What to Do when Traditional Diversification Strategies Fail – Revisited

An Updated Diversification and Asset Correlation Study Accounting for Zero-Commission Exchange Traded Funds

2010 Volume 13 Issue 4

Reduced costs of trading commissions are a welcome new benefit of using ETFs as portfolio building blocks, but the cost of the bid-ask spread can be significant if low-volume ETFs are mixed into a diversified portfolio.

[powerpress: http://gsbm-med.pepperdine.edu/gbr/audio/fall2010/dilellio-diversification.mp3]

Online investments going down

The market events of 2008 stressed the ability of diversification to protect against loss due to rapidly changing correlation amongst assets. But, as demonstrated in the initial article, “What to Do When Traditional Diversification Strategies Fail,” there is still a simple, repeatable approach based on utilizing previous year correlation coefficients to construct a diversified portfolio that reduces loss of principle.[1] The significant market gains of 2009 further challenge the benefits of diversification. So, the question now is: Does this approach to diversification also provide opportunity for significant positive gains? To answer this question, we revisit the simple diversification strategy featured in the previous article, which exploits correlation to reduce risk, to see if opportunities for gains exist.

Furthermore, a recent competition between brokers has been driving down commissions for online trades. In addition to lower commissions, some brokers have selected a subset of ETFs from a single provider, such as iShares’ affiliation with Fidelity, and waived all commissions when trading these financial products within their online platform. These reduced costs are important and may have a direct influence on the optimal reallocation frequency. So, a new question now is: With the reduction or elimination of trade commissions, is a more active strategy optimal? This article also examines this practical issue, and quantifies the overall benefits from $0 ETF commissions currently in the marketplace.

Hypothesis Revisited

This study revisits many of the hypotheses established in the previous study. The correlation coefficient threshold is validated from an updated illustration containing four asset classes: U.S. Large Caps, U.S. Small Caps, International, and Bonds. As seen in Table 1, correlations observed over 2008 suggest the same allocations against U.S. Large Caps (SPDR S&P 500 fund, symbol: SPY) and Bonds (iShares Aggregate Bond Fund, symbol: AGG) as suggested from correlations observed over 2007.[1] But, because of the continuing trend of lower commission costs, consideration must also be given to volume in the process of identifying uncorrelated assets. Volume is known to be inversely related to costs from bid-ask spreads and is empirically modeled in the following section. So, to provide a preference to higher volume funds that minimize the resulting bid-ask spread, the correlation matrix rows are generated in order of decreasing volume before eliminating highly correlated investment options. The result to the right of the arrow illustrates the result, applying this process to a four-asset class example.


Table 1- DiLellio

Table 1: Correlation Coefficients from Daily Returns Adjusted for Dividends in 2008, sorted by Average Daily Volume.


Table 2 shows the associated 2009 performance, based on holding both the four-asset portfolio as well as the suggested two asset portfolio based on the 80 percent correlation threshold. The diversification effect observed in 2008 reduced the 2009 portfolio gain from 21 percent to 14.3 percent. Reviewing the 2008 portfolio returns (illustrated in the previous article), we observe a loss of 27 percent and 15 percent, respectively, where the smaller loss occurrs when we apply the correlation threshold to portfolio construction. Thus, the two-year cumulative return from this simple illustration is -12 percent when no correlation threshold is applied, versus -3 percent when it is applied.


Table 2- DiLellio

Table 2: 2009 Performance of Naïve Allocation with and without use of 2008 Correlation Coefficients.


This updated simple illustration continues to suggest a benefit of multi-asset diversification or wide diversification, consistent with other research.[2][11] While these studies use longer history market indices, we show a more pragmatic view in the following sections, since the ETFs examined are easily traded by individuals, investment advisors, hedge funds, and institutional investors. Furthermore, ETF transaction costs can be accurately modeled, as shown in the next section. Unfortunately, ETFs are still fairly new investment products, so they do not offer the long histories available for many asset allocation studies employing equity, bond, and commodity-based indices used in the aforementioned studies.

Analysis Assumptions and Methodology

Continuing with the nine asset classes identified in the previous article, including the 136 unique ETFs available since January 2004, we have added an analysis of new zero-commission ETFs now being offered by Schwab, Fidelity, and Vanguard. Six of the asset classes are equity-based and consist of large cap domestic, large cap foreign, emerging markets, midcap domestic, small cap domestic, and domestic sectors. The three non-equity classes include commodities, bonds, and real estate. A summary of the nine asset classes represented by these ETFs appears in Table 3, where sector and large cap domestic assets have the largest representation, while bonds and real estate assets have the smallest.


Table 3 - DiLellio

Table 3: Asset Classes represented by 136 Exchange Traded Funds available since January 2004 (values are rounded to the nearest percent).


Based on the updated simple illustration from above, we continue to define uncorrelated assets using a correlation matrix generated by volume. We then eliminate lower volume assets that are more than 80 percent correlated with higher volume assets. All correlation coefficients were calculated based upon 12 months of daily historical returns developed from adjusted closing prices that included dividends and splits. For consistency, volume was also estimated using a 12-month average daily volume. This methodology follows the same rationale established in the initial paper.

Revisiting the existing assumption regarding switching costs, we have updated our methodology to address the practice of investment managers seeking “most liquid” ETFs.[4] To further improve the fidelity of the back-testing, we have also incorporated a nonlinear regression model for a bid-ask spread that grows rapidly with low volume. The model parameters are based on empirical data provided by Pankaj Agrrawal and John M. Clark in their 2009 article, “Determinants of ETF Liquidity in the Secondary Market: A Five-Factor Ranking Algorithm.”[3] This data is represented in Figure 1. The value of R2 = 94 percent obtained from the power-law model suggests that a significant amount of the variation has been explained between the bid-ask spread and the trailing volume, providing high confidence in the model’s ability to accurately reflect bid-ask costs based on volume.


Figure 1 - DiLellio

Figure 1: Bid-Ask Spread, in Basis Points (BP) versus Average Volume, with Power Law Regression model and Goodness of Fit Measure.


The model in Figure 1 is applied against hypothetical trades using month-end adjusted closing price and volume. Returns were calculated based on a naïve allocation approach that evenly spreads assets across uncorrelated ETFs. The purpose is to examine the data’s sensitivity to annual, biannual, and quarterly rebalances. To reflect the latest updates in commissions from discount brokerages such as Vanguard, trade commission are reduced from $10 to $5 per trade against a portfolio starting with $100,000 in a tax-free account.[7]

Empirical Results

Figure 2 appears to have a very similar downward trend, but contains a full five years of history. Once again, the increased correlation amongst assets classes increases over time, yielding fewer uncorrelated funds. Also note that including volume as part of the process to determine uncorrelated funds has had a marginal effect on the total number of uncorrelated funds, but the downward trend from 2005-2009 remains.


Figure 2 - DiLellio

Figure 2: Number of ETFs that are less than 80 percent correlated over previous year with higher volume ETFs (2005 – 2009).


Tables 4, 5, and 6 list the portfolio allocations against each of the nine asset classes for the annual, biannual, and quarterly rebalancing periods. In each case, the allocations begin in 2005 with a majority of holdings in large foreign equities, emerging markets, and domestic sectors. By 2009, large domestic equity increases significantly, while large foreign equities and emerging market allocations shrink drastically, as highlighted in orange. Highlighted in yellow, bond funds continue to grow to become 43 percent of the allocation, one of the largest percentages seen over the five-year study. Lastly, domestic sectors remain a significant percentage of the allocation throughout the five-year study, suggesting a cyclical pattern between the range of approximately 25 percent and 45 percent. In summary, these results indicate that the naïve allocation strategy appears to be achieving wide diversification, based on the portfolio containing between five and eight asset classes throughout the five-year testing period.[2] Furthermore, the strategy appears to have a dynamic component that, in times such as early 2009, approaches the classic allocation of 50/50 bond-equity allocation.


Table 4 - DiLellio

Table 4: Annual Portfolio Allocation Percentages with Naïve Allocation Approach and 80-Percent Correlation Threshold



Table 5 - DiLellio

Table 5: Biannual Portfolio Allocation Percentages with Naïve Allocation Approach and 80-Percent Correlation Threshold.



Table 6 - DiLellio

Table 6: Quarterly Portfolio Allocation Percentages with Naïve Allocation Approach and 80-Percent Correlation Threshold.


Table 7 summarizes the net returns based on the three reallocation intervals and includes the effect of modified and new positions incurring a bid-ask spread cost and the flat-rate $5 commission cost. Once again, the annual reallocation period appears optimal. Also, the commission costs do not appear to be driving the lower performance. When set to $0, returns increase by 0.6 percent, 1 percent, and 1.9 percent over the five-year period for annual, bi-annual, and quarterly reallocations, respectively. But, this increase is not sufficient to offset the larger gross returns provided by the annual reallocation frequency.


Table 7 - DiLellio

Table 7: Net Returns with Naïve Allocation



Table 8 - DiLellio

Table 8: Sharpe Ratio with Naïve Allocation


Alternatively, Table 8 shows the risk adjusted returns using data from Ibbotson & Associates’ one-month T-bill for the risk-free rate and William F. Sharpe’s methodology based on excess return and standard deviations.[5] Once again, annual reallocation provides the greatest risk-adjusted returns.

The cost impact on the portfolio due to the bid-ask spread is somewhat more complex than the flat-rate commission discussed above. While the the aim was to select higher volume uncorrelated funds, it is likely that a few of the uncorrelated funds had significantly lower volume. To examine the relative effect of the portfolio’s bid-ask spread against number of positions in the allocation, a scatter plot appears in Figure 3 from the quarterly allocation data. Interestingly, the lowest bid-ask spread cost incurred for a given allocation is achieved when 20 to 30 uncorrelated funds are identified. Alternatively, when only a dozen or so funds are available, the resulting bid-ask spread becomes significant. The larger bid-ask spread is also seen for portfolios with more than 40 uncorrelated funds, but to a lesser degree. The larger portfolio bid-ask spread is the result of a few low-volume ETFs needed to provide portfolio diversification, which were not available from higher volume alternatives. And because of the rapid growth of the bid-ask spread for low volume, a small fraction of the allocation towards low-volume ETFs can increase the portfolio bid-ask spread substantially.


Figure 3 - DiLellio

Figure 3: Portfolio Bid-ask spread (basis points) vs. number of uncorrelated funds is nonlinear.


Observations and Current Market Offerings

Revisiting the simple methodology previously established, we see that using correlation coefficients continues to provide a practical approach to obtaining the benefits of diversification. Reduced costs of trading commissions are a welcome new benefit of using ETFs as portfolio building blocks, but the cost of the bid-ask spread can be significant if low-volume ETFs are mixed into a diversified portfolio. Furthermore, based on a correlation threshold, the methodology applied here can include these low-volume ETFs in portfolios with smaller and larger numbers of uncorrelated funds.

These are important observations because, as of May 2010, Fidelity, Vanguard, and Schwab all offer $0 commissions on trades. These brokerage firms appear to be using this offer along with lower expense ratios, better exposure to asset classes, and lower tracking error as a discriminator.[8][9] But, expense ratios and bid-ask spreads are important costs to consider, particularly for lower volume $0 commission ETFs.[10] Table 9 summarizes the median cost for the 6 ETFs from Schwab, 26 from Fidelity, and 46 from Vanguard that are currently offered with $0 commissions when traded online. The costs are based on buying and selling the median ETF over a one-year holding period, and the bid-ask spread is based on the model in Figure 1 using average volume from February to April 2010.

Table 9 suggests that annual transaction costs associated with buying and selling $0 commission ETFs can quickly exceed 100 basis points, or 1 percent, when traded quarterly. While such evidence still may not deter day-trading of ETFs, one broker has announced limitations on trading their $0 commission ETFs. Vanguard incorporates a limit of 25 buys/sells of its $0 commission ETFs per year.[6] This announcement is clearly associated with Vanguard’s founder, John Bogle, and his belief in keeping costs low for long-term investments. Investors would be wise to consider this fundamental philosophy.


Table 9 - DiLellio

Table 9: Annual Median Transaction Cost of Reallocation using $0 Commission ETFs


DISCLAIMER: The exchange trade products analyzed in this article were chosen from those publicly available. They do not represent the author’s recommendations and were only used to support observations. Investment advice is neither implied, nor suggested.


[1] DiLellio, James, “What to Do When Traditional Diversification Strategies Fail,” The Graziadio Business Report, 12, no. 4 (2009).

[2] Mulvey, John M., Cenk Ural and Zhoujuan Zhang. “Improving Performance for Long-Term Investors: Wide Diversification, Leverage, and Overlay Strategies,” Quantitative Finance, 7.2 (2007): 175-187.

[3] Agrrawal, Pankaj and John M. Clark, “Determinants of ETF Liquidity in the Secondary Market: A Five-Factor Ranking Algorithm,” Institutional Investor Journals. Fall: 59-66.

[4] Hight, Gregory N., “Diversification Effect: Isolating the Effect of Correlationon Portfolio Risk,” Journal of Financial Planning, October (2010).

[5] Sharpe, William F. “The Sharpe Ratio,” Journal of Portfolio Management, Fall (1994): 49-59.

[6] Wiener, Dan, “Free Trading Vanguard’s Shotguns,” Forbes.com, May 4, 2010.

[7] Maxey, Daisy, “Vanguard Joins Cuts of ETF-Trading Fees,” The Wall Street Journal, May 5, 2010.

[8] Spence, John, “BlackRock, Vanguard Battle for ETF Assets – Being First Mover isn’t So Advantageous,” The Wall Street Journal, April 27, 2010.

[9] Kapadia, Reshma, “Identical Twins? Nope.” WSJ.com, April 5, 2010.

[10] Randall, David K., “Why Bargain Trades Are No Bargain“, Forbes, March 15, 2010.

[11] Gibson, Roger C., “The Rewards of Multiple-Asset-Class Investing,” Journal of Financial Planning, July (2004):58-71.

[14] Vanguard.com, Vanguard ETFs® https://personal.vanguard.com/us/funds/etf.



[i]Expense ratios and volumes were obtained from Brokerage Web sites in April 2010, including Fidelity.com, Vanguard.com, ishares.com, as well as finance.yahoo.com, SeekingAlpha.com, and are subject to change.

About the Author(s)

James DiLellio, PhD, MBA, is a practitioner faculty of decision sciences at the Graziadio School of Business and Management at Pepperdine University, where he teaches undergraduate and graduate business courses in applied statistics and quantitative analysis. His research interests are primarily in the area of nonlinear optimization and Kalman filtering techniques for solving decision analysis problems in investing and finance.

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