Harry Markowitz

"A good portfolio is more than a long list of good stocks and bonds. It is a balanced whole, providing the investor with protections and opportunities with respect to a wide range of contingencies."

— Harry Markowitz, Nobel Laureate in Economic Sciences, Professor of Economics at University of California at San Diego

Merton Miller

"Diversification is your buddy."

— Merton Miller, 1990

Eugene Fama Jr

"Investment planning is about structuring exposure to risk factors."

— Eugene Fama Jr., The Error Term, December 2001

Roger Ibbotson

"We can extrapolate from the study that for the long term individual investor who maintains a consistent asset allocation and leans toward index funds, asset allocation determines about 100% of performance."

— Roger Ibbotson, The True Impact of Asset Allocation on Returns, 2001


In the early 1950s, Harry Markowitz applied his mathematical expertise to investing. Markowitz, then a Ph.D. candidate in economics at the University of Chicago, believed investment professionals erred by urging investors to focus solely on returns of individual stocks with no consideration of the concept of risk exposure. He set out to reveal how investors could improve their stock market performance by optimizing the trade-off between risk and return. In his 1952 Nobel Prize-winning paper, "Portfolio Selection,"1 Markowitz established the importance of diversification. He asserted the best portfolios include non-correlated stocks that act and move independently from each other. Today trillions of dollars worldwide are invested according to his principles of risk and return, known collectively as Modern Portfolio Theory.

The blend of investments that is appropriate for a particular investor is known as asset allocation, also called risk exposure, and is based on an investor's risk capacity. Asset allocation is the most important factor in optimizing a portfolio's expected returns, thus it is essentially the most important decision an individual investor can make. This concept also extends to larger institutional investments, such as state pension funds, fire and police pension plans, non-profit and for-profit defined contribution plans, church funds, college endowments, and any other funds governed by committees.

As presented in Step 8, Eugene Fama and Kenneth French identified that as much as 96% of equity returns are explained by a portfolio's exposure to market, size and value. Their research expanded upon Markowitz's and Sharpe's initial findings regarding risk and return. While Fama and French demonstrated that indexes constructed of small and value companies have historically outperformed the total market index over the long term, the risks associated with these small and value indexes have also been higher.



Investors Frequently Take the Wrong Risks

Some investors tend to avoid risk when it comes to their investments. They want returns without any risks, but avoiding all risk is the same as avoiding potential returns. Others take on too much risk, while many take risks that just don't reward. All these "wrong risk" behaviors are the crux of the poor performance many investors experience. Risk should be embraced in appropriate doses that match an investor's risk capacity. There is a right amount and type of risk for every investor. Risk provides opportunity, and a taste for appropriate risk is a good thing.

As was shown in Step 9, certain asset classes, such as small and value, have a long history of sufficiently rewarding investors for the risks associated with them. However, there are also several asset classes that carry risk but have been inefficient in delivering returns commensurate with the risks taken. This kind of risk is not worth taking. As such, many investors struggle to develop an asset allocation that captures the right blend of the markets that have maximized returns at given levels of risk. Case in point, many investors seem comfortable investing in companies that are best described as glamour or growth stocks, presuming they perform better than small or value companies. These investors would be surprised to learn that growth companies actually have a poor history of delivering risk-commensurate returns. Commodities, private equity and technology indexes have also failed to historically maximize returns for risks taken. Failing to understand which blend of investments are worth their risk causes investors to earn lower returns than they could if they simply bought, held and rebalanced a blend of indexes that optimizes risks and returns.


Investors Get Commodity Fever

Commodities have developed a reputation for providing a hedge against inflation and an apparent negative correlation to equities. Further research into this subject reveals that no such advantage proves true. A compelling study2 by former USC finance professor, Truman Clarke, details the lack of substantiation for the bold claims made by commodities proponents. A commodity is a hard asset, an item that is purchased on the hope that an increased demand or a decreased supply for the item will cause its value to increase. "Remember when you buy a commodity, you're not buying something that generates earnings and profit. You're buying a hard asset and hoping another buyer will be willing to pay more for that asset in the future," wrote Matt Krantz in a June 2008 USA Today article titled, "Read this before you jump on the commodities bandwagon."3

Commodity investments differ from stock investments in that companies, as a whole, have earned profits that have translated into an average return of about 9.5% per year. Under most conditions, their stock value is expected to increase in line with their growth in profits. The expectation of price appreciation for commodities is not based on profits, but rather on supply and demand. In short, commodities have not provided expected returns.

In November 2010, noted economist and professor of finance at Dartmouth, Kenneth French, conveyed his findings regarding commodities. He stated, "The high volatility of commodity prices makes it impossible to accurately estimate the expected returns, volatilities and covariances of commodity funds, but theory suggests that if commodity returns are negatively correlated with the rest of the market, the expected risk premium on commodities is small, perhaps negative. Finally, commodity funds are poor inflation hedges. Most of the variation in commodity prices is unrelated to inflation. In fact, commodity indices are typically 10 to 15 times more volatile than inflation. As a result, investors who use commodity funds to hedge inflation almost certainly increase the risk of their portfolios."4

Contrary to what many investors presume, commodities are not a panacea for hedging one’s portfolio against inflation and are frequently more risky than they are led to believe.


Efficient Diversification: The Key to Success

A diversified portfolio which captures the right blend of market indexes reaps the benefit of carrying the systematic risk of the entire market while minimizing exposure to the unsystematic and concentrated risk associated with individual stocks and bonds, countries, industries, or sectors. The only risk that remains is the risk of the market itself, a risk that must be taken in order to capture market returns.

As capitalism has expanded throughout the world, it has become increasingly important to allocate a significant portion of one's portfolio to international securities. In the 1970's, the U.S. comprised more than 68% of global equity value, but today it comprises less than 50%. Investors achieve an enormous benefit of increasing diversification and capturing the expected returns of global capitalism by investing in index funds comprised of international developed countries and emerging markets countries in risk-appropriate doses.

An additional important aspect of diversification is diversifying across time. When investors maintain a globally diversified portfolio for long periods of time, they are able to maximize their ability to capture the complete range of returns that are offered by the global markets. Index portfolios with a high exposure to stock equities require a longer holding period than fixed income portfolios in order to efficiently maximize their ability to achieve an expected outcome.

The hypothetical stock certificate represents an investment in Capitalism, Inc., showing estimates for year-end 2011 of total market value, sales, net profits, number of CEO's, and number of employees who work for an investor who buys and holds a globally diversified index portfolio. With a total market cap of $30 trillion, over 12 thousand CEO's worldwide, and over 61 million employees selling products in 192 countries, it is not reasonable to ever believe that Capitalism, Inc. will go out of business. And if it did, your money would be worthless.


Risk-Calibrated Portfolios

The stacked chart of Figure 11-1 shows the general asset class allocations for 20 of 100 different risk-calibrated Index Portfolios. The Index Portfolio number matches the equities (stocks) allocation of that portfolio; i.e. Index Portfolio 20 has a 20% equities allocation, and Index Portfolio 80 has an 80% equities allocation. The Index Portfolios have a higher degree of tilt toward small cap and value as the portfolio numbers increase. In the chart, gold represents each portfolio’s weighting in fixed income, and red represents its percentage of equities. Almost all of the asset allocations carry the same asset class components—fixed income, U.S. stocks and non-U.S. stocks—but weighs each differently. For example, the least risky index portfolio displayed, number 5, is heavily weighted in fixed income, carrying very little global equity exposure. This portfolio is well suited to an investor with a very low risk capacity—in general, someone with a short investment time horizon and current liquidity needs. An example of this type of investor would be an older retiree.

Figure 11-1

In contrast, the most risky index portfolio numbered 100 is an all-equity portfolio that is invested entirely in equity funds and carries greater concentration in international and emerging markets. This high risk portfolio is suitable for either a young 21-year old just starting out or someone who generally is very fluent in the language of riskese, will not need to liquidate investments for a minimum of 15 years, has a high net worth and net income, and a strong stomach for volatility.

The Index Portfolios shown in Figure 11-2 have diversified away uncompensated risks, so that the risk of investing in the markets is all that remains. The higher risk Index Portfolios 75 and 100 have a very high market exposure and a considerable tilt toward small and value indexes. The increased volatility of these higher risk index portfolios had higher returns over the 50+ year period starting January 1, 1964, relative to the less volatile Index Portfolios 25 and 50. This example provides sound proof for the importance of establishing the efficient asset allocation that is best matched to an investor’s risk capacity.

Figure 11-2


Portfolio Construction

Once investors identify the asset allocation that matches their risk capacity, they have a choice to make as to how to best implement that asset allocation. A handful of passively managed fund providers offer asset class indexes, namely Vanguard and Dimensional Fund Advisors (DFA). The index portfolios referenced in this book are implemented with funds from DFA, a highly regarded fund company which provides pure implementations of Modern Portfolio Theory and the Fama/French Five-Factor Model, purposefully isolating risk factors to efficiently capture higher expected returns for the level of risk chosen. This isolation is beneficial because it allows the DFA funds to achieve a stronger tilt toward the small and value risk factors that have shown to deliver higher returns at comparable levels of risk.

Figure 11-3 illustrates a 15-year comparison between 20 index portfolios comprised of funds from DFA and 20 Vanguard portfolios which carry the same asset allocation weightings. This time period was used due to live data available. Results are net of fund fees and a 0.9% advisor fee for both strategies. The chart shows that at every level of risk, the index portfolios utilizing DFA funds had a higher annualized return than the index portfolios using Vanguard funds.

Figure 11-3

Figure 11-4 is a similar chart that shows a 13-year comparison between the same 20 index portfolios comprised of DFA funds and portfolios of iShares exchange-traded funds. The beginning date is two years later (due to the limited availability of live ETF data), but the results are similar. The size of the DFA advantage is directly proportional to the risk level of the portfolio. Although several brokerage firms offer a "free-trades" promotion with select ETFs, investors should proceed cautiously with their trades, staying cognizant of the bid/ask spread, the depth of the order book, and the possible divergence between market price and net asset value. Investors who don't know what any of that means probably should refrain from trading ETFs. Finally, investors must avoid the temptation to use ETFs as market-timing tools.

Figure 11-4

DFA funds are available through a select group of registered investment advisors to whom the company provides comprehensive data from CRSP on numerous indexes dating all the way back to 1928. This allows for analysis of data that is usually only available to academic researchers.

DFA's emphasis on training advisors to educate investors has contributed immensely to the ability of investors to capture the returns offered by the compensated risk factors of the market.

Dalbar surveyed investment advisors four times between 1997 and 2004. The study was titled, "The Professionals' Pick." Dalbar rated DFA the best overall no-load mutual fund company in 1997, 2000, 2002, and number two in 2004. DFA was also rated #1 by Barron's in 2010 and #1 in different categories by Cogent Research in 2010, 2011, and again in 2013. See Figure 11-5.

Figure 11-5


It's All in the Mix

A globally diversified index portfolio has historically delivered efficient returns for the risk that is built into each individual portfolio. Figure 11-6 plots the risk and reward optimizations for 20 index portfolios and various indexes, alongside an S&P 500 Index over a long time period. Note the higher annualized returns of the index portfolios that have similar risk (annualized standard deviation) as the S&P 500 Index. Also note the returns of the emerging market asset classes when isolated on their own (high risk with compensated returns). The index portfolios shown are all comprised of an efficient blend of indexes. This chart shows the value of diversifying beyond large cap companies in the U.S., as reflected in the S&P 500. 

Figure 11-6

Figure 11-7 shows 50 years of monthly return distributions for four index portfolios. These histograms represent 600 months of risk and return data from January 1, 1963 to December 31, 2012. Note the wider bell curve distributions in the higher risk Index Portfolios 100 and 75 as compared to the lower risk Index Portfolios 50 and 25. This indicates that the riskier portfolios had a larger range of outcomes over time.

Figure 11-7

This wider range or increased volatility has also carried a higher degree of return. Of the four portfolios shown, the least risky Index Portfolio 25 had the narrowest range of monthly return outcomes over the 50-year period. This narrower range or decreased volatility is the trade-off for lower returns, relative to Index Portfolios 100, 75 and 50 that had higher risk and higher returns. The charts also reflect the growth of a $1 investment in each portfolio over the 50-year period. Remember that an investor's actual returns will vary from these asset class allocations due to the timing of withdrawals and contributions, rebalancing strategies and costs, fees, and other factors.

As was shown in the previous charts and discussions, efficient diversification among lower-cost index funds is a very effective means for investing one's assets. Further, index portfolios that carry risk-appropriate blends of the indexes that have historically rewarded investors is a highly prudent strategy. Indeed, while one cannot obtain any guarantee of future success based on the past, the 85 years of data associated with the style-pure index portfolio allocations is arguably as good as it gets for any investor, individual or institutional.

The data table in Figure 11-8 represents the short-term and long-term risk and return data for the S&P 500 and 20 index portfolios with varying degrees of exposure to fixed income and stock market equities. Growth of $1 is also shown for each portfolio. When seeking to construct a portfolio with a high degree of probability of success, it is advisable for investors to pay very careful attention to the 20, 35, 50 and 86+ year data columns on the right hand side. The 50-year return is largely considered the historic return and a good estimate of the future or expected return. The left columns which show the year-to-date, 1, 3 and 5-year returns are shown in order to make investors aware of the short-term volatility of the various investments and should not be considered useful for determining which portfolio is right for an investor.

Figure 11-8

Notice in the 50-year column the correlation between the higher risk numbers and the impact on returns as measured in percentages and dollars over time. Also notice the benefits of diversification that efficiently implemented risk and captured higher returns compared to the S&P 500. Index Portfolios 60-80 outstripped returns at a lower level of risk, and Index Portfolios 90-100 substantially improved returns relative to the S&P 500 at similar levels of risk. As you can see from the abundance of data shown, a knowledge of the long-term risk and return characteristics of the index portfolios enables an investor to make a sound investment choice that is based on history and probabilities, thus avoiding the hazards of speculation.


Matching Risk Exposure to Risk Capacity

Unlike horseshoes, close enough isn't good enough for investors who want to maximize their ability to capitalize on the exchange between risk and return. For this reason, when selecting a diversified portfolio, the primary consideration should be identifying and investing in a blend of indexes that most closely matches risk capacity.

Many investors choose a common 60/40 asset allocation, regardless of their risk capacity. As you now know, a more optimal strategy is to invest in a portfolio that directly corresponds to a particular risk capacity. This sophisticated approach enables investors to take on just the right amount of risk—not too much or not too little—allowing them to maximize their expected outcome.

The significant benefits associated with capturing just the right amount of risk are elegantly displayed in Figure 11-9, which shows the growth of $1,000 in 100 different index portfolios in the time period starting January 1, 1963. Each of these engineered portfolios is designed with different blends of equities and fixed income. This continuum of risk and return provides investors the opportunity to invest in a targeted asset allocation that matches their risk capacity score between 1 and 100. The chart further validates the value of carefully matching an investor's risk capacity to a corresponding risk exposure, avoiding the rounding up or down of the analysis. As you can see, a small change in risk made a substantial difference in the growth of $1,000 over this 50+ year period.

Figure 11-9


Prudent Investing

The process of prudent long-term investing requires thorough and thoughtful discernment. The best way to earn optimal returns is by buying and holding a passively managed and globally diversified index portfolio, matching an investor's risk exposure to his or her risk capacity and relying on historical risk and returns data that goes as far back as 1928. In Step 10, an explanation of four unique risk capacities was provided for risk capacity scores 100, 75, 50, and 25. Links to portfolio page for the four index portfolios that match those risk capacity scores are provided below.

IFA Index Portfolios 100

IFA Index Portfolios 75

IFA Index Portfolios 50

IFA Index Portfolios 25

These portfolio fact sheets consist of a list of the indexes contained in each portfolio, simulated returns and volatility data, charts that represent annual returns and growth of $1, a 50-year monthly rolling period analysis, and a histogram of monthly rolling periods for the time intervals matched to the average holding period for each level of risk capacity. For an investment period of a given length; e.g. 3 years, this rolling period table will show how many periods there were in the entire 50-year period, the median annualized return over all these periods, as well as both the highest and the lowest returns that occurred in these periods. The very clear pattern that emerges is that as the period length increases, the median return changes very little, but the range of returns narrows considerably. We refer to this as the timediversification of returns.

To reiterate, the most important question an investor can ask is, "What mix of indexes is best for me?"

  • 1Harry Markowitz, Portfolio Selection, The Journal of Finance, Vol. 7, No. 1. (Mar., 1952), pgs. 77-91.
  • 2Truman Clarke, "Commodity Futures in Portfolios," Dimensional Fund Advisors (2004).
  • 3Matt Krantz, "Read this before you jump on the commodities bandwagon," USA Today (McLean, VA), Jun. 24, 2008.
  • 4 Kenneth French, "Q&A: What Role for Commodities?," Fama/French Forum, November 1, 2010, http://www.dimensional.com/famafrench/2010/11/what-role-for-commodities.html.
step 11introductionharry markowitzmodern portfolio theoryportfolio selectiondiversificationeugene famakenneth frenchsharperiskrewardwrong riskasset allocationcommoditiestruman clarkematt krantzcapitalismstock certificateportfoliorisk-calibratedasset classallocationsrisk capacityvanguarddimensional fund advisorsdfafive-factor modelisharesetfsdalbarcogent researchbarron'ss&p 500globally diversified portfolioportfolio allocationsreturnvolatilityrisk exposurebuy and holdprudentoptimal returnsglobally diversified index portfoliorisk capacity scorefact sheets

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