A Practical Demonstration of the Value of Portfolio Theory 20 comments
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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 (DJP), utilities (XLU), REITs (VNQ),
and Malaysia (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 (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 (FE), AFLAC (AFL), Pepsi (PEP), FTI Consulting (FCN), Lockheed Martin (LMT), Chesapeake Utilities (CPK), Southwest Gas (SWX), The Southern Company (SO), Northwest Natural Gas (NWN), WGL (WGL), United Utilities (UUPLY.PK), General Mills (GIS), Johnson & Johnson (JNJ), Enbridge (ENB), Municipal Mortgage & Equity (MMA) and Clorox (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 (BUD), JNJ, Kellog (K), GIS, DJP, DTE Energy (DTE) and Northrop Grumman (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.
Summary
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.
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This article has 20 comments:
30% Domestic Equity
15% Foreign Developed Equity
5% Emerging Markets Equity
20% REITS
15% Treasury Bonds
15% TIPS
seekingalpha.com/artic...
The kind of basic asset allocation that Foust cites from Mr. Swensen is precisely the kind of generic asset allocation that can be improved using portfolio theory to deliver more return with less risk. Thats the point of Phil's article and, in fact, uses the same approach to maximizing diversification that has made Mr. Swensen so successful.
Big G seems to be saying that he can make a portfolio that will outperform Mr. Swensen via adding timing to Mr. Swensen's approach to portfolio theory. Thats a big claim.
First and foremost is you are assuming a normal distribution in your analysis. Sharpe and Mandelbrot rebuke normal (arithmetic) distributions in favor of stable (logarithmic) distributions. In a normal distribution the odds of a 5σ (std. Dev.) event is one in 7000 years when in reality its one in every 3-4 years (as seen in a stable distribution). Any model using a normal distribution is blind to the real world and the results are merely academic.
The second major flaw is your attachment to Mean Variance Optimization (MVO). Who cares what the recommended asset mix is when its averaged over a long historical time frame. You can be in a bullish of bearish state for 20 years. To assume MVO works is akin to assuming a broken clock works because it properly tells time twice a day. Add three months of new data to an MVO model and tell me if it changes your recommended allocation. It doesn’t because what can 3 months of data do to a model when averaged with decades of information? Had you elected to use the works of more recent Noble laureates (not those from the 1950’s) you would come across the GARCH models (awarded in 2002). MVO is to the Farmer’s Almanac as GARCH is the Doppler radar.
The final obvious flaw is using Monte-Carlo in conjunction with MVO. What good is it when it relies on long-term data that has been averaged over time? Try using M-C simulations on Stable Student-t distributions combined with GARCH and you would find yourself at the start of this year in 50% 1-3 year Treasuries and other risk adverse securities after enjoying a banner 2006 & 2007. The worse thing to happen is that ‘old schoolers’ will call you a market-timer as you laugh your way to the bank.
I suggest you read ‘The (Mis) Behavior of Markets” by Benoit Mandelbrot to get you out of the 50’s and upgrade yourself to the 21st century.
Foust: The Swensen portfolio you cite was down 7.4% over the study period, and that with a 30% fixed income buffer. Is there any evidence of Swensen's long-term outperformance of the market using only liquid, publicly-traded securities? I thought these were only a small fraction of the Yale endowment, and that his track record was really based on private equity and hedge funds and illiquid securities that have little to do with the transparent and efficient markets in which the rest of us fish. I do like Swensen's Boglesque stress on low fees and indexing, though.
Big G: If you have the ability to consistently move in and out of markets as they rise and fall then I congratulate you. This skill is elusive, for all the reasons William Sharpe pointed out in his 1975 essay on market timing. As I go down the Forbes 400 list, I cannot find anyone who made his fortune in this manner. I don't know how people possessing this knack could have avoided becoming billionaires.
Mark McHugh: I agree -- anyone who can consistently pick the top-performing asset class in advance is going to outperform a diversified portfolio. Diversification is only valuable to people who can't do this.
Locke: The movie hasn't even edited into its final form; why not hold fire until you see it? I think you have been misinformed as to its content.
Smart ETF: Mandelbrot urges portfolio managers build portfolios using precisely the kind of Monte Carlo simulations we perform here ("The (Mis)Behavior of Markets" p. 267). He confesses of the people trying to apply his methods in finance, "...in truth, our knowledge is still so limited that no one has yet to report great success." (ibid, p. 256). It sounds like your experience is an outlier.
DMB: I think the 1-in-20 calculation of a 10% correction is excellent modeling. The MC-tested portfolios tend to beat market-indexed portfolios with less risk; if you have a better mousetrap then please tell how you do it.
1. Correlation between all the poor return probabilities, ie. uncorrelated markets will frequently become highly correlated during bear markets
2. By going back only 3 years you missed the key business cycle correlations, such as correlation between sectors, interest rates, etc. during various phases of the business cycle
These correlations are not random and need to be taken into account. They cannot be taken into account with 3 years of data since business cycles last on average 6 years, and you need to go back multiple business cycles for a program to pick up these correlations.
By reading only the one article, I am afraid that you have missed something very important. I have tested QPP out-of-sample through both up and down markets. The representation of correlation effects is more sophisticated than you think, apparently. I am well aware of the fact that things often get more correlated in market declines--and the model has handled these periods with aplomb. Also, the model combines the short-term data with much longer term cross-asset capital markets data. It knows about more than just the last few years. The model has been tested through bear-markets out-of-sample.
As to the Forbes 400, why exclude inherited wealth? The wealth came from somewhere; if market timing were the original source, it would be evident, or if market timing were so lucrative, then market timers would have long ago displaced the idle rich layabouts and Daddy Warbucks types still remaining on the list.
Even though people like Buffett and Zell buy low I would not call them "market timers" in the sense that term is ordinarily used. They are really doing long-term market valuation, which I would endorse, and is a skill that can be acquired by will and discipline, to use your words.
I definitely agree that hedge fund managers may use market timing (in nanoseconds, sometimes) to great profit, but these usually are frontrunning (="quantitative") strategies or market-manipulation strategies based on their ability to briefly dominate certain markets with their massive trading firepower. Just my opinion.
Whatever it is that hedge funds might be doing, it is not a strategy that can be appropriated by retail investors or anything that bears much resemblance to the brand of short-swing market timing based on technical analysis or forecasts of macro economic trends (or newsletters doing the same). I would call skill in this domain elusive. This conventional definition of market timing is what I was referring to and what Sharpe criticized. But certainly it has many devotees.
I just read your other article, and I feel like I owe you an apology for my wisecrack. First of all, I do believe in diversification. I thought you were one of the "re-balance 'til your broke" types. You touched on the tax consequences and costs and I think that's a key point. Most times, you are better off letting your winners ride until you at least get the long-term gains tax break. Furthermore, devices like trailing stop orders can help in making those decisions for you. The bee in my bonnet about diversification just for the sake of diversification is that it ignores trends and changing market conditions. In other words, it lacks conviction. I'm not a very good chess player, but I know enough not to make a move "just to see what will happen." Your other artcle, "Rebalancing can be hazardous...", speaks much louder to me.
Thanks for your comment. The lack of conviction implied by diversification is a strategy for dealing with uncertainty. But even where one has conviction, it can be very useful. Let's say we have a strong conviction that China will dominate global markets in the 21st century. Even so, are we 100% sure? Well...probably not. China is great, but who knows what might go wrong? So let's overweight China but also keep some investments in other things that are going to still be there even if China goes down the drain. Here is where Monte Carlo can help us estimate what to add in what proportion to what plausible effect on our future risks and returns. It's not a time machine but it is as good a tool as we have at present for dealing with this kind of issue.
I would like to thank you and Ben writing your latest book. And it goes without saying that Geoff needs a big "Thank You" for having developed QPP.
Question, does Ben have a Seeking Alpha site? I find it to be refreshing that all of us can communicate to those of you who have contributed your time and talent and communicate about these matters. I appreciate you willingness to share and at times 'get hammered' in this process, however at the end of the day the truth surfaces above the background noise. I look forward to your next portfolio up-date on the above porfolios -- maybe in 6 months.
Ben does not have a Seeking Alpha site, but his writings can be found all over: he's a regular columnist for Yahoo! Finance and the Sunday New York Times Business Section (available online as well). He's also a regular on "Cavuto on Business" on Fox and "Kudlow & Company" on CNBC.
Nice work.