Fibonacci Levels and a Silver Lining for Stocks

Assessing whether Fibonacci retracements after rallies are a cause for concern

Senior Quantitative Analyst
May 13, 2020 at 7:35 AM
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The S&P 500 Index (SPX) continues to rally after the coronavirus market crash that started in March. The index, however, is running right into its 61.8% Fibonacci retracement level after being rejected there around the end of April. These levels are accessible on most charting software because they are popular support/resistance levels. Is there any quantifiable evidence that these seemingly random levels should affect a stock price? In the study below, I consider prior 20% market crashes and look for evidence that Fibonacci levels impede the recovery.

SPX Fib Levels

Method & Benchmark

For this study, I went back to 1950 and found each time the S&P 500 fell at least 20% from an all-time high. Using the all-time high and the lowest point since that time, I calculated the Fibonacci levels. Then I found the specific dates at which the S&P 500 closed to within 2% of the levels. It had to be below that level for at least 10 trading days. If those criteria were met, I looked at how the market did going forward. Here are the periods I identified where the S&P 500 fell by at least 20%.

SPX 20percent corrections

I also needed a benchmark for comparison. My first inclination was to use anytime returns on the index since 1950. That, however, does not account for the environment in which these signals are taking place. Since all the signals are occurring after a market bottom, the signals are occurring in a bullish environment. To account for the environment, I just eyeballed the chart during each pullback and found the time where I considered the recovery complete. It’s a haphazard way of doing it, but I think it made for a more apt comparison. The tables below compare the anytime returns of the S&P 500 since 1950 and the returns during these recoveries. The returns during the recoveries were significantly better than typical returns. I’ll be using those recovery returns as a benchmark.

SPX Returns Benchmark

Testing Fibonacci Levels as Resistance

Since the index is currently right at that 61.8% level, let’s look at that Fibonacci retracement first. Again, looking at 20% pullbacks, these are S&P 500 returns after the index gets to within 2% of the level, given that it has been under that level for at least ten straight trading days. I compare the returns after those signals to the recovery returns mentioned above.

There’s no reason to fear the nearby 61.8% retracement level, according to these numbers. The short-term results are almost identical to typical returns during the recovery. Looking out to a month, there’s a little bit of bullishness to the returns after these signals; the S&P 500 averages a 2% return after a month with 74% of the returns positive. Typically, during these recoveries, you would get a 1.3% return with 66% of the returns positive a month out.

SPX Fib Level 618

It’s not a Fibonacci level, but a 50% retracement is still often pointed out as potential resistance. The table below summarizes the returns after the S&P 500 gets up near one of these levels. Once again, the one-week return after one of these signals matches the usual recovery return. After that, you would have done well buying the index when it gets near a 50% retracement level. The index averages a 5.5% return three months after a signal at this level.

SPX 50 retracement

Finally, I looked at one more Fibonacci level; 38.2%. In this case, the one-week average return is negative after a signal, despite the percent positive very near what you’d expect anytime during a recovery. There must have been some big down moves after the index hit this level. After that one week, however, the summarized returns are once again bullish in comparison to typical returns for the index during these recoveries.

SPX 382 retracement

Based on these numbers, I would conclude that Fibonacci retracement levels, by themselves, are not levels to be feared after large pullbacks.


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