Death to the Policy Portfolio
William Jahnke (Rough Draft Not for Circulation: March 25, 2004)
Peter Bernstein (2003) caused an uproar with his Economics and Portfolio Strategy publication when he proclaimed “policy portfolios are obsolete.”[1] The policy portfolio is the term Bernstein uses to describe the common practice in financial planning of setting a fixed asset allocation mix as part of investment policy and avoiding market timing. In challenging the policy portfolio, Bernstein is challenges the core belief supporting it, “Equilibrium and central values are myths,” he says “not the foundations on which we (should) build our structures.” Bernstein is calling for flexible asset allocation that recognized the changing investment opportunities and risks, evaluates the prospects for extreme financial outcomes from an economic perspective not a statistical perspective, and hedges some of the risks associated with extreme outcomes.
Bernstein is ruffling all kind of feathers. For many financial planners the policy portfolio is a cornerstone of investment practice. How could something with such wide appeal and acceptance in the financial planning community be ideologically wrong? How can the policy portfolio with seemingly irrefutable theoretical and empirical credentials be judged obsolete by one of the foremost authorities on investing? The answers have been there from the start. Indeed, the story behind of the policy portfolio and its rise to prominence in the practice of financial planning – a chronicles as troubling as it is fascinating – is one worth telling.
Faulty Assumptions
The theoretical foundation of the policy portfolio is the random walk model. As first conceived by Louis Bachelier (1900), the random walk model assumes that successive price changes are independent, identically distributed, and normally distributed.[2] What is meant by independent is that no investor can use his knowledge of past data to increase his expected profit. What is meant by identically distributed is that the means and standard deviations from sample period to sample period will converge on being identical as the sample sizes get larger. What is meant by normally distributed is that the distribution of time series of periodic returns can be described by the well known bell shape curve. For the assumptions of the random walk model to hold the process that generates returns across time must be stable.
The common practice of forecasting returns and portfolio volatility based on historical mean returns and standard deviations requires the belief that the return generating process is stable and the assumptions of the random walk model are valid. If the return generating process is not stable or does not conform to the random walk model assumptions, then the practice of forecasting future returns from historical returns is unreliable because investment opportunities vary from period to period, and thus the appropriate investment solution is subject to change. Without the random walk model there is no theoretical foundation for the policy portfolio.
Confusion abounds among academics and financial writers when it comes to terminology. By random walk some writers simply mean that future steps in the market can not be predicted. This is the definition that Burton G. Malkiel uses in “A Random Walk Down Wall Street.”[3] Malkiel’s definition of random walk is better suited to defining the term efficient market. According the efficient market model the market is a “fair game” where prices are set fairly and there are no market inefficiencies for investors to exploit. The efficient market model says nothing about stability in the process generating returns. The random walk model is a special and more restrictive case of the efficient market model which carries the added assumptions that successive returns be independent and identically distributed. Malkiel is not alone; other financial writers confuse financial planner with their use of the terms random walk and efficient market. It is little wonder that many financial planners have been confused in thinking that the policy portfolio is supported by efficient market theory, or that studies in support of the efficient market model necessarily support the random walk model and the policy portfolio.
While the random walk model requires the return generating process be stable, the efficient market model does not require stability in the return generating process. If the return generating process is unstable, then statisticians have difficulty applying their techniques. If the return generating process is stable and produces normal distributions then statisticians have and easy job. It return distributions are stable but non-normal then statisticians have their work cut out for them because the standard statistical tool kit assumes that return distributions are normal. It is common for statisticians to assume that distributions are normal when the empirical data does not appear to be normal, because of the lack of tools to work with non-normal distributions. When Peter Bernstein observes equilibrium and central values myths, he is implicitly challenging the assumption that successive returns are being generated from a stable return generating process.
The efficient market model can claim theoretical legitimacy in classical financial theory even if empirically it does not perfectly fit the real world. However, there is no economic theory supporting the random walk model. The assumptions that successive returns are independent and identically distributed are among the most extreme and implausible assumptions in all of economics. The idea that returns are drawn from a stable return generating process defies any appreciation of the instability, discontinuities, and inflection points common in the real world of business, finance and investing.
What’s troubling is few financial planners know that the assumptions underpinning the statistical work on the policy portfolio have been under attack practically from inception a century ago. There is overwhelming and conclusive evidence that asset class returns do not behave in accordance with the normal distribution. Virtually all of the early researchers observed that empirical return distributions had “fat tails” relative to the normal distribution. The solutions to the fat tail problem varied; some researchers ignore the fact, some threw out the offensive outliers, some adjusted the numbers, some rejected the random walk model, and some tried to salvage the random walk model by replacing the normal distribution assumption with another stable distribution that better fit the data.
Just how poorly the random walk model fits empirical data can be gleaned from the Ibbotson Associates publication “Stocks, Bonds, Bills and Inflation.” Among the derived statistics are asset class returns and standard deviations by decade, and rolling sample mean returns, standard deviations and correlations. Looking at the tables and charts, how can anyone not be struck by the lack of stability? How can anyone believe that the average return, standard deviation, and cross correlation computed with all the data, whether inflation adjusted or not, provides accurate forecasts for the purpose of financial planning and asset allocation?
According to Benoit Mandelbrot (1967), the father of Fractal Geometry, all of the assumptions supporting the random walk model “are working assumptions and should not be made into dogma.” Mandelbrot goes on to say that Bachelier writing in 1914 made no mention of his earlier claims of empirical evidence for the random walk model and noted the existence of empirical evidence contrary to the random walk model; standard deviations vary from sample period to sample period and the tails of the distributions are fatter than those predicted by the normal distribution. Mandelbrot gives Bachelier not only the credit for being the first to propose the random walk model, but also he gives him credit for being the first to expose its major weaknesses.[4]
Mandelbrot was well aware that empirical data for many financial time series do not conform to the normal distribution assumption of the random walk model. Mandelbrot (1967) notes that virtually every student of price series has commented on the fact that empirical return distributions are fat tailed. In discussing stationarity, Mandelbrot states, “One of the implications of stationarity is that sample moments vary little from sample to sample, as long as the sample length is sufficient. In fact, it is notorious that price moments often ‘misbehave’ from this viewpoint (though this fact is understated in the literature, since ‘negative’ results are seldom published).” Mandelbrot’s stated goal was to save the random walk model by accounting for the fat tails with a family of stable non-normal distributions called stable Paretian. Mandelbrot acknowledged that there are other explanations for fat tails, including distributions that are not stable but are “haphazard.” According to Mandelbrot, if sample returns distributions from period to period are haphazard, i.e. not capable of being treated by probability theory, “why bother to construct complicated statistical models for the behavior of prices if one expects this behavior to change before the model has time to unfold?” Bachelier believed he was looking a haphazard distributions; Mandelbrot’s mission was to prove Bachelier wrong.
Bad Science?
The random walk model languished in obscurity until Leonard Jimmie Savage rediscovered it sometime around 1954. Savage a gifted statistician at the University of Chicago introduced the random walk model to U.S. academics including Paul Samuelson. Samuelson, the first American to win the Nobel Prize in Economics. Samuelson was enamored with Bachelier's work and a believer in the theory that market prices are the best gauge of intrinsic value published a paper in 1965 “Proof that Properly Anticipated Prices Fluctuate Randomly.” Much has been made of Samuelson’s proof; indeed, Peter Bernstein devotes a chapter in his book Capital Ideas to Samuelson and his proof. Here Bernstein quotes Samuelson’s reservations: “The theorem is so general that I must confess to having oscillated over the years in my own mind between regarding it as trivially obvious (and almost trivially vacuous) and regarding it as remarkably sweeping.”[5] Samuelson’s proof that prices fluctuate randomly is not a proof of the random walk model but rather a proof that in an efficient market prices fluctuate randomly.
Mandelbrot joined the faculty at the University of Chicago where he influenced his student Eugene Fama, who was to become the leading academic advocate for the random walk model. Fama (1963) in an article “Mandelbrot and the Stable Paretian Hypothesis,” discusses the issue of fat tailed distributions and Mandelbrot’s fix for the random walk model.[6] The stable Paretian distribution defines the distribution of returns in terms of four parameters instead of the normal distribution’s two (mean and standard deviation). The four parameters of the stable Paretian distribution determine the mean of the distribution, the symmetry of the distribution (skewness), and the tails of the distribution (kurtosis) and how the distribution scales. The normal distribution is a special case in the family of stable Paretian distributions. Fama noted that the stable Paretian distribution has “extreme” implications. Unless the return distribution is normal, the sample standard deviation in probably a meaningless measure of dispersion and statistical tools such as least squares regression will be at best considerably weakened and may in fact give very misleading answers. Fama warned “Before the hypothesis can be accepted as a general model for speculative prices, however, the basis of testing must be broadened to include other speculative series.”
The fact that it can “explain” the existence of fat tails and other complexities observed in empirical data it does not mean that the return generation process actually conforms to the stable Paretian hypothesis. How realistic is it that returns from one period to another are governed by a fixed set of four numbers? An alternative explanation for the fat tails is that the process that generates returns is unstable. A periodic reading of the Financial Times and the Wall Street Journal does not suggest an underlying mathematical order in the return generating process; rather it suggests that investing offers an ever changing set of risky bets with variable rewards for risk taking. After proposing the stable Paretian hypothesis, Mandelbrot was never able to make good on his goal to successfully demonstrating the value of his work in forecasting returns. Later, Mandelbrot moved on to more fertile applications of non-normal stable distributions in the natural sciences.
The random walk model was a marketing success in large part due to the efforts of Fama. Fama’s (1965) Ph.D. thesis “The Behavior of Stock Prices” dealt extensively with the violations of the normality assumption in the random walk model and Mandelbrot’s attempt to salvage the random walk model by introducing the stable Paretian distribution.[7] Fama presented his own research that finds fat tails in the time series of returns for Dow stocks. He also reviewed some of the studies he found to support the independence assumption over short time horizons as well as the inconsistency in performance in one mutual fund performance study, and comes to number of conclusions including; a large and impressive body research supports the random walk model, the stable Paretian distribution fits empirical data better than the normal distribution, statistical tools using variance and standard deviations are invalidated including Markowitz mean-variance portfolio selection.
In 1965 Fama took the debate on the random walk model to the investment profession when he published “Random Walks in the Stock Market” in the Financial Analysts Journal.[8] Fama not only challenges the practice of technical analysis he attacks the usefulness of fundamental analysis. Fama limits his discussion on the random walk model to whether the independence assumption fits the empirical data. He never referred to fat tails, non-normal distributions, or whether the return generating process is stable. In the article, Fama concluded “The evidence to date strongly supports the random walk model.”
One of the early works for which Fama (1970) is known in the investment community is his 1970 paper “Efficient Capital Markets: A Review of the Theory and Empirical Work,” which sorts the empirical work into weak, semi-strong, and strong form tests of efficient market theory.[9] Here, Fama clearly distinguished the efficient market model from the random walk model and reaffirmed his support for the efficient market theory, “For the purposes of most investors the efficient markets model seems a good first (and second) approximation to reality. In short, the evidence in support of the efficient markets model is extensive and (somewhat uniquely in economic) contradictory evidence is sparse.” Fama claims to being “surprised” that the evidence against the independent assumption of random walk model is as weak as it is. “Indeed, at least for price changes or returns covering a day or longer, there isn’t much evidence against the ‘fair game’ model’s more ambitious off-spring, the random walk.”