Recent Portfolio Theory - Advice in a Multifactor World John H. Cochrane, Federal Reserve Bank of Chicago By Jim Wiandt June 7, 2000

Click here to link to a pdf file of the research paper

A bewildering array of new portfolio theories confront the investor as he tries to put together an investment strategy. Cochrane's paper touches on some of the more important studies, and ultimately comes to a number of conclusions that should come as no surprise to index investors.

Taking a machete through thickets of data-mining and the occasional suspect conclusion, Cochrane emerges with some lucid thoughts. Know your risk factors. Apply multifactor efficient-frontier logic to your portfolio. Remember the law of averages. Avoid fees, taxes, and snake oil salesmen.

Risk Factors

1) Know how much certainty you are willing to sacrifice for the promise of high returns. Do you have the fortitude to carry your plans through? For Cochrane it is just a matter of deciding whether or not you are more risk tolerant that the average investor. If you are, you'll invest 60% of your money in equities. If not, you will invest less. The exact ratio, of course depends largely on point two.

2) Understand your investment horizon. The shorter your horizon, the less risk you want to take. A graphic illustration of this point can be found in Larry Swedroe's risk article. Over most longterm periods, stocks outperform other asset classes.

3) What are and are not your risks? You should adjust the factors in your portfolio analysis to match the risks you face. If your job is at the front end of the New Economy for instance, you may want to diversify away from the market. Conversely, if you are living on investment income and are unconcerned about a recession, you will want to invest in recession-sensitive sectors of the economy that hedging investors avoid, driving up their risk premiums.

Apply multifactor efficient-frontier theory to your portfolio

The market has a balancing point between different rates of return and risk or volatility. The efficient frontier refers to portfolio asset allocation which outperforms this mean. The goal is to find the optimal balance between returns and risk, seeking less risk and higher returns. For a graphic explanation of this point, see Figure 1. The straight line indicates the mean-variance frontier, the market's mean balance between average returns and volatility. Investors want allocations that place their portolios to the upper left of the chart, enjoying higher returns with less volatility. Investors using this traditional two-factor models can achieve efficient portfolios through a combination of two asset classes, equity index funds and risk free investments, including bonds and money market funds.

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The next step if for the investor to add additional pertinent factors in determining the portfolio's efficient frontier. For example, a small businessman might want equities that are less sensitive to a recession to hedge against the decline of his own business. This investor would be willing to sacrifice a certain degree of higher returns and lower volatility to gain safety in the event of a recession.

Adding a third factor provides a new mean-variance frontier, which appears in Figure 2 as a three-dimensional cone. Illustration B shows the mean frontier that is formed with the inclusion of a risk-free investment, like a government bond or a money market fund. In this case, the principal is the same as the two-factor model, except that portfolios that find their way into the efficient frontier can now be achieved with combinations of three types of funds: equities, bonds or money market funds, and a portfolio that is adjusted for the investor's chosen third factor.

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Look at apparent free lunches with healthy skeptism

Never forget that for every investor who is buying a stock or asset class for its risk premium, there is another investor who is avoiding it because he feels that the risk is too high. This is an issue that is really on the front edge of the index investing debate. Current data tends to indicate that some asset classes, such as small cap. and value stocks carry a risk premium, meaning investors can expect higher returns from these asset classes. Some economists (such as Fama and French) believe that the premiums of certain asset classes are caused by higher risk. Others believe that this imbalance in pricing is caused by the irrational behavior of investors, who flock to equities that are in favor, and shy away from those that aren't. Cochrane sees economists as being about evenly divided between the two camps.

Understanding the reason for the market's behavior is critical to making the best investment decisions. If the risk is real, then you can invest in these equities - but with the understanding that you are gaining higher returns at the expense of additional risk. If the higher returns are indicative of irrational investor behavior, you would be a fool not to invest in the underbelly of a market inefficiency that is certain to revert back to the mean. However, if the irrational behavior is ingrained into the human psyche like, say flying in airplanes, it is for all intents and purposes the same as real risk. Cochrane advances another argument: that the risks are real, but narrowly held - thus a few investors are capturing a risk premium at a cheap price.

Understanding market behavior comes down to a question of reversion to the mean. If, like Fama and French, you believe that the risk in small cap and value stocks is real, and therefore the premium is real and will endure, even with the market turning against these stocks, we can eventually expect the return of their historical premiums. This is a critical point for asset allocation. If we can expect equity premiums and risk levels to continue at historical levels, we can feel confident investing in equity index funds over a longterm horizon, gradually decreasing our holdings in riskier equities and increasing our holding in bonds and money market funds as we near retirement. If equity pricing is more akin to a "random walk," or a coin flip, then (per Merton and Samuelson) it may make sense to determine an asset allocation and simply maintain it through continuous rebalancing.

Think Twice Before Trying to Time the Market

If there is some consistency in historical equity returns and valuations, the most obvious benefit to the savvy investor would seem to be an ability to time the market. Cochrane analyzes some recent studies dealing with market timing and emerges with healthy skepticism. The fact that the studies necessarily select limited ranges of data leaves their claims of extraordinary market-timing premiums open to suspicion. In the case of a study by Campell and Vicera, which holds that investors should buy into markets with a high dividend/price ratio and sell into markets with a low dividend/price ratio, returns predictablility in the 50-year sample were sliced in half by the past two years of low d/p ratios and high returns.

If there were a magical timing solution to the market, one would think that something more than one in four actively managed funds would be able to beat the market. As Cochrane so eloquently puts it "If the strategy is real and implementable, one must argue that funds simply failed to follow it." You can argue predictive theories until you are blue in the face. It is difficult to argue with returns. (though Fama and French attempt to do this in a forthcoming publication by arguing that the premium that equities have over risk-free investments may very well be much smaller than is held by conventional wisdom).

Remember the Basics

While it may be possible to come up with numbers that conform to virtually any economic theory imaginable, there are things you can control. Fees. Taxes. Narrowing the gap between your real returns and mean market returns.

Most basically, it doesn't seem to make a lot of sense to absorb the higher expense ratios and tax consequences of actively managed mutual funds for lower returns. It is all a lot of to-do to come back to one simple solution for your portfolio: index funds.

John H. Cochrane is the Sigmund E. Edelstone Professor of Finance at the Graduate School of Busniess at the University of Chicago, and works as a consultant for the Federal Reserve Bank of Chicago