Tuesday, June 3, 2008

MPT Part VII: Revised Asset Allocation Tables Using Monthly Data

Yesterday we compared asset allocations based on a simple average versus a compounded average. Today we'll be comparing allocation tables derived from monthly versus annual data. In previous MPT segments, my asset allocation calculations were based on annual data for the past 81 years. My goal has always been to do these calculations based on monthly data but this involved manually inputting almost 6000 pieces of data which took me a while, especially since I rechecked every input for accuracy. I hope you'll forgive me for not doing this in the first place! In my defense, the allocation tables derived from annual data are by no means invalid; they're just not quite as accurate as the ones I'm about to show you. The fact is that the more data points you have, the more accurately will your results reflect reality.

The Revised Allocation Table Based on an Arithmetic Average
So without further apologies, let's look the newly derived monthly tables. The first one is based on arithmetic averages (compare it to the annual chart shown in yesterday's blog):

The toughest part of annualizing returns based on monthly data is in the conversion of monthly standard deviations. Remember that the standard deviation is another term for portfolio risk. [For you academicians who revel in hairy mathematical equations, the conversion formula is given at the end of this article.*] The standard deviations in these tables generally reflect the smaller variations that occur over a greater number of shorter time intervals, at least for the more conservative portfolio allocations.

Note that this table begins at the lower Required Return level of 3.8%. In general, the optimum allocations based on monthly data compared with allocations derived from annual data reveal that the percentage of total portfolio funds allocated to Large Stocks should be slightly decreased in favor of increasing funds to Small Stocks and Long-Term Corporate Bonds.

The Revised Allocation Table Based on a Compounded Average
The table below represents the optimum allocations using monthly data with compounded averages. Compare these results with the table given in yesterday's blog (and also in MPT Part II).

As we saw yesterday, the allocations for the same risk level (standard deviation) are only the same at the low end of the Required Annual Return. Comparing the above chart with the annual chart, we again see that Large Stocks are also slightly deemphasized until about the 11% level of Required Return in favor of Small Stocks and Long-Term Corporate Bonds.

Revised Asset Class Correlation Table
You'll recall from MPT Part IV (April 24th blog) that the more that asset classes are uncorrelated with each other, the less risky is your overall portfolio. The asset allocation table given previously was based on annual data, and if you compare it with the one below that was derived using monthly data, you'll see that in most cases there is less correlation in the monthly table which is what we want.

This concludes my discussion of Modern Portfolio Theory, at least for the time being. Tomorrow I'll be introducing some concepts of Post-Modern Portfolio as well as my opinions on the subject.

*Calculation of Annualized Standard Deviation
The annualized standard deviation values were derived using the exact form of the period conversion formula shown below rather than the common approximation,

Posted by Prof. Pat

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