Mathematical Investment Decisions, Inc.

Sector Rotation Scientifically Applied

Sector rotation is a complex process with many aspects to consider, but, properly applied, it can yield superior investment results.

Some of these aspects are:

  1. What population of assets will be rotated?
  2. How is the population to be culled for suitable candidates?
  3. How will assets be ranked?
  4. How many assets will be traded at one time?
  5. How will money be initially allocated and how will it be reallocated in response to changing conditions?
  6. What is the overall strategy?
    a)                  Long only or long and short?
    b)                  Always in the market or sometimes in alternative investments
                (strategic overlays)?
    c)                  Hedged (market neutral) to control risk?

We will consider these questions in order, and discuss Mathematical Investment Decisions’ approach to each one.

  1. What population of assets will be rotated?

We have considered a number of different asset populations, including sectors of the U.S. market, particularly those sectors that correspond to ETF’s, country ETFs, and managed Small-Cap, Mid-Cap and Large-Cap funds.

We have also considered cash and bonds as alternative investments under a variety of strategies.

  1. How is the population to be culled for suitable candidates?

One important criterion is that the cross correlations of assets traded should be as low as reasonably possible.  We set up a cross correlation matrix, and use it to eliminate assets that we view as too highly correlated to the other assets.  This process is not exact or mechanical, but relies on judgment, and needs to be redone every few months.

We put our cross correlations in a spreadsheet like the one shown below.  That spread sheet shows cross correlations for 16 domestic ETFs that we wished to sector rotate.  The cross correlations that exceed 0.7 are highlighted in yellow.  Some of the ETF sectors have correlations of 0.8 or 0.9 with a number of the others; and therefore, they do not provide true diversification.


Figure 1

The information illustrated above was used to reduce the population of domestic ETFs to 11 sector ETFs, which are:

Assets also need to be liquid and free of restrictions that make practical trading difficult. In another case, we wished to rotate a population of Small-Cap funds.  These had to be culled to make sure that:

a)      They were large enough to accept the funds we wished to place
b)      They were open to new investments
c)      They were no load funds
d)      The funds did not have unreasonable rules related to entry and exit.

  1. How will assets be ranked?

Mathematical Investment Decisions uses a number of statistical tools.  One of the tools computes a rate of return by using a moving regression line (as illustrated in Figure 2).


Figure 2

The look back periods considered are 1, 2, and 3 months, and 6 weeks.  The slope of the moving regression of prices is divided by the beginning values in order to make the result price independent.

Figure 3 below illustrates this process.  The top frame shows moving quarterly rates of change for closing prices of stocks (red) and bonds (blue).  The bottom frame shows the same prices and the moving slope rate of change over the same time window.

The extra smoothness gives stability to scoring methods, and avoids short-term whiplash. 


Figure 3

Figure 4 is a comparison of results we obtained using this method of ranking, versus similar results obtained by a well known sector rotation fund (named here as the “Rotator Cuff” Fund). The latter uses ordinary rates of change whereas MathInvest uses our own moving slope rate of change ranking method.


Figure 4

We also use a variety of risk adjustment methods in our scoring, including a ‘moving Sortino Ratio’ that we have developed, as well as the usual statistical methods that employ standard deviation.

  1. How many assets will be traded at one time?

We find that trading just one or two assets produces more volatility than we desire, although it sometimes produces exceptional returns.  Also, the fall off in returns becomes significant when we trade more than about one-third to one-sixth of the total, depending on the assets and their number.

  1. How will money be initially allocated and how will it be reallocated in response to changing conditions?

There are many possible regimes to be investigated here, and we have pursued most of them.

  1. Money is allocated equally in a fixed number of accounts (first-place, second-place, etc.), and these accounts are assigned to the best scoring assets at each point.  Monies are never subsequently redistributed equally to the other accounts.  That is, you do not reallocate the funds, although the assigned assets may change.
  2. You proceed initially as in 1, but whenever the list of currently traded assets changes, you redistribute the money equally among the new assets.
  3. You can proceed as in 1 or 2, but have an unequal distribution of funds, allocating greater percentages to the higher ranking assets.
  4. You can insist on rebalancing the accounts each day, or each time you initiate trades.

       An example of results obtained with these strategies.

Below we illustrate the type of returns that can be achieved with the methods discussed above.  Figure 5 shows the results of trading the 11 ETF sectors discussed above from 1990 to present.  We scored the assets with moving slope rate of return, and traded the top four scorers at all times.  We initially allocated funds equally to the top scorers, and rebalanced the allocations to be equal whenever the assets being traded changed. 

For comparison we show the S&P 500 during that time, and the result of a constantly compounded 10% rate (a target for many companies with pension fund obligations).


Figure 5

  1. What is the overall strategy?

a)      Long only or long and short?

Our primary strategies are long only, although on occasion we will implement a hedging strategy by going short futures.

b)      Always in the market or sometimes in alternative investments
            (strategic overlays)?

By a Strategic Overlay we mean an overriding market indicator that will tell us whether we should be in equities or in an alternative investment – usually bonds.  Some of the possible uses of such an indicator are:

        I.      Based on a strategic overlay, we will either be fully in equities, rotating our chosen assets, or fully in the alternative investment – usually bonds.

     II.      Based on a strategic overlay, and the current behavior of stocks and bonds, we will be fully in equities, rotating our chosen assets, fully in bonds, or fully in cash or treasury bills (if stocks and bonds are both in decline).

   III.      The equity regime will be altered to include cash assets, which will be scored along with the stocks.  If we are planning to trade the top five assets, then an equal number of cash assets will be included with the stock assets and all will be scored in the usual way.  At any time, the top five scorers might consist of four stocks and one cash asset, putting us 20% in cash.  Similarly any number from two to five could be cash, the latter putting us completely in cash for that time period.  We change the alternative investment similarly, scoring (say) bonds and cash.  Finally, we use the strategic overlay to switch between these two regimes.  These things are illustrated schematically in Figure 6.

 


Figure 6

Figure 7 shows charts of the S & P and treasuries.  These charts illustrate why they are frequently good alternative investments.  Our basic strategic overlay follows the “Fed Model” of competition between bond yields and stock yields for investment dollars, and is a based on moving correlations of those two markets.


Figure 7

Other strategic overlay models are possible as well, and may be more useful in certain situations.  Among the possibilities are.

a)      Use moving correlations of leading-to-lagging indicators.  Positive correlations over the look back period will favor equities, and negative ones will favor the alternative.

b)      Use moving correlations of equal weighted to cap weighted S&P.  Take positive correlations to be favorable to equities and negative ones to be favorable to the alternative investment.

A more complete description of these alternative overlays, complete with graphs, is given in the appendix.

In Figure 8 below we show the result of applying our simple stock vs. bond moving correlation overlay strategy.  Here we are either long S&P (no rotation between sectors) or in bonds.  The result of this investment strategy is shown in green.


Figure 8

One important test of a good Strategic Overlay is its affect on drawdowns.  The strategy shown above slightly outperforms the market, but has far superior drawdown behavior.  One possible consequence of this is that the strategy could be levered without sustaining unacceptable risk.  That is, a leveraged investment using only the strategic overlay has less risk than the S&P unleveraged.  The result is shown below in Figure 9.


Figure 9

The best results are obtained when rotation methods and overlays are combined.  Results of rotating the 11 ETFs previously described, and trading the top 3, combined with our basic strategic overlay, are shown in figure 10.

:
Figure 10

The comparison between results of these ETFs with and without strategic overlay can be seen by comparing figures 5 and 10.  Similar results can be produced from international ETF’s, as shown in Figure 11


Figure 11

You can also use these techniques with actively managed funds, as shown below in figures 12, 13, and 14.


Figure 12

 


Figure 13

Text Box: 1 20
Figure 14

In addition, we can combine these techniques with more traditional methods of diversification of risk.  Illustrated below, in Figure 15, is the result of keeping funds arranged 60% in stocks and 40% in bonds, while rotating both sectors.


Figure 15

c)    Hedged (market neutral) to control risk?

Another way of reducing risk, while staying in the market at all times is through the use of hedging strategies.  One of our programs rotates over 100 Small-Cap managed funds, and trades the top 6 by the methods previously outlined.

The results are shown in Figure 16.  Also shown are the results of hedging this investment by buying a 2.5 times levered inverse Russell 2000 fund and dividing resources in various proportions.  This has the advantage of never being short, for those who cannot or do not wish to take such positions.  The disadvantage is that about 28% of the assets are diverted from the main investment, but drawdowns are significantly reduced.  The percentage in the hedge is fixed throughout the investment.


Figure 16

A much more efficient way to hedge is by selling Russell 2000 futures.  This is more or less equivalent with using an inverse fund with (at least) a 10 to 1 ratio.  The result of using a full hedge acquired in this way is shown in Figure 17.


Figure 17

Another way to hedge is to adjust the hedge based on a strategic overlay (the same basic one we used before).  In Figure 18 we show that result, with varying percentages of hedge coverage.  Whenever the overlay indicates caution in the equities markets, the labeled percentage of both initial capital and profits is hedged.  Whereas, when the caution warning is removed, the hedge remains unadjusted to let subsequent profits accumulate without being hedged. 


Figure 18

With a given set of assets comes a statistical history that may favor one choice over another in the allocation regime.  Typically Mathematical Investment Decisions will perform hundreds or thousands of automated computer runs, experimenting with different scoring periods, number of traded assets, and risk reduction strategies.  Our main principles are these:

1.      Every run must involve a long enough period (typically 10 to 20 years) to include bull, bear, and neutral markets, and a wide variety of economic conditions.  Scoring, risk reduction methods, and traded asset numbers are always kept fixed throughout the entire run to ensure that no curve fitting or use of improper information is permitted.

2.      The best resulting combinations are set aside for further examination.  If a run produces a superior result, many additional and similar runs are made, each modifying one or more of the factors of the run in a small way.  The results should be similar to the optimal result in their general shape and nature, and differ in returns and drawdowns by no more than a modest amount.  This ensures that results are statistically stable and avoids historical aberrations that would not be likely to persist.

3.      No results are accepted unless Monte Carlo simulations with random choices of assets conclude that the probability that given results could have been produced randomly is less than 1 in 500.

 


Appendix - Strategic Overlays

A strategic overlay is a tool or model for deciding whether you are safe to pursue your specific investment tactics, or should you adopt defensive positions.  For example, if your investment program is essentially a “long” investment in equities that would suffer if equities as a whole were to decline, a good strategic overlay would define overall bullish periods for the equities markets. 

If not equities, then what?  That is, should your strategic overlay raise the caution flag on the equities markets, you must have alternative places to employ your capital.  These could be a variety of other investments, but the more common ones are cash (i.e. the money market), or U.S. Treasury notes and bonds.  Note that the Treasury market really did not become active until 1970, before which the most common alternative to equities was corporate bonds.  However with the full development of the Treasury markets, corporate bonds have gradually grown too highly correlated to equities to be of much use as a diversion or diversification. 

A strategic overlay is not limited to guiding your other investments, but can be used as an investment model by itself.  In fact one of the most useful ways of illustrating an overlay is to test its performance by trading surrogates for your various investment choices in the form of ETFs or index funds.  Such is essentially a sector rotation program in which the sectors are “supersectors” of indices of equities, treasuries, cash, gold or whatever. 

MathInvest has constructed a variety of strategic overlays, all of which work well.  Interestingly, they can be derived from “fundamental” data, “technical” data, or from a statistical combination of both.  Let us give you examples of the variety:

Fundamental Models

The U.S. Department of Commerce has identified various indicators of the economy and characterized them as leading, coincident and lagging indicators.  Around the end of each month, they release this data, and most of the attention is focused on the “Index of Leading Economic Indicators”.  MathInvest takes the Commerce Department’s data and from their components builds a Leading/Lagging indicator, whose effect is illustrated in below in Figure A1:


Figure A1

The bottom panel demonstrates when the Leading Indicator is positively correlated to the Lagging Indicator (the blue dots), and negatively correlated (red line).  Corresponding periods are illustrated in the chart of the S&P 500 Index in the top panel.  As is evident, the blue periods are generally bullish periods for the stock market.  Fundamental models are disadvantaged by the infrequency of data, and the fact that data is often revised.  In this case, we are relying on data issued monthly.

Technical Models

Market-based or technical data can also be used to create a strategic overlay.  For example, here we illustrate the relationship between the correlation of equally-weighted S&P 500 Index and the standard (capitalization-weighted) version of same.  The highly correlated (or bullish) periods of Figure A2 are in blue, and the less-correlated (cautionary) periods are in orange. 


Figure A2

Technical models make the assumption that players in the market have some inkling as to a change in fundamentals and act upon that inkling.  However, market-based data is available daily in most cases, and is rarely revised. 

Statistical Models

It is also possible to use quantitative analysis to turn more-frequent (than fundamental) data into statistical forecasts.  The so-called “Fed Model” computes forecasted stock yields from earnings forecasts and current market prices, and then relates those expected yields to current yields exhibited by the Treasury markets.  Effectively the Fed Model ranks stock and Treasury yields as competitors and chooses the best competitor.  MathInvest’s standard strategic overlay operates in a similar fashion (see Figure A3).


Figure A3

MathInvest has also created a “Payroll Tax Model” that uses payroll withholding figures released daily by the U.S. Department of the Treasury as a surrogate for U.S. growth.  Since the U.S. economy is dominated by service-sector jobs, taxes paid by those jobholders are a better indicator of activity than the month-delayed weekly unemployment numbers which dominate the media and political landscape.  The Payroll Tax model thus serves as a further check on the accuracy of our standard strategic overlay.