolio allocation reaches a 56% stock, 44% bond mix at retirement.

To create a fair comparison, we assume that the benchmark allocation follows the same glidepath. In other words, we don’t assume Betterment’s allocation management process provides any greater level of efficiency than individual investors could achieve on their own.

### 4. Rebalancing and the Efficiency of Sorting Tax Lots

Since we’re assuming the typical investor maintains a target allocation, we also are assuming some rebalancing behavior that maintains the allocation.

We assume that the benchmark investor rebalances to the target allocation annually, around year-end. Annual rebalancing is a common low-maintenance approach to rebalancing endorsed by a variety of investment firms. We assume that the benchmark investor does not rebalance with tax implications in mind, meaning that short- and long-term gains and losses may be realized. Specifically, we assume that lots are sold in a First-In-First-Out (FIFO) order, as this is the standard way that the IRS calculates your taxes on capital gains if you do not otherwise specify which lots you sold.

For Betterment, we assume that rebalancing is done according to our rebalancing algorithm, which is proprietary and built in to every account. Our rebalancing methodology aims to limit tax consequences by using your cashflow, and it also uses drift-based rebalancing, aiming to keep the allocation within 3% of the target weights. Our rebalancing approach also refrains from causing short-term gains, as these are particularly tax inefficient.

### 5. Account Types and Asset Location

Given that the typical investor is investing for retirement, we assume the accounts used are a mix of Roth and traditional IRAs and taxable investment accounts. The mix is the same for both the Betterment user and the benchmark investor.

Meanwhile, at Betterment, we typically recommend accounts within a retirement goal utilize Tax Coordination, which is Betterment’s automated approach to asset location. Asset location is the practice of keeping tax-inefficient assets in tax-advantaged accounts, and tax-efficient assets in taxable accounts. Asset location can provide a lot of value when done correctly, but it requires a great deal of manual work, making Tax Coordination an important service. So, we assume that the typical Betterment investor’s portfolio is asset located according to our Tax Coordination methodology, while the comparison investor’s portfolio is not.

### 6. Tax-Loss Harvesting

Since a portion of the typical investor’s portfolio is assumed to be in a taxable account, the investor has the opportunity to harvest capital losses. This means selling an asset that’s depreciated in value, while purchasing a different asset to retain upside, allowing you to offset other gains up to $3,000 of earned income. Given the time and effort required, we assume the benchmark will not harvest losses at all.

Meanwhile, Betterment automates the process with Tax Loss Harvesting+ completely, making it a common part of taxable investing at Betterment. We assume a typical Betterment investor uses Tax Loss Harvesting+ and that harvesting opportunities are evaluated daily.

### 7. Management Fees

We assume the Betterment investor is charged a fee of 0.25% per year. In the simulations, we assume that this fee is charged quarterly and calculated based on the average account balance over the preceding quarter.

We assume that the benchmark investor has no added fee applied, as they are managing their own investments. We don’t assume they face any costs per trade, even though most brokerages for individuals charge per trade.

### 8. The Typical Investor’s Income and Tax Information

Given that many Betterment features are designed to help optimize taxes for customers, we also have to make some assumptions about the characteristics and income of the investor to quantify the value of these features.

For our simulations, we assume that both the benchmark investor and Betterment customer are residents of California, as this is both the most populous state and the state in which more Betterment customers reside than any other. To estimate the value of Betterment’s offering for a wider range of customers, we run our simulations for two different income-level assumptions (“moderate” and “high”), which also affects the assumed tax brackets.

We summarize these assumptions in the table below.

Assumption | Typical investor with moderate income | Typical investor with high income |
---|---|---|

Location | California | California |

Age | 35 | 35 |

Tax Filing status | Single | Single |

Pre-tax annual income (USD) | 120,000 | 562,000 |

Federal marginal tax rate | 24.0% | 37.0% |

State marginal tax rate | 9.3% | 12.3% |

Net-investment income tax | 0.0% | 3.8% |

Short-term capital-gains / non-qualified dividend income rate | 33.3% | 53.1% |

Long-term capital-gains / qualified dividend income rate | 24.3% | 36.1% |

### 9. An Investors’ Initial Savings and Future Investments

We don’t assume the typical investor starts with nothing. Rather, we assume that by age 35, the typical investor (whether at Betterment and elsewhere) has already saved an amount equal to their current annual income in total, spread across three accounts (Taxable, Roth IRA, Traditional IRA).

Moreover, we assume the typical investor will save and invest in the future based on the Bureau of Labor Statistics’ data for marginal propensity to save. Then, we assume the investor will use our calculator on “Which IRA Should You Choose?” to estimate how much to put in each of their three accounts.

Of course, investors have to adhere to income and contribution limits on IRA accounts, currently $6,000 per year. At the time the simulations were run, the limits were still $5,500 per year, which are the limits we used in the simulations, and we assumed an increase in these deposit limits of 2% per year.

The table below summarizes how we assume a typical investor will invest.

Assumption | Typical investor with moderate income | Typical investor with high income |
---|---|---|

Initial balance | 120,000 | 562,000 |

Accounts | Taxable, Roth IRA and Traditional IRA | Taxable, Roth IRA and Traditional IRA |

Tax filing status | Single | Single |

Monthly (annual) taxable deposits | $708 ($8,500) | $11,833 ($142,000) |

Monthly (annual) Roth IRA deposits | $229 ($2,750) | $0 ($0) |

Monthly (annual) Traditional IRA deposits | $229 ($2,750) | $458 ($5,500) |

### 10. The Investor’s Timeline and Way of Liquidating

We assume the typical investor saving for retirement will be invested for 30 years, from age 35 to 65. We then assume they can liquidate and withdraw their money at the last date of the simulation in three different ways:

- Liquidating 100% of their portfolio – Full liquidation all at once.
- Liquidating 50% of their portfolio – Half liquidation all at once.
- Liquidating none of their portfolio – Zero liquidation.

These three different ways of liquidating allow us to simulate an additional dimension of possible outcomes.

## III. Simulating Uncertain Future Markets and Investors Over Time to Understand Betterment’s Value

Now that we have a framework for simulating investment strategies, and a set of assumptions we want to test, we can get to the good stuff:

- Calculating the distribution of outcomes from our Monte-Carlo simulation.
- Selecting the set of outcomes that best reflect Betterment’s overall value to the public.

While we’ve already explained how our simulation framework will work overall, let’s replace the coin-toss example from the first section with the real simulation scenario we used: a projection of market conditions.

### Simulating Market Changes and Dividends

We begin by simulating hundreds of different market scenarios, over a 30-year simulation horizon. These scenarios encompass everything from surging bull markets, to crushing bear markets and anything in between.

We generate forward-looking scenarios by sampling daily returns for each asset from what statisticians call a multivariate normal distribution. This underlying distribution of possible returns is driven by the same model of expected returns that underpins the Betterment Portfolio Strategy.

We simulate dividends by looking at historical dividend yields, and fixing a univariate normal distribution for each asset, with the mean based on one-year trailing dividend yields as of the date of simulation, and the variance based on five-year trailing dividend yields.

The discrepancy in sampling lengths here is due to rising interest rates making a five-year look-back period for mean dividend yields overly conservative, as we expect dividend yields for a bond fund over the next 30 years to be higher than they have been over the past 5 years. We’ve made this adjustment based on the fact that after the financial crisis of 2008, the Federal Reserve set the Federal Funds rate at a historically low 0%. Since then, the Fed has increased the rate. Since the interest of most bonds is highly dependent on this rate, we believe that incorporating the full past 5 years in our sampling would underestimate the dividend yields on bond funds for the foreseeable future.

We then simulate dividends for each asset at the frequency which the asset currently pays dividends, e.g. monthly for the short-term U.S. treasury bond ETF, SHV and quarterly for the emerging markets stock ETF, VWO. We subtract our calculated dividend yield for each asset from the expected return estimates before simulating prices so that we simulate price-returns, rather than total returns. We account for the tax liability created by dividends within the simulation by keeping a record of all dividends that were paid to an account, and then paying taxes on those dividends accordingly at the end of the simulated year.

### Simulation Results and Selected Outcomes

We simulate both the Betterment investor’s portfolio and the benchmark investor’s portfolio in these conditions. However, as mentioned above, due to differences in a benchmark investor’s portfolio expenses, we’ve simulated comparisons between the two portfolios both with and without the effects of the average fund’s expense ratio in the 2018 SPIVA mid-year report, creating two simulation sets. Then, since investors can withdraw and liquidate their money, we have projections for three different ways of doing so.

The result of our simulations is a rich set of results, including everything from trades, losses harvested, drifts from the benchmark and so on.

You’ll see the simulation outcomes as annualized internal rate of return, which we often call “money-weighted return.” This value is the average annualized return at which each cash-flow grew to reach the resulting final portfolio value. This gives us an estimate of the annualized performance. These performance figures vary by path, and the full range of internal rates of return (IRR) can vary significantly based on path.

Then, we’ll explore the added value (i.e. alpha) of Betterment compared to the benchmark investor, our chief analytical objective.

Let’s explore each set of simulations.

### Simulating Internal Rate of Return

Here, you can review internal rates of return for each scenario—each set of portfolio assumptions, liquidation type and tax bracket scenario.

In the chart above, we plot the IRR for each simulation as a distribution. There are a few things to note here:

- The return, which we plot on the x-axis, varies quite significantly between the simulations. For both the benchmark investor and the Betterment investor, the 30-year annualized returns could be anywhere from 0% to roughly 13%. This distribution of values exists as we considered a large number of market scenarios.
- The distribution of returns for the benchmark investor is narrower than that of the Betterment investor. This means that the range of possible IRRs is smaller than that of the Betterment investor.
- In all panes of the chart, we see that the distribution of returns for the Betterment investor is shifted to the right of the benchmark investor. This means that the Betterment investor generally had higher returns than the benchmark investor over the 30-year simulation period.

Next, we calculate the average return for each investor so that we can more easily compare the strategies. The results can be seen in the table below:

Mean IRR | |||
---|---|---|---|

Liquidation | Strategy | In a moderate tax bracket | In a high tax bracket |

Full | Benchmark | 6.01% | 5.32% |

Betterment | 6.96% | 6.09% | |

Half | Benchmark | 6.34% | 5.79% |

Betterment | 7.24% | 6.60% | |

Zero | Benchmark | 6.59% | 6.04% |

Betterment | 7.46% | 6.91% |

When we add in the fund fees and account for the differences between asset-class returns and fund returns as outlined in the SPIVA report, we get a different set of results:

As before, we plot the distribution of IRRs for each investor, with the panes representing the various liquidation and tax assumptions. In general we see slightly lower IRRs across all panes, which is expected since we have additional costs baked into these simulations. The table below shows the average IRR across the various scenarios:

Mean IRR | |||
---|---|---|---|

Liquidation | Strategy | In a moderate tax bracket | In a high tax bracket |

Full | Benchmark | 5.24% | 4.60% |

Betterment | 6.76% | 5.88% | |

Half | Benchmark | 5.56% | 5.03% |

Betterment | 7.04% | 6.34% | |

Zero | Benchmark | 5.81% | 5.27% |

Betterment | 7.27% | 6.63% |

### Simulating Betterment’s Added Value (i.e. Alpha)

Now that we’ve compared simulated internal rates of return, we can simplify this view to answer the question: Based on our assumptions, what is Betterment’s value add to the typical investor saving for retirement? In analyst terms, what is Betterment’s alpha? You can explore this in each scenario, and we’ll also describe the situation we point to as applicable for an investor comparing Betterment customers who follow our investing recommendations to benchmark investors who self-direct their investments.

The most notable insight from the chart above is that, in all panes, the vast majority of the distribution lies above 0%. This means that in almost all of the simulations, the Betterment investor outperformed the benchmark investor. The difference in returns covers a relatively wide range, where in the worst case (for the Betterment investor) the benchmark investor outperforms by around 1% per year, and in the best case the Betterment investor outperforms by around 3% per year.

To simplify and give you a single number, we take the average of the simulated alpha values—the mean—for each tax bracket and liquidation scenario.

Added value (mean) of Betterment over the benchmark | ||
---|---|---|

Liquidation | In a moderate tax bracket | In a high tax bracket |

Full | 0.96% | 0.77% |

Half | 0.90% | 0.81% |

Zero | 0.87% | 0.87% |

From here, if we judge the half-liquidation, moderate tax bracket investor as the representative sample, we see that a Betterment customer can expect to make about 1.03% more per year after taxes and fees than the benchmark.

We can also calculate what the extra take-home money could be for a Betterment customer versus the benchmark investor. By simulating the initial and periodic deposits according to the internal rates of return at full-liquidation (e.g. 6.01% for the benchmark investor in the moderate tax case, and 7.10% for the Betterment investor in the same tax case), we can calculate the estimated total amount of cash a customer could have after 30 years for each path. From there, we can calculate the increase in after-tax cash that the Betterment customer would have over the benchmark investor.

Tax bracket | Projected increased cash (mean percentage) after 30 years |
---|---|

Moderate | 23.7% |

High | 16.8% |

Remember that added value is a projection without fund fees and the typical costs as reported by SPIVA. Now, let’s review the impact taking into account those fees.

The added value is even higher now in all scenarios, with the maximum alpha even approaching 4% in some cases. The average added value can be seen in the table below:

Added value (mean) of Betterment over the benchmark | ||
---|---|---|

Liquidation | Moderate Tax | High Tax |

Full | 1.53% | 1.28% |

Half | 1.48% | 1.30% |

Zero | 1.47% | 1.36% |

Similarly as before, we can pick the half-liquidation, moderate tax bracket as the representative situation, and see that the typical investor who uses average-cost funds as opposed to low-cost funds could gain an extra 1.48% per year from investing with Betterment. We also calculate the mean percentage of extra cash after a 30-year investment horizon.

Tax bracket | Projected increased cash (mean percentage) after 30 years |
---|---|

Moderate | 38.8% |

High | 27.9% |

## Summarizing Betterment’s Added Value

In this methodology, we’ve shown you our robust (and yet conservative) approach to calculating the added value Betterment offers the typical investor.

It’s worth mentioning the significant handicap we’ve placed on Betterment, in fact. In our assumptions, we removed any possible value of de-risking the asset-allocation over time, of more tax-efficient allocation adjustment, or the behavioral benefits that advisors like Betterment aim to produce for customers.

What we have shown is that when you’re investing for retirement with Betterment, our goal-based portfolio advice and tax-smart technology offer an important value add. In the tables above, we’ve shown how typical investors can see a range of varying possible outcomes, but in every simulation—including taking into account fund fees or not; moderate tax bracket or high; zero liquidation to full—Betterment projects an added value to the typical investor.

In summarizing this range of possibilities to just one number for the public, we suggest that the most typical simulation for typical investors is the moderate scenario: A moderate tax bracket where the investor invests in a portfolio with fees as high as SPIVA’s report and liquidates 50% of the portfolio. In that case, we project Betterment’s value add to be an estimated 1.48% in added investment returns per year. Based on the size and timing of the cash-flows within the simulations, this can lead to approximately 38% more cash after tax after 30 years.

Real outcomes will vary. Simulations are inherently limited, but at Betterment, as we strive to maximize your money, this projected added value—and building more to enhance it—is our focal point as your investment advisor.

Read more about the calculations above in our full disclosure.

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