Sunday , 20 August 2017

Attn. Financial Advisors: How Much Asset Class Diversification Is Really Necessary?


The ideal tool for performing the analysis  is Modern Portfolio Theory (MPT), a Nobel Prize-winning approach utilizing complex mathematics to tell you how to best allocate your funds among various asset classes to minimize risk.

Risk can be looked at as fluctuations in portfolio returns. In MPT, risk is measured by a statistical term called the standard deviation. [For more on MPT read: Understanding Systematic Risk, Modern Portfolio Theory and the Efficient Frontier] It is this quantity that MPT seeks to minimize in recommending portfolio allocations…

The portfolios considered here used monthly total return data taken from January 1928 through May 2011 for each of the following 10 asset classes:

  1. Large-Cap U.S. Stocks
  2. Small U.S. Stocks
  3. Long-Term Corporate Bonds
  4. Long-Term Government Bonds
  5. Intermediate-Term Government Bonds
  6. 30-day U.S. Treasury Bills
  7. Real Estate Investment Trusts (REITs)
  8. International Stocks
  9. International Bonds
  10. Gold

Each of these asset classes are themselves composed of a broad diversification of assets within that class. This article does not address that need, only the benefits of diversification among various classes.


The methodology used in this analysis was to first establish a baseline return/risk table using all 10 candidate asset classes (Table 1 below). You’ll see that the table contains certain measures of risk defined as follows:

  1. Standard Deviation – statistical measure of portfolio return fluctuation around the target return.
  2. Probability of Loss – chance of that portfolio losing value in any one year.
  3. Sharpe Ratio – a measure of risk versus reward with larger numbers being better.

This baseline data is shown in Table 1 along with the current ten asset class portfolio allocations (through May 2011.)

Table 1. Baseline portfolio incorporating all ten candidate asset classes.

[Click all to enlarge]

Click to Enlarge


The next step was to remove each asset class one by one in each of successive rounds and to assess its effect on the measures of risk. At the end of each round we chose to eliminate that asset class that increased the measures of risk the most. This was repeated for eight rounds until only two asset classes remained. Eliminations required examination of 52 separate portfolios (10+9+8+7+6+5+4+3).

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By using the above measures of risk as our benchmark, asset classes were eliminated from consideration in each successive round in the following order:

  1. International Bonds
  2. Long-Term Government Bonds
  3. Real Estate Investment Trusts
  4. Gold
  5. International Stocks
  6. 30-day U.S. Treasury Bills
  7. Large U.S. Stocks
  8. Either Intermediate-Term Government Bonds or Long-Term Corporate Bonds depending on target return


Tables 2a and 2b show the measures of risk using only two asset classes in the MPT analysis. There are two tables because different asset class combinations are preferable for the most conservative portfolios (target returns up to and including 7%) and the more aggressive ones (target returns 8% and above).

Table 2a. Two asset class allocations and risk measures for conservative portfolios

Required Standard Probability Sharpe Small Medium-Term
Annual Deviation Of Ratio Company Government
Return   Loss   Stocks Bonds
5.5% 4.6% 0.12 1.19 1.8% 98.2%
6.0% 5.3% 0.13 1.14 10.1% 89.9%
7.0% 8.7% 0.21 0.81 25.0% 75.0%

Table 2b. Two asset class allocations and risk measures for more aggressive portfolios

Required Standard Probability Sharpe Small Long-Term
Annual Deviation Of Ratio Company Corporate
Return   Loss   Stocks Bonds
8.0% 12.8% 0.27 0.62 34.3% 65.7%
9.0% 17.3% 0.30 0.52 50.4% 49.6%
10.0% 22.4% 0.33 0.45 66.3% 33.7%
11.0% 27.8% 0.35 0.40 82.1% 17.9%
12.0% 33.6% 0.36 0.36 97.8% 2.2%
12.1% 34.4% 0.36 0.35 100.0%  

You can see from the tables that returns are best realized by small-cap stocks and medium-term government bonds in conservative portfolios, and by small-cap stocks and long-term corporate bonds (investment grade) in the more aggressive ones. The inclusion of small-cap stocks especially in the more aggressive portfolios should come as no surprise because it is this asset class that is capable of generating the highest returns over the long haul. In fact, it is because of using only small-cap stocks to generate returns in the two candidate model that returns below 5.5% are completely unachievable (but so are very low levels of risk).

Now let’s see how these results compare to the classical model of using 10 asset classes.

Comparison of results

Table 3 presents the risk differences associated with reducing ten asset classes to only two.

Table 3. Risk difference between two and ten asset classes

Required Standard Probability Sharpe
Annual Deviation Of Ratio
Return   Loss  
6.0% 0.2% 0.01 -0.04
7.0% 0.4% 0.01 -0.03
8.0% 0.4% 0.01 -0.03
9.0% 0.5% 0.00 -0.02
10.0% 0.6% 0.01 -0.01
11.0% 0.7% 0.01 -0.01
12.0% 0.2% 0.00 0.00


What this analysis shows is truly astonishing and surprising. You can see that the reduction in the number of asset classes has a relatively insignificant effect on risk. I’m betting few folks would have expected this result!

To summarize all this into one number, you are increasing your overall level of portfolio risk by only about 1 part in 20 by decreasing the number of candidate asset classes from ten all the way down to two. This is based on the general numerical increase in the values of the risk measures as measured from their baselines.

An historical comparison

Looking at this from a historical perspective, let’s see how well a portfolio with only two asset classes would have fared against a traditional portfolio with all ten. Table 4 shows the results of actually following the recommended MPT allocations – with monthly rebalancing – from January of 1928 through May of 2011.

Table 4. Comparison of actual returns achieved utilizing ten asset classes versus two asset classes.

Required Ten Asset Classes Two Asset Classes Differences
Return Return SD Return SD Return SD
6.0% 7.1% 7.3% 8.0% 8.9% 0.9% 1.6%
7.0% 8.2% 10.1% 9.1% 11.1% 0.9% 1.0%
8.0% 8.6% 12.6% 10.2% 13.5% 1.6% 0.9%
9.0% 9.1% 14.5% 10.9% 15.7% 1.8% 1.2%
10.0% 10.1% 16.7% 11.4% 17.6% 1.3% 0.9%
11.0% 10.9% 18.8% 11.7% 19.2% 0.8% 0.4%
12.0% 11.8% 19.9% 11.8% 20.5% 0.0% 0.6%

To read this table, the Return under each model is the actual return the portfolio would have realized at the required return level given in the first column, and SD is the risk defined by the standard deviation.

Let’s look at an example. To achieve a 10% required compounded average annual return, a 10 candidate asset class portfolio would have achieved its goal and would have actually returned 10.1% at a risk of 16.7%. That same 10% targeted return attempted using only two asset classes would have actually produced a greater return, 11.4%, with only a slightly higher standard deviation of 17.6%. [Read: Warren Buffett: Diversification is Nothing More Than Protection Against Ignorance]

It is interesting to note that the portfolios composed of only two asset classes exceeded their targets more so than their ten asset class counterparts. This is due to the fewer choices available to the mathematics of MPT in its attempts to achieve, at least, the required return while also minimizing the level of risk but in so doing, the level of resultant risk is commensurately slightly higher.


The takeaway from this article should be to note that it doesn’t take broad asset class diversification to adequately achieve one’s investment goals with a reasonable level of reward versus risk. [In fact,] your nest egg needn’t be diversified among more than the two carefully selected asset classes discussed above for you to realize your desired long-term return at minimum risk…

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Editor’s Note: The above article has been has edited ([ ]), abridged (…), and reformatted (including the title, some sub-titles and bold/italics emphases) for the sake of clarity and brevity to ensure a fast and easy read. The article’s views and conclusions are unaltered and no personal comments have been included to maintain the integrity of the original article.

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