Modern Portfolio Theory-Part II: Asset Allocation

Today we continue with the column of guest blogger Professor Pat who provides us with the second installment of his treatise on Modern Portfolio Theory. Yesterday's blog provided an introduction to Modern Portfolio Theory (MPT) and today he'll be discussing how to optimize your portfolio using the results of MPT. Although the Professor doesn't like to toot his own horn, I just want to say that some of the data presented in the table today and in the next installment are derived from historical data run through the Professor's own MPT algorithms and won't be found anywhere except for perhaps in brokerage firms. So lead on, Professor Pat!

Portfolio Construction & Optimum Asset Allocation
Last time I introduced the concept of Modern Portfolio Theory (MPT) and described what it was and why it might be of interest to a certain type of investor. This time we will look at some actual data and examine the results.

The core philosophy behind MPT is to construct a portfolio of uncorrelated (or relatively uncorrelated) asset classes. Two assets are said to be uncorrelated if they react differently to market events. For example, the stock market and the bond market are two asset classes that are relatively uncorrelated as bonds usually perform better when the stock market is suffering and vice versa. The point of MPT is to construct a portfolio consisting of relatively uncorrelated assets in ratios that will give the investor the return he expects while minimizing risk.

Ibbotson & Associates, a firm with expertise in asset allocation and recently acquired by Morningstar, publishes a yearbook where they present time series data for six major U.S. asset classes back to the late 1920's. These classes are:

1. Large U.S. Stocks as currently represented by the S&P 500 Index.
2. Small U.S. Stocks defined by the Dimensional Fund Advisors (DFA) Microcap Portfolio.
3. Long-Term Corporate Bonds measured by the Citigroup High-Grade Corporate Bond Index.
4. Long-Term Government Bonds, currently a 20-year Treasury Bond.
5. Intermediate-Term Government Bonds, a 5-year Treasury Note.
6. 30-day U.S. Treasury Bills.

Using annual total return performance data for each of these individual asset classes from 1927 through 2007 and applying the mathematics of MPT to that data, I was able to construct the following table.

To use this table, you must choose the desired rate of return incorporating your tolerance for volatility or risk. (The standard deviation, the second column in the above table, is the measure of portfolio risk.) You should not merely chase the highest potential return; you should also consider your ability to accept years in which sharp draw-downs in the overall portfolio value may occur. This is the major tenet of MPT.

Investors nearing retirement, when they will start to withdraw investment funds, will need to avoid the possibility of those declines happening just when they will be selling. In that case an aggressive allocation should be converted to a more conservative one. For example, the average return from the most conservative portfolio would be 4.1% which would be achieved with a portfolio of 1.7% Small Stocks, 5.4% Long-Term Corporate Bonds, and 92.9% Treasury Bills. This represents the safest possible portfolio in that it provides the smallest variation in return from year to year. In any one year there is an approximate 68% chance (see the last installment of this article) that the actual return will be within one standard deviation. In this case, the return can be expected to vary between 1.1% and 7.1% (4.1% +/- 3.0%) In other words, the chance of a decline in overall portfolio value over any given year is small.

A more aggressive investor with a longer time horizon, such as a person in his 20s -30s, might choose a higher yielding allocation but he must also be willing to accept the risk of short-term market declines or intermediate-term lackluster returns. He must do this so that he will be properly invested during those times where the previously underperforming assets become out-performers.

Small stocks have historically produced the highest overall returns over the long haul as indicated by the table. We can see that an average annual return of 17.3% can be achieved by a portfolio that is 100% invested in small-cap stocks. This return, though, is realized at the cost of very high volatility. In 1973, for example, the loss in the small stock asset class was about 31% followed in the next year by another 20% hit. The following nine years, however, saw a nice recovery with a whopping average annual appreciation of 36%. Regardless of your risk tolerance, the table does indicate that some exposure to small-cap, high-growth stocks is advantageous.

It is interesting to note that the above table recommends that Long-Term Government Bonds are not an attractive investment to hold in any portfolio. Who knew?

Most investors will want to choose an allocation that moderates the volatility risk while still providing a healthy average return. One such selection is at the 11% level. For such a return there are chances of small declines in any one year but reliable gains over time for most years. The portfolio would consist of approximately 27% Large stocks, 30% Small stocks, 16% Long-Term Corporate Bonds, and 26% Intermediate Term Government Bonds. This allocation has the advantage of including one additional asset class over the 10% level for greater diversification.

If the reader is interested in following a course of action along the lines of MPT using these asset classes I recommend the Vanguard family of funds for their low expense ratios and respectable performance. (Note: I have no affiliation with Vanguard other than being a satisfied customer.) It's also good to note that index funds have very low to no year-end capital gains distributions which means your taxes on them will be minimal to none.

In my next installment, I'll discuss the effects of expanding the number of asset classes to include international stocks and bonds as well as real-estate investment trusts (REITs). See you tomorrow!