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How Much Diversification is Enough

Whenever we come across road kill on the investment highway, we ask ourselves: “How could this happen?” The fact is, absent gross failure of investment policy and/or implementation, it should never happen.

There are a variety of proven techniques that lead directly to portfolio destruction. High up on the list is the failure to properly diversify. Diversification is the one free lunch in finance and investment practice. Prudent diversification is a prime responsibility of fiduciaries under common law, UPIA and ERISA. We diversify first and foremost to reduce risk to its lowest possible value.

But what should the standard be, and how much diversification is enough? This paper will look at how systematically diversifying a portfolio can reduce risk at the portfolio level while maintaining and/or enhancing returns. While the balance between risky and risk-free assets is critical for each investor, to illustrate the benefits of diversification, we first focus on the risky asset portion of the portfolio.

Risk and Return

Few investors are able to meet their reasonable economic objectives while investing in zero risk instruments, so they must assume some risk in their portfolios.

The trick is not to avoid risk, because investors are systematically rewarded for bearing risk. The trick is to manage it prudently within their risk tolerance, time horizon and liquidity needs to meet their unique objectives.

Financial economists have defined risk in the investment process as the standard deviation around the expected return of the portfolio. That’s a concept that doesn’t resonate with many investors who naturally think in terms of avoiding running out of money, preventing a financial disaster, or some other more personal definition. But the two concepts are directly related: The higher a portfolio’s standard deviation, the higher the probability that something awful might happen. It’s not a far stretch to think of standard deviation as a “danger index.” That’s why it is a required practice for all fiduciaries to model the risk reward characteristics of the portfolio.

Over time, investors are compensated for bearing discrete factors of market risk, and not compensated for anything else. So the investor’s job is to ruthlessly pare away any uncompensated risk. Why would anybody take a risk for which they are not likely to be rewarded? While there are others, the biggest example of uncompensated risk is any risk that could be diversified away.

Risk and reward may be related in the global sense, but they certainly don’t have to be in your portfolio!

It’s true – risk and reward are related. There are no high return investments that do not carry high risks. That’s certainly not new news. However, the equation cannot be reversed. We have all seen lots of high-risk strategies with disastrous results. Stated as clearly as possible, high-risk strategies may not (and most often do not) produce high rewards. Investors lose sight of this at their peril.

It is important to understand that excessive risk will most often not work itself out to an average return. A flameout anywhere along the way can destroy the entire financial future of the investor. Investors only get one chance to get it right. 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 only in a special case: Risk and reward are related only for securities in a fully diversified asset class portfolio. As the investor moves from a fully diversified portfolio, he has no expectation of higher return, but he bears more risk. Since this additional risk earns no more return, it is uncompensated risk.

It is absolutely 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.

The optimum equity portfolio will be defined as the one equity portfolio that has the highest expected return per unit of risk.

If asset class returns are plotted against risk as measured by standard deviation, the appropriate relationship is obvious.  For instance, 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, and yield higher total returns over time than larger companies. Investors demand that additional return for putting up with the additional risk. These additional rewards are called risk premiums, and spring from priced risk factors.

It is no great mystery how this system works. The market’s self-regulating, self-adjusting, self-correcting price mechanism almost instantly adjusts prices of stocks to the point where future returns justify their risks. The Invisible Hand never sleeps as millions of investors examine securities around the clock with an eye to future returns and risk levels.

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 almost instantly be pushed up 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 travels at the speed of light, and the opportunity to reap excess profits consistently is practically nonexistent.

Of course, individual stocks do have widely different returns. Because none of us can tell 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 that will be. So unless you think you know better than a few hundred million of your closest friends who are looking at the same data, it’s delusional to think you can consistently pick winners.

In trying to “beat the market”, investors pay a high price. Of course, there are transaction costs and taxes. These must be subtracted from whatever return is generated. As a result, the highest probability is that rate of return will go down. But by holding less than the full market portfolio, there is then a lot of uncompensated risk. That’s risk for which one cannot expect additional return. True, the variation of returns is staggering. But in the net, the returns will not (and cannot) be higher. Lower return and higher risk is nobody’s definition of an optimum portfolio.

Individual Stocks

The higher the concentration of holdings, the higher the uncompensated risk. At the far extreme, there is an Enron only portfolio. On the other end, there is the 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. Here are a few well known stocks with their annual standard deviation. However, the chance of total loss is not adequately captured by standard deviation at this level. Think Enron, Global Crossing, Eastern Airlines, etc. While the probability of a total blow up is small, the consequences are catastrophic.

Company Name 10 Yr Standard  Deviation
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

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. Ask any tech fund investor how he enjoyed 2000 to 2002.

Sector Fund Ticker Morningstar Category 10 Yr Standard Deviation 10 Yr Return
Old Mutual Col Cir Tech A OATCX Specialty-Technology 44.90 0.38
US Global Inv Gold Shares USERX Specialty-Precious Metals 40.03 -0.84
Fidelity Sel Energy Serv FSESX Specialty-Natural Res 36.84 17.21
Fidelity Sel Devel Comm FSDCX Specialty-Communications 34.87 6.85
Fidelity Sel Biotech FBIOX Specialty-Health 32.02 10.05
Prudent Bear C PBRCX Bear-Market 25.22 -2.30
Fidelity Sel Brokerage FSLBX Specialty-Financial 25.14 18.11
Alpine U.S. Real Estate EUEYX Specialty-Real Estate 22.04 16.33
Fidelity Select Utilities FSUTX Specialty-Utilities 17.18 8.53

The S&P 500

Most investors define the market as being the S&P 500. That’s an index of large domestic companies. Many investors still use this as an appropriate benchmark for the market.

Portfolio 10 Yr Standard Deviation 10 Yr  Return
Standard & Poor’s 500 15.66 8.32

 

An International Portfolio

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

Portfolio 10 Yr Standard Deviation 10 Yr  Return
50 % S&P 500- 50%  MSCI EFA 14.40 7.63

 

Global Portfolios

But the S&P 500 and EAFE omit many mid-sized and small companies. Addition of smaller companies will further lower risk at the portfolio level because they track differently from their larger cousins (low correlation).

Portfolio 10 Yr Standard Deviation 10 Yr Return
Global Portfolio Including Small Company Stocks 14.52 9.49

 

As it turns out, the optimum market portfolio is the global market. It would be ideal to hold a little pro rata share of every traded stock in the world. But one cannot expect to get every traded stock in every exchange in the world. Today’s index funds and ETF’s 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. If a portfolio is only domestic large companies, an investor is taking far more risk than he or she needs to.

Portfolio 10 Yr Standard Deviation 10 Yr  Return
Global Portfolio Including Emerging Markets 14.55 11.12

 

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

As a default portfolio, every investor should consider the global equity market portfolio. In fact, any investor that rejects the global equity market portfolio should have a very strong belief set to justify his/her position. Unfortunately, many investors have flawed belief sets, or none at all. So it’s not unusual to hear variations of the following:

 

Not all of these people will crash and burn. A few 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.

That’s not quite the end of the story. As it turns out, subsequent research indicates that investors may wish to overweight distressed companies (value stocks) on a global basis to capture additional returns. Value stocks may be considered as separate asset classes with low correlation to the traditional large capitalization market (The S&P 500 and EAFE). While these risks are different, the total risk at least as measured by standard deviation, is not increased. Inclusion in a portfolio may actually decrease risk

Portfolio 10 Yr Standard Deviation 10 Yr Return
Global Portfolio Including Value Stocks 14.42 10.84

 

Investors may correctly have different tastes for these additional risk factors, so the amount of overweight (if any) may be adjusted for individual preferences.

Beyond traditional stocks

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

Portfolio 10 Yr Standard Deviation 10 Yr Return
Global Portfolio Including REITs and Commodities 13.97 11.10

 

In both theory and practice, the portfolio with the widest diversification will have the lowest risk. Capital Asset Pricing Model (CAP-M) indicates 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 picks up a large amount of uncompensated risk.

Diversification between stocks and bonds

Of course, even an optimum risky portfolio may be far too much risk for a particular investor’s unique situation. An investor should water down the risk level to accommodate his risk tolerance, need for liquidity, and time horizon. The appropriate way to accomplish this is to vary the mix of risky and risk-free assets. The academic answer is to utilize the local zero risk asset (The T-Bill in the U.S.), but in practice, a very high quality short duration bond fund is substituted.

Portfolio 10 Yr Standard Deviation 10 Yr Return
100% Global Equity Portfolio 13.97 11.10
70% Global Equity 30% Global Bond Portfolio 9.26 9.16
60% Global Equity 40% Global Bond Portfolio 7.83 8.48
50% Global Equity 50% Global Bond Portfolio 6.36 7.80
40% Global Equity 60% Global Bond Portfolio 5.02 7.10

As you can see, 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. Investing at the appropriate level of risk is the key consideration for investment 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 true no load index funds and ETFs at an average weighted annual cost well below 0.5% at the fund level. It holds over 15,000 companies which represent over 95% of the value of the world’s traded stocks.

Conclusions:

Investors do the darndest things! Left to their own devices, they can find an almost endless variety of creative ways to self-destruct. The do-it-yourselfers may have only themselves to blame, but when an investor consults a “financial advisor” he has every right to expect high level practice standards, professional knowledge and fiduciary prudence.

The benchmark for prudent diversification is the global market. Anything less is a real 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, and/or may wish to tailor his exposure to either small companies or value. The tailored policy should be described in the Investment Policy Statement in detail, accompanied by appropriate capital market assumptions, and contain a risk reward model designed to meet the investor’s unique requirements.

All investors need to spend as much effort on the risk side of the problem as on returns. Within broad limits, managing risk is more important to success than attempting to drive up returns. Investing should be the ultimate Tortoise and Hare story. Avoiding unpleasant surprises is the name of the game. 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, and the eventual winner.


Disclaimer: This model is for general education purposes to illustrate the effects of diversification and could not have been implemented as described on the inception date. In developing our models we used data from Morningstar on real world mutual funds and ETF’s. Some past index data is simulated where funds did not exist to implement asset classes. Additionally, past performance is no guarantee of future performance. Transaction fees, advisor fees and taxes would have reduced returns.

Category Fund
Small Cap DFA Small Cap Portfolio
Small Cap Value DFA Small Cap Value Portfolio
Large Cap DFA Large Cap Portfolio
Large Cap Value DFA Large Cap Value Portfolio
International Small Cap DFA Intl Small Cap Value
International Small Cap Value DFA Intl Small Cap Value
International Large Cap DFA Intl Large Cap
International Large Cap Value DFA International Large Cap Value
Emerging Markets DFA Emerging Mkts Portfolio
REIT Vanguard REIT Index Viper
Commodities Pimco Commodities Real Return D
Fixed Income DFA One Year Fixed Income