How Does Asset Allocation Work?

"There are lies, damned lies, and statistics," the 19th century British politician Benjamin Disraeli once remarked.

In spite of Disraeli's apparent loathing, statistics have played a vital role in developing modern portfolio investment theory. Indeed, it was the comprehensive use of statistical analysis during World War II that helped the Allied Air Corps clear the Normandy beaches of mines in preparation for D-Day landings.¹

Out of this work on statistical risk analysis during World War II, the modern portfolio theory of asset allocation was developed. In some form or other, statistical analysis is used by the majority of professional portfolio managers.

There are three basic statistical terms you should be familiar with in order to improve your understanding of the scientific concept behind asset allocation.

The mean rate of return is quite simply the average return on your investment. Let's look at a simplified case in which you purchase a stock that produces returns of –4, 8, 15, and 21 percent over a four-year period. Your mean rate of return is 10 percent annually. This assumes that all cash distributions (if any) are reinvested in the portfolio.

In most instances, like the simple example we have here, your return may well prove to be more or less than the mean rate of return. The spread of returns around the mean rate of return is known as the standard deviation.

The importance of standard deviation for an investor lies in the fact that it measues the variability of returns over time. Thus, the standard deviation helps you quantify the risk associated with your investment. It is a statistical fact that, 68 percent of the time, the return on your investment will fall between two figures on either side of the mean, which corresponds to one standard deviation.²

In our example, if the stock has a mean return of 10 percent and a standard deviation of 12, then 68 percent of the time your return will lie somewhere between –2 and 22 percent (i.e., 10 + 12 = 22 and 10 – 12 = –2).

The wider the spread of results you are prepared to accept, the more certain you can be in predicting them. So if you go to the second standard deviation, statistics show that, 95 percent of the time, your actual return should fall within plus or minus two standard deviations of the mean.³ In our example, this would mean that 95 percent of all returns are likely to fall between –14 and 34 percent.

The final concept you should be familiar with is correlation. If you wish to improve your chances of achieving the average return annually, you need to diversify over a number of different investments with the same potential average return.

If the prices of two stocks always move together, so that when one moves up so does the other, they are said to have positive correlation.

Alternatively, if the prices of two stocks always move in opposite directions, they have negative correlation. Theoretically, if you could find two investments with perfect negative correlation, it is possible to eliminate risk while maintaining your average rate of return.

The real art of asset allocation is to use the historical statistical information that is available on thousands of investments to build an integrated and diversified portfolio that will meet your expectations.

Asset Allocation is a method of diversification which positions assets among major investment categories. This tool may be used in an effort to manage risk and enhance returns. However, it does not guarantee a profit or protect against loss.

Sources: 1) American Statistical Association, The Origins of Statistical Computing, by David Alan Grier, 2006; 2-3) Morningstar Investing Classroom, Standard Deviation, 2006

This material was written and prepared by Emerald Publications.
© 2008 Emerald Publications

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