A Practical Demonstration of the Value of Portfolio Theory

Includes: DJP, EWC, EWM, VNQ, XLU
by: Phil DeMuth

Ben Stein and I wrote Yes, You Can Supercharge Your Portfolio to demonstrate the practical value of Modern Portfolio Theory to a mass audience. It had long struck us that many investors still operate under a pre-Markowitz paradigm, trying to outperform the market by picking hot stocks and five-star mutual funds. In the book, we argue that a better approach is to seek massive diversification among and within asset classes in order to attain the best risk/return tradeoff for a portfolio. We further recommend that portfolios should be checked through forward-looking Monte Carlo simulations, and provide some practical examples. In contrast, merely extrapolating from historical returns to an asset allocation can lead to poorly-performing allocations, as shown in William Bernstein’s The Intelligent Asset Allocator. Forward-looking models can provide more realistic estimates of future risk and return.

We didn’t know then that stock markets would be in the middle of a major correction by the time the book was released. The analysis and results in the book all had been generated using market data available through 2006. The portfolios we presented as examples all looked fine as we went to press (thanks to Geoff Considine’s Quantext Monte Carlo simulator, QPP), but they were to be severely tested as the book reached the stands. This paper examines the performance of three teaching portfolios we discuss in the book during the recent market decline from 10/31/2007 to 1/31/2008.

A key point of the book is that standard ‘pie chart’ asset allocations often can be improved using forward-looking analyses via Monte Carlo simulations. Standard allocations can be engineered to deliver more estimated return for less estimated risk. Our initial examples set fairly modest goals, looking for around one percent per year in additional return with risk levels at or below those of the original portfolios upon which they were based. This approach allows investors to ease into portfolio theory because the core of the portfolio is still quite familiar.

Apple Pie

The first portfolio we considered we called the “Apple Pie” portfolio: 70 percent total U.S. Stock Market [TSMX] 25 percent MSCI EAFE Index [FSIIX], and 5 percent MSCI Emerging Markets Index [VEIEX]. This is the kind of low-expense, indexed pie chart portfolio we often see recommended for the equity side of investors’ holdings.

We tried to “supercharge” this portfolio – that is, enhance its risk/return characteristics -- by adding small quantities of few exchange-traded funds: funds tracking a commodities index (NYSEARCA:DJP), utilities (NYSEARCA:XLU), REITs (NYSEARCA:VNQ), and Malaysia (NYSEARCA:EWM). We called the resulting portfolio “Apple Pie a la Mode” and claimed that it had better portfolio characteristics than the original. We designed this modified portfolio using a forward-looking Monte Carlo simulator (Quantext Portfolio Planner). Our new version had less projected risk than the Apple Pie portfolio, but with an increase in expected return of 0.8% per year (p.63-66).

I analyzed both portfolios to see what happened to them from 10/31/2007 through 1/31/2008. During this time, Vanguard’s flagship S&P 500 Index fund [VFINX] fell 10.57 percent.

The plain “Apple Pie” portfolio is down 11.97 percent over the same period. This portfolio supposedly improves on the S&P 500 by adding small cap stocks, foreign developed market stocks and emerging market stocks, but they did not help here. This illustrates a basic theme of our book: simply adding highly correlated assets to a portfolio does not significantly improve its risk/return profile, even if the asset classes seem impressionistically like they should. We argue that instead, investors should examine the actual behavior of portfolio components. To do this they need portfolio analysis tools like the Monte Carlo simulator.

What about the “Apple Pie a la Mode” portfolio? It was down 10.28 percent. It had the same 100 percent equity exposure, but with improved performance over three months in a down market courtesy of the free lunch of increased diversification. This is important because, unlike market timing or stock or fund picking, the ‘free lunch’ of diversification, like that of low expenses, is on the table for the taking.

The difference between the less- and more-diversified portfolios was 1.7 percent over three months. But imagine that the difference amounted to only 1 percent annually. Over the course of 30 years, that would mean an investor would have about 35 percent more money in his or her retirement account. Investors focus a lot of attention trying to capture big differences in performance to make a killing today, but they would be better advised to seek out incremental differences in performance that are reliable and compound over time.

Global Cap-Weighted Portfolio

Next, we tried a variation. We took a portfolio that was indexed by capitalization weighting to the global economy as a whole. This ends up being allocated 46 percent to the total U.S. stock market [VTSMX], 44 percent to foreign developed stock markets [FSIIX], 7 percent to emerging markets [VEIEX], and 3 percent to Canada (which was omitted from the original EAFE Index but is here reinserted as iShares MSCI Canada Index ETF (NYSEARCA:EWC)). This portfolio is considerably more weighted to international stocks than the “Apple Pie” portfolio.

This time, we wanted to show how portfolio diversification could be improved by the judicious addition of individual securities – even for a portfolio that already is diversified by thousands of companies from all over the world. We added 16 individual stock positions at 1 percent each. The companies were primarily drawn from utilities and consumer staples, and included a few others whose returns had a low correlation to the rest of the global portfolio: FirstEnergy (NYSE:FE), AFLAC (NYSE:AFL), Pepsi (NYSE:PEP), FTI Consulting (NYSE:FCN), Lockheed Martin (NYSE:LMT), Chesapeake Utilities (NYSE:CPK), Southwest Gas (NYSE:SWX), The Southern Company (NYSE:SO), Northwest Natural Gas (NYSE:NWN), WGL (NYSE:WGL), United Utilities (OTC:UUPLY), General Mills (NYSE:GIS), Johnson & Johnson (NYSE:JNJ), Enbridge (NYSE:ENB), Municipal Mortgage & Equity (MMA) and Clorox (NYSE:CLX). We called it the “Global Cap-Weighted Portfolio with Fries.” The forward-looking Monte Carlo analysis calculated that this portfolio had an expected future return that was 0.9% per year higher than the Global Cap-Weighted Portfolio, with less than 90% of the total volatility (p.72-75).

The global capitalization-weighted portfolio was down 12.81 percent from 10/31/2007 through 1/31/2008. Once again, international diversification worked against us. Our more diversified portfolio performed better: it was down only (although one greatly hesitates to use the word “only” in this context) 10.35 percent, or about a two and a half percentage point improvement over three very bad months.

Six Ways from Sunday

The third allocation we examined was Scott Burn’s “Six Ways from Sunday” portfolio. We chose it because it had the best performance of any of the canned portfolios we had called out in earlier chapters. Its outperformance was due to a heavy allocation to two of the top performing sectors of the previous three years: REITs [VGSIX] and energy [VGENX]. We generally argue against making big bets on recent big winners (this being a major difference between a forward-looking Monte Carlo-based portfolio and one based on historical Mean-Variance Optimization). It does not generally make sense to us to invest as much in a single sector as one would in the entire U.S. or international stock market. Scott Burns would be the first to admit that this is not a performance record you could bank on repeating. The rest of the portfolio is allocated to total U.S. stock market [VTSMX], total international stock market, [VGSTX] Treasury inflation-protected securities [VIPSX], and foreign unhedged bonds [BEGBX] – all at an equal 16.66% weighting.

We wondered if even an extremely lucky portfolio such as this could be improved. As Nobelist James Tobin pointed out in 1958, the way to suppress volatility in a portfolio is to lend money against it by adding bonds. We wanted to explore whether substituting low-volatility individual stocks (the list was composed of FCN, LMT, AFL, Anheuser-Busch (NYSE:BUD), JNJ, Kellog (NYSE:K), GIS, DJP, DTE Energy (NYSE:DTE) and Northrop Grumman (NYSE:NOC)) for most of the highly meaningful bond allocation in the “Six Ways from Sunday” portfolio could preserve its downside protection while securing a potential improvement in an up market from the increased equity exposure overall. In effect, we wanted to we have our safety and the returns, too.

As we ran the numbers over the down market, we anticipated that the “Six Ways from Sunday” portfolio would fare significantly better than ours, since ours had less than half as many bonds (15.2 percent vs. 33.3 percent). The “Six Ways” portfolio lost 6.02 percent of its value during the period, but our “Supercharged” version went down just slightly more, 6.05 percent. As we had correctly observed in the book (p. 87), “In practice, you might want to increase the percentage of bonds slightly beyond this to account for the possibility of increased correlation among portfolio assets going forward.” The close score of the two portfolios in this instance adds evidence that individual securities with low correlations to a portfolio and that are low in volatility can have an effective, bond-like role in dampening volatility, while still preserving the possibility of more equity-like returns in favorable markets.

Potential Loss and Forward-Looking Volatility

Another interesting finding is the role of the Quantext Monte Carlo simulator not only in “stress-testing” portfolios on paper before real money is committed to the markets, but also in educating users to the potential future volatility their portfolios might face. The future volatility projected for the model portfolios shown in the book was roughly twice the historical volatility of the portfolios over the most recent three years. The Monte Carlo simulator assigned the original “Apple Pie” portfolio a 1-in-20 risk of a minus 11 percent return over a three-month period. Users might have been unhappy, but cannot claim to have been dumbfounded, by the negative 11.97 percent return they subsequently realized. The simulator forecast a 1-in-20 risk of minus 10 percent for the “Apple Pie a la Mode” portfolio, and anyone who bought that portfolio should not have been stunned by the 10.28 percent loss he or she would have actually experienced. Both are well within the probabilities of our everyday experience: 1-in-20 events are hardly “Black Swans.”

Losses of this magnitude would have come as a greater shock, however, to investors who assumed that the low-volatility conditions prevailing in equity markets over recent years to be normative. Projecting from the experience of the past three years only, a 1-in-20 loss would have been on the order of minus 3 percent. The actual losses were over three times greater. Indeed, it was precisely the soporific effects of the placid investment environment that led investors to take on more risk than they realized, until it was too late. Investors using forward-looking models were forewarned.


While a three month period provides only anecdotal evidence, the dramatic recent downturn in the stock market offers an interesting window on to the predictive validity of Yes, You Can Supercharge Your Portfolio. These results are consistent with the body of evidence supporting the use of forward-looking models for better portfolio design. These results may help investors to understand the practical value of portfolio theory in investment planning and asset allocation.