# Defining an Asset Class

Asset allocation is one of the most important decisions investors face, however there are no universally accepted criteria that define exactly what an asset class is. Some investments take on the status of an asset class because managers feel that investors are more inclined to allocate funds to products if they are defined as an asset class, rather than merely as an investment strategy. Alternatively, the investment industry tends to overlook investment categories that legitimately qualify as an asset class because investors are reluctant to defy tradition.

# What are the real consequences of NOT defining an asset class?

The undefined nature of an asset class reduces the efficiency of the asset allocation process in at least two ways.

1. If dissimilar investments are wrongly grouped together into an asset class, the portfolio will not be diversified efficiently.

2. If an asset class is inappropriately partitioned into redundant components, the investor will be required to deploy resources unproductively to analyze irrelevant expected returns, standard deviations, and correlations.

Furthermore, the investor may waste additional resources in search of relevant investment managers. For these reasons, it is important to establish criteria for the purpose of identifying legitimate asset classes.

# Proposed Asset Classes

The list of proposed asset classes is long and diverse. The traditional candidates are:

• Domestic Stocks

• Foreign Stocks

• Real Estate

• Domestic Bonds

• Foreign Bonds

• Cash Equivalents

The stock and bonds are often subdivided into more specific groups:

• Large Cap Stocks

• Mid Cap Stocks

• Small Cap Stocks

• Growth Stocks

• Value Stocks

• Financial Stocks

• Developed Market Foreign Stocks

• Emerging Market Foreign Stocks

• Long Term Government Bonds

• Long Term Corporate Bonds

• Intermediate Term Government Bonds

• Intermediate Term Corporate Bonds

• High Yield Bonds

• Municipal Bonds

• Developed Market Foreign Bonds

• Emerging Market Foreign Bonds

Finally, there are the so-called alternative investments:

• Commodities

• Currencies

• Hedge Funds

• Managed Futures

• Market Neutral Funds

• Private Equity

• Timberland

• Venture Capital

We propose four criteria for determining asset class status:

1. An asset class should be relatively independent of other classes in the investor’s portfolio

2. An asset class should be expected to raise the utility of the investor’s portfolio without requiring selection skill

3. An asset class should be comprised of homogeneous investments

4. An asset class should have the capitalization capacity to absorb a meaningful fraction of the investor’s portfolio

## (1) Relative Independence

Relative independence address whether or not a new asset class will help diversify more efficiently. An asset class will not improve diversification if combinations of asset classes already in the portfolio could duplicate the new asset class’s risk characteristics. The redundancy doesn’t have to be with a single asset class, but with any linear combination of asset classes.

### How can we test for independence?

We can test for independence of a proposed asset class by identifying the combination of asset classes that minimizes tracking error with the proposed new asset class. We call this portfolio a mimicking portfolio. Then, we judge whether the tracking error of the mimicking portfolio is sufficiently large to suggest independence. Tracking error is computer as the square root of the average of the squared differences between the mimicking portfolio’s returns and the returns of the proposed asset class. In other words, it is the standard deviation of the return differences.

For example, suppose we allocate our portfolio among U.S. stocks, foreign stocks, U.S. long-term bonds, and U.S. cash equivalents. We want to determine whether or not we should include U.S. intermediate-term bonds in this portfolio. Based on monthly returns from the beginning of 1985 through the end of 1997, a mimicking portfolio consisting of 0.21% U.S. stocks, 0.56% foreign stocks, 48.86% long-term bonds, and 52.38% short-term instruments produces tracking error of only 1.32% with intermediate-term bonds. Compare this value to the tracking error between each of the current asset classes and its mimicking portfolio constructed from other assets in the portfolio, based on the same historical return sample.

 ​ Tracking Error of Mimicking Portfolioswith Current Asset Classes U.S. Stocks 12.15% Foreign Stocks 16.34% Long-term Bonds 6.46% Short-term Instruments 6.94%

It is reasonable to conclude from these tracking errors that immediate-term bonds are redundant to the other asset classes and therefore should not be considered as an asset class in this situation.

## (2) Expected Utility

The second criterion for asset class status raises two critical distinctions: the distinction between expected utility and expected return, and the distinction between random selection and skillful selection on the part of the investor.

Expected utility refers to happiness or satisfaction, which comes from either the expectation of higher returns or of less risk. Consider commodities, for example. You may believe that their expected return is insufficient to raise the expected return due technological advances outpacing the depletion of scarce resources. However, because commodities offer diversification against financial assets, especially in environments of high unanticipated inflation, their inclusion in a portfolio might lower risk sufficiently enough to more than offset their expected reduction of return.

$\text{Expected Utility}=\text{Expected Return}-\text{Risk Aversion}\times \text{Variance}$

Suppose our portfolio consists of a single asset with an expected return of 10.00% and a standard deviation of 12.00%. Also assume that our risk aversion equals 1.5, which indicates that we are willing to give up 1.5 units of expected return in order to lower portfolio variance by one unit. With these assumptions, and remembering that variance equals standard deviation squared, we calculate expected utility to equal 7.84% $\left( 0.10-1.5 \times 0.122 \right)$.

Let’s assume that we estimate commodities to have an expected return of 9% and a standard deviation of 12%. At first, it doesn’t appear that an allocation to commodities would improve the risk/return profile of our portfolio because commodities have the same risk but less expected return. However, we must not ignore the correlation of commodities within our portfolio. Suppose we estimate the correlation of commodities with our portfolio to equal 5.00%. If we shifted 38% of our portfolio’s assets to commodities, its expected return would decline from 10.00% to 9.62%, but its standard deviation would fall from 12.00% to 8.92%. Based on risk aversion of 1.5, the expected utility of this new portfolio equals 8.43% $\left( 0.0962-1.5 \times 0.08922 \right)$. Given our willingness to exchange expected return for risk reduction, we would be happier to allocate some of our portfolio to commodities even though this shift reduces the expected return we expect to achieve. The point is that expected return, by itself, is insufficient for gauging an asset’s impact on investor satisfaction.

### Random Selection vs. Skillful Selection

The distinction between random selection and skillful selection is subtle, yet important. An asset class should raise a portfolio’s expected utility not because the investor is skillful in identifying superior portfolio managers within that asset class. Rather the investor should expect the asset class to raise utility even if managers within an asset class are selected randomly. It does not follow, however, that an asset class is disqualified if improvement in expected utility requires skillful managers within the asset class.

Assume that passive exposure to domestic stocks is expected to raise a portfolio’s utility. Domestic stocks therefore might qualify as an asset class. Let’s also assume that the top quartile growth stock managers would also be expected to raise utility. If growth stock managers on average are note expected to raise utility, and only a skillful investor would be able to identify top quartile growth stock managers before the fact, than top quarter growth stock managers would not qualify as an asset class.

### Are Hedge Funds an Asset Class?

Finally, let’s consider hedge funds. Let us first acknowledge the conjecture that hedge funds would raise a portfolio’s utility because their managers, on average, perform better than do non-hedge fund investors who invest in the same assets. In other words, random compositions of the assets that typically constitute hedge funds are not expected to raise utility, but a random selection of hedge fund managers would be. This unusual conjecture arises from the fact that hedge funds typically require a lock-up period; that is, their investors are precluded from withdrawing funds for a pre-specified period of time. Therefore, hedge fund managers are in a position to collect a liquidity premium, which may explain why their performance exceeds the average performance of the assets in which they invest. If this conjecture were indeed true, a naïve or random selection of hedge fund managers, requiring no skill selection on the part of the investor, would be expected utility because hedge fund managers as a group are skillful in extracting a liquidity premium. Hence, hedge funds might qualify as a legitimate asset class, even if their constituent investments do not.

## (3) Homogeneity

The requirement for homogeneity among the components of an asset ensures that we do not ignore opportunities for diversification. If an asset class comprises dissimilar components, then by investing in that asset class we implicitly impose the unnecessary and potentially harmful constraint that the components must be held in the same relative proportions as their weights in the asset class. We could achieve a more efficient portfolio if we partitioned the dissimilar components into multiple asset classes.

For example, foreign stocks are typically viewed as a single asset class. For this example, let’s define foreign stocks as a 40% allocation to German stocks, a 30% allocation to UK stocks, and a 30% allocation to Japanese stocks—all unhedged. This construction is not significantly different in its risk profile from the EAFE index. Based on the returns, standard deviations, and correlations from the beginning of 1980 through the end of 1997, a portfolio comprised of 25% U.S. stocks, 50% U.S. bonds, and 25% foreign stocks, has an expected return of 14.54% and a standard deviation of 9.20%.

Now suppose we partition foreign stocks into six components: hedged and unhedged German stocks, hedged and unhedged UK stocks, and hedged and unhedged Japanese stocks. If we retain the same weights in U.S. stocks, U.S. bonds, and foreign stocks as a group, but allow the allocations within foreign stocks to vary among the six components, we could achieve a more efficient portfolio. By recognizing that foreign stocks are not homogeneous, we can segment this asset class into several homogeneous components and improve our portfolio’s expected return and risk significantly.

## (4) Capacity

The final criterion for asset class status — that it has to be sufficiently large to absorb a meaningful fraction of our portfolio — is self-evident. If we invested in an asset class with inadequate capacity, we would likely drive up the cost of investment and reduce our portfolio’s liquidity. The consequence might be to lower our portfolio’s expected return and increase its risk to the point at which the proposed asset class would no longer be expected to improve our portfolio’s utility.