Asset allocation: all classes and Greeks

The right level of diversification based on several assets of different asset classes, as portfolio theory tells us, is the basis for an efficient and successful investment portfolio. But what are "asset classes" and do they also encompass managed futures?

What is an asset class?

This takes us back to our original question: what is an asset class? Interestingly, there is still no universally recognized definition. The online dictionary Investopedia offers the following definition: “A group of securities that exhibit similar characteristics, behave similarly in the marketplace, and are subject to the same laws and regulations. The three main asset classes are equities (stocks), fixed-income (bonds) and cash equivalents (money market instruments).“ However, that doesn‘t much help the investor whose aim is the optimum distribution of asset classes and individual assets within the framework of asset allocation. The definition isn‘t much use to theorists either. One solution to our dilemma would be to determine the effect of an asset class on optimum asset allocation in relation to the desired process. The various contributions to portfolio theory are based on the premise that an efficient portfolio comprises parts (assets), each with positive earnings expectations, but which post these earnings in different market phases - they must therefore be low or non-correlated. Hence, we could say that an asset class is a group of assets which

1.) shows a (virtually) identical distribution of profit and loss in the same time periods (i.e. there is a highly positive correlation),
2.) has a comparable risk to earnings ratio,
3.) delivers a (more or less) uncorrelated yield for another group of securities which also meets the two criteria above.

We could summarize it more succinctly based on the Capital Asset Pricing Model (CAPM), as Bernard Winograd, then CEO of Prudential Investment Management, proposed in a working paper in a bid to settle the longstanding debate: an asset class, he suggested, is a class of investments with similar beta characteristics (B. Winograd, “Alpha and Beta - Translated from the Greek“, October 2004).

Beta: an asset and the market portfolio

At this point, let‘s try to make things clearer by looking at the practical applications of portfolio theory. In this context, beta was introduced by William Sharpe as a term to indicate firstly whether two time series which are being compared have a tendency to move in the same or opposite directions and, secondly, the extent to which they fluctuate in relation to one another. Experienced statisticians will recognize the beta coefficient of the linear regression model, which is calculated using a regression analysis. In William Sharpe‘s CAPM risk model, beta represents the systematic risk (in short, the market risk) of an investment. Beta (ß) is calculated for a specific fractional value of a market (W) in relation to the entire market (the “market portfolio“ M) based on the relative value fluctuations (e.g. monthly or daily performances in percent). The formula:

ß = Covar (W:M) / Var (M)
or alternatively:
ß = Correl (W:M) * StDev(W)/StDev(M)

where Covar stands for covariance, Var for variance, Correl for correlation coefficient and StDev for standard deviation. Two of these four functions from the statistical armory say something about the volatility of the measured time series: variance and standard deviation indicate the extent to which the individual markets fluctuate around the average of all market changes. The higher the (always positive) value of variance or standard deviation, the higher the risk.
The other two functions tell us about the directional correlation between the two time series: covariance and correlation measure whether and how frequently the two comparison values move in the same (positive sign) or opposite (negative sign) direction.
The beta sign therefore also indicates the directional correlation of the two measured variables.
The absolute value of beta (i.e. the number which follows the sign) indicates the strength of the value fluctuations of the individual value in relation to a 1% move of the market portfolio. If the value of beta is greater than 1 (or smaller than -1), then the average volatility of the individual value is higher than that of the market portfolio. A beta of 1.5 would lead us to expect the individual value to rise or fall by 1.5%, whereas the market portfolio would move just 1% in the same direction. If, by contrast, beta is between -1 and 1, then the volatility of the individual value is probably lower. A beta of -0.5 indicates that the individual value would fall by 0.5% if the overall market were to move 1% in the opposite direction.
Caution is advised. A low beta can, in certain circumstances, tell us nothing about the volatility of the individual value in question. If there is a near-zero correlation with the market portfolio, then the beta of the individual value can be very low, although its value fluctuations are significantly higher than those of the market portfolio - simply because zero divided by whatever value equals zero. This would be refered to as uncorrelated beta, which will be discussed in greater detail later. The market portfolio itself has by nature and definition a beta of 1.

The portfolio models of Markowitz and Tobin. In Markowitz‘s modern portfolio theory there is no riskless investment and all possible portfolios lie within the area enclosed by a hyperbola. Efficient portfolios are grouped on the efficiency line („Efficient Frontier“). Tobin introduces the riskless asset. This gives rise to an extended universe of possible portfolios which are located in the imaginary area below the capital market line (the tangent on the market portfolio which links the riskless asset with the market portfolio). All efficient portfolios are located here. Whereas Markowitz and Tobin define risk as the variance of the returns (standard deviation, volatility), Sharpe later introduces beta as the risk variable.

What is the market portfolio?

In order to return to the aforementioned deliberations, the only point which remains to be established is what is meant by the market portfolio. It is a portfolio comprising every - not riskless - security on the market, weighted according to their value in circulation, that is to say a capital-weighted mega index. Any intelligent investor not completely averse to risk would, in line with the theory and depending on risk propensity, add a large proportion of the market portfolio to a riskless investment. In practice, it is frequently assumed that this riskless investment centers on government bonds (which strictly speaking are in no way riskless) or money market interest rates. Due to the fact that nobody is in a position to calculate a market portfolio in line with Sharpe‘s definition, in practice we tend to take one of the usual, broadly diversified stock indices or a combination of such an index with bonds in order to create the market portfolio.

Alpha: skill or fortune

It is current practice in portfolio management to analyze assets in terms of their beta in relation to an index of this kind (i.e. their possible additional performance contribution with simultaneous change in the level of risk). Such a portfolio will (hopefully, in any case) move in the same direction as the combination of bonds and a stock index, but will fluctuate to a greater or lesser degree - whereby a premium is given for the risk taken (higher beta). If the portfolio‘s return ultimately exceeds this premium (i.e. more than the “leverage“ expected from the greater risk), then the investor would appear to have had the right touch, having bought just the right individual assets at just the right time. This surplus is referred to as alpha and whether the art of the portfolio manager is rooted in fortune or chance is a matter of debate.

Zero beta vs. alpha exposure

This approach and the subsequent application of the portfolio construction is logical if you intend to put together an individual portfolio of positively correlated individual values - in particular stocks of one market - which is tailored to the risk level of the investor. Looking beyond the world of stocks and bonds to the wider universe of modern financial instruments, the limitations of the model quickly become apparent. Of course assets can be treated like hedge funds or managed futures like stocks. In this case you will see that calculations very often reveal a near-zero beta. Does this mean that the measured zero-beta asset moves by an average of zero percent? Of course not. An investment of this kind would never have been considered in the first place. A near-zero beta rather suggests that for the period in question there is no directional correlation between the asset and the index used (market portfolio). Because the correlation (or covariance) is zero and the solution of the beta formula also yields zero, as such an asset would essentially be no cause for concern but is, quite on the contrary, an absolute gem. As Harry Markowitz also says, thanks to the right proportion of slightly or zero-correlated assets (with positive earnings expectation) a portfolio has a better chance of yielding returns and the risk is reduced.

Individual assets or classes?

Zero-beta assets merely give rise to a pseudo problem rooted in the fact that we are want to remain within the traditional categorization of asset classes. There are two different solutions and there has been considerable debate as to which is the “right one“. Solution number 1: since the returns of the measured assets obviously cannot come from the beta, they must come from the alpha. Logically, such assets are referred to as either “alpha strategies“ or “market-neutral“. Both frequently throw up yet further questions. Ultimately, nobody could claim that a crude oil certificate which, in relation to a broad stock index can have a beta of zero, will increase in value thanks to exceptional management skills or is even “market-neutral“ (except in relation to the stock index used). In order to find the best gems (zero-beta assets with above average performance), each one would have to be analyzed individually in terms of its (assumed) effect within the portfolio, given the skyrocketing number of individual values an impossible task, even with today‘s computer power.
However, there is a more elegant solution. If an asset has no correlation with the benchmark “stock index“ used (and therefore has no beta), then this benchmark is unsuitable for the purposes of comparison. But maybe there is an entire group of such assets with very similar characteristics to the asset just found - an asset class. All of the assets within the group should in turn have a highly correlated beta in relation to this class. Which takes us back to the elegant solution describing an asset class minimalistically and simply on the basis of common beta characteristics.
The big advantage of this approach: an efficient combination of asset classes matching the risk profile of the investor can be determined for this portfolio construction - just as the classic theory proposes with interest, bonds and stocks. And After that it‘s just a matter of addressing the best individual assets of the relevant class instead of the complex minefield of individual zero-beta assets.
Thanks to the numerous benchmarks now available for virtually every far-away galaxy of the financial market universe, we now have no problem identifying the appropriate categorization for almost all individual assets. Whether each benchmark is coupled with an asset class (or simply a category within a class) cannot always be definitively determined, as even with the help of our elegant beta definition, it is, pragmatically speaking, just splitting hairs. It is a particularly enthusiastic debate fuelled by the growing number of alternative investment styles.
The aforementioned includes hedge funds, points to the question whether they represent one or even several separate asset classes within the aforementioned criteria. This is at least to some extent a matter of opinion. Several products and subcategories of the hedge fund universe have, for example, heavily correlated betas in relation to the stock market. No wonder. Styles such as long/short equity or event-driven are essentially stock investments with extended instruments (leverage and short selling). Therefore, they could also be regarded as categories of the stock class.

Correlation (blue) and betas (red) of different hedge fund styles and selected managed futures examples in relation to the stock market (MSCIW). Managed futures are the only category with an almost perfect zero correlation.

The ideal: managed futures

In terms of alternative investments, managed futures are the ideal zero-beta asset. Their correlation and their beta in relation to the major stock indices is, in the long term, an ideal zero target, but the performance is without question a match for stocks. What‘s more, the correlation with bonds is so weak that we find uncorrelated beta here as well. This is something which John Lintner, co-founder of the CAPM, analyzed back in 1983 in a study which is even today still regarded as groundbreaking. He determined that a stock/bond portfolio diversified with managed futures showed materially less risk at every possible level of expected return compared with the traditional portfolio alone (“The Valuation of Risk Assets and the Selection of Risk Investments in Stock Portfolios and Capital Budgets”, Review of Economics and Statistics, Feb. 1983). Do these circumstances predestine managed futures as a separate asset class? For the investor searching for the portfolio with just the right risk-return ratio for him, definitely.

All about alpha?

As far as the academic community is concerned, the case is far from closed. If we stick within the limitations of the current theoretical model, in particular within the CAPM, then managed futures throw up a whole range of questions. So we could argue that the expected value of the entire market (market portfolio) is always precisely zero, because futures markets are inherently zero-sum games. Thus the systematic risk would also equal zero and the beta of this market would also be zero. The returns of individual managed futures products could not, therefore, result from the beta and would be down either to chance or the individual alpha.
The flip side is that managed futures, in particular the majority of managers who trade in line with technical/systematic models - have been delivering data for over 20 years, which show high correlation with one another and post long-term returns considerably higher than the expected zero.

A riddle, wrapped in a mystery inside an enigma

Two US economists, Davide Accomazzo and Michael Frankfurter, address the resulting dilemma in a recently published study (“Is Managed Futures an Asset Class? The Search for the Beta of Commodity Futures“, Cervino Capital Management LLC and Managed Account Research, 2007). The authors describe the search for the beta of managed futures as “a riddle, wrapped in a mystery inside an enigma“. Indeed, managed futures do put the classic capital market theory and the strict form of modern portfolio theory to the test. Nevertheless, as investors we believe that a synthesis is possible between the two seemingly contradictory facts that managed futures enjoys the best of health and that there has been no better model for portfolio selection other than that developed by Markowitz, Sharpe, Lintner and others. More about that in a future edition of Futures.