Thursday, April 24, 2008

MPT-Part IV: Asset Class Correlation & Fund Proxies

Today is the final installment of Professor Pat's dissertation on Modern Portfolio Theory (MPT). In it, he'll be looking at the correlation among asset classes and will also provide you with fund recommendations that you can use as proxies with which to construct your own portfolio. But before I hand this over to the Professor, I want to thank him for providing us with his insight into MPT and for generating these tables which involved research trips to the local university's business library and many hours of computer modeling. I am deeply grateful for his valuable time, knowledge, and effort.

Tomorrow we will return to our regularly scheduled programming. Take it away, Pat!

Correlation Among Various Asset Classes
Additional asset classes added for consideration should preferably be uncorrelated or negatively correlated to the other asset classes for best results. The relation between how asset classes or securities move relative to each other is defined by what is known as the Pearson correlation coefficient. The table below shows the Pearson correlation coefficients for each of the asset classes to one another. A value of +1. indicates perfect correlation while a value of -1. would reveal total negative correlation in the sense that when one asset goes up in value the other would go down in the same proportion, and vice versa. A value of zero demonstrates no correlation between the two asset classes; that is, they behave independently. (Note: The Pearson coefficient assumes a Normal distribution of data.)

As expected, large stocks and small stocks are highly correlated to each other. That is, when one class goes up or down in value there is a good chance that the other class also goes up or down commensurately. On the other hand Long Term Government bonds and REITs behave as two uncorrelated processes totally independent of each other. What this table confirms is that there is a sufficient lack of correlation between the various asset classes to present a suitable set of alternatives from which to compile a portfolio that can be counted on to behave according to the precepts of MPT.

Let's now look at a comparison of the returns and risks of an optimally allocated portfolio with those that contains just one asset class. The table below shows the average annual return and volatility of the individual asset classes over the 1927-2007 time frame for the expanded list of asset classes.

We can see, for example, that a portfolio holding only large stocks would yield an average annual return of 12.3% but do so with a standard deviation (our measure of risk) of 20.0%. Compare that with an optimally allocated portfolio (given in the chart in yesterday's blog) where the return is 13% but the risk has been reduced to 19.0%. Similarly, a completely conservative portfolio of safe U.S. Treasuries would return an average of 3.8% annually with a standard deviation of 3.1%. We saw yesterday that an optimum conservative portfolio can return a higher 4.2% at an even lower risk level of 3.0% just by adding long-term corporate bonds and some REITs to the mix.

There are many interesting observations to be gleaned from these tables such as the high volatility of REITs and the counterintuitive performance of Long-Term Corporate bonds versus Long-Term U.S. Government bonds where Corporate bond returns display the expected risk premium but the volatility is actually lower. Perhaps a closer examination of the actual composition of the comparative fund holdings might provide an explanation for this.

Asset Class Proxy Recommendations
Earlier, I recommended Vanguard as an excellent family of mutual funds. I do not work for Vanguard and know them only as a satisfied customer. An investor interested in forming a portfolio along the lines of the nine asset classes discussed here will find the following Vanguard funds as suitable proxies for them. Vanguard does not currently offer an International Bond fund so a T. Rowe Price no load fund with a reasonable expense ratio is listed. (Dr.K Note: Vanguard isn't the only firm offering these type of funds. Check Morningstar for other comparable funds and note transfer fees among fund families.)

The 500 Index Fund (VFINX) for Large Stocks.
The Small Cap Index Fund (NAESX) for Small Stocks.
The Long-Term Investment Grade Fund (VWESX) for Long-Term Corporate Bonds.
The Long-Term Treasury Fund (VUSTX) for Long-Term Government Bonds.
The Intermediate-Term Treasury Fund (VFITX) for Intermediate-Term Government Bonds.
The Treasury Money Market Fund (VMPXX) for U.S. Treasury Bills.
The REIT Index Fund (VGSIX) for U.S Real-Estate Securities.
The Total International Stock Index Fund (VGTSX) for International Stocks.
The T. Rowe Price International Bond Fund (RPIBX) for International Bonds.

In summary, we have shown that diversification provides real measurable benefits and that you, the investor, can use the tools of MPT to quantitatively measure reward versus risk in forming an investment portfolio that is suitable for your circumstances.

Thank you for allowing me to introduce you to the concepts of Modern Portfolio Theory.

Note from Dr. Kris: Pat has expressed a desire to provide one or two future articles on the evolution of MPT into PMPT, or Post Modern Portfolio Theory which challenges some of the assumptions inherent in MPT. (Don't worry, the information provided here is still valid.) We'll be looking forward to further installments. Thanks again, Professor Pat!


H Jarvis said...

Hi there

I am interested in correlation coefficients for various asset classes and am keen to find out from exactly which source you found the Pearson correlation coefficient matrix (data 1927 - 2007). Is this table published in a journal or book that is easily accessible?

Many thanks

Dr. Kris said...


I emailed your comment to Professor Pat and here's his response:

The matrix of Pearson coefficients was computed by my elf (oops, I mean myself) using a short Java program to apply Pearson's formula to the annual historical (1927-2007) total return data for each of the asset classes. This particular table was prepared exclusively for Dr. Kris' Stock Market Cookbook and appears nowhere else. The historical total return data are from Ibbotson & Associates and Dimensional Fund Advisors.

H Jarvis said...

Thanks a lot for getting back to me! That is very helpful.

Dr. Kris said...


Since you showed interest in the MPT discussion, I wanted to update you personally on the tables listed in Parts II-IV. Prof. Pat informed me that he input one piece of data incorrectly. He revised the tables and discussions pertinent to them. The April 22-24 blogs have modified to reflect these changes.