Asset Allocation: A Primer

At the beginning of March, the U.K. Treasury published the results of an extensive study it has undertaken into institutional investment in the U.K. We would highly recommend reading it, as it offers a particularly lucid overview of the investment management industry in general. From our perspective, one of its most interesting findings was that "asset allocation -- the selection of which markets, as opposed to which individual stocks, to invest in -- is an under-resourced activity. This is especially unfortunate given the weight of academic evidence suggesting that [asset allocation] decisions can be the critical determinant of investment performance." It went on to recommend that "the attention devoted to asset allocation decisions [by fund trustees] should fully reflect the contribution they can make to achieving the fund's investment objective.

"Smart asset allocation lies at the heart of what The Index Investor's mission. With that in mind, we'd like to respond to a number of subscriber requests for a short asset allocation primer. Here it is:

What is Asset Allocation?

How you choose to allocate your investments between different types of assets (that is, between "asset classes") is the most important decision you make when it comes to determining whether or not over time you will earn the minimum rate of return you need to meet your goals. Unfortunately, this "asset allocation" decision is one that most people don’t spend nearly enough time thinking about before they make it.

Given this, let’s start with the basics. First, what is an asset class? To some extent, this is a theological question, on which experts can argue for hours without reaching agreement. For example, you may hear some people define "mid-cap U.S. value stocks" as an asset class, while someone else calls "European stocks" or "U.S. government bonds" an asset class. The basic concept of an asset class is relatively straightforward. An "asset class" is a group of securities of some type (bonds or stocks) that have more in common with each other than they do with securities from outside the group. The rate of return on an asset class is measured by an index. So far, so good. But how and where does one draw the lines? What does "have more in common with each other" mean?

Here is how we’ve approached this question at The Index Investor. The basic purpose of dividing securities into asset classes is so that they (the asset classes) can be combined into portfolios that are "optimal." In this case, optimal means that there is not another combination of asset classes that generates a higher ratio of return to risk (for those of you who are familiar with modern portfolio theory, we’re talking about the efficient frontier).

When you are calculating the expected return and risk of different portfolios (that is, different combination of asset classes whose weights sum to 100%), return is pretty easy to calculate: it is simply the weighted average of the expected returns of the different asset classes included in the portfolio.

Calculating risk, however, isn’t as easy. Why? Because the riskiness of an asset class depends not only on how variable its returns are relative to their historical average (that is, their standard deviation), but also on the extent and direction in which the asset class’s returns vary with those of other asset classes (that is, its correlation). For example, an asset class with a relatively low rate of return might be a very good one to hold in a portfolio if those returns tended to go up when other asset classes’ returns went down.

This brings us to the crux of the argument about what constitutes an asset class: the real question (in our eyes, at least), is where you draw the line on maximum correlation of returns you will accept between two "asset classes." Consider the following correlations (of monthly returns from January, 1988 through December, 2000). Between the Russell 3000 (an index that measures the performance of the broad U.S. equity market) and the S&P 500, the correlation of returns was .99; with the S&P 400 (a mid-cap index) it was .92, and with the Russell 2000 (a small cap index) it was .78. However, the Russell 3000’s correlation with the Lehman Brothers Aggregate Bond Index (a broad measure of returns in the U.S. bond market) was only .38; with the MSCI Europe Index (which measures returns on European equities), it was .61, and with the MSCI Emerging Markets Index (emerging market equities) it was .55.

By now you can see where we’re going with this. Given that the real power of diversifying your portfolio across asset classes comes from reducing risk as much as it does increasing returns, at The Index Investor we think it makes sense to define asset classes broadly enough so that their returns have a relatively low degree of correlation with each other. So for our purposes, European, Emerging Markets, and U.S. Equities (represented by the Russell 3000) are asset classes, while the S&P 500 or the Russell 2000/Value are not. Rather than being asset classes in themselves, the latter two represent, respectively, size-based and value-based "tilts" within the U.S. Equity asset class which, depending on your point of view, may or may not be worth making in pursuit of a better return versus risk tradeoff.

Is Asset Allocation Important?

One of the most important lessons about asset allocation is that, assuming you define your asset classes correctly, investing in more of them often increases your expected returns while asking you to take on no more risk than you would with a mix that uses fewer classes.

Here’s an example. Assume that for the period between January, 1988 and December, 2000, you had invested 60% of your portfolio in a broad U.S. equity index fund (for which we’ll use the Russell 3000 Index as a good proxy), and 40% in a broad U.S. bond index fund (for which we’ll use the Lehman Brothers Aggregate Bond Index). Your portfolio would have earned an average annual return of 13.83% per year, with a standard deviation of 9.99% (standard deviation measures the dispersion of returns around the mean, and is often used as a measure of risk).

By adding three additional asset classes to this mix (international equities, non-U.S. bonds, and commodities), you could have raised your average return to 14.57%, while taking on no more risk (that is, while keeping standard deviation at 9.99%).

By breaking down international equities into three different asset classes (European equities, Pacific equities, and Emerging Market equities), and by adding high yield U.S. bonds, you could have raised your average annual return to 14.64 %, while still taking on no more risk.

Finally, by making it possible to take size tilts within U.S. equities (by substituting the S&P 500 large cap, 400 mid cap, and 600 small cap indexes for the Russell 3000), and maturity tilts within U.S. Bonds (dividing them into short, intermediate, and long maturity indexes to replace the Lehman Brothers Aggregate), you could have raised your average annual return to 15.23% per year, again while holding standard deviation (risk) constant at 9.99%.

Does this matter? Over time it sure does. Over a ten year holding period, the expected value of the 15.23% return portfolio is 12% higher than the 2 class, 13.83% return portfolio. And after twenty-five years, the difference in expected values grows to 35%. Can you actually achieve this kind of performance improvement in practice? All we can say is that if you implement your asset allocation strategy by using no-load index funds that have very low expense charges, you can come very close to improvements of this magnitude. And sometimes, you can even do much better. For example, last year our model U.S. dollar portfolio outperformed its benchmark of 80% equities and 20% bonds by over 500 basis points (5%).

How Do You Do It?

The quantitative approach to asset allocation is part science and part art. Let’s look at the science first.

Technically, asset allocation is about optimization – that is, the science of how to make the best decision when you are confronted with a range of possible choices. In the case of investments, the range of choices is clear. The challenge is to make the best decision.

The first step in the science side of the process is to define what you mean by the "best" decision. Most of the theory that underlies asset allocation assumes that this refers to the identification of a portfolio (that is, the weights one gives to different assets) that is expected to produce the highest possible return for a given level of expected risk, or, the lowest level of expected risk for a given level of expected return. The expected return of a portfolio is simply the sum of the expected return for each asset times its weight in the portfolio. The expected risk of a portfolio presents a bit more of a challenge. First of all, there is the basic question of what we mean by risk. The theory that underlies most of the asset allocation literature defines risk as the standard deviation of an asset’s returns, which measures how tightly they cluster around the asset’s average return. An asset with a high standard deviation is deemed to be more risky, because its annual returns tend to be widely distributed around their average, while one with a low standard deviation is deemed to be less risky. Things get a bit more complicated when you calculate the expected standard deviation of a portfolio’s returns. Without going into the math, the key issue here is that a portfolio’s standard deviation is a function not only of the weighted standard deviations of its underlying assets, but also of the extent to which those assets’ returns are related to each other. All other things being equal, if the assets’ returns have a low degree of correlation with each other, the portfolio will have less risk.In its simplest form, quantitative asset allocation involves building an optimization model (or using a readily available piece of software like Excel’s solver function), inputting expected returns, standard deviations, and correlations for the potential assets in the portfolio, and specifying the goal of the optimization process: for example, maximizing the portfolio’s return subject to it having an expected standard deviation of no more than 12 percent (this is termed "setting a constraint" on the optimization).

The output of this model is a set of weights for the different assets that, together, sum to 100%, along with an expected return and standard deviation for the portfolio. When this process is repeated for different risk constraints (e.g., standard deviations of 6%, 8%, 10%, etc.), the line graph of the resulting portfolios’ expected returns against their expected levels of risk is termed "the efficient frontier", because it describes the set of portfolio combinations that are optimal for the set of assets you have specified. To repeat: these portfolios are termed "optimal" because no other combination of asset weights can produce a higher level of expected return and still stay within the risk constrains you have specified.

So far, so good. The science seems straightforward enough. So what’s with the art? The artistic side of asset allocation comes into play because, as is so often the case in life, the apparent science isn’t quite as precise as it first appears. Let’s start by reviewing the main criticisms that have been raised about the use of quantitative optimization models to determine asset allocations within a portfolio.

The biggest criticisms revolve around the nature of the expected returns, standard deviations, and correlations that are used as inputs into the optimization model. To begin with, where do they come from? General practice is to use historical standard deviations and correlations. One question here is the extent to which the past will be a good guide to the future. If, for example, the conditions that gave rise to a particular asset’s returns in the past do not hold in the future, then an asset allocation based on the historical data will, when viewed in hindsight, turn out to have been sub-optimal (one thinks, for example, about an asset allocation done when Japan was at the height of its bubble economy in the late eighties). What, however, is the alternative to using historical data? For standard deviations and correlations, the general answer seems to be that there aren’t any alternatives that are viable. In the case of returns, however, some users of asset allocation models have taken various approaches to develop "forward looking" estimates of future returns for different assets. Unfortunately, in one way or another, all of these approaches rely on some type of historical information, and are thus subject to the same criticism.

Here’s an example. One approach to developing estimates of future returns is to start with a basic building block – say the rate on short term U.S. government bonds. To this basic "risk free" rate, one can then add additional amounts to reflect the incremental riskiness of different types of assets – say, add 1.5% to reflect the additional risk of holding long term instead of short term government bonds, or add 7% to reflect the incremental risk of holding U.S. equities (as an asset class). But where did 1.5% and 7% come from? From history. As you can see, the criticism that the assumptions used in asset allocation models are based on historical relationships that may not hold in the future pretty quickly bogs down. Either you’re going to rely on history and admit it, or you’re going to rely on someone else’s judgment, which, absent either divine intervention, tarot cards, or other such means will itself also be based on history.

A second criticism, that is closely related to the first is that financial markets have recently become more irrational (due, perhaps, to the greater number of individuals owning shares), which has invalidated the assumptions that underlie asset allocation models. Because this argument is often raised by active investment managers, it is well to look carefully at its different parts, and to test its implications. Let’s start with the evidence. How could you tell if financial markets had "become more irrational"? One way would be to look at changes in standard deviations over time for different asset classes. Presumably, if markets were indeed becoming more irrational, this would be reflected in sharper price swings, and higher standard deviations of returns. Unfortunately, this is not what one observes in the data. We divided the historical data into three periods, 1971-1980, 1981-1990, and 1991-2000, and looked at the standard deviations for the Russell 3000 Index (a broad U.S. equity market index) and the Lehman Brothers Aggregate Bond Index (a broad U.S. bond market index). The values for the former were 22.13%, 19.01%, and 15.69%. The values for the latter were 8.45%, 7.97%, and 4.02%. Not exactly the signs of an increasingly irrational market.

However, let’s assume that this premise is true, and markets have in fact become more irrational over time. Does this argue for or against increased use of active investment managers (leaving the fee and tax questions aside for a moment). If markets are indeed more irrational, the superior information and/or superior models claimed by active investment managers should be less useful, because they assume rationality on the part of other investors. If this isn’t the case, then they should deliver lower than expected returns. An exception might be models based on human psychology. However, if these were in widespread use, then one would expect to see a lot of active managers using them and delivering returns that are consistently above the indexes, even after taking fees and taxes into account. However, as we all know, this hasn’t been the case. In sum, the criticism that increased market irrationality has invalidated quantitative asset allocation doesn’t seem to hold water.

A third, and more valid criticism of of quantitative asset allocation models is that their assumptions about asset returns, standard deviations, and correlations are all subject to measurement error. This is undoubtedly true, as it is for most other measurement techniques, particularly those used to capture economic or social phenomenon. The reason this is important is that, if the assets being used are quite similar (that is, they have roughly equal levels of expected return and risk, and are highly correlated), then even a slight measurement error could result in an asset allocation that, in hindsight, will turn out to be sub-optimal.

This criticism is closely related to a fourth one, which is that, where the returns and risks of the assets used are very similar, and highly correlated, the solutions produced by an optimization model will be highly unstable – that is, a small change in one variable, say expected return, will produce a very different asset allocation recommendation.

At The Index Investor, we have taken a two step approach to these valid criticisms of quantitative asset allocation modeling. First, in developing our model portfolios we use asset classes that are defined sufficiently broadly that they have correlations with each other that are generally lower than .60. Mathematically, this makes our model solutions much more stable, in the sense that a change in expected return or risk is not likely to result in a significant change in our recommended asset weightings. In our view, this offsets most of the impact of potential measurement errors.

Just to be sure, however, we also take a second step, and place further constraints on the maximum weight that the optimization model may give to any asset class in our recommended portfolios. This also offsets another criticism of quantitative asset allocation models – that they sometimes produce "solutions" that are impractical, such as placing 70% of one’s portfolio in emerging markets equities.

A fifth criticism of quantitative asset allocation models is that standard deviation is a poor measure of risk. More specifically, for while standard deviation is based on returns that are both above and below the average return, most investors are far more concerned with falling short of their goals than they are of exceeding them. In other words, this argument says most investors focus on "shortfall risk." We believe that this criticism is valid. For that reason, at The Index Investor one set of our model portfolios is based on target return levels, whose goal is to maximize the probability of achieving a given return over a given period while taking on as little risk as possible.

As a result of our approach, our asset allocation models typically produce recommended portfolios that are both stable and in line with most investors’ common sense guidelines. Will they perfectly stand the test of time? Almost certainly not – in ten years, hindsight will undoubtedly show us where our portfolios could have been improved. But this isn’t the question to ask. The real issue is whether or not there is a better way to decide on an asset allocation strategy. We don’t think there is. Like democracy, the approach we have chosen to take is undoubtedly subject to criticism, some of which is quite valid. But in comparison with the alternatives, it is still the best way to go.