How Much Diversification Is Enough?
Crafting a Portfolio That Minimizes Uncompensated Risk

By Frank Armstrong III

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JANUARY 2008 - How could this happen?” investors ask when they read about market disasters in the headlines. In fact, without the gross failure of investment policy or implementation, they should never happen.

Portfolios can be destroyed through a variety of well-known failures. High up on the list is the failure to diversify properly. Diversification is the one free lunch in finance and investment practice, and prudent diversification is a prime responsibility of fiduciaries under common law, UPIA, and ERISA. Diversification first and foremost reduces risk to its lowest possible value.

How much diversification is enough? This article will look at how systematically diversifying a portfolio can reduce risk at the portfolio level while maintaining or even enhancing returns. While the balance between risky and riskless assets is critical for each investor, in order to illustrate the benefits of diversification, the first place to focus on is the risky portion of the portfolio.

Risk and Return

Because few investors are able to meet their economic objectives while investing in zero-risk instruments, they must assume some risk in their portfolios. The trick is not to avoid risk entirely, because investors are systematically rewarded for bearing risk. Instead, the challenge is to manage risk prudently within each investor’s risk tolerance, time horizon, and liquidity needs to meet personal financial objectives.

Financial economists define risk in the investment process as the standard deviation around the expected return of the portfolio. This concept doesn’t resonate with many investors, who naturally think in terms of not running out of money, not having a financial disaster, or some other more personal definition of risk. But the link is this: The higher a portfolio’s standard deviation, the higher the probability that something awful might happen to the portfolio. It’s not a far stretch to think of standard deviation as a “danger index.” That is why all fiduciaries must model the risk/reward characteristics of a portfolio.

Over time, while investors are compensated for bearing discrete factors of market risk, they are not compensated for anything else. An investor should ruthlessly pare away any uncompensated risk. Why would investors bear a risk for which they are not likely to be rewarded? The prime example of uncompensated risk is any risk that can be diversified away.

Risk and reward may be related in the global sense, but they certainly don’t have to be related in a portfolio. It is true that all high-return investments carry high risks; however, the equation can’t be reversed. Stated as clearly as possible, high-risk strategies may not—and often do not—produce high rewards. Investors lose sight of this at their peril.

It is important to understand that excessive risk usually doesn’t work itself out to an average return. A flameout anywhere along the way can destroy the entire financial future of an individual investor. In real life, investors can’t hit rewind and start over. Relying on averages to bail out a flawed strategy rarely works.

The often-quoted, much misunderstood relationship between risk and reward holds true just in a special case: Risk and reward are related only for securities in a fully diversified asset class portfolio. As an investor moves away from a fully diversified portfolio, he has no expectation of higher return, yet he bears more risk. Because this additional risk earns no higher return, it is uncompensated risk.

The optimal equity portfolio will be defined as the one equity portfolio that has the highest expected return per unit of risk. It is possible to construct an infinite number of portfolios with a 10% expected return. Some of them will have absurdly high risk. But one of them will have the minimum risk necessary to generate that rate of return. That portfolio dominates all other strategies, and every investor shooting for a 10% return should want to hold it.

If asset class returns are plotted against risk as measured by standard deviation, the appropriate relationship should be obvious. For example, it is well known that stocks have a higher past and expected return than Treasury bills, but carry more risk. Small companies carry more risk than large companies, and yield higher returns over time than larger companies. Investors demand that additional return for bearing the additional risk. These additional rewards are called risk premiums and spring from priced risk factors.

In an efficient market, no stock can be expected to have a higher return than any other with similar characteristics. If it did, buyers would push the price up until the expected return was equal to other similar stocks. If most investors agreed that one small company stock had an expected return of 12%, while the other stocks of similar size and book-to-market ratio (BTM) had only an 11% expected return, the price of the first stock would adjust to where it yielded 11% to the next purchaser.

If a company’s prospects suddenly improve, that improvement will quickly be reflected in its stock price, adjusting its future expected return to the market average. News today travels at the speed of light, and the opportunity to reap excess profits consistently is practically nonexistent.

Of course, individual stocks have widely different returns. Because no one can predict the future, there is an enormous amount of noise and uncertainty in the process. Some companies will do better than average, and some will crash. But no one can know consistently in advance which ones those will be. So unless one can outpick millions of other investors looking at the same data, it’s delusional to think any individual can consistently pick winners.

Investors pay a high price when they try to beat the market. Of course, transaction costs and taxes must be subtracted from whatever returns are generated, lowering the effective rate of return. But by holding less than the full market portfolio, an investor is bearing risk without an expectation of higher returns. True, the variation of returns is staggering. But in the net, the full market’s returns will not be (cannot be) higher. Lower return and higher risk is nobody’s definition of an optimal portfolio.

Individual Stocks

The higher the concentration of holdings, the higher the uncompensated risk. At the far extreme, consider an “Enron only” portfolio. On the other end, consider a full market portfolio. Both had the same estimated rate of return. But one portfolio is still standing and growing, while the other vaporized.

Individual stocks have a very high level of risk. The list below shows a few well-known stocks with their annual standard deviation (std. dev.):

Company Name
10-Yr Std. Dev.
Sirius Satellite Radio 114.13
Lucent Technologies 63.81
Dell 49.82
Starbucks 40.53
Microsoft 40.01
General Motors 35.73
Amgen 34.78
AT&T 29.03
Pfizer 25.16
General Electric 24.03

The chance of total loss is not adequately captured by standard deviation at this level. Think of failures like Enron, Global Crossing, and Eastern Airlines. While the probability of a total blowup is small, the consequences are catastrophic.

Sector Investing

Sector funds are diversified within an industry group, but hardly a properly diversified portfolio. Sector-fund investing is demonstrably not prudent. Extreme variations in total valuation are possible. For a sampling of how the risk of sector funds can match up with their returns, see Exhibit 1.

Diversifying a Portfolio

Many investors use the S&P 500 as an appropriate benchmark for the entire stock market.

But the S&P 500 is only one part of the optimum market portfolio. Adding an equal weighting of large foreign companies in developed markets will lower risk substantially (Exhibit 2). The most widely quoted benchmark representing this asset class is the Morgan Stanley Europe, Australia, and Far East Index (EAFE).

But the S&P 500 and EAFE omit many midsized and small companies. The addition of smaller companies to the portfolio (Exhibit 3) will further lower risk overall, because such stocks track differently from their larger cousins (i.e., they have a low correlation).

The optimum market portfolio must be global in nature. It would be ideal, but unfeasible, to hold a proportionate share of every traded stock in the world. Today’s index funds and exchange traded funds will capture in excess of 95% of the value of the world’s capital markets. The risk level for the S&P 500 is substantially higher than the global market. International investing offers substantial risk reduction for long-term investors. A portfolio that includes only large, domestic companies includes far more risk than is necessary.

Emerging markets offer another opportunity to spread risk (Exhibit 4). While higher in volatility, their low correlation to developed economies reduces risk at the portfolio level while enhancing returns.

Every investor should consider the global equity market portfolio as a default. Any investor who rejects the global equity market portfolio should have a very strong belief set to justify such a position. Unfortunately, it’s not unusual to hear variations of the following justifications for an unbalanced portfolio:

  • I work for Enron. It’s a great company. I know what’s going on there.
  • I can pick individual stocks that will beat the market.
  • The United States is the only place to invest. The rest of the word is too risky.
  • Energy will outperform the rest of the market.
  • I’m a doctor. I understand healthcare stocks.

Not all of these people will see their portfolios crash and burn. The lucky ones will prosper—after all, somebody wins the lottery every week. But the majority will pay a heavy price for failing to manage their risk properly.

There’s more to diversification than just location. Research indicates that investors may wish to overweight distressed companies (i.e., value stocks) to capture additional returns. Value stocks may be viewed as a separate asset class with a low correlation to the traditional large capitalization market (S&P 500 and EAFE). While these risks are different, the total risk, at least as measured by standard deviation, does not increase, and may even decrease, when value stocks are included in a portfolio (see Exhibit 5).

Investors may correctly have different tastes for these additional risk factors, so the weight of each within a portfolio may be adjusted for individual preferences.

If the definition of markets is expanded to include real estate and commodities futures (see Exhibit 6), there will be additional opportunities to diversify a portfolio and reduce risk.

In both theory and practice, the portfolio with the widest diversification will have the lowest risk. The Capital Asset Pricing Model (CAP-M) tells us that the optimum equity portfolio is the whole market. It’s the one with the highest return per unit of risk. Anything less than the global portfolio is a bet against the efficient market and subjects an investor to uncompensated risk.

Including Bonds in a Portfolio

Of course, even an optimum risky portfolio may be far too much risk for a particular investor. The level of risk in an investor’s portfolio should accommodate his risk tolerance, liquidity needs, and time horizon. The appropriate way to accomplish this is to vary the mix of high- and low-risk assets. The academic answer is to utilize local zero-risk assets (Treasury bills in the United States), but in practice, investors can substitute a very high-quality, short-duration bond fund:

Global Portfolio
10-Year Std. Dev.
10-Year Return
100% Equity 13.97 11.10
70% Equity/30% Bond 9.26 9.16
60%/40% 7.83 8.48
50%/50% 6.36 7.80
40%/60% 5.02 7.10

By including bonds, investors obtain a great deal of protection against volatile markets. Risk drops off a great deal faster than return when bonds are introduced into a portfolio. Investing at the appropriate level of risk is the key consideration for success.

Fortunately, financial markets allow investors to diversify their holdings, and today’s investment tools and products can provide effective diversification at extremely low cost. The illustrated global portfolio can be obtained by using a combination of traditional no-load index funds and exchange-traded funds (ETF) at an average weighted annual cost well below 0.5% at the fund level. It holds more than 15,000 companies that represent more than 95% of the value of the world’s traded stocks.

Slow and Steady Wins the Race

Left to their own devices, investors can find an almost endless variety of creative ways to self-destruct. Do-it-yourselfers may have only themselves to blame, but when an investor consults a financial advisor, he has every right to expect a high level of practice standards, professional knowledge, and fiduciary prudence.

The benchmark for prudent diversification is the global market. Anything less is a disservice to investors that fails to properly control risk.

Reasonable people may disagree on the finer points of investment policy. For instance, an individual investor may prefer to exclude either REITs or commodities, or may wish to tailor exposure to small companies or value stocks. Any policy tailored in such a fashion should be described in detail in the investment policy statement, accompanied by appropriate capital market assumptions and a risk/reward model designed to meet the investor’s unique requirements.

All investors should spend as much effort on the risk side of investment problems as on the return side. Within broad limits, managing risk is more important than driving up returns. Successful investing over an individual’s lifetime should resemble the story of the tortoise and the hare. If you think you just can’t stand to have a boring portfolio, especially when everybody around you is talking about today’s hot thing, just remember the tortoise. He’s the guy with the low-volatility, fully diversified portfolio who avoids unpleasant surprises and eventually wins the race.

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Frank Armstrong III is the founder and principal of Investor Solutions, Inc., a fee-only, SEC-registered investment advisor ( He is also the author of The Informed Investor: A Hype-Free Guide to Constructing a Sound Financial Portfolio (Amacom, 2003), now available in paperback.




















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