Portfolio Theory
Thomas E. Berghage
As a lead in to this discussion lets review a little security analysis history. Current security analysis techniques trace their beginning back over 100 years to the early 1900’s. The techniques were finally formalized in 1934 when Benjamin Graham and David Dodd wrote their now famous (and in our view, miss-titled) book, Security Analysis. In this book they set forth the basic metrics of financial analysis.
You have to understand that this book was written before the establishment of the SEC (Securities and Exchange Commission), current corporate reporting requirements, derivatives, computers, Spiders, Webs, Leaps, and a host of other products and changes. The shear size of equity markets today has altered the interpretation of the raw numbers. Daily trading volumes of over a billion shares were not even feasible a few short years ago and authorities would have shut down the markets before even approaching these kinds of volumes. Online trading with thousands if not millions of individual day traders has changed the way we view markets and the equities that trade on them.
At the time Graham and Dodd’s book was written it was heralded as the first objective way of establishing investment value, or as it was later termed, intrinsic value.
The intrinsic value of a business or other investment can be defined, in both a theoretical and practical sense, as the present value of the future cash flows of that business or investment. To determine the intrinsic value, the expected future cash flows of a business or other investment are discounted back to the present at an appropriate discount rate. The formula for determining intrinsic value is shown below. While simple to define, the estimation of the factors that determine the intrinsic value are much more complex and requires an understanding of financial and investment theory as well as experience in analyzing businesses and in making the estimates needed for the discount model. In short the discount model is a overly precise way of expressing rather nebulous, imprecise, often subjective estimates of future events.
The general formula, or model, for the calculation of the intrinsic value of a business or investment is:
Vj = C1 + C2 + C3 + . . . . . C¥
(1+k) (1+k)2 (1+k)3 (1+k)¥
where:
Vj = value of business j or investment j
Ct = cash flow during period t
K = required rate of return on business j or investment j
While gaining popularity in the 1900’s because of Graham and others, the use of the term intrinsic value can actually be traced as far back as the mid 1800’s. The exact meaning of the term intrinsic value has been debated for over a century, and there is still no conclusive consensus. Every financial theorist and practitioner has his or her own slightly different definition and way of using the concept. Nevertheless, most definitions of the term and uses of the concept revolve around the general formula given above. J.B. Williams, a mathematician and financial writer, first set forth the general formula for the calculation of intrinsic value in the mid 1930’s (although J.B. Williams actually cites Robert F. Wiese as his source for the model). It was later reintroduced and expanded by Myron J. Gordon, for whom the constant-growth version of the popular dividend discount model, known as the Gordon model was named.
Warren Buffett, one of the wealthiest and most successful investors in the world has long been an advocate of the use of the intrinsic value concept and includes an extensive discussion of his definition for intrinsic value in the Berkshire Hathaway Owner’s Manual. Buffett learned about the concept from Benjamin Graham while he was a student of Graham’s at Columbia University. J.B. Williams and his book, The Theory of Investment Value, influenced both Buffett and Graham in the development of their own definitions of intrinsic value.
By estimating the intrinsic value of a business or investment, one can, in theory, make a determination as to whether a particular business or investment is overvalued or undervalued. The advocates of this approach to security analysis suggest that over the long-term, which is typically 3 to 5 years; they expect the average market price of a particular company to converge with the company’s intrinsic value. In the interim (the short-term periods), the market typically continues to miss-price the security creating overvalued and undervalued conditions that create investment opportunities. As we documented in Chapter 2 the intrinsic value, despite its mathematical elegance and attractive logic, does not appear to have much predictive power when it comes to forecasting future security performance. For time horizons out to one-year intrinsic value has close to a zero correlation with security performance. We will reserve judgment for longer time periods until we see a definitive study.
Regardless of whether you call it intrinsic value or fundamental value you are basically talking about a theoretical concept that is in constant fluctuation and impossible to define. Psychologists have been struggling with a similar problem regarding human intelligence or IQ for years. Both ideas, intrinsic value and I.Q, are conceptually very appealing, but both are impossible to define. Both concepts could improve predictability in their respective fields if they were not so nebulous. The pursuit of both are interesting exercises, but not very useful. The measurement of I.Q. and its use for identifying individuals that are going to excel in school, business, or as community or political leaders has fallen into disrepute. Psychologists now days are much more likely to look at past performance as an indicator of future performance. They prefer to look for behavior patterns as an indication of what an individual is likely to do in the future. Perhaps it is time to start doing the same thing with regard to intrinsic value. Maybe we should abandon the search for this nebulous value and focus on trying to identify the “corporate behavior patterns” that are indicative of future success.
Like the Quantum Mechanics revolution demolished its rivals in the early 1920’s so too will Corporate Behavioral Pattern Recognition put to rest the concept of Corporate Intrinsic Value. Just like the Heisenberg Uncertainty Principle in Quantum Mechanics says, we can never be sure where an electron is or what its velocity is, so too can we never know what a company’s true value is or what its rate of change is. The best we can do is calculate the probability that an electron will appear at a certain place with a certain velocity and that a company’s stock will be at a certain value and appreciating at a certain rate.
This lack of predictive power among traditional accounting based financial variables and security performance lead Eugene Famma and others to suggest that markets are extremely efficient at digesting new information and that a security’s price reflects everything that is known about a company’s current situation and future potential. This assertion has been widely accepted in the academic community and is referred to as, “The Efficient Market Hypothesis.” Regardless of whether one accepts the idea of the efficient market hypothesis, and many do not, the fact remains that traditional financial measures have very little predictive power for forecasting future security performance. The relationship between financial analysis and security performance is weak at best. This lack of predictability could be due to a number of factors including market efficiency, but for whatever reason traditional accounting measures appear not to be effective tools for use in security analysis. The studies that have been done in support of the efficient market hypothesis demonstrate the inability of financial analysts to add value to investment portfolios.
The inability of financial analysis to add value to the investment process has led many in the financial community to abandon the use of financial analysis altogether and focus their efforts on asset allocation and portfolio structure. Equity allocations are represented by baskets of stocks (Indexes) structured to track the performance of the market as a whole or various sectors of the market. The growth in the use of index funds is the fastest growing investment segment and it eliminates the need for analysis of individual companies and securities.
The academic literature is full of studies that provide support for the efficient market hypothesis. So overwhelming has been the support, that it became the cornerstone for the economic model that has dominated finance for the last fifty years. The Nobel Prize Committee in 1990 recognized the importance of the Capital Asset Pricing Model (CAPM) and its underlying assumption of market efficiency when it awarded its prize in economics to Harry Markowitz, Merton Miller, and William Sharpe.
The Capital Asset Pricing Model (CAPM) as put forth by Markowitz (1959) and Sharpe (1963) is based upon a number of underlying assumptions such as all investors having the same investment time horizon, identical borrowing and lending rates, and no transaction costs or taxes. All of these assumptions were necessary because all of these conditions differ among investors. An even more basic assumption is that investors are rational decision makers and that given the choice they prefer, lower risk versus higher risk, for the same level of return, and for a given level of risk, they prefer higher returns over lower ones. This idea of the rational investor has permeated economic thinking and model making ever since. A number of people have questioned this assumption and have provided extensive experimental evidence to indicate that it is a shaky premise at best. The assumption is now so widely questioned that it has given rise to its own school of business thought called, Behavioral Finance, and has had a special issue of the Financial Analyst Journal devoted to its research findings. We will review some of the research in support of Behavior Finance in the next chapter.
Rather than throwing out the Capital Asset Pricing Model because of the weakness of one of its underlying assumptions, I think it would be more productive and profitable to shore up the underlying assumption by replacing the irrational human decision maker with a totally rational intelligent machine. We will discuss the possibility of doing this in Chapter 13. We now have the ability to build machines with computational intelligence that surpass the capability of we poor humans, and this will allow us to reenergize the CAPM by strengthen the underlying assumption of the rational investor. Through the use of intelligent systems we can build a totally rational investor that is completely devoid of emotion, and able to analyze investments far better than anything that has been attempted up to now; systems that can learn and adapt to changing conditions far more readily then anything now available.
Most financial text used in universities today address the topic of investment risk and talk about modern portfolio theory as a way to understand and handle the volatility associated with individual securities. They suggest that there are three or four levels of risk, risk associated with the individual corporation, risk associated with industry sectors, risk associated with related or similar companies, and over-all market risk. Modern Portfolio Theory suggest that the first three risk factors can be handled by appropriate diversification while the remaining market risk is handled by hedging or portfolio insurance.
The Capital Asset Pricing Model describes the way prices of individual assets are determined in markets where information is freely available and reflected instantaneously in asset prices – that is, efficient markets. To describe the relationship between risk and return, the CAPM introduced two new terms to the investment vernacular, “Alpha” and “Beta”. These two terms are the coefficients used to calculate the relationship between risk and return in the CAPM. They are defined as:
Alpha (a) – The constant term in the equation relating the risk premium on an asset to the risk premium on the market. Its expected value is zero, but its actual value may differ from zero.
Beta (b) – The coefficient that expresses the sensitivity of rates of return on a portfolio or on a particular security to general market movements. If the beta is 1.0, a 1 percent increase in the return on the market will result, on average, in a 1 percent increase in the return on the particular portfolio or asset. If beta is less than 1.0, the portfolio or asset is considered to be less risky than the market. Beta is the regression coefficient of the rate of return on the market in the market model equation,
Ri = ai + biRM + ei
Ri = Rate of return on security i
ai = Alpha for security i
bi = Beta for security i
RM = Rate of return on the market
ei = A random variable for security i
An estimate of the beta coefficient of a portfolio is a weighted average of the betas of the portfolio’s component assets.
A favorite pastime for institutional investors and their consultants has been the search for managers that can produce consistent Excess Alpha, i.e. portfolios with returns above the Capital Market Line. They like to use what is now called the Sharpe Ratio for evaluating return-per-unit-of-risk. To calculate the Sharpe Ratio you take an investment’s return minus the “risk-free” rate, (generally considered to be the return on the 90 day treasury bill) divided by the standard deviation of the investment’s return over some period of time. A number of techniques have been used to find these elusive excess alpha investments that provide above average, risk adjusted, returns, and none has been successful. As we pointed out in Chapter 3 the use of traditional financial analysis techniques has failed to have much value when it comes to analyzing securities. Without the development of some new approach to the security analysis problem, we will continue to struggle in our attempts to produce consistent excess market returns and index investing will remain the investor’s best option.