The Standard and Poor’s (S&P) 500 index is a value-weighted stock index based on the market capitalizations of 500 large companies in the US. This index was introduced in 1957 and intended to be a representative sample of leading companies in leading industries within the US economy. Stocks in the index are chosen for market size, liquidity, and industry group representation. The S&P 500 index appeared as a result of the expansion of the Standard and Poor’s Composite index that was introduced in 1926 and consisted of only 90 stocks.

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This index is probably the most commonly followed equity index and many consider it one of the best representations of the US stock market. Many index funds attempt to replicate the performance of the S&P 500 index by holding the same stocks as the index, in the same proportions. The first example of such a fund was the Vanguard Group’s Vanguard 500 that appeared already in 1976. In addition to the index funds, there are exchange-traded funds (ETF) that also replicate the performance of the S&P 500 index.

Because of the widespread popularity of the S&P 500 index, low cost and ease of investing in the S&P 500 index fund, there are lots of studies that investigated the profitability of trend following rules in trading this index. Unfortunately, practically all of these studies used back-tests without correcting for the data-mining bias and ignored such an important market friction as transaction costs. The results of these studies gave birth to lots of myths about the superior performance of trend following trading strategies.

Two examples of such myths are as follows:

  • First, one can easily beat the market by using a trend following strategy.
  • Second, as compared to its passive counterpart, the trend following strategy has greater returns with lower risk. So there is no downside in implementing the trend following strategy.

In other words, you can have your cake and eat it too.

We, on the other hand, use a forward-testing methodology, account for realistic transaction costs, and comprehensively evaluate the profitability of various trend following rules in trading the S&P 500 index. The results of this study allow us to revisit the myths regarding the superior performance of the trend following rules in this well-known stock market and fully understand their advantages and disadvantages.

The Structure of Our Trend-Following Tests

In our tests we use the following 5 trend following rules: MOM, P-MA, MAC, MAE, and MACD. We estimate the profitability of each single rule and the combined rule (COMBI). In the combined rule, the performance of each single trading rule is evaluated in the in-sample segment of data; then the best trading rule is selected and its returns are simulated in the out-of-sample segment of data. See Part 6 of this blog series for the detailed description of the forward testing procedure.

Note that a practical realization of 4 out of 5 single rules requires choosing a particular moving average (SMA, LMA, EMA, etc). In addition, when a trading rule generates a Sell signal, there are two possible actions: either move to cash or sell short the stocks. Finally, because there are several alternative performance measures, the selection of the best trading strategy may depend on the choice of performance measure. To reduce the dimensionality of testing procedure, first of all we conduct a few minor studies to answer the following questions: Does the choice of performance measure influence the selection of the best trading strategy? Does the choice of moving average influence the performance of the best trading strategy? Is it sensible to consider the strategy with short sales?

The results of these studies allow us to make the following conclusions:

  • The short selling strategy is risky and does not pay off. Specifically, the performance of the short selling strategy is substantially worse than the performance of the corresponding strategy where the trader switches to cash (or stays invested in cash) after a Sell signal is generated. The reason for the poor performance of the short selling strategy is that a trend following rule identifies the direction of a trend with far from perfect accuracy;
  • From a practical point of view, the choice of performance measure does not influence the ranking of trading strategies. When the performance is measured using either daily or monthly returns, all performance measures produce virtually identical ranking of trading strategies. Therefore the Sharpe ratio, which has become the industry standard for measuring risk-adjusted performance, is superior to other performance measures from a practitioner’s point of view;
  • From a practical point of view, the choice of moving average does not have a crucial influence on the performance of trend following strategies. In particular, regardless of the choice of moving average, the performance of the best trading strategy remains virtually intact. In this regard, the SMA can be preferred as the simplest, best known and best understood moving average. Note that our analysis of the properties of ordinary moving averages (see Part 2 of this blog series) suggested that, theoretically, LMA and EMA might have some potential advantages over SMA. Unfortunately, in practical applications these advantages are not realized.

We remind the reader that, even though forward-tests are supposed to be purely objective tests that allow the trader to evaluate the true profitability of a trading rule, in reality the outcome of a forward test depends generally on the choice of a historical period and on the choice of split point between the in-sample and out-of-sample segment of data (see Part 6 of this blog series). This fact gives the possibility to manipulate the results of a forward test. In particular, the choice of the historical period and/or the split point can be a decisive factor that determines whether or not a trend following strategy outperforms its passive counterpart.

In our forward tests we use monthly data from January 1926 to December 2015; January 1950 is used as the split point between the in-sample and out-of-sample segment of data. Our choices are motivated by the following considerations. First, even though the data for the S&P Composite index can be extended back in time to 1800, the post-1926 data are more reliable than the pre-1926 data. Second, we identified the presence of a major structural break around year 1944 in the growth rate of the index. Therefore the historical profitability of trend following rules after the break can be used as a reliable indicator of their future profitability. Still, there are multiple choices to select the split point. Depending on the choice of the split point, the p-value of the outperformance test can vary from virtually 0% to almost 100%. However, our analysis reveals that for the majority of choices the p-value of the outperformance tests lies in between 15% and 25%. So using January 1950 as

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