*Dr. Kris is out of town this week and is rerunning her series written by guest contributor, Professor Pat on the topic of Modern Portfolio Theory. These posts originally appeared in April 21-24, 2008. The content has been edited and data updated to current values where appropriate.
Introduction
Yesterday, we saw that the aim of MPT is to provide the investor with a desired return value while minimizing risk. It achieves this by allocating portfolio resources among appropriately selected asset classes of varying volatilities and inter correlations. Today we’ll look at some actual data and examine the results.
Note that the data presented here represents monthly data collected from 1928 to the present. You probably won’t find these results anywhere except perhaps in institutions of higher learning or in large brokerage houses. This is a rare opportunity to view it first-hand.
Portfolio Construction: Selection of Asset Classes
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.
In order that the recommendations provided by MPT be robust, it’s necessary to have enough asset classes of varying risks and inter correlations. The reason to include higher risk asset classes such as small-cap/high-growth stocks is that they’re precisely the ones that can provide the investor with higher returns, if needed. It’s also important to include a mixture of relatively uncorrelated as well as negatively correlated asset classes, such as stocks and bonds. The nature of the correlations among the asset classes is the factor that minimizes risk.
Description of the Selected Asset Classes
We’ve selected nine asset classes that are not only popular investment vehicles but also represent a collection of asset classes with the required volatilities and correlations. They are the following:
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, a 20-year Treasury Bond.
5. Intermediate-Term Government Bonds, a 5-year Treasury Note.
6. 30-day U.S. Treasury Bills
7. Real-Estate Investment Trusts (REITs) defined by the DFA US Real-Estate Securities Index
8. International Stocks per the DFA Global Equity Portfolio
9. International Bonds per the DFA 5-Year Global Fixed Income Index Fund
Optimum Asset Allocations at required levels of return
Using annual total return performance data for each of these individual asset classes from January,1928 through April, 2009 and applying the mathematics of MPT to that data, the following table can be constructed:
To use this table, you, the investor, would choose the desired rate of return (given in the first column) that lies within your tolerance for risk. The risk is defined by the standard deviation located in the second column. You should not merely chase the highest potential return but also consider your ability to accept years in which sharp draw-downs in the overall portfolio value may occur. It is of utmost importance to note that variations in returns are smoothed out and tend towards the desired return, but this usually requires a long time horizon—sometimes on the order of 40 to 50 years.
Portfolio allocations for investors with shorter time frames
Investors nearing retirement will need to avoid the possibility of sharp declines happening just when they will be needing to withdraw funds. In this case, an aggressive allocation should be converted to a more conservative one. For example, the average return from the most conservative portfolio is 3.7% which is achieved with a portfolio of 0.1% Small Stocks, 0.2% Long-Term Corporate Bonds, 0.1% International Stocks, and the bulk of the portfolio, 99.6% in Treasury Bills, an essentially riskless asset class.
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 2.8% and 4.6% (3.9% +/- 0.9%) In other words, the chance of a decline in overall portfolio value over any given year is small.
Portfolio allocations for those with longer time frames
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. This must be done so that the portfolio will be properly invested during those times where the previously underperforming assets become out-performers.
Portfolio allocations for those with intermediate time frames
Most investors will want to choose an allocation that moderates the risk while still providing a healthy average return. Returns between 7% – 9% are particularly attractive because as there’s a chance of a small decline in any one year, there will be reliable gains for most years over time. Right now, these portfolios would be allocated among the Small-cap stocks, Medium-term government bonds, and International stocks.
Observations gleaned from the above asset allocation table
Small stocks have historically produced the highest overall returns over the long haul as indicated by the table. To achieve the higher returns, the portfolio must be heavily weighted in small-cap stocks. But as MPT shows, higher returns come only with higher risk.
In 1973, for example, the loss in small stocks 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 Large-cap stocks, Long-Term Government Bonds, REITS, and International Bonds are not an attractive investment to hold in any portfolio right now.
In the next MPT installment, we’ll suggest some proxies for these asset classes. We’ll also look at the correlation table between them.