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Problems with CAPM and EMH suggest that Modern Portfolio Theory is not useful for individual investors. As a result, modern finance is in the midst of a paradigm shift similar to those discussed by Kuhn (1962). On an interim basis, using James Montier’s trinity of risk plus behavioral finance as an overlay may work. James Montier, the famous value investor now at GMO Asset Management, has written extensively about the huge contradictions between academic theory and real world observations when it comes to the dynamic between risk and reward in the markets. This is a topic I have been interested in for a long time, because the disjunction between theory and practice should (but usually doesn’t) strongly affect how investment managers view risk and construct client portfolios. Montier began his argument with a review of the evolution of market theory, and especially that part of theory called the Capital Asset Pricing Model, or CAPM. In the 1950’s future Nobel Laureate Harry Markowitz wrote his Ph.D. thesis on a mathematical model for asset allocation called portfolio optimization. His model could theoretically be used to construct portfolios that combined maximum gain with minimum risk for any investor whose assets were diversified. Eventually this approach led, in conjunction with the CAPM, to what is now called Modern Portfolio Theory (MPT). Many institutions today use a modified version of MPT to develop their recommended asset allocations. The CAPM part of modern theory was introduced by Nobel Laureate William Sharpe and his colleagues in the 1960’s. In brief, the CAPM assumed that all investors would use Markowitz’s optimization method, so that a single mathematical factor could be isolated that would distinguish between stocks of differing risk levels, and that factor is called beta (i.e., beta is that part of a stock’s risk that can be attributed to market fluctuations that are systematic and undiversifiable, and this in turn depends in part on a stock’s correlation to the market, as represented by the S & P 500). The final component of MPT was the development of a concept called the Efficient Market Hypothesis by Nobel Laureate Eugene Fama. As part of his work Fama attempted to prove that information is equally available to all players in the markets, so therefore the markets are efficient and all stocks are correctly priced. Over time this idea led directly to the notion that the best investment approach is to use passive indexes to fill out a portfolio allocation, since no one should expect to beat efficient markets for any substantial period of time. It is important to note that this idea of efficient markets is really just an assumption used to make mathematical treatment possible. There is abundant evidence that the assumption of market efficiency is false, as has been discussed by Warren Buffett, John Mauldin and many others. One only needs to think back to the NASDAQ bubble in the late 1990’s and its subsequent collapse, or the carnage of the Great Financial Crisis in 2008, to find glaring examples of inefficient markets. A basic tenet of CAPM is that risk and reward are directly proportional. This means that as risk increases, so does reward. However, a study in the late 2000s by JPMorgan has shown just the opposite trend for real world data. In other words, when 20 years of actual market (the Russell indexes) data through 2008 were plotted, they indicated a strong linear relationship between risk and reward all right, but it was reciprocal. Thus, if risk increases in the real markets, reward can actually decrease. Indeed, Fama and his long-time colleague French published a paper in 2004 showing that for the period from 1923 to 2003, using all stocks on the NYSE, AMEX and NASDAQ, the highest risk (highest beta) stocks considerably underperformed relative to the predictions of the CAPM. The reverse was also true, in that the lowest risk (lowest beta) stocks considerably outperformed relative to the predictions of the CAPM. Over the long run, there was essentially no relationship between beta and stock returns. Yet another study was conducted a few years ago by Jeremy Grantham of GMO Asset Management, who found that for the 600 largest U.S. stocks (for the time period from 1963 to 2006), those with the lowest beta have had the highest returns. Montier himself has studied the risk-return relationship for European stocks for the period from 1986 to 2006 as well, with essentially the same result. Montier’s explanation for the failure of the CAPM over shorter time frames is based on the many questionable assumptions that have to be made for the model to “work” mathematically. Amongst the more questionable assumptions are: 1) no taxes are paid, so investors are indifferent between dividends and capital gains; 2) all investors use Markowitz portfolio optimization at all times; and 3) investors can take any position (long or short) without affecting the market price. These assumptions are implicitly accepted by all who use MPT and CAPM to manage portfolios, such as many institutional asset managers. These may indeed be valid over very long time frames, but then they may not be appropriate for mere mortals to use with their personal investments. This assumed validity reaches its ultimate level of absurdity in the obsession many financial institutions have for so-called short term “tracking error”. Tracking error measures the variability in the difference between a fund manager’s portfolio returns and the returns of the appropriate stock index. Many institutional managers have been compensated on the basis of tracking error. Thus, the variance in investor portfolio returns has not always been considered; rather, a manager’s relative performance against an index is the criterion by which they are commonly judged. This means that if the market loses 20% in a given year and the manager only loses 18%, that manager may very well bonus for outperformance on a tracking error basis, even though their clients lost significant money. Modern hedge funds are in part the profession’s response to client angst over this state of affairs. Many hedge funds attempt to provide steady absolute returns, and that is why they have become so popular amongst high net worth clients. Unfortunately, retail clients until recently had no sophisticated risk-control strategies available to them, but that is changing. If you accept for the purposes of argument that both CAPM and the Efficient Markets Hypothesis are invalid or at least suspect, then you are presented with a dilemma. MPT doesn’t really work except during 50 year periods and longer, which is way too long for use with retail clients, but it is the only theory with any mathematical rigor that is widely accepted. This situation is reminiscent of the problems faced in the physical sciences when an old foundational theory or paradigm has been tossed out, but a new one has not yet appeared. The classic examples are the paradigm shift that occurred when Newton proposed his gravitational theory, and again when Einstein proposed his theories about relativity. This problem was written about brilliantly by Thomas S. Kuhn in his book on “The Structure of Scientific Revolutions,” published in 1962. What generally happens is that the old guard defends the old paradigm even while it is being destroyed as an explanatory tool by new data, so that only younger scientists like Newton and Einstein can break through to new paradigms, and then only when the old guard stops fighting. A famous quote on the matter is attributed to the physicist Max Planck in the early 1900s: “Science progresses one funeral at a time.” I believe, as do others, that this is where we now find ourselves with respect to MPT. Grad schools still teach it, but applying it during the sequential bubbles of the last 20 years has yielded awful results on a risk-adjusted basis. Over an even longer period, since 1982, 30-year zero coupon bonds have beaten the S & P 500 by an absolutely huge margin, as Gary Shilling has been pointing out for many years. The careful practitioner then has a dilemma, assuming that he or she now rejects the old MPT paradigm: there is no mathematically rigorous new paradigm to replace it with. How do we go about asset allocation then? Many others have explored this question in recent years, but with a possible new bear market ahead of us sometime in 2016 or 2017, there is renewed urgency to the quest for answers. Behavioral finance has provided a rich and powerful explanation for what happens in the real world of the markets. It should be a major part of the equation, and goes a long way towards explaining the problems with MPT, but it is not inherently mathematical itself. I am reconciled to thinking that since human beings are involved in economics and markets, there will be no mathematical solution. I personally have been using Montier’s “trinity of risk” concept as a template for making allocation decisions. His trinity consists of valuation risk, business/earnings risk, and balance sheet/financial risk. These can be applied in some way to most asset classes. But a behavioral finance overlay can be useful as well. It is on this basis that I have written elsewhere that I strongly favor certain bonds over stocks, and possibly even over cash, in 2016. The most important conclusion for investors to draw from this discussion is that the assumptions that underlie an asset manager’s approach should be examined carefully and judged for their conformity with that investor’s investment goals. Most will reject the notion that periodic 50% losses are acceptable, so a more risk-aware approach is needed. I realize that I have not really answered all of the questions I have posed; clearly this is a work in progress.