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Revisiting Modern Portfolio Theory and Portfolio Construction FEATURE | REvisiting ModeRn PoRtfolio THEORy and PoRtfolio CONSTRUCTION Revisiting Modern Portfolio Theory and Portfolio Construction By Bryce James ears ago, I was speaking at an invest- Figure 1: Standard Deviation Probabilities from the Mean Return ment industry conference when a Probability of Return at 1, 2, and 3 Standard Deviations Yman in the front row yelled out, “Is this just another rubber chicken pre- 5% 1σ sentation on asset allocation?” I responded 4% with, “Fasten your seatbelt!” and I’ll say it 3% again here, because this is not your generic 2% 2σ 2σ article on post-modern portfolio theory. 1% I’m going to challenge you to question what Probability Density 3σ 3σ 0% you think you know about asset allocation 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% and ask you to keep an open mind to what –9% –8% –7% –6% –5% –4% –3% –2% –1% 10% –10% is possible. DJIA Daily Return 99.7% Probability of Return 95.4% Probability of Return 68.3% Probability of Return Birth of a New Technology Source: Internal calculation using Excel. Data from Thomson-Reuters Computer technology was born in the 1950s with the first commercial com- return, and linear correlation (ρ) for which academics named the efficient market puter—the UNIVAC 1—delivered in 1951, correlation. hypothesis (EMH). The person credited followed by the first hard disk in 1955, 3. Optimize the portfolio using a covari- with this integration of the EMH was Fortran computer language in 1957, and ance matrix to seek the optimal effi- Eugene Fama at the University of Chicago. the modem in 1958. This era also gave cient frontier, i.e., asset mix. birth to modern portfolio theory (MPT). Standardized risk metrics in finance took You know about Harry Markowitz and In a classic MPT model, which is based hold in the 1950s when top economists, what he accomplished. All asset allocation upon probability theory, many assumptions such as Maurice Kendall (London School of work henceforth is a manifestation of his are made. The core assumption was Economics), Paul Samuelson (MIT), Harry concepts, founded on the principles of founded on the work of Louis Bachelier Markowitz (University of Chicago), and diversification. Implementing MPT is to (Mandelbrot and Hudson 2004, 9), who in William Sharpe (University of Washington apply a process called mean-variance 1900 introduced a probability-based model and University of California, Los Angeles), optimization (MVO). following the random walk theory, which is observed that over the long term, changes named after the unpredictable path of a in security prices plotted on a histogram An MVO model is a three-step process for drunken man (Fox 2009, 40–41; Sornette chart (frequency distribution) resembled portfolio construction: 2002, 38). Bachelier postulated that the the shape of the symmetrical bell curve market is like a 50-50 coin toss and that (Gaussian distribution) (see figure 1). 1. Collect a large amount of historical most market moves are measurable. This Combining all these pieces gave birth to price data on each security in your led him to conclude that markets are effi- the “science of investing.” fund universe (typically 30 years of cient. He calculated that 68.3 percent of daily prices and dividends). the changes up and down are small, falling As MPT took hold in the early 1960s, folks 2. Calculate the risk and return of each within one standard deviation (1σ) from such as Jack Treynor and William Sharpe security and the correlation between the mean return; that 95.4 percent of the introduced the capital asset pricing model pairs of securities. In traditional MPT, changes fall within 2σ; and that 99.7 per- (CAPM), improving upon Markowitz’s this is performed using standard devia- cent fall within 3σ. Markowitz (1952, 1959) capital allocation line. Risk finally could tion (σ) for risk, mean return (μ) for fit snugly into this random walk theory, be measured, as ratios, in various ways JANUARY / FEBRUARY 2017 5 © 2017 Investment Management Consultants Association Inc. Reprinted with permission. All rights reserved. FEATURE | REvisiting ModeRn PoRtfolio THEORy and PoRtfolio CONSTRUCTION through the metrics created by Sharpe, Data bonds instead of non-callable bonds. In Treynor, and Sortino. Today, these theo- In 2005, a law firm representing a group of addition, they were using bond proxies ries, known for their risk metrics, stand as investors hired me as an expert witness. The when no long bond was issued (which is the foundation of investing. But as tech- clients, all retired, claimed their broker was most of the time) in calculating the long- nology has significantly changed over the imprudent in managing their assets, creating term bond index. The net effect was an over- past half century, is it possible finance has losses exceeding 40 percent. The brokerage allocation to equities and an undervaluing been asleep? firm’s asset allocation software, based on an of bond returns. The net result, according to MVO model, recommended the usual 60/40 Ryan, created a massive performance dif- MPT assumes all information is priced into mix. However, the firm chose to use 18 years ference of 45.3 percent (from 1941–1991). the security and that yesterday’s price has of historical data rather than the 28 years Furthermore, investors would have experi- no influence on today’s price; each price recommended by the software vendor. As enced a standard deviation of 9.04 percent change is independent from the previous a result, the Monte Carlo simulations esti- using the Ibbotson Long Treasury portfolio move. The market, and each security, is mated a 16-percent return on equities into compared to 5.96 percent standard devia- fairly priced and moves are completely ran- the future instead of the 9-percent estimate tion with the actual Treasury composite; dom, with no regard for human emotion. (as of December 31, 1999) using the software a difference of 45.6 percent more risk Therefore, MPT assumes: (1) returns are vendor’s default 28-year time series. Yet this (Ryan 1992). normally distributed, (2) risk (σ) is accu- was not the main issue. The broker himself, rately captured using a normal distribution, using his own personal asset allocation soft- In a response to Ryan’s claims, Ibbotson (3) historical prices (mean-variance) can be ware, decided to load only three years’ worth colleagues Laurence B. Siegel and Scott L. used to predict future prices, (4) linear cor- of history (ending December 31, 1999) into Lummer (1993) wrote: relation accurately represents the relation- the asset allocation software. Recall that this ship between pairs of securities, (5) data was one of the best-performing periods for Today, however, only a very naïve investor acquired from data providers is accurate, the stock market, if not the best, in history. In would use our 20-year constant maturity and (6) markets are efficient, thus ignoring doing so, the broker’s MVO model forecasted series as a benchmark for evaluating a the behavioral science of fear and greed. a 27-percent return, which he presented to diversified bond portfolio. Mr. Ryan I’m here to tell you that all these assump- his retirement-age clients. As you know, the makes a valid point in suggesting an asset tions are false. Stock markets do not follow dotcom bubble soon burst and it took the allocator could be fooled by the Ibbotson random walks (see, e.g., Lo and MacKinlay S&P a decade to break even and 14 years data into underweighting in bonds. This 1988; Grossman and Stiglitz 1980; for the NASDAQ. The case was an easy win is a danger only if the asset allocator liter- Colander et al. 2009). for our side. Selection of time series is a form ally believes the disappointing historical of momentum. return on long-term bonds will be It’s so hard to let go of judgments and repeated. Again, this is a naïve view. The beliefs. It’s human nature to hang on to The time series is such a critical piece of expected return on a default-free bond is what’s familiar. In our business, it’s best to data, yet so overlooked. I argue that all its yield. This, not the historical return, stay safe by doing what everyone else does. models are momentum models, because should be used for asset allocation. We also stay safe by keeping things simple. any time you select a time series, you are If it’s not simple, clients’ eyes roll back in making an assumption and making a bet. Asset allocation models should be expec- their heads and you’ve lost the sale. This is To buy and hold is making a bet that past tational; they require expected returns as why even the newest financial technology— performance is indicative of future results, inputs. For bonds, the expected return is robo-advisors—rely upon the MPT/MVO contrary to our marketing disclaimers. observable in the market as a yield and math from 1952; it’s fast and easy. The first does not have to be extracted from his- person to expose the naked truth about the Back in the days of the UNIVAC 1, the tory. To use a historical average as the mathematics was Benoit Mandelbrot term GIGO (garbage in, garbage out) was expected return for bonds, as Mr. Ryan (1964). He criticized the use of normal dis- born. Financial companies have been built has done, is conceptually improper and tributions and warned that markets are around delivering quality data. I’m here to leads to poorly constructed portfolios. influenced by human behavior.
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