SPX Monthly Returns And Tail Risk

I had some time yesterday while waiting for an appointment, and re-read "A Comparison of Tail Risk Protection Strategies in the U.S. Market".  One particular sentence in the paper caught my attention:

"Remarkably, of the 24 months with greater than 5% loss in the S&P 500 between March 1990 and March 2011, 17 of them (or 71%) occurred with the S&P 500 below its 10-month moving average.7"

The footnote associated with this sentence stated:

"The ten-month or 200-day moving average is a popular technical indicator among market participants; its effectiveness in asset class timing is documented by Faber (2005)"

I ran the same study in AmiBroker and Excel using the monthly closing prices of the SPX.  I calculated the 10 month moving average of SPX closing prices, and compared this value with the closing value of the first day of the next month.  For example, on March 1 1990, the closing price was 332.74, and the 10 month average of monthly closing prices was 338.59 (May 1989 through Feb 1990).  In this situation, March 1990 started below it's 10 month moving average.

Looking at the same period of time as the Tail Risk Article (March 1990 - March 2011; 253 months), I found the following:

• 70 of 253 months started below the 10 month moving average (28%)
• 183 of 253 months started above the 10 month moving average (72%)
• 25 of 253 months experienced a loss of 5% or more
• 16 of these 25 months occurred when the month started below the 10 month moving average (64%)

There were a few other points to note regarding winning and losing months:

• 103 of 253 months were losing months (41%)
• 36 of these 103 losing months occurred when the month started below the 10 month moving average (35%)
• 150 of 253 months were winning months (59%)
• 34 of these 150 winning months occurred when the month started below the 10 month moving average (23%)
• 29 of these 150 winning months had monthly returns of greater than 5% (19%)
• 14 of these 29 occurred when the month started below the 10 month moving average (48%)

A few takeaways:

• A greater percentage of the 5%+ monthly losses occurred when a month stated below the 10 month moving average
• A month starting below the 10 month moving average is not a good indicator of whether the month will end with any loss ... the SPX has a positive bias
• A month starting above the 10 month moving average is a good indicator of whether the month will end as a win (77%)
• The numbers are similar when the range is expanded through March 2017

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