The Forgotten Dimensions Of Diversification

by: Marc Cohn


Rules-based asset allocation strategies are diverse across a range of asset classes.

But these systems are generally focused on one set of rules and one set of time-frames for implementation.

Additional diversification can be obtained by combining multiple sets of rules at different times.

The article discusses one way to implement a more diversified approach to rules-based asset allocation.

Rules-based asset allocation strategies, particularly momentum-based strategies, have been discussed thoroughly on this site and elsewhere. Some examples are Herr's Dual Momentum, Grossman's GMR, Faber's GTAA, Varan's analyses, and this author's trading systems here and here. These systems generally seek diversification by applying the same rules across a broad group of asset classes. For instance, each relies on a narrow set of parameters for measuring the momentum of an asset class in the group. GTAA recommends a 10-month lookback period. Mr. Herr's Dual Momentum applies a combination of 60-day and 100-day lookbacks, along with a volatility component. Grossman used a 3-month lookback.

While these rules have been backtested well in the study period of each strategy, other studies have shown that fixed momentum look-backs generally do not operate robustly across all time periods. For example, GestaltU provides an article showing the apparent randomness of optimal x-day lookback periods in a simple momentum-based asset allocation system applied to a broad set of asset classes, as shown in the below image reproduced from the article:

While no single x-day lookback period performed the best in all periods, what the GestaltU study did show was that a combination of all portfolios in the study beat the VTI. (Query whether that was an appropriate benchmark, but that question is not for this article.) Thus, the article confirmed decades of research showing that momentum is a factor that can create alpha. For another example of this research, click here.

Measuring momentum in a narrow manner can result in volatility that is similar to what one sees when trading a single asset class. A lack of diversification exposes the investor to large risks of drawdown. This author explored ways to implement a combination of portfolios that measure momentum differently and at different times.

In addition, the decision of when to trade, e.g., in a monthly system, which day of the month, can also present a luck-of-the-day risk that might be good or bad, but which is not known ex ante. Mr. Herr addresses this risk in his "tranche" modelling, in which he uses a spreadsheet to model the same portfolio implemented once for each of the previous 12 days. Each implementation contributes one-twelfth to the overall asset allocation.

This author proposes applying a model similar to Mr. Herr's tranche model to both the timing and the lookback parameters of a momentum-based trading system. The example system discussed herein is applied to a diverse group of asset classes:

  • Vanguard Total Stock Market ETF (NYSEARCA:VTI)
  • Vanguard High Dividend Yield ETF (NYSEARCA:VYM)
  • Vanguard Small Cap Growth ETF (NYSEARCA:VBK)
  • Consumer Staples Select Sector SPDR ETF (NYSEARCA:XLP)
  • Utilities Select Sector SPDR ETF (NYSEARCA:XLU)
  • Vanguard FTSE Developed Markets ETF (NYSEARCA:VEA)
  • Vanguard FTSE Emerging Markets ETF (NYSEARCA:VWO)
  • SPDR Dow Jones International Real Estate ETF (NYSEARCA:RWX)
  • Vanguard REIT Index ETF (NYSEARCA:VNQ)
  • PowerShares DB Commodity Index Tracking ETF (NYSE:DBC)
  • iShares Gold Trust ETF (NYSEARCA:IAU)
  • Vanguard Intermediate-Term Bond ETF (NYSEARCA:BIV)
  • iShares 20+ Year Treasury Bond ETF (NYSEARCA:TLT)
  • iShares Floating Rate Bond ETF (NYSEARCA:FLOT)
  • iShares TIPS Bond ETF (NYSEARCA:TIP)
  • iShares 1-3 Year Treasury Bond ETF (NYSEARCA:SHY)

The author's system would apply an x-day lookback for measuring momentum (Po/Px) using 14 different lookback periods. It would calculate the x-day price performance at the close of each of the previous six days, and each portfolio would select the top three performing ETFs in which to invest equally.

Thus, the author has prepared a matrix for each of the first, second, and third picks for each portfolio, as shown below as of 2/2/2017:

Table of performance based on data from

(Based on the author's algorithms described above and data from

As can be seen, the results vary widely depending on which lookback is used and the day on which the rule was implemented.

The construction of the portfolio is then straightforward. There are three 6x14 tables for a total of 252 entries. Each entry, therefore, is 1/252th of the total portfolio. Note, however, that only a portion of the ETFs in the basket appear in the table. To find the respective allocations, add up the number of times each ETF appears in the tables and divide by 252. For the tables in the example above, the allocations are as follows:

(Based on the author's algorithms described above and data from

The author generally applies some subjective allocation rules to make trading and rebalancing easier and less expensive. For example, allocations smaller than 5% are moved to cash, and allocations are rounded down to the nearest 10 share increment. The following table shows the application of these rules to the allocations above on a $100,000 portfolio:

(Based on the author's algorithms described above and data from

One method of implementing this system would be to rebalance every 22 trading days, which is often commission free in most 401k accounts (e.g., like the author's TDAmeritrade account). Other rebalancing periods could be used including bi-weekly, monthly, or quarterly. One could even diversify across rebalancing periods, implementing, for example, 33% of their portfolio with a bi-weekly rebalancing, 33% with a monthly rebalancing, and 33% with a quarterly rebalancing. Of course, the more trading that is done, generally the higher one's trading costs.

The foregoing principles provide diversification across parameter measurement risk (lookback) and day-of-the-month risk. These principles could be applied to any rules-based asset allocation approach with the goal of maximizing diversification across all known risks.

Disclosure: I am/we are long DBC, GLD, HYG, IWD, IWM, IWN, REM, VTI.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.