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Trend following has its supporters and detractors. Here is one view into the data that may be helpful in establishing context for the debate regarding the persistence and utility of trends.

R^{2} (the coefficient of determination) is a measure of the proportion of variability in a data set that is accounted for by a statistical model. It provides a metric of how well future outcomes are likely to be predicted by the model. A value of 1 means the data fits the model perfectly and at a value of zero the model offers no explanation of the data.

For this example we have taken the SP 500 daily adjusted closing price from 1955 to 2012 and calculated the first derivative (trend) of an arbitrary 150 day moving average. We then look at the future returns (150 day) and calculate the R^{2} value between those two data sets. If the value is high it implies that the trend is highly correlated with those future returns, if it is low then it isn't. Below is the graph of the results of that exercise.

The solid line is the actual rolling daily value of R^{2} of the data. The green line is a simple 1 year moving average of the R^{2} value for clarity. The dashed line is a 5th order polynomial best fit to the data. The data shows strong predictive periods and weak predictive periods. The variability of R^{2} over time may explain why there is such disagreement over the effectiveness of a trend following indicator.

What jumps out is the recent and dramatic rise in the R^{2} value. How long this relationship will be sustained is unknown. It may point to the influence of an increasingly correlated world entering and exiting a major correction, wide investor access to the same market data, behavioral trading, or the interconnectedness of it all.

So what happens if you actually apply such a metric? The math of looking at the first derivative of a moving average to establish a trend metric and applying it can be a bit tedious, but there is a web app that does it automatically for any stock, mutual fund, ETF or index: www.InvestEngines.com.

Below are the results from that site for the SP 500 going back to 1950. The first chart below shows the adjusted price of the SP 500 (green line) and the effective price of the SP if you had simply gone to cash when indicated by the metric (blue line). During the relatively stable broadly rising period from 1950 to 2000 there was little benefit to applying a trend following metric such as this. But the last 10 plus years depict a very different period, both in terms of the performance of the SP and the benefit of using a trend following metric to protect the downside.

The next chart taken from the web site shows the detailed data for the SP 500 and compares the buy and hold performance relative to applying the trend following metric. Over the long run this type of metric acts as an insurance policy against major negative corrections by reducing the max drawdown. The price paid is the trading activity, false positives and missed potential upside. This data is shown in the table below. It indicates that there was less than one round trip per year on average. Max drawdown was significantly reduced and most of the potential benefit has been from activity over the past 10 years. The metric has been green (positive) without change since October of 2011. The values shown do not take into account trading costs or tax implications.

Trend following as an indicator begs for further study. But it may represent a helpful tool to protect on the downside, especially now, if current market imbalances correct at some point.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

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## Trend Following May Have Its Time 0 comments

Trend following has its supporters and detractors. Here is one view into the data that may be helpful in establishing context for the debate regarding the persistence and utility of trends.

R

^{2}(the coefficient of determination) is a measure of the proportion of variability in a data set that is accounted for by a statistical model. It provides a metric of how well future outcomes are likely to be predicted by the model. A value of 1 means the data fits the model perfectly and at a value of zero the model offers no explanation of the data.For this example we have taken the SP 500 daily adjusted closing price from 1955 to 2012 and calculated the first derivative (trend) of an arbitrary 150 day moving average. We then look at the future returns (150 day) and calculate the R

^{2}value between those two data sets. If the value is high it implies that the trend is highly correlated with those future returns, if it is low then it isn't. Below is the graph of the results of that exercise.The solid line is the actual rolling daily value of R

^{2}of the data. The green line is a simple 1 year moving average of the R^{2}value for clarity. The dashed line is a 5th order polynomial best fit to the data. The data shows strong predictive periods and weak predictive periods. The variability of R^{2}over time may explain why there is such disagreement over the effectiveness of a trend following indicator.What jumps out is the recent and dramatic rise in the R

^{2}value. How long this relationship will be sustained is unknown. It may point to the influence of an increasingly correlated world entering and exiting a major correction, wide investor access to the same market data, behavioral trading, or the interconnectedness of it all.So what happens if you actually apply such a metric? The math of looking at the first derivative of a moving average to establish a trend metric and applying it can be a bit tedious, but there is a web app that does it automatically for any stock, mutual fund, ETF or index: www.InvestEngines.com.

Below are the results from that site for the SP 500 going back to 1950. The first chart below shows the adjusted price of the SP 500 (green line) and the effective price of the SP if you had simply gone to cash when indicated by the metric (blue line). During the relatively stable broadly rising period from 1950 to 2000 there was little benefit to applying a trend following metric such as this. But the last 10 plus years depict a very different period, both in terms of the performance of the SP and the benefit of using a trend following metric to protect the downside.

The next chart taken from the web site shows the detailed data for the SP 500 and compares the buy and hold performance relative to applying the trend following metric. Over the long run this type of metric acts as an insurance policy against major negative corrections by reducing the max drawdown. The price paid is the trading activity, false positives and missed potential upside. This data is shown in the table below. It indicates that there was less than one round trip per year on average. Max drawdown was significantly reduced and most of the potential benefit has been from activity over the past 10 years. The metric has been green (positive) without change since October of 2011. The values shown do not take into account trading costs or tax implications.

Trend following as an indicator begs for further study. But it may represent a helpful tool to protect on the downside, especially now, if current market imbalances correct at some point.

Disclosure:I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.Instablogsare blogs which are instantly set up and networked within the Seeking Alpha community. Instablog posts are not selected, edited or screened by Seeking Alpha editors, in contrast to contributors' articles.## Share this Instablog with a colleague

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