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How Robo Advisers Allocate Your Money


We've always known it's important to allocate assets among stocks, bonds, etc. in a reasonable manner. But when it comes to implementation, the more we think we understand, the more we realize we don't understand. So more often than anyone likes to admit, we're pulling allocations out of folklore, stereotype, gut instinct, etc. So if you decide to go robo, you need to understand how such prototypically human judgments are made.

Focusing on Wealthfront

I'm going to focus today on Wealthfront. They're one of the big gorillas in this field so that alone makes it reasonable to do so.

Another consideration: They have been far and away the most transparent among the group, having made a detailed and thoughtful white paper available even to those who haven't registered as clients. This is important. An investment adviser is a fiduciary and that doesn't change even if the adviser's brain consists of microchips rather than gooey substance. And when it comes to fiduciary relationships, transparency counts for a lot. So on this very important matter, Wealthfront wins hands down among the large generalist robo firms.

Also, in terms of the kind of portfolio you're likely to wind up with if you go robo, at least with a big generalists, they are almost carbon copes of one another, so if you analyze one, you've pretty much analyzed them all. (I'll point out little differences as they become relevant to any discussion.)

The Heavy Art and Lite Science of Asset Allocation

Given that the science of asset allocation has a pedigree that includes two Nobel Prizes (Modern Portfolio theory, or MPT and the Capital. Asset Pricing Model or CAPM), you might wonder about my characterization of it as "lite." Bear in mind that these prizes were in the category of "Economic Sciences," a field that has often been dubbed "the dismal science." How dismal? When it comes to asset allocation, we'll see that it's dismal on steroids.

We can easily articulate the problems to be solved, and our Nobel Laureates gave us methodologies for solving them. Once upon a time, these algorithms were hogs requiring lots of heavy-duty computing power. But nowadays, like many things I.T., it's a piece of cake. CAPM can easily be dashed off with a free calculator app and even the complex MPT can be done with Solver, a free add-on that comes with Excel (the existence of which you may or may not be aware). And those who want to work on an Apple or Android tablet, where implementations of Excel can't readily handle the heavy stuff, it can be done on-line through Google Sheets (it's created by Frontline Solvers, the same folks that supply the one used in Excel).

The hard part is coming up with credible inputs for the models:

  • Expected return of each asset
  • Expected volatility (or standard deviation) of each asset's returns
  • Expected correlation between the returns of each asset with the returns of each other asset

Free shareware implementations of MPT presume you'll use historical data to generate those inputs, and often don't even feel a need to allow you to override that approach. So, too, do classroom exercises, where professors can make darn sure they concoct historical data sets that can, indeed, serve as reliable proxies for the expectations regarding the future (i.e. assets whose expected returns should be positive are given histories that are free from inconvenient negative averages, no one asset is allowed to be so far superior to the potters in terms of risk and/or reward that it "dominates" the result set, etc.). But in real life, nobody in his or her right mind would even think of doing anything like that since the only thing that never changes is the fact that things change and since no matter what sample periods you use, there are likely to some assets whose results were pumped up or atypically depressed by factors that are unlikely to be sustained in the future.

Another implementation challenge involves how one decides which assets to even consider. This is often brushed over by so-called passive-investing advocates who simply say "buy the market." But as discussed last week, defining the market is a huge and complex task.

How Wealthfront Decides Which Asset Classes to Allocate

There's no science here. It all comes down to judgment, which, according to Welathfront is handled as follows:

We consider each asset class's long-term historical behavior in different economic scenarios, risk-return relationship conceptualized in asset pricing theories, and expected behavior going forward based on long-term secular trends and the macroeconomic environment. We also evaluate each asset class on its potential for capital growth and income generation, volatility, correlation with the other asset classes (diversification), inflation protection, cost to implement via ETF and tax efficiency.

Phew. That's a lot to think about - and a lot to actually do. There's no way to know whether or to what extent they really did study all that, or the extent to which the language is more reflective of public posturing. Either way, at the end of the day, Figure 1 shows the asset classes Welthfront defined. These are the ones they're going to allocate within client portfolios:

Figure 1

Are these good choices? We'll see as we go along and assess portfolio performance.

How Wealthfront Makes Its Asset-Class Predictions

I don't want to elaborate here on why naïve use of historic data can produce ridiculous results. But you can easily see for yourself if you get a shareware MPT program and give it a whirl.

So how the heck can we, Wealtfront, Betterment, Wise Banyan, Schwab, Vanguard or anyone else do this sort of thing? The unfortunate reality is that however bad past data is, we're pretty much stuck looking at it at as a jumping off point because it does offer one big advantage; it exists.

For expected return, Wealthfront starts by using CAPM to derive "expected returns in market equilibrium under certain assumptions" with "the expected return of an asset class . . . dictated by its systematic risk as measured by beta." That endeavor alone is more suited to degree holders from the Art Institute of Chicago than the famed University of Chicago Finance department because you need to do a ton of creative fudging to come up with non-absurd numbers for equity risk premium and beta, two out of three CAPM inputs. But even that isn't enough. Wealthfront continues:

We also form views on long-term return expectations for each asset class based on interest rates, credit spreads, dividend yields, GDP growth and other macroeconomic variables. We use the Black-Litterman model (Black & Litterman, 1992) and the Gordon growth model (Gordon, 1959) to adjust the CAPM returns with our views.

Black & Litterman is a math-heavy algorithm that does not eliminate fudging. What it does is help users implement the fudging more effectively by making sure there's a mathematically valid consistency between fudged and non-fudged numbers. As to the Gordon growth model, this is actually another name for the Dividend Discount Model, the one that you can't use in the real world without adapting the daylights out of it because of all the non-dividend payers and because if your growth-rate assumption is for any time horizon other than infinity (which is even harder to estimate than the 3- to 5-year spans analysts typically use as proxies for long term), you're likely to wind up with many stocks, probably most stocks, having negative fair values.

Moving on to expected volatility, Wealthfront says:

To estimate each asset class's standard deviation (volatility), we consider its long-term historical standard deviation, its short-term standard deviation, and the expected volatility implied by its pricing in the options markets. Long-term historical estimates benefit from a larger sample size, short-term estimates capture market evolution and the option markets imply forward-looking volatility.

In other words, they do several different things and aggregate them through eyeballing or who knows what.

Expected correlation is approached similarly: "To estimate correlation, we consider long-term historical correlation and short-term correlation."

Actually, as asset allocation processes go, what Wealthfront does is actually pretty sensible and if Portfolio123 eventually gets involved with this sort of thing, we're likely to follow a similar approach. My problems with Wealthfront and the other robos that work this way is that they try to pass this off an objective, automated, passive process. It's not. It is, as noted, heavy on art and lite on science. And that means that instead of evaluating robos based on how pretty and easy-to-use their web sites are, we need to be evaluating their so-called-passive-but-really-active investment-related decisions.

Anyway, Figure 2 shows the Expected Return assumptions Wealthfront's active judgments came up with. (The column labeled "Black Litterman Gross Return" is the end result of the actual process. The two rightmost columns are there, most likely, to promote their low fees and their tax-loss harvesting services.)

Figure 2: Expected "Real" Returns (Over and Above An Assumed 2% Annual Inflation Rate)

This strikes me as a somewhat safe set of assumptions in that it seems in line with many others I've seen elsewhere. It's like the way analysts allow themselves to be guided toward a "consensus." You hate turning out to be wrong, but you can comfortably live with that if everybody else is just as wrong as you are.

Figures 3 and 4 show Wealthfront's assumptions regarding volatility (standard deviation) and correlations among asset pairs.

Figure 3

Figure 4

Putting It All together in a Portfolio

This is done through Mean Variance Optimization (NYSE:MVO), which is an aspect of Nobel Prize winning MPT (Modern Portfolio theory). The goal here is to identify the asset weightings that will, for a specified level of risk, produce the highest possible expected return. (This could be turned around to calculate the weightings that will, for a given level of expected return, produce the lowest possible level of risk.)

There are many different level of possible risk ranging from "Cowardly Lion" to "Evel Knievel's Got Nothing On Me" and everything in between. So for each of these possible levels of risk, you calculate the one and only set of asset-class weightings that produces the highest level of expected return that can be achieved without taking on more risk. Each such best-bang-for-the-level-of-risk portfolio can be called "efficient" or "optimum." Which level of risk, i.e. which efficient portfolio, is best? There is no answer. As long as they are all efficient (show the most possible expected return for a given level of expected risk), they are all equally good. (If reality turns out to be markedly different form what was expected, then they may all turn out equally bad.) Academicians, being what they are, can't help but plot all these possible expected return-risk combinations on graph paper, and coming up with something that looks like this:

Figure 5

When you go through Wealthfront's questionnaire, they'll figure out, from your answers (we hope), how much risk you're willing to take (this will translate to a number plotted along the horizontal axis) and then give you a set of asset class weightings that have an overall expected return consistent with what you'd get if go straight up vertically from your risk plot and stop at the black line, which is known as the "efficient frontier." That expected return, the corresponding number on the vertical axis, is the best you can rationally expect given where, on the horizontal axis, your level of risk is located.

Is this a good way to allocate assets? If the assets selected for consideration (Figure 1) and the inputs needed by the model (Figures 2, 3 and 4) are reasonable, then heck yes, this would be a great thing to do, as was recognized by the Nobel Prize Committee. But if the asset selection and/or inputs are bad, you're likely to have a hot mess on your hands.

How confident is Wealthfront in its assumptions? Well, let's put it this way. Despite all they do, they still won't use the weights they get without protecting themsleves through one more human override: Based on subjective judgment, Wealthfront decided that no asset class can be more than 35% and that no asset class can be less than 5% (except for TIPS which can go as low as zero) of the portfolio. Accordingly, these "constraints" were programmed into the efficient-frontier-calculating model. (This is a commonplace practice. Excel -Google Sheets Solver and MPT shareware allow for this.)

Summing Up

So there it is. Now you know how Wealthfront puts together the portfolios it establishes for clients. (I presume you are aware that each asset class is represented by an ETF.) That's also the way the other robos do it. The process is sensible - as long as you understand that it's driven by subjective human judgment and not by fancy automated mathematical wizardry. The next step is to start evaluating all of these judgments and see how they play out in real-world robo portfolios.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.