MPT Redux-Part III: Asset Class Correlations & Fund Proxies

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 the April 21-24, 2008 blogs. The content has been edited and data updated to reflect current values where appropriate.

Today is the final installment on Modern Portfolio Theory (MPT) where we’ll be looking at the correlation among asset classes. We’ll also provide you with proxies for these asset classes drawing from the mutual fund and ETF pool so that you, too, can construct your own portfolio.

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 we discussed yesterday.)


As expected, all of the stock asset classes have high correlations with each other and low correlations to government bonds, especially T-bills, where the correlation there is slightly negative. As for bonds, the Long & Medium Term Government, Corporate, and International Bond asset classes are highly correlated with each other. T-bills, on the other hand, don’t show much of a correlation to any other asset class except for Medium Term Gov’t and International Bonds.

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.

Historical volatilities & returns of the asset classes
Let’s now look at a comparison of the returns and risks of an optimally allocated portfolio with those that contain just one asset class. The table below shows the average annual return and volatility of each of the nine asset classes using data from 1928 to the end of April, 2009.


You can see that to get a higher return requires that the investor take a higher risk. To achieve higher returns, MPT would allocate the portfolio chiefly among the stock and REIT asset classes, with some component of bonds thrown in to minimize risk. This is why young investors should concentrate their portfolios into these asset classes while those nearing retirement should focus on minimizing risk to preserve needed capital. Bonds are the least risky asset classes which is where the older investor’s portfolio woukd be concentrated. But, MPT would likely throw in a small percentage of stocks in order that the desired return can be achieved.

For example, we saw yesterday that the most conservative portfolio of 99.6% in T-bills would return an average of 3.7% annually with an associated risk of 0.9%. However, by increasing our risk by only 0.1% to 1.0% we can achieve a return of 4.0%, or 0.3% over the previous return, just by adding Medium Term Gov’t bonds to the mix.

You can see why it’s important to not only include a mix of asset classes of differing correlations but of differing expected returns. MPT uses the higher volatility (i.e. the higher return) asset classes to maximize portfolio return and uses the correlation coefficients to minimize portfolio risk. It’s important to note that no portfolio can achieve a higher return than that of its highest returning asset class.

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 Proxies
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 some of 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 as well as one by Oppenheimer.

The electronically traded funds listed in the following table are also suitable proxies for the named asset classes.

ETF or Mutual Funds?
This is really a subject for another blog but I thought I’d touch on it because it’s relevent. One main reason to use mutual funds, especially if you hold many funds within the same fund family, is that you can exchange among them at little or, even better, no cost (like Vanguard).

One reason to use ETFs is that you don’t have to wait until the end of the day to transfer in and out of them because they trade exactly like stocks. (But also like stocks there’s a spread between the bid and ask prices.) If you’re judicious in your trading, you could actually do better in the transaction, especially if you’re trading among negatively correlated asset classes.

The other reason to use ETFs is that, in general, they’re not subject to as many tax consequences as mutual funds. This is because that instead of selling stocks like a mutual fund is forced to do, and by so doing incur short or long-term capital gains, the equivalent ETF has the legal right to “swap” in and out of stocks avoiding capital gains altogether.

The choice is yours, and you should do your homework on both strategies.

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.

Note: All of the above calculations were determined using the SMC Analyzer. To see how the Analyzer achieved these results, click here to view the Demo.

*Disclaimer: No one at the StockMarketCookBook has any affiliation with Vanguard, but we like their low management fees and the ease with which one can move among their funds at no cost. You can check out more about them and other mutual funds and ETFs at Morningstar.

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