| "Nothing is more dangerous than an idea, when you have only one idea." |
| -- Alain |
IVERSIFICATION, DIVERSIFICATION, DIVERSIFICATION. Just like location in real estate, diversification is the most important thing in a portfolio -- at least that's what you hear, over and over again. We were a little curious about this so we decided to take a closer look. What we found surprised us and it may surprise you, too.
You see, most of us see diversification as the division of our portfolios 
into stocks, bonds, and cash. That's a good starting point, but it's what comes after that that gets a little hazy. Once we decide on the percentages for each of these classes, we go out and buy whatever stocks or bonds are available while using the cash in whatever way we're most comfortable. This doesn't necessarily satisify the purpose of diversification because the types of stocks and bonds we buy are important, too.
To check this out, we turned to Ibbotson Associates, the folks who compile historical performance numbers for -- you guessed it -- stocks, bonds, and cash. Based on this data, we constructed five different efficient portfolios with differing degrees of risk and return. Needless to say, we didn't get the results we expected.
Risk, Return, and Correlation
As you probably already know, there's a trade-off between risk and return. In general, the more risk you can bear, the more return you can expect over the long-run. That's why riskier investments usually offer greater potential return.Return is typically measured by the asset's expected annual return. Risk is usually given in terms of the asset's "standard deviation". This is a measure of the variability of an asset's return. The more the return varies from the average, the greater the risk. Riskier investments have higher standard deviations while more conservative ones have lower standard deviations.
Different types of investments have different risk and return profiles. For example, many investors are concerned with three major asset classes: 
stocks, bonds, and cash which are often represented by the S&P 500, U.S. Treasury Bonds and, U.S. 90-Day Treasury Bills, respectively.
The expected returns and standard deviations for each are shown on the accompanying graph. (For tables of all the information used in this presentation, click here.) As you would expect, Treasury Bills have the least risk, stocks have the most, and government bonds fall in between. Also since there is a direct relation between risk and return, the same ordering applies to anticipated return.
Only the most conservative investor would use 100% Treasury Bills while only the most aggressive would hold 100% stocks. By devising the right combination of holdings, you can increase your expected return while minimizing the associated risk. This is the essence of diversification.
But the benefits of diversification don't come to just any random mix. Some are better than others. The effectiveness of a particular mix is determined by how the constituent assets perform relative to one another. This is referred to as their "correlation".
Some asset classes tend to behave in similar manners. For example, common stocks and high yield ("junk") bonds tend to go up at the same time and down at the same time. While the magnitude of their movement may differ, they do tend to move in the same directions.
On the other hand, bonds and real estate are "negatively correlated" -- when one goes up, the other goes down. This is understandable since real estate performs well when inflation is high. This is precisely when bonds turn in their worst performance. The opposite also holds: When inflation is low, bonds appreciate while real estate languishes.
The Efficient Frontier
As investors, we each want our portfolio to provide the highest return for the amount of risk we are willing to assume. You may be willing to take on more than me, so you can expect a higher return. I'll have to live with my lower return so I can be comfortable with my portfolio's risk level. This suggests that there's a target asset mix that's right for me and a different one that's right for you.In essence, once we determine the risk level we want (or the return we need) there's a specific asset mix that will maximize our expected return (or minimize our risk). This set of portfolios can be plotted on a graph tracking risk (measured by standard deviation) vs. return. If you draw a line connecting each portfolio that provides the highest return at each level of risk, you create what has been named the "efficient frontier".
Below is the graph of the efficient frontier derived from the past 15 years of historical performance. Asset mixes falling along the line provide the greatest return for their given level of risk. You can always increase your expected return by moving along the line to the right, but as you'd expect, you'll also increase your level of risk.
Obviously, you'd like to create a portfolio that would put you above the line in the top left corner of the graph. This would provide high expected returns and low risk. Everybody wants that, but given the available investments, it's unattainable. Remember, the efficient frontier shows the highest return you can achieve at any given level of risk. No mix of assets can provide returns above the line.
Unfortunately, portfolios can (and most do) fall below the line. This means they offer lower returns for greater risk. By moving back to the efficient frontier, and investor can anticipate greater return for the same risk, or lower risk for the same return.
When we make our investment decisions based on "instinct" or some hokey asset allocation from Money magazine, we're bound to fall off the efficient frontier. Only through analyzing risk, return, and correlation, can we create the efficient mix.
Input
That's what we set out to do. Using data from Ibbotson Associates, we created the efficient frontier illustrated above. We then created five portfolios running from the most conservative to most aggressive. There's no magic here, they're simply evenly spaced along the risk spectrum that appears on the graph's horizontal axis.There's a tremendous number of asset classes that can be included in creating the efficient frontier. In making ours, we wanted to stick to what most investors would consider purchasing. As a result, real estate and specific commodities weren't included. Neither were foreign bonds or U.S. stock sectors. The following table shows the asset classes that did make the cut. (For more detailed information, click here.)
| Proxies and Classes | |
| Series | Asset Class |
|---|---|
| Smith Barney 90-Day T-Bill | Cash |
| U.S. Intermediate Term Govt. Index | Intermediate Govt. Bonds |
| Lehman Brothers Govt. Index | Long-Term Govt. Bonds |
| Lehman Brothers Mortgage Index | Mortgage Bonds |
| Lehman Brothers Corporate Index | Corporate Bonds |
| S&P 500 Index | Large Cap Stocks |
| S&P 400 Index | Mid Cap Stocks |
| S&P 600 Index | Small Cap Stocks |
| EAFE Index | International Stocks |
As you can see, we wanted a broad representation of investment alternatives. We didn't just want stocks, bonds, and cash, but also various types of stocks and bonds. We assumed that different risk levels would call for different asset classes. It turns out we assumed wrong.
Output
Surprisingly, none of the efficient portfolios included any type of
government bond. This is true not only for the five portfolios, but all along the efficient frontier. You might have thought the more conservative portfolios would have included them. Apparently you'd have thought wrong.
You might have also figured small and mid-cap stocks would have a representation in the more aggressive portfolios. Wrong again. Instead, the efficient portfolios rely on large-cap stocks represented by the S&P 500 and 
international stocks in the EAFE index. Curiously, only the conservative portfolio utilized small-cap stocks shown by the S&P 600. Didn't you think they were risky? What's going on here?
It all comes back to risk, return, and correlation. Small-cap stocks are used to a minor extent in the conservative portfolio because they have a 0.06 negative correlation with T-Bills, the dominant asset. By including a fractional percentage of small-caps, return can be enhanced with no additional risk.
Government bonds don't appear in the portfolios because they are closely correlated with corporates and mortgages, have similar risk characteristics yet have lower returns. By using corporates and mortgages, returns can be increased with little additional risk.
In regard to stocks, the EAFE index has a relatively low correlation with 
large-caps stocks (.49) vs that of mid and small-cap stocks (.92 and .85, respectively). The EAFE's return exceeds that of small-caps and is only slightly below mid-cap's. While its risk is slightly higher, using foreign stocks over small or mid-cap domestic stocks can improve portfolio performance through enhanced return and lower correlation with large-cap stocks.
Conclusions and Conditions
So should you sell all your government bonds and dump all but your large-cap stocks? Probably not. While the efficient frontier and the portfolios found along it appear to be optimal, this concept must be kept in perspective.
First, you need to realize that there isn't just one efficient frontier. The frontier we created is a function of the asset classes we included. If you add or subtract classes, the line shifts, changing both expected return and risk.
Secondly, as financial markets gyrate relative to one another, the line will shift even if you continue to use the same inputs. This is because over time, returns, risk profiles, and even asset correlations change. These changes call for reallocation of the efficient portfolios and may even require addition or deletion of specific holdings. While you don't need government bonds or mid-cap stocks now, you might next year or maybe even next month.
Thirdly, the time-span for the series effects the frontier. We only looked back 15 years because some of the series didn't go back any further. Data for other series is available back to the turn of the century. The past 15 years has seen a major bull market for stocks. (Did you notice the high expected return figures for each portfolio?) Sure, it includes the mini-crash of 1987 but certainly nothing as devastating as the crash of 1929 or even the bear market of the 70's. An efficient frontier with series covering these periods would certainly offer different efficient portfolios. This isn't rocket science. Like anything else, garbage in, garbage out.
Finally, the portfolios falling along the efficient frontier can suggest how you should structure your portfolio, but they can't make you feel better about it. For example, you may be like a number of investors who fear using foreign stocks. They don't understand them and fear the effects of external events. After all, it doesn't do you any good to own stock in a great foreign country if its newly empowered dictator nationalizes it. You also can't control exchange rates, foreign withholding taxes, and trade restraints. If this is the case, you just don't want foreign stocks in your portfolio.
Well then, unless you're not the most conservative or aggressive investor, your portfolio won't be efficient. You can add other domestic stock classes to increase your return, but you still won't make it back to the efficient frontier.
But you know what? That's OK. That's right, you don't have to be on the frontier to have a well-constructed portfolio. At best, efficient portfolios provide models we should try to approach. Since it's constantly changing, it's a moving target anyway. The closer you can get to the efficient models, the better, but you've got to feel comfortable with what you own.
If you don't want foreign stocks that's fine. Just try to get your portfolio as close to the frontier as you can. If you've always perferred mid and small-cap stocks to large-caps, don't change now. You may not find your portfolio on the efficient frontier, but you'll still be pretty close. The efficient frontier may indicate you don't need government bonds, but if you've always felt comfortable with their stability and liquidity, you may need them.
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