iM-Best9(Russell 1000) – Large-Cap Portfolio Management System

This model invests in highly liquid large-cap stocks selected from those making up the Russell 1000 Index which represents the large-cap segment of the U.S. equity universe.  When adverse stock market conditions exist the model reduces the size of the stock holdings by 50% and buys the -1x leveraged ProShares Short S&P500 ETF (SH).

Using a web-based stock trading simulation platform with our ranking system, and periodically rebalancing the portfolio to hold 9 of the highest ranked stocks would have produced survivorship biased free average annual returns of about 53% from Jan-2000 to end of Nov-2013.  Over any 1-year period, starting at any day from Jan-2000 to Nov-2012, the return would never have been less than 14.7%.  The model is appropriately named Best9(Russell1000) and is hereinafter referred to as Best9.

(An alternative to reducing the size of the stock holdings and buying SH is to sell short SPY.  This would have produced an average annual return of about 58% as shown in Figures 9 & 10 in Appendix D.)

Ranking System and Trading Rules

Ranking System and Trading Rules are described in this article.  Additionally liquidity has been assured by stipulating that for a stock to be bought its average daily $-volume over the last 50 trading days must have been greater than $7-million.  The only sell rule is rank less than 97.

Figures 6 to 8 in Appendix C show comparison of performance when the following govern:

1. only the ranking system,
2. the ranking system and market timing in the buy-rules,
3. the ranking system, market timing, and when the model reduces the size of the stock holdings by 50% to buy SH, which occurred 8 times from 2000-2013.  (Note: The inception date of SH was June 19, 2006. Prior to this date values are “synthetic”, derived from the S&P 500.)

The model assumes stocks to be bought and sold at the next day’s opening price after weekly weekend rebalancing generates the signals for Monday.  Variable slippage accounting for brokerage fees and transaction slippage was taken into account.  Taxes were not considered.

The model was backtested from Jan-2-2000 onwards, as this was the first full year when the algorithm had access to all the required indicators.

 Performance

The trading performance of the system is shown in Figure 1 further down.  The annualized return from January 2000 to end of November 2013 was a high 53%;  $100 grew to about $37,000 over this period.  The maximum drawdown of 22% occurred early in October 2011.

Annualized returns for periods of 1 to 13 years were all higher than 32%, with the average being 52%; they are listed in Table 2 in Appendix A.

The model assumes an initial investment of $20,000 on Jan-2,2000.  It normally holds no more than 9 stocks.  To November 29, 2013 there were 1346 trades completed, 939 of these were winners and 407 losers as summarized in the tables below.  The amounts shown include transaction fees of $457,425 arising from slippage and brokerage commission.

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In above graph, the green line is the ratio of the Best9 to SPY, the general rising trend of that graph indicating that the Best9 continuously outperformed SPY over longer periods; to end of Nov-2013 it produced 235 times the value which one would have had from a Jan-2000 buy and hold investment in the SPY.  Note, that over shorter periods the model had sometimes underperformed relative to SPY, which is indicated by the segments of the green graph with negative slopes.

Annual Returns

Annual performance from January to December ranged from a maximum of 114% for 2009 to a minimum of 33% for 2011, as can be seen in Figure 2.

Rolling Annual Returns

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Figure 3 shows the 3-day average rolling 1-year returns starting each day from 2000 to 2012. There was never a loss over any 1-year period. The minimum return over 1 year was 14.7% and the maximum was 178%.  One can see that Best9 always outperformed SPY over a 12 months period, which is indicated by the golden graph never being below  the blue graph at any time.  For rolling 1-year returns starting every 3 months the Sharpe ratio was a reasonably high 1.9, indicating that the returns were of similar magnitude.

2-year Returns

Performance over 2 years from January to December ranged from a maximum of 346% from 2008-09 to a minimum of 79% from 2011-12, as can be seen in Figure 4.

Distribution of Monthly Returns

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Figure 5 shows the distribution of monthly returns.  There were a total of 167 months in the period under consideration. Best9 produced positive returns during 123 months and only 44 months of negative returns, as is evident from the chart above.  SPY had 73 months of negative returns.

Terminal Values

To simulate savings over time, terminal values were calculated to the end of May 2013 for annual hypothetical investments of $1. Starting with a dollar during each of the 13 years from 2000 to 2012, one would have invested a total of $13 cumulatively by the end. Summing the 13 terminal values, this strategy would have netted this dollar-per-year investor $875 at the end of 13 years.

Following a buy-and-hold strategy in SPY, one would have only $20.42, about 2.3% of what Best9 would have provided. Furthermore, the lowest annualized return, for any of the 13 time periods would have been 33% and the average for all the periods would have been 52%. This is shown in Table 1 and 2 in the Appendix A.

Correlation with other “Best” models

The correlation between Best9 with Best10 and Best8+ is a high 0.76 and 0.75, respectively, with 1.0 signifying 100% correlation.  Therefore the signals from Best9 would produce many stock duplications of the stocks selected by the other two models.

However, the correlation with Best(SPY-SH) is only 0.35.  Thus a combination of Best9 and Best(SPY-SH) should be advantageous.  This was tested with a combo of 70%Best9 and 30%Best(SPY-SH).   The combo showed an average annual returns of about 46% from Jan-2000 to end of Nov-2013 with a maximum draw-down of only -17%.  Also, over any 1-year period, starting at any day from Jan-2000 to Nov-2012, the return from the combo would never have been less than 20.5%.

Conclusion

As shown in Table 3 this portfolio management system made on average about 90 completed trades per year, resulting in an moderate average annual portfolio turnover of 825%.  This is equivalent to making 3 to 4 trades each week, not an unreasonable effort considering the good returns.

A simple ranking system with only 8 variables (which a sensitivity study showed to be very robust) is applied to the stock selection process.  This is this not a complex, high risk system with many parameters which could easily break down. Robustness is a function of the number of parameters in a model. It is well known that increasing the number of parameters in a model improves the goodness of the fit, but also makes the model less robust.  Simply put, the more rules a model has the more likely it is being curve fitted.  For example, the Akaike information criterion not only rewards goodness of fit (which would be maximum return in our case), but also includes a penalty that is an increasing function of the number of estimated parameters in a model.

The backtesting returns are not distorted by survivorship bias because the model uses a point-in-time database. Based on the past performance one could expect this model to continue to outperform in the future as well. However, please be aware that all performance results are hypothetical and the result of backtesting only. Out-of-sample performance may be much different.  We can make no claims about future performance of this signal, which may include significant potential for losses.

Appendix A

Appendix B

Risk Analysis

Note the risk measurements, particularly the reasonably low drawdown and high Sharpe- and Sortino Ratios.

Liquidity

 Table 3 in Appendix A shows the number of realized trades according to market capitalization.  One can see that over the last 5 years the model only bought stocks from large- and mid-cap companies.  The maximum portfolio size is dependent on the liquidity of the stocks in the model.  To calculate the maximum dollar-value of a portfolio without incurring too much slippage the following formula was recommended by P123:

($LiquidityBottom20Pct * #Position * 5%) / WeeklyTurnover%
where 5% is the maximum amount traded without affecting the stock price.

$LiquidityBottom20Pct = $ 12.8MM
#Positions = 9
Annual Turnover% = 825%
WeeklyTurnover% = 15.9%
Maximum Portfolio Size = ($12.8MM * 9 * 5%) / 15.9% = $36MM

Thus, this model could accommodate a good number of individual investors and  also professional fund managers.

 Appendix C

Note: All performance values are for an initial investment of $100,000 made on Jan-2-2000.

Fig. 6 –  Performance with only the Ranking System governing
(CAGR= 39.0% max DD= -60.0%)

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Fig. 7 – Performance with Ranking System + Market Timing Rules governing
(CAGR= 45.5%  max DD= -22.4%)

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Fig. 8 – Performance with Ranking System + Market Timing Rules + 50% SH governing
(CAGR=53.1%  max DD= -22.4%)

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The vertical shaded stripes indicate when the model reduced the size of the stock holdings by 50% to buy SH, which occurred 8 times from 2000-2013.

 Appendix D

Note: All performance values are for an initial investment of $100,000 made on Jan-2-2000.

Performance with Ranking System + Market Timing Rules + 100% short SPY
(CAGR=58.1%  max DD= -22.4%)

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