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An Introduction to Modern Portfolio Theory. The following is a very simplified discussion of modern portfolio theory, but is intended for the advanced investor. The goal is to introduce portfolio theory in order for the investor to gain an insight into its basic concepts . For a more detailed discussion of portfolio theory see our reading list and/or visit Dimensional Fund Advisor’s website. In 1952 Harry Markowitz, then a Ph.D. candidate at the University of Chicago, introduced his doctoral thesis entitled Portfolio Selection. His ideas have transformed the way money is managed and subsequently was awarded the Nobel Prize in economics in 1990. Many other brilliant financial economists have added to this body of research, including Eugene Fama of the University of Chicago and Kenneth French of Dartmouth College. Understanding this research and applying it to the practical world of investing is necessary to achieve superior results. In simple terms, Markowitz starts out with the assumption that investors would like to avoid risk as much as possible. He defines risk as the standard deviation of future expected returns. Prior to 1952 risk was assessed on the individual security level. Markowitz proposed that instead of focusing on the risk of a particular security, focus on how that particular security affects the overall risk of the entire portfolio. He then considered how the different securities in the portfolio move in relation to one another in the same time frame. This is “correlation” and is central to the idea that an investor can actually reduce the overall risk of a portfolio by introducing riskier asset classes to the portfolio. Ultimately however, this leads us to the “efficient frontier”.
The efficient frontier line represents all portfolios that have the maximum rate of return for every given level of risk, or the minimum risk for every level of return. In figure 1, point C represents the portfolio that has the maximum return, point B, for the given amount of risk, point A. Point D represents an inefficient portfolio because it is not maximizing the return for the amount of risk taken. This is essentially the main theme of portfolio theory: Maximize return for amount of risk taken.
Numerous problems arise at this point. Simply using historical data can lead to disastrous results. As you know, history does not always repeat itself. How does one estimate future expected rates of return? One method is to use the Gordon Equation: Expected Return = Current Dividend Yield + Dividend Growth Rate The historical dividend growth rate has been approximately 5%. Add this to the entire stock market yield of approximately 1.7% (as of 1/12003) and you get an expected stock return of 6.7%. Applying this to the bond market using the Lehman Brothers Aggregate Bond Index yields the following: Current dividend (interest) yield of 5.0% (as of 1/1/2003) with no dividend growth rate gives an expected bond return of 5%. The expected bond yield is almost identical to the long-term average of the bond market but the expected stock return is well below the long-term average of approximately 10%. Hatton Consulting believes it is appropriate to use the historical numbers for standard deviations and correlations. Once these variables are determined a sophisticated type of software called “portfolio optimization” can be used to determine the optimal portfolio. Hatton Consulting believes that are so many potential pitfalls to this type of software that its use should be restricted to a tool not an answer for the final asset allocation. If one does decide to use portfolio optimization we recommend including at a minimum the total stock and bond market asset classes and at a maximum the following five asset classes:
The above process will, in theory, provide an investor with an asset allocation that will deliver the highest expected return for a given level of risk. The reality is that a majority of amateur and professionally managed portfolios are similar to point D in figure 1; they are not being compensated fully for the risk taken. Efficient Market Hypothesis Quoting from Dimensional Fund Advisors website, where Fama serves as a director and board member. “The efficient markets hypothesis holds that markets are full of people trying to make a profit by predicting the future values of securities based on freely available information. Many intelligent participants compete to trade at a profit. The price they strike in trading a stock is the same for everyone, so is the value. The price the market strikes is therefore based on all the available information about a stock, everything the investors know that has happened in the past and everything they predict will happen in the future. In this sense, markets assemble and evaluate information so effectively that the price of a stock is usually our best estimate of its intrinsic value. Prices are not always perfectly correct, nor is that a condition for market efficiency. The consensus view of investors can temporarily result in prices well above or well below a stock’s intrinsic value. The only condition efficient markets require is that a disproportionate number of market participants do not consistently profit over other participants. Since “mispricings” tend to occur in both directions and since managers seem to over-and under-perform with random frequency when adjusted for risk and costs, markets seem to be efficient.” The above is the reason there is an ongoing debate about passive vs. active management. We include it our discussion because the empirical data supports its findings. It is also a segue into the Fama/French Three Factor Equity Model. Eugene Fama, of the University of Chicago and Kenneth French, of Dartmouth College have identified what they believe to be are the sources of risk within the capital markets. They are leading candidates for a Nobel Prize for this model. The three equity factors are:
Within the bond market they believe the following:
Table 1 highlights their findings for the period 1927-2001. International stocks 1975-2001, Emerging markets 1988- 2001.
Table 1 Understanding the three-factor model is one more building block in achieving the ultimate goal of return maximization for a chosen level of risk. Many investors try to “beat the market” through specific security selection, market timing or trying to identify the best mutual funds or money managers. Portfolio theory aims to provide superior returns than the market through proper risk exposure. From table 1, you will see the S&P 500 has delivered a 10.7% annual rate of return with a standard deviation of 20.2. To achieve a return in excess of the market the portfolio needs to be exposed to greater risk than the market. In other words, invest in asset classes that have demonstrated long term that, even though there is higher risk, they deliver higher returns (for instance, even though small cap growth stocks have higher risk than the large cap market stocks, as represented by the S&P 500, they have not delivered higher returns). The trick is to determine what riskier asset classes, when combined together (low to negative correlation) will deliver above market returns with less than market risk. Note, that this form of investment does not employ specific security selection or market timing. Therefore, the three factor model suggests to beat the market one must structure the portfolio to have a smaller than average market capitalization in addition to holding companies that exhibit “value” characteristics. To incrementally beat the market by a larger margin one must incrementally expose the portfolio to the two factors of “size” and “price”.
Figure 2 Modern portfolio theory is an ongoing body of research that aims to determine how the capital markets work. There is no one person or idea that dominates, but rather a collection of ideas accumulated over the last 50 years. It is immense and complex. Applying its findings to the practical world of investing is itself very complex but also very rewarding when executed properly. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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