July 2003
The Third Factor
| "The whole is more than the sum of its parts." |
| --Aristotle |
HERE ARE CERTAIN TRUISMS THAT everyone learns when they begin investing. You know them, they're the basics such as:
- The more risk you can handle, the greater your potential return.
- Stocks are riskier than bonds.
- Small cap stocks are riskier than large cap stocks.
But perhaps we should think about them once in a while, maybe even critically. Like all generally accepted "facts", they can be used to reach erroneous conclusions.
Now this isn't because the "truisms" aren't true, but rather because we apply them incorrectly. For example, a representative of a major trust bank recently said something to the effect of
Most of our customers are quite conservative. Because of this, we always emphasize large cap stocks, even in the most aggressive portfolios. In the most conservative, we'll only consider large cap stocks while we'll use some small caps in the most aggressive, but always to a lesser extent than large caps.That makes sense, right? The clients are conservative and large caps are the least risky equity class, so it stands to reason they would be emphasized.
This is exactly how many investors handle their own portfolios. The strategy seems so obvious, most don't give it a second thought, but maybe they should.
General Theory, Real Returns
Just consider how this approach would have worked over the past three years. The grey bars in Chart 1 show the returns of the S&P 500, small cap U.S. stocks and the 30-Day U.S. Treasury Bill, a proxy for cash. The measurement period is January 2000 through April 2003.|
Chart 1 Returns and Risk-Adjusted Returns January 2000 - April 2003 |
 Data Source: Ibbotson Associates |
This doesn't paint a pretty picture for those conservative trust accounts. From January 2000 through April 2003, large cap stocks were off 10.44% while small caps actually gained 6.25%. Short-term Treasury Bills returned 3.51%.
But then again, conservative investors wouldn't have been fully invested in any kind of stock, but rather in a combination of equity and fixed income investments. To get a feel for how a more balanced portfolio would have performed, we created four different ones consisting of 30% large cap stocks and cash, 50% large cap stocks and cash, and the same percentage small cap stocks and cash. These mixes seemed most appropriate for conservative investors.
The black and blue bars show the results for the large cap portfolios while the green and red show those of the small caps. Once again investors in the "safer" large cap portfolios fared considerably worse than those utilizing "riskier" small caps.
And no, it wasn't simply a reward to shouldering more risk. The dots in Chart 1 show the Sharpe Ratio for each index and portfolio. The Sharpe Ratio is a way of measuring risk-adjusted return so obviously, the higher the better. As you'll notice from Chart 1, small cap stocks and the portfolios utilizing them also had higher risk-adjusted returns than the "safer" alternatives.
Of course just looking at three years doesn't really paint a very comprehensive picture. There will always be short-term time periods where one asset class does better or worse than others. Not even the three truisms listed above hold in every short-term time frame.
If you consider a longer time frame, you clearly see the basis for all three truisms. Chart 2 plots the index series as well as the four portfolios in risk/return space. Risk, as measured by standard deviation, is measured on the horizontal axis while annualized return is shown on the vertical axis.
Chart 2's results are derived from January 1930 - December 1999. This time frame was selected since the Ibbotson data series start in 1926 and a little later we'll look at 10-year periods covering seven decades.
The best investments will fall in the upper left of the graph (high return, low risk) while the most inefficient ones will fall towards the bottom right (high risk, low return). The dotted line in Chart 2 is the Capital Market Line (CML) and is constructed by drawing a line connecting the "riskless" investment (30-Day T-Bill) and the S&P 500. According to the Capital Asset Pricing Model (CAPM), efficient portfolios will fall along or above the Capital Market Line.
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Chart 2 Risk vs. Return January 1930 - December 1999 |
 Source: Ibbotson Associates |
From a risk standpoint, you can clearly see why conservative investors are somewhat afraid of small cap stocks. Notice that small caps fall far to the right of all other alternatives on Chart 2. With a standard deviation of over 33%, they're clearly more "risky".
By the same token, they've also compensated investors for the additional risk with additional return. Not only do small caps fall to the right of all other alternatives, they also are much higher on the return scale. In fact, they fall only slightly below the CML, which also explains why their Sharpe Ratio is in line with the other alternatives.
Also notice that from an efficiency standpoint, all four stock/cash portfolios are roughly equivalent. Each falls slightly above the CML and their Sharpe Ratios are all within 0.17% of one another. In essence, they're only differentiated by their respective risk and return levels. That's how efficient series should work, according to the CAPM.
There's one other, and possibly the most important, thing to notice: Consider how closely the large cap 50/50 and small cap 30/70 portfolios map on Chart 2. The former is a "safer" mix, yet it plots almost identically with a "riskier" one.
Perhaps even more striking is the fact that the large cap portfolio requires the conservative investor to place 50% of his or her assets in equities while the purportedly riskier small cap portfolio only has a 30% equity exposure. What's up with that?
Same Through the Decades
First off, this isn't some kind of fluke. As you can see from Chart 3, the small cap 30/70 portfolio (red line) led the large cap 50/50 portfolio (black line) in four of the last seven decades of the 20th Century. Despite trailing in the last two decades, the former's annual arithmetic average was 8.05%, vs. 8.28% for the latter.Over on the risk side, the mixes tracked remarkably closely. This is shown on Chart 4. The actual annual standard deviation was lower for the small cap 30/70 portfolio (9.46% vs. 9.95%). That's probably because it had less equity exposure than the large cap mix.
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Chart 3 10-Year Returns January 1930 - December 1999 |
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Chart 4 10-Year Risk January 1930 - December 1999 |
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Chart 5 10-Year Sharpe Ratio January 1930 - December 1999 |
 Data Source: Ibbotson Associates |
Both mixes performed quite similarly on a risk-adjusted basis, too. Chart 5 shows the Sharpe Ratios for all the mixes and again, the small cap 30/70 and large cap 50/50 track tightly together. Over the entire period, the annual value for the small cap 30/70 was slightly higher (0.8509 vs. 0.8325).
The second point is that none of this contradicts any of the three truisms. Chart 2 definitely showed that indexes and portfolios -- at least those being considered here -- with more risk produced greater returns over the long-term. That's why they all fell around the upward sloping CML.
Over the long-term, stocks are riskier than fixed income investments. That's why on Chart 2 both the S&P 500 and small cap stocks fell well to the right of T-Bills and U.S. Long-Term Government Bonds.
Small cap stocks are riskier than large caps over the long term. That's why they have a higher standard deviation and fall to the right on Chart 2.
But here's the main difference: In considering the performance of the small cap 30/70 and large cap 50/50 portfolio, we're no longer focusing on the relative performance of large and small stocks, but rather that of portfolios that mix asset classes.
That's a tremendous difference because when you combine risky asset classes, it's possible to actually reduce the risk of the resultant portfolio. When you create portfolios, there is another element at work in addition to risk and return: correlation.
Correlation measures the way asset classes track relative to one another. Those that are highly correlated move in the same direction and to similar degrees. They're said to be positively correlated. On the other hand, classes that tend to move in opposite directions, even if at varying degrees, are said to be negatively correlated.
Portfolios that combine highly correlated classes can magnify the risk of the constituents, but those that utilize low or negatively correlated classes can actually minimize or even reduce the risk of the overall portfolio. This is a key tenet of Modern Portfolio Theory.
Over the period January 1930-December 1999, both large cap and small cap stocks have had a slightly negative correlation with 30-Day T-Bills, 
-0.0146 and -0.0900, respectively. When these risky asset classes are mixed with T-Bills, the resultant portfolios have a greater return potential but not proportionately higher risk. That's why they're able to stay near but move up the CML on Chart 2.
The negative correlation with T-Bills has almost always been greater for small caps than large caps so that allows the 30/70 portfolio's risk to remain similar to that of the 50/50 portfolio (see Chart 5) while delivering similar returns.
In this case, by utilizing the "riskier" asset class, you can create a portfolio with less equity exposure and comparable return to one with a higher percent holding in a more "conservative" equity class. While the truisms still hold, certain trust banks may need to rethink their approach.
Not an Isolated Incident
Finally, we realize most conservative investors also utilize bonds in their portfolios. Stocks have historically had a higher correlation with bonds than with the T-Bill. From January 1930-December 1999, long-term government bonds have had a 0.1996 correlation with large caps and 0.0202 with small caps, yet this doesn't mean that small caps shouldn't still play an important role in risk-averse portfolios.|
Chart 6 Efficient Portfolios January 1930 - December 1999 |
 Source: Ibbotson Associates |
Chart 6 graphically displays the mix of assets that would have been efficient portfolios over the last seven decades of the 20th Century. Each color represents one of the four asset classes: large and small cap stocks, long-term government bonds, and 30-Day T-Bills.
The vertical axis runs from 0-100% and represents weights of the various asset classes. The horizontal axis moves from conservative to more aggressive mixes as you move from left to right.
You can determine the efficient mix at any point along the way by simply drawing a vertical line and estimating the percentage weights represented by each color. On this chart, small cap stocks are represented by the black area.
Notice how even the most conservative portfolios (those to the left) have a considerable small cap component. As you move further toward the right, the small cap weight grows substantially, even at the expense of large caps (blue area).
So what do you tell the conservative investor (or money manager) who is afraid to utilize small cap stocks because they're riskier than large caps? It's not that the three truisms mentioned at the outset don't hold; they do. Small stocks are riskier than large caps and fixed income alternatives.
But you can capitalize on the potentially greater return that comes with that risk by mixing them with other, perhaps less risky, asset classes. Sometimes it's more conservative for a portfolio to hold what by themselves, are riskier assets.
Correlation really does matter, it's just not the subject of too many truisms.
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