Using a third party small-cap model from the web-based trading simulation platform in combination with our iM-Best(SPY-SH), we demonstrate the benefits of combining this model with iM-Best(SPY-SH), these include a reduced volatility, constant positive rolling returns, and high annualized returns with low drawdowns. The model was chosen because its algorithm does not include market-timing, and also because it holds 50 stocks, has a low annual turnover, and should be able to support a relatively high total portfolio size of $3.5-million on its own.
It is interesting that this combination of a small/micro-cap and iM-Best(SPY-SH) model would have produced virtually the identical return as the large-cap Combo5, not only from inception, but also over different time periods as shown in the table below.
Combo Mode Performance
The component models and their percentage weights in the combination are listed below:
- 50% Best(SPY-SH): Switches between SPY and SH.
- 50% Keating’s 50 stk low turnover 50-350m: Holds small- and micro-cap stocks
This combination model is always trading long, and has a low average annual turnover of about 350%.
The combination, Combo2, would have produced, an annualized return of 33.6% with a maximum drawdown of only -18% as shown in Figure 1. The in-between-recession segments of the ratio graph Combo2 to SPY have a fairly constant upward slope, indicating that Combo2 out-performed SPY most of the time.
Had one left out the iM-Best(SPY-SH), then the annualized return for the Keating model alone would have been 35.3% with a maximum drawdown of -47.7%, as shown in Figure 1a. This is almost the same as Combo2’s return, but with a much worse drawdown. However, the ratio graph Keating to SPY shows the undesirable erratic performance of the Keating model relative to SPY without the stabilizing effect of iM-Best(SPY-SH).
Figure 2 shows the annual returns for Combo2. Note that all returns were positive, which is not the case when iM-Best(SPY-SH) is omitted, as can be seen in Figure 2.a.
Figure 3 shows the rolling 1-year returns for Combo2, starting each trading day from 2000 to 2012. The lowest return was +3.6%. The rolling returns were always greater than for SPY, except for one week in March 2010. For rolling 1-year returns starting every 3 months the Sharpe ratio was a reasonably high 2.3, indicating that the returns were of similar magnitude.
Without iM-Best(SPY-SH) and in the combination, then as shown in Figure 3a, the lowest rolling return would have been a very low -39.0%. One can see that the negative rolling returns lasted for more than a year from the middle of 2008 onward, and there was another period in 2011-12 when the minimum was about -10%, with the Keating model under-performing SPY.
The correlation between the two models was calculated to be zero. From a portfolio construction standpoint, the combination should be more robust than any single system on its own.
Note that the risk measurements for the combination are better than for any of the individual models, indicating that the combination should be more robust than any single system on its own. Particularly the reasonably low drawdown and higher Sharpe- and Sortino Ratios for the combination are noteworthy.
Performance Statistics from 1/2/2000 to 10/25/2013
Distribution of Monthly Returns from 1/2/2000 to 10/31/2013
There were a total of 166 months in the period under consideration. Combo2 produced positive returns during 125 months and only 41 months of negative returns, as is evident from the chart above.
(click to enlarge)
The maximum portfolio size is dependent on the liquidity of the stocks and ETFs in the model. The ETFs have huge liquidity and will not place a constraint on portfolio size. To calculate the maximum size a portfolio can handle without incurring too much slippage the following formula is recommended:
($LiquidityBottom20Pct * #Position * 5%) / WeeklyTurnover%
where 5% is the maximum amount traded without affecting the stock price.
The Keating model has the lowest liquidity of the bottom 20 Pct, and is thus the critical model in the combination. It represents 50% of the total portfolio.
$LiquidityBottom20Pct = $0.07MM
#Positions = 50
Annual Turnover% = 257%
WeeklyTurnover% = 4.9%
Max Port Size for Keating model= ($0.07MM * 50 * 5%) / 4.9% = $3.5MM
Maximum Portfolio Size Combo2= $3.5MM / 0.5= $7.0MM.
Thus, this combination model could accommodate 20 investors with a $350,000 portfolio each, and $175,000 allocated to each component model.