• KEY TAKEAWAYS

• We adjust our recommendation over time, taking less risk as you approach your goal, but the amount of risk and path to get there may differ for each goal.

• We are constantly optimizing your portfolio and savings or withdrawal recommendations based on a quantitative assessment of potential outcomes.

By Dan Egan

## Introduction

If you have ever worked with a traditional investment manager or have a 401(k) plan at work, you have likely answered a “standard” risk questionnaire. It often starts with your estimated retirement date and how much money you have, and then ask you what kind of returns you want to see.

But these questionnaires measure what kind of risk-taker you think you are, not what kind you need to be in order to achieve your goals.

At Betterment, we believe that your investment horizon—how long until you will need your money—is one of the most important determinants of how much risk you should take. The more long-term your investing goals, the more risk you can afford to safely take. Money saved for short- and medium-term goals, such as saving for a house or buying a car, can be invested at a different risk level than a longer-term goal, such as retirement.

Another consideration is how you plan to use the money when you need it. Will you take out the investment in a lump sum or will you gradually make withdrawals over time and use that money for income? These are key pieces of information we use when providing personalized investment advice.

Below, we walk you through the rationale of our risk advice model. Unlike the standard risk questionnaires, our algorithm weights investment time horizon and downside risk more heavily, and allows you to deviate from our advice if you want to deviate.

This is the heart of Betterment’s risk advice algorithm.

First, let’s talk about goals. At Betterment, you can think of goals like different investment buckets. They are technically subaccounts that you can use to silo your retirement savings from vacation savings, for example. Every goal you set up at Betterment (and every customer can set up several) will have its own customized allocation of stocks and bonds.

Each goal has different final liquidation assumptions, so it is important to select the one that most closely matches your real intentions. Below we can see the diversity of goals you can manage at Betterment.

##### …and then look at your investment horizon.

Once we know your goal, we next consider how long you will be invested in that goal, as well as the withdrawal plan for that goal. Is it a goal that you plan on cashing out in 10 years, or a goal such as retirement in 30 years, give or take a few years? That actually makes a big difference in the advice we’ll give.

We assume you will spend your Major Purchase goal savings at a specific point in time. You might withdraw your entire House goal investment after 10 years when you have hit the savings mark for your down payment. In contrast, with a Retirement goal, we assume you will spend funds over a number of years rather than in one lump sum withdrawal. That’s the nature of a nest egg—it’s the basis for your monthly income in retirement.

If you don’t have a specific investment horizon or target amount, we will use your age to set your investment horizon (our default target date is your 65th birthday) in a General Investing goal. It has a similar spending assumption as retirement, but maintains a slightly riskier portfolio even when you hit the target date, since it’s not clear you’ll liquidate those investments soon.

With this information about your time horizon and goals, we can determine an optimal risk level for your investment horizon. We do this by assessing the possible outcomes for your time horizon across a wide variety of bad to average markets.

Getting to an optimal risk level, generally attained through exposure to stocks versus bonds, involves weighing the trade-offs between potential gains from higher risk investments and the potential for falling short by playing it safe. We have designed our formula so that it works especially well with our portfolio, which contains multiple globally diversified asset classes.

Now, we know we can’t predict what the future will be. So we use a projection model that includes this uncertainty by including many possible futures, weighted by how likely we believe they are.  We use these probability-weighted futures to build our recommendation based on a range of outcomes, giving slightly more weight to potential negative outcomes and building in a margin of safety—which technically is called ‘downside risk’ and uncertainty optimization. If you’re interested, you can also read more about our projection methodology.

Paying particular attention to below-average scenarios we are able to select a level of risk that aims to minimize potential downside risk at every investment horizon. By some standards, we have a fairly conservative allocation model—but as we mentioned above, our mission is to help you get to your goal through steady saving and appropriate allocation, rather than taking on unnecessary risk.

## How we balance risk and time

Now, let’s consider now how risk and time work together. The example below shows the forecasted growth of $100,000 in a 70% stock portfolio over three years. The expected return, or median outcome, for this portfolio is$121,917, but the range of possible outcomes moves from at least $180,580 for the top 5% of potential outcomes to no better than$82,312 for the bottom 5%. This is a great example of how stocks can bring both a lot of upside—as well as downside in the short-term.

#### Outcome and risk over a three-year term

If the graph above shows an example of the predicted volatility that stocks can bring to very short-term time horizons, what happens to the same portfolio over a 10-year time horizon?

#### Outcome and risk over a 10-year term

After 10 years, our models predict that you are less likely to lose money and more likely to come out ahead on an absolute dollar basis.

## How we manage downside risk

Now that the relationship between risk and time is clear, let’s turn back to allocation.

In order to make an appropriate recommendation of stocks and bonds, we have to look at potential outcomes for everything from 0% stocks to 100% stocks. To do this, we evaluate stock allocations and look at how they might perform at similar percentiles over a fixed investment horizon. This analysis helps us finely tune the stock-and-bond ratio.

In the example below, we see the 15th percentile outcome for every stock allocation over a 20-year investment horizon. We use the 15th percentile to represent a ‘bad’ outcome, i.e., poor predicted market performance. With shorter-term horizons (seven years and less), our modeling shows a majority bond portfolio beats a majority stock portfolio in this ‘bad case.’  However, by year 12, the same model predicts higher stock allocations begin to overcome bond-heavy portfolios. By year 20 all majority stock portfolios (at least 50.1%) have better outcomes than majority bond portfolios, even though this is still a ‘bad’ outcome in terms of investment performance.

#### Returns at the 15th percentile, or a ‘bad case’ scenario

Within this bad outcome scenario let’s focus on the best allocation at each time period. Measured by returns, the best expected outcomes are equivalent to the top of this graph (traced in red).

Another way to view this best allocation line is to change the y-axis from absolute value in dollars to the stock allocation. If we plot the same 15th percentile best allocation line on a new plot we get the following graph.

#### Portfolio value as a measure of stock allocation at the 15th percentile

This new view of the same line clearly shows which allocation would have performed best for a given period. For example, in the ‘bad’ scenario, a 65% stock portfolio would have performed best over a period that lasted 10 years and nine months on the predicted model.

#### Allocation and time

Our advice doesn’t only consider the bad outcomes. We seek to find the best stock allocation for outcomes from the expected 50th percentile to the 5th percentile (a ‘worst case’ scenario, but not THE worst case scenario). You can see the result of this exercise in the graph below, which maps investment horizon against best stock allocation, given the percentile chosen.

#### Percentiles by 5%, from 5th to 50th

Our goal is to provide the best possible expected returns. That means aiming to provide you with the best chance of making money and not losing it. To do that, we then must look at the the median outcome—and an average of all the outcomes that are considered bad, which is everything from the 5th percentile to the 50th. (Why 50th? Percentiles over the 50th, the median will always show that 100% stocks are the best allocation.)

The dark blue line represents the average ‘best’ stock allocation across all percentiles. Since we have included more downside scenarios in this average, it weighs the potential for loss more than equivalent upside. But note that over longer time periods, even with a downside risk focus, we predict that it is still better to be in a majority stock portfolio compared to a majority bond portfolio.

#### Average of all percentiles

For long-term goals, those with time horizons over 20 years or more, we recommend 90% stocks. For short-term time horizons, we recommend 10% stocks. And for intermediate-term goals, the recommended stock allocation rises very quickly. This is based on a conservative downside-weighted risk measure which accounts for your specific time horizon in each goal to help ensure you are taking on the right risk for the level of return you should realize.

## The result is Betterment’s glide path

The result is a general framework for the risk allocation advice Betterment uses across all goals, which can supply a goal-specific glide path recommendation.

In investing, a glide path is the formula used for asset allocation that progressively gets more and more conservative as the liquidation date nears. Many retirement-oriented target-date funds are based on a glide path (though every firm has its own formula.)

At Betterment, we adjust the recommended allocation and portfolio weights of the glide path based on your specific goal and time horizon. This means Betterment glide path recommendations are more personalized to your specific goals and investment horizons.

For example, in our Major Purchase goals, shown below, the recommended glide path takes a more conservative path than a recommended retirement glide path—moving to near-zero risk—for very short time horizons. Why is that? This is because we expect that you will fully liquidate your investment at the intended date and will need the full balance.

With Retirement goals, in contrast, the glide path we recommend remains at a higher risk allocation even when the target date is reached, as we assume liquidation will be gradual, and you still have years in retirement for your investments to grow before they are liquidated. If you’d like to understand how this advice varies by goal type, you can read more here.

#### Mixing bonds and stocks across percentiles

The bottom line: Our allocation advice is designed at a goal level to help ensure you’re taking on the right level of risk based on your personal situation, unlike the impersonal and often unexplained glide path offered by target-date funds.

## Including customer risk preference

How should we modify this analysis for a conservative or aggressive approach?

The glidepath derived above is downside optimized because it gives equal weight to each percentile outcome from the median down to the first percentile over a given time horizon. To tailor this guidance to a more conservative or aggressive approach, we’ll change the weights to reflect the degree to which investors care about the worse outcomes versus median average outcomes.

### A quantitative approach

We’ll define a ‘conservative’ approach as giving the median (50th percentile outcome) about 40% of the weight of the 5th percentile outcome. Conversely, the ‘aggressive’ approach gives the 5th percentile outcome about 40% of the weight of the median.

#### Weight Given to Outcome for Different Approaches

The result is a set of optimal aggressive and conservative glidepaths, as shown below for a major purchase goal.

#### Deviation from the Recommended Approach

This approach does allow for deviation by risk level, which produces a non-linear guidance range. It is wider at moderate allocations, and tighter at the bottom and top of the risk range.

#### Optimal Stock Allocation

One reason is simply mechanical: at higher risk levels, you can’t deviate up very much. At lower risk levels, you can’t deviate down much.

Taken across the entire range our outcomes, we have determined that ± 7% is a reasonable deviation. We believe a stable range across recommended levels is easier to understand and follow, and there is sufficient noise in the more extreme tails of these estimates to justify allowing a higher range at the tails. We therefore give guidance that the acceptable range of deviation is -7% for customers wanting a conservative approach, and +7% for customers wanting an aggressive approach to that goal.

### Goal-term guidance

Our quantitative approach above allows us to establish a set of recommended risk ranges given our goals. However, an investor may choose to deviate from our risk guidance if they see fit, and there may be appropriate reasons for those deviations. That being said, we provide investors with feedback regarding the potential implications of such deviations and, in doing so, we treat upwards and downwards deviations differently.

If an investor decides to take on more risk than we recommend, we communicate the fact that we believe their approach is “too aggressive” given their goal and time horizon. We flag this because even in a setting where an investor cares about the downsides less than the average outcome, it still isn’t rational to take on more risk (viewing this particular goal in isolation). If the investor is unlucky with returns over that period, the losses in a portfolio flagged as “too aggressive” will be very difficult to recover from.

In contrast, if an investor chooses a risk level lower than our “conservative” band, we’ll communicate that their choice is “very conservative.” This is because the downside of taking on a lower risk level in a moderate outcome scenario is simply needing to save more. And we believe investors should choose a level of risk which is aligned with their ability to stay the course through the short term.

### Aligning risk level with short-term risk tolerance

An allocation cannot be optimal if the investor is not comfortable committing to it in both good markets and bad ones. As a point of reference, our 70% stock portfolio would have lost 46% from Nov. 2007 to Mar. 2009, and been in the red until 2011. While this performance would have been very disappointing, it is important to remember we only recommend 70% stock allocations for goals expected to be held eight years or longer. To ensure that investors understand and feel comfortable with the short term risk in their portfolios, we present them with both extremely good and extremely poor return scenarios for their selection over a one-year time period.