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Future stock market returns are difficult to forecast. That hasn't stopped some high-profile analysts from predicting for some time now a very low return environment for stocks, incorrectly, at least thus far. Investors interested in better returns than predicted can possibly improve performance by managing their own stock portfolio with stock trading systems and asset-allocation/timing models.

The period from January 1999 to September 2012 can be classified as a low stock return environment. The S&P 500 with dividends reinvested provided a low nominal average return of 2.9% per annum, similar to the 1.5% real returns predicted for the next 15 years. My investigation showed that despite the stock market's poor performance over the last 14 years it would have been possible to achieve much higher returns over this period by investing following the signals from stock trading and asset-allocation/timing models.

**The stock trading system**

For my investigation I selected a model from a web-based stock trading system which according to the performance results on the web-site had produced an average annual return of 28.4% from January 1999 to September 2012. Here is a summary of how the system works.

Initially a "universe" is chosen from which stocks can be selected. Then a ranking system has to be specified based on fundamental and technical parameters likely to produce the best equity returns. The ranking system then assigns rank numbers from low to high to all stocks in the universe and groups the stocks according to rank.

The next step is to define the model's rules, such as:

- Rebalancing frequency, trading costs, and slippage losses of the stock price between the time of the signal and the time of execution.
- The approximate number of stock positions in the portfolio.
- Buy and sell rules which incorporate the stock ranks.
- The start- and end-dates for the simulation, and out-of-stock-market periods.

The system then generates a list of stocks to start the investment with and continues to give periodic information on rebalancing the holdings, eliminating stocks which no longer meet the required standards, and replacing them with stocks that conform to the buy rules of the model.

To better reflect slippage when trading stocks of small-capitalization companies which this model concentrated on, I assumed more realistic slippage losses of 1.0% instead of 0.5% which the original model used. My results for this amended model (referred to as model A from here onwards) confirmed that trading returns were normally better than from buy-and-hold, but there were extended periods when this was not always the case. Additional limitations of the trading system are discussed in appendix A.

**Performance**

For model A the holdings were rebalanced weekly and a $8.00 commission per trade together with a slippage rate of 1.0% of each trade amount was applied. Model A provided a compound annual growth rate (CAGR) of 18.5% from January 2, 1999 to September 25, 2012 with dividends reinvested, which is significantly better than the low 2.9% CAGR of the S&P for the same period, as measured by the ETF SPY, also with dividends reinvested. An initial amount of $100,000 would have grown to $1,035,000 over 13.75 years as shown in figure 1.

The effect of 1% slippage is reflected by the lower average annual return for model A, about 10% less than the original model's return which assumed a 0.5% slippage rate.

The Value/SPY ratio shows that an initial investment made in January of 1999 would have been about 7 times greater by September 2012 than that obtained from a buy-and-hold strategy of the SPY. For the periods 1999-2001 and 2006-2012 the ratio remained more or less constant, indicating that the model's performance over these periods was not better than that of SPY - the period from 2001 to 2006 producing all the excess returns as reflected by the upward slope of the ratio graph over this time-span.

Although the performance appears satisfactory now, one would have been greatly distressed when the portfolio lost more than 60% of its value during the great recession from October 2007 to March 2009, more than the S&P's drawdown at the time. However, drawdowns can be significantly reduced by applying the buy- and sell signals from the IBH stock market timing model, and exiting and entering the stock market accordingly, as shown in figure 2. This would have reduced the maximum drawdown to 18.7%, and increased the CAGR to 21.5% from the previous simulation's 18.5% growth rate. The periods when the investment was in cash are indicated by the horizontal sections of the Value graph between the vertical sell and buy signal lines.

The Value/SPY ratio indicates that an initial investment made in January of 1999 would have been about 10 times greater by September 2012 than what buy-and-hold of SPY would have provided. Also one can see from the approximately constant level of this ratio prevailing over the periods 1999-2001, 2006-2007 and 2010-2012 that performance was not better during those time-spans than that of SPY.

Returns can be increased by placing the portfolio's funds, when not in the stock market, into treasury bond funds selected according to the signals from the BVR model. The BVR model provides information as to whether funds should go into high-beta bond funds or a low-beta funds depending on bond market direction. For the low-beta funds I used the ETF MBB which tracks mortgage backed securities, and for the high-beta funds the 20+ Year Treasury Bond ETF TLT. (Before inception of these ETFs I used mutual funds VUSTX and VFIIX for the high-beta bond funds and low-beta funds, respectively.)

Figure 3 shows the Bond-Value-Ratio (BVR) with the stock market buy- and sell signals from the IBH model superimposed. One can see that the sell signals from IBH coincided with up-bond-markets when funds are placed into high-beta Treasury bond funds until an upper switch point is reached, after which they go into low-beta bond funds, and so on, until a buy signal from the IBH model appears, whereupon the funds are transferred back to the stock market and managed according to model A's rules.

The performance with funds invested in the bond market when not in the stock market is shown in figure 4 below. The CAGR is now 29.6% and the maximum drawdown remained at a low 18.7%. An initial investment amount of $100,000 would have grown to $3,520,000 over 13.75 years, 24 times as much than what one would have had from a buy-and-hold investment of SPY over this period.

It is apparent that performance was significantly increased by the returns from the bond market which are listed in the table below.

**Conclusion**

Stock trading systems should increase investment returns if the model is well designed and the assumed slippage rate reasonably reflects slippage from actual trading conditions. Performance from trading systems is not immune to extreme drawdowns. Drawdowns can possibly be minimized by exiting and entering the stock market following the signals from an effective market timing model. Further improvements to return could be achieved by investing in the bond market during periods when the timing model avoids stocks, provided bonds are reasonably priced.

**Appendix A**

Stock trading systems have limitations and do not always improve on buy-and-hold. The slippage rate and rebalance frequency have a significant influence on performance. Other limitations are portfolio size and the possible under-performance of the system relative to buy-and-hold over periods which were in some instances longer than 3 years for model A. (Under-performance does not necessarily indicate that the portfolio lost money, it means it did less well than buy-and-hold of SPY.)

**Slippage rate and rebalance frequency**

There was quite a big variation in the daily prices for the type of stocks that the model selected to buy or sell. I found that for a representative number of stocks the daily high and low prices varied from the opening price by 2.4% on average. Assuming that one wanted to buy a large number of shares at the opening price, then one would probably not be able to do this without driving the price higher, and vice versa, one would drive the price lower if one wanted to sell a large number of shares.

In my simulations I assumed a slippage rate of 1.0% of the trade amount and a rebalance frequency of one week. Model A would have performed better had it been rebalanced every two weeks instead of once a week as is evident from the table below. The table shows the effect of slippage and rebalance frequency on the performance of this model. It is apparent that as slippage rate increases, rebalance frequency should be decreased for optimal performance.

**Portfolio size could limit performance**

At the end of September 2012 the model A stock portfolio had a value of $3,519,910 (see figure 4) allocated as follows:

I found that in some instances the required number of shares to be bought or sold according to the model's requirements exceeded the actual daily trading volume for the particular stocks. In one particular case it would have taken 4 days to sell all the shares and one would have realized only about 99% of the price which the model used. This would also have delayed buying the replacement stocks which were trading at the later date about 5% higher than what the model assumed. Thus the average slippage rate would have been about 3% for those two transactions. This may be an extreme example, but it is impossible to check all of the 2,800 trades which this model made from 1999 to 2012.

Therefore, one has to be conservative in the assumption of the slippage rate for calculating the performance for the model. One could possibly apply a lower slippage rate for low value portfolios and increase the rate as the investment's value becomes bigger to simulate performance more realistically. Trading systems should work reasonably well for smaller portfolios with low slippage rates, but bigger portfolios with a high proportion of micro-cap and small-cap stocks could be handicapped by the inefficiencies of having to trade a large number of illiquid stocks.

**The trading system can under-perform the S&P**

One should not immediately expect a superior performance from stock trading systems. A detailed analysis showed that for some shorter periods model A produced lower returns than SPY. However, after 40 months the returns from model A were always better than the returns from SPY as is apparent from the table below.

For example, when comparing the performance of the trading system relative to buy-and-hold over a 12-month period, the minimum difference between the percentage value change over 12 months for model A and the percentage value change of SPY over the same period was -28.9% (model A performance worse than SPY), the maximum difference over 12 months was 129.5% (model A performance better than SPY), and the chance that model A would under-perform SPY over a year at any point in time is a relatively high 19.2%.

When using the IBH macro signals to exit and enter the stock market one can shorten the length of the period of possible under-performance by the model relative to buy-and-hold of SPY and also reduce the probability of under-performing SPY as is shown in the table below.

*Georg Vrba is a professional engineer who has been a consulting engineer for many years. In his opinion, mathematical models provide better guidance to market direction than financial "experts." He has developed financial models for the stock market, the bond market and the yield curve, all published in Advisor Perspectives. The models are updated weekly. If you are interested to receive theses updates at no cost send email request to vrba@snet.net.*

*Past performance is no guarantee of future returns or that the models referred to in this article will be profitable at all. The opinions stated here could be wrong due to false signals generated by the models, or that the models were incorrectly structured and/or interpreted.*