Linear fitting and trend trading
Vladimir Daragan, STTA Consulting Inc.

Let us shortly consider using linear fitting curves for trading trends. The idea is very simple. Let P(i) are the closing prices. Using N points

P(i) (points A or B on the figure)
P(i-1)
P((i-2)
...
P(i-N+1)

one draw the fitting line as it is shown on the figure. If the slope of the line is positive (green on the figure) one can say that the trend is positive within N day frame. If the slope of the line is negative (red on the figure) one can say that the trend is negative within N day frame.

One can hold stock (or index shares) as long as the trend is positive and start selling short when the trend turns negative. Using N > 4 one can expect that this method will eliminate price fluctuations and reduce the number of the false buy/sell signals.

We have performed computer analysis of the historical prices of the Dow Jones Industrial Average (DJIA) for the period from 1900 to 2001. Next figure shows the results of trading the Dow Jones index for the period from 1901 to 2001 for various periods of MA (from 20 to 200 days). We showed the relative capital growth: trading capital after 101 year trading using MA divided to the investing capital, i.e. after using buy and hold strategy. It was supposed that initial capital was equal to $10,000 and the brokerage commissions = $10. We assumed that a trader was not able to buy and sell exactly at closing prices. The bid-ask spread slippage was equal to 0.1% for our calculations.

One can see that for very short N (4 - 6 days) the results of using this strategy is much better than the result of the buy and hold strategy. For long periods (from 90 to 150 days) the results are also very good. However, we would not make any conclusion at this time. One should check the stability of any strategy for various periods.

We have calculated the relative capital growth using described strategies for the period form 1975 to 2001. The results are presented on the next figure. One can see that the results of using this strategy are much worse than the result of the buy and hold strategy. It is similar to using the moving average strategies. This period of time was very bad for using these strategies.

Conclusion: Using linear fitting lines for trend trading is very unstable. We would not recommend these strategies to trade index shares.