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Bear markets have notorious reputations for stock price volatility, where big daily changes in stock prices are a characteristic that distinguishes bear markets from bull markets.
These periods include bear market rallies, which often see outsized upward movements in stock prices that punctuate periods of corrections or bear markets and often extend into the early phases of recoveries from them.
That's relevant today because we've just seen two such rallies in the last two weeks, one on Wednesday, 26 December 2018 and Friday, 4 January 2018, where the S&P 500 (Index: SPX) rallied by an outsized amount with respect to its typical level of volatility.
What is an outsized amount for the stock market to go up in a single day? Building on our statistical analysis to quantify daily market volatility for the S&P 500 since 3 January 1950, we can put the threshold for identifying an outsized upward movement in its level at a 2.92% increase above its previous day's closing value, which is three standard deviations above the mean daily change of 0.34% for the index, where the variation in the percentage change is well-described by a normal distribution.
For the 17,364 daily observations we have covering the 69 years from 3 January 1950 through 4 January 2019, we count a total of 115 days where stock prices closed more than 2.92% above their previous days close, accounting for 0.66%, or roughly 1 in 151, of the total observations.
These outsized rallies are not evenly distributed throughout the period however. Going year by year, here's are the main periods where they are concentrated, which cover 100 of the 115 outsized single day rallies:
Aside from 1955, all of these periods where the S&P 500 experienced single day price gains of 2.92% or more have coincided with or closely followed negative corrections or bear markets for the S&P 500.
Yahoo! Finance. S&P 500 (^GSPC) Historical Prices, 3 January 1950 through 4 January 2019. [Online Database]. Accessed 4 January 2018.
Yardeni Research. Stock Market Briefing: S&P 500 Bull & Bear Market Tables. [PDF Document]. 13 February 2018.