Category Archives: Volatility

Increasing Day-to-Day Volatility for the S&P 500

Statistically speaking, day-to-day changes in the S&P 500 (Index: SPX) don't start to be interesting until the index changes by more than two percent from its previous day's closing value. But those day-to-day changes get really interesting when the S&P 500 changes by more than three percent from its previous day's closing value.

That's because big changes like that don't happen very often. Going back to 3 January 1950, for the 18,198 days through 27 April 2022 where we have the data to tell how much the index gained or lost from where it ended on the previous day's trading, just 239 involved the index gaining or losing more than 3.00%. That's 1.3% of all the trading days in the index' modern era.

The following chart updates our visualization of that day to day volatility, where the dashed red lines roughly coincide with when the S&P 500's volatility has gotten really interesting.

S&P 500 Daily Volatility, 3 January 1950 - 27 April 2022

The index has experienced two trading days in the past week where it has gotten close to becoming really interesting. Friday, 22 April 2022 saw the index fall by 2.77%, while Tuesday, 26 April 2022 saw the S&P drop by 2.81%. We're pointing these recent changes out because when the S&P 500 experiences big changes like these, they tend to be clustered together in time. Which is to say that once they show up, they tend to keep showing up until the market's volatility dies down.

They also tend to be roughly balanced between gains and losses, with the number of big daily gains being nearly equal to the number of big daily losses. Today, the market's big gain/loss ratio is 118/121.

Here's the question to answer: How long might it be until what looks like a developing volatility cluster for the S&P 500 causes the index to cross the line and become really interesting by our standards?

Growing Day-to-Day Volatility in Stock Prices

Long streaks and especially long losing streaks in the S&P 500 have become much less common during the past 20 years.

That change has come however as stock prices themselves have become more volatile. The following chart visualizes the daily percentage change from the previous days close for the S&P 500 from 3 January 1950 through 30 June 2021.

S&P 500 Daily Volatility (Percent Change Between Closing Value and Previous Trading Day's Closing Value), 3 January 1950 - 30 June 2021

In this chart, we see that large daily percentage changes have become more common in recent decades. To simplify the visualization of that change, we're calculated the standard deviation of the daily percentage change in the S&P 500 by decade, presented in the next chart, where we find the typical volatility among the U.S. stock market's largest stocks by market capitalization has increased.

Daily Volatility by Decade for S&P 500, Standard Deviation of Daily Percentage Change from Previous Close, 3 January 1950 - 30 June 2021

The final bar, for the 2020's, differs from the others in that it doesn't cover a full decade's worth of stock price changes. It covers the typical volatility observed to date in the year and a half from 2 January 2020 through 30 June 2021.

Still, it's a big jump over the preceding decade long periods, where we also see that the S&P 500 index in the decades of the 2000s have been considerably more volatile than the five decades that preceded them. The increase in the typical standard deviation indicates by decade bigger daily changes in stock prices have become more common in the 2000s.

That change offers a potential explanation for why losing streaks have become less common over the same period. Since the stock price volatility as measured by standard deviation has become larger than in previous decades, indicating larger daily changes when volatility breaks out, stock prices more quickly reach thresholds where investors buy the dips, which translates into shorter losing streaks.

Exit question: how profitable is buying big dips as a trading strategy?

References

Yahoo! Finance. S&P 500 Historical Data. [Online Database]. Accessed 2 July 2021.

Previously on Political Calculations

17/9/20: Exploding errors: COVID19 and VUCA world of economic growth forecasts

 

Just as I covered the latest changes in Eurozone growth indicators (https://trueeconomics.blogspot.com/2020/09/17920-eurocoin-leading-growth-indicator.html), it is worth noting the absolutely massive explosion in forecast errors triggered by the VUCA environment around COVID19 pandemic.

My past and current students know that I am a big fan of looking at risk analysis frameworks from the point of view of their incompleteness, as they exclude environments of deeper uncertainty, complexity and ambiguity in which we live in the real world. Well, here is a good illustration:


You can see an absolute explosion in the error term for growth forecasts vs actual outrun in the three quarters of 2020 so far. The errors are off-the-scale compared to what we witnessed in prior recessions/crises. 

This highlights the fact that during periods of elevated deeper uncertainty, any and all forecasting models run into the technical problem of risk (probabilities and impact assessments) not being representative of the true underlying environment with which we are forced to work.  


The S&P 500’s Worst Ever One Day Declines

Prompted by China's latest escalation of its trade war with the United States, with China's central bank allowing the Chinese yuan to decline in value relative to the U.S. dollar with the apparent blessing of top Chinese government officials, the S&P 500 (Index: SPX) suffered a 2.98% drop on Monday, 5 August 2019, with the index closing the day at $2,844.74.

In doing so, the S&P 500 completed its fourth Lévy flight event of 2019 as investors fully shifted their forward-looking focus from the distant future quarter of 2020-Q1 just a week earlier toward the nearer future quarter of 2019-Q4.

Alternative Futures - S&P 500 - 2019Q3 - Standard Model - Snapshot on 5 August 2019

That large percentage change qualifies the stock market's volatility on Monday, 5 August 2019 as interesting, where we consider an interesting level of volatility as occurring whenever the closing daily value of stock prices changes by more than 2% from the previous trading day's closing value, for statistical reasons.

But with a change in value of nearly 3% from the previous day's close, that represents an even more interesting threshold for "interesting", as that level falls more than three standard deviations outside of the mean day-to-day change recorded in the S&P 500 over every trading day from 3 January 1950 through 5 August 2019, where only 1.4% of all 17,510 trading days recorded during this period have seen similarly large changes from the previous day's closing value, which are roughly equally split between increases and decreases.

S&P 500 Daily Volatility, 3 January 1950 through 5 August 2019

Focusing on just the decreases, there have been just 131 recorded in the more than 69 years from 3 January 1950 through 5 August 2019. We've recorded the data for each the S&P 500's worst ever one day declines recorded during the modern era of the U.S. stock market in the following dynamic table, where you can click the column headings for Date, Open, High, Low, Close, and Percent Change from Previous Close, you can sort the data from either high-to-low, or from low-to high. If you're accessing this article from a site that republishes our RSS news feed, please click through to our site to access a working version of the dynamic table.

Worst 131 Single Day Declines in S&P 500 During Modern Era for U.S. Stock Market
Date Previous Day's
Close
Open High Low Close Percent Change
from Previous Close
1950-06-26 $19.14 $18.11 $18.11 $18.11 $18.11 -5.38%
1950-06-29 $18.11 $17.44 $17.44 $17.44 $17.44 -3.70%
1950-11-28 $20.18 $19.56 $19.56 $19.56 $19.56 -3.07%
1950-12-04 $19.66 $19.00 $19.00 $19.00 $19.00 -3.36%
1953-02-09 $26.51 $25.69 $25.69 $25.69 $25.69 -3.09%
1955-09-26 $45.63 $42.61 $42.61 $42.61 $42.61 -6.62%
1955-10-10 $42.38 $41.15 $41.15 $41.15 $41.15 -2.90%
1957-10-21 $40.33 $39.15 $39.15 $39.15 $39.15 -2.93%
1961-04-18 $68.68 $66.20 $66.20 $66.20 $66.20 -3.61%
1962-05-28 $59.47 $59.15 $59.15 $55.42 $55.50 -6.68%
1962-06-04 $59.38 $59.12 $59.12 $57.14 $57.27 -3.55%
1973-11-19 $103.88 $103.65 $103.65 $100.37 $100.71 -3.05%
1973-11-26 $99.44 $98.64 $98.64 $95.79 $96.58 -2.88%
1974-07-08 $83.66 $83.13 $83.13 $80.48 $81.09 -3.07%
1974-10-23 $73.13 $72.81 $72.81 $70.40 $71.03 -2.87%
1974-11-18 $71.91 $71.10 $71.10 $68.95 $69.27 -3.67%
1979-10-09 $109.88 $109.43 $109.43 $106.04 $106.63 -2.96%
1980-03-17 $105.43 $105.23 $105.23 $101.82 $102.26 -3.01%
1980-03-24 $102.31 $102.18 $102.18 $98.88 $99.28 -2.96%
1981-08-24 $129.23 $128.59 $128.59 $125.02 $125.50 -2.89%
1982-10-25 $138.83 $138.81 $138.81 $133.32 $133.32 -3.97%
1986-07-07 $251.79 $251.79 $251.81 $243.63 $244.05 -3.07%
1986-09-11 $247.06 $247.06 $247.06 $234.67 $235.18 -4.81%
1987-10-14 $314.52 $314.52 $314.52 $304.78 $305.23 -2.95%
1987-10-16 $298.08 $298.08 $298.92 $281.52 $282.70 -5.16%
1987-10-19 $282.70 $282.70 $282.70 $224.83 $224.84 -20.47%
1987-10-22 $258.38 $258.24 $258.38 $242.99 $248.25 -3.92%
1987-10-26 $248.22 $248.20 $248.22 $227.26 $227.67 -8.28%
1987-11-09 $250.41 $250.41 $250.41 $243.01 $243.17 -2.89%
1987-11-30 $240.34 $240.27 $240.34 $225.75 $230.30 -4.18%
1987-12-03 $233.45 $233.46 $233.90 $225.21 $225.21 -3.53%
1988-01-08 $261.07 $261.05 $261.07 $242.95 $243.40 -6.77%
1988-04-14 $271.58 $271.55 $271.57 $259.37 $259.75 -4.36%
1989-10-13 $355.39 $355.39 $355.53 $332.81 $333.65 -6.12%
1990-08-06 $344.86 $344.86 $344.86 $333.27 $334.43 -3.02%
1990-08-23 $316.55 $316.55 $316.55 $306.56 $307.06 -3.00%
1991-11-15 $397.15 $397.15 $397.16 $382.62 $382.62 -3.66%
1996-03-08 $653.65 $653.65 $653.65 $627.63 $633.50 -3.08%
1997-10-27 $941.64 $941.64 $941.64 $876.73 $876.99 -6.87%
1998-01-09 $956.05 $956.05 $956.05 $921.72 $927.69 -2.97%
1998-08-04 $1,112.44 $1,112.44 $1,119.73 $1,071.82 $1,072.12 -3.62%
1998-08-27 $1,084.19 $1,084.19 $1,084.19 $1,037.61 $1,042.59 -3.84%
1998-08-31 $1,027.14 $1,027.14 $1,033.47 $957.28 $957.28 -6.80%
1998-09-30 $1,049.02 $1,049.02 $1,049.02 $1,015.73 $1,017.01 -3.05%
1998-10-01 $1,017.01 $1,017.01 $1,017.01 $981.29 $986.39 -3.01%
2000-01-04 $1,455.22 $1,455.22 $1,455.22 $1,397.43 $1,399.42 -3.83%
2000-02-18 $1,388.26 $1,388.26 $1,388.59 $1,345.32 $1,346.09 -3.04%
2000-04-14 $1,440.51 $1,440.51 $1,440.51 $1,339.40 $1,356.56 -5.83%
2000-12-20 $1,305.60 $1,305.60 $1,305.60 $1,261.16 $1,264.74 -3.13%
2001-03-12 $1,233.42 $1,233.42 $1,233.42 $1,176.78 $1,180.16 -4.32%
2001-04-03 $1,145.87 $1,145.87 $1,145.87 $1,100.19 $1,106.46 -3.44%
2001-09-17 $1,092.54 $1,092.54 $1,092.54 $1,037.46 $1,038.77 -4.92%
2001-09-20 $1,016.10 $1,016.10 $1,016.10 $984.49 $984.54 -3.11%
2002-01-29 $1,133.06 $1,133.06 $1,137.47 $1,098.74 $1,100.64 -2.86%
2002-07-10 $952.83 $952.83 $956.34 $920.29 $920.47 -3.40%
2002-07-19 $881.56 $881.56 $881.56 $842.07 $847.75 -3.84%
2002-07-22 $847.75 $847.76 $854.13 $813.26 $819.85 -3.29%
2002-08-01 $911.62 $911.62 $911.62 $882.48 $884.66 -2.96%
2002-08-05 $864.24 $864.24 $864.24 $833.44 $834.60 -3.43%
2002-09-03 $916.07 $916.07 $916.07 $877.51 $878.02 -4.15%
2002-09-19 $869.46 $869.46 $869.46 $843.09 $843.32 -3.01%
2002-09-27 $854.95 $854.95 $854.95 $826.84 $827.37 -3.23%
2003-01-24 $887.34 $887.34 $887.34 $859.71 $861.40 -2.92%
2003-03-24 $895.79 $895.79 $895.79 $862.02 $864.23 -3.52%
2007-02-27 $1,449.37 $1,449.25 $1,449.25 $1,389.42 $1,399.04 -3.47%
2007-08-09 $1,497.49 $1,497.21 $1,497.21 $1,453.09 $1,453.09 -2.96%
2007-11-07 $1,520.27 $1,515.46 $1,515.46 $1,475.04 $1,475.62 -2.94%
2008-01-17 $1,373.20 $1,374.79 $1,377.72 $1,330.67 $1,333.25 -2.91%
2008-02-05 $1,380.82 $1,380.28 $1,380.28 $1,336.64 $1,336.64 -3.20%
2008-06-06 $1,404.05 $1,400.06 $1,400.06 $1,359.90 $1,360.68 -3.09%
2008-06-26 $1,321.97 $1,316.29 $1,316.29 $1,283.15 $1,283.15 -2.94%
2008-09-04 $1,274.98 $1,271.80 $1,271.80 $1,232.83 $1,236.83 -2.99%
2008-09-09 $1,267.79 $1,267.98 $1,268.66 $1,224.51 $1,224.51 -3.41%
2008-09-15 $1,251.70 $1,250.92 $1,250.92 $1,192.70 $1,192.70 -4.71%
2008-09-17 $1,213.60 $1,210.34 $1,210.34 $1,155.88 $1,156.39 -4.71%
2008-09-22 $1,255.08 $1,255.37 $1,255.37 $1,205.61 $1,207.09 -3.82%
2008-09-29 $1,213.27 $1,209.07 $1,209.07 $1,106.42 $1,106.42 -8.81%
2008-10-02 $1,161.06 $1,160.64 $1,160.64 $1,111.43 $1,114.28 -4.03%
2008-10-06 $1,099.23 $1,097.56 $1,097.56 $1,007.97 $1,056.89 -3.85%
2008-10-07 $1,056.89 $1,057.60 $1,072.91 $996.23 $996.23 -5.74%
2008-10-09 $984.94 $988.42 $1,005.25 $909.19 $909.92 -7.62%
2008-10-15 $998.01 $994.60 $994.60 $903.99 $907.84 -9.03%
2008-10-21 $985.40 $980.40 $985.44 $952.47 $955.05 -3.08%
2008-10-22 $955.05 $951.67 $951.67 $875.81 $896.78 -6.10%
2008-10-24 $908.11 $895.22 $896.30 $852.85 $876.77 -3.45%
2008-10-27 $876.77 $874.28 $893.78 $846.75 $848.92 -3.18%
2008-11-05 $1,005.75 $1,001.84 $1,001.84 $949.86 $952.77 -5.27%
2008-11-06 $952.77 $952.40 $952.40 $899.73 $904.88 -5.03%
2008-11-12 $898.95 $893.39 $893.39 $850.48 $852.30 -5.19%
2008-11-14 $911.29 $904.36 $916.88 $869.88 $873.29 -4.17%
2008-11-19 $859.12 $859.03 $864.57 $806.18 $806.58 -6.12%
2008-11-20 $806.58 $805.87 $820.52 $747.78 $752.44 -6.71%
2008-12-01 $896.24 $888.61 $888.61 $815.69 $816.21 -8.93%
2008-12-04 $870.74 $869.75 $875.60 $833.60 $845.22 -2.93%
2008-12-11 $899.24 $898.35 $904.63 $868.73 $873.59 -2.85%
2009-01-07 $934.70 $927.45 $927.45 $902.37 $906.65 -3.00%
2009-01-14 $871.79 $867.28 $867.28 $836.93 $842.62 -3.35%
2009-01-20 $850.12 $849.64 $849.64 $804.47 $805.22 -5.28%
2009-01-29 $874.09 $868.89 $868.89 $844.15 $845.14 -3.31%
2009-02-10 $869.89 $866.87 $868.05 $822.99 $827.16 -4.91%
2009-02-17 $826.84 $818.61 $818.61 $789.17 $789.17 -4.56%
2009-02-23 $770.05 $773.25 $777.85 $742.37 $743.33 -3.47%
2009-03-02 $735.09 $729.57 $729.57 $699.70 $700.82 -4.66%
2009-03-05 $712.87 $708.27 $708.27 $677.93 $682.55 -4.25%
2009-03-30 $815.94 $809.07 $809.07 $779.81 $787.53 -3.48%
2009-04-20 $869.60 $868.27 $868.27 $832.39 $832.39 -4.28%
2009-06-22 $921.23 $918.13 $918.13 $893.04 $893.04 -3.06%
2009-07-02 $923.33 $921.24 $921.24 $896.42 $896.42 -2.91%
2010-02-04 $1,097.28 $1,097.25 $1,097.25 $1,062.78 $1,063.11 -3.11%
2010-05-06 $1,165.87 $1,164.38 $1,167.58 $1,065.79 $1,128.15 -3.24%
2010-05-20 $1,115.05 $1,107.34 $1,107.34 $1,071.58 $1,071.59 -3.90%
2010-06-04 $1,102.83 $1,098.43 $1,098.43 $1,060.50 $1,064.88 -3.44%
2010-06-29 $1,074.57 $1,071.10 $1,071.10 $1,035.18 $1,041.24 -3.10%
2010-07-16 $1,096.48 $1,093.85 $1,093.85 $1,063.32 $1,064.88 -2.88%
2011-08-04 $1,260.34 $1,260.23 $1,260.23 $1,199.54 $1,200.07 -4.78%
2011-08-08 $1,199.38 $1,198.48 $1,198.48 $1,119.28 $1,119.46 -6.66%
2011-08-10 $1,172.53 $1,171.77 $1,171.77 $1,118.01 $1,120.76 -4.42%
2011-08-18 $1,193.89 $1,189.62 $1,189.62 $1,131.03 $1,140.65 -4.46%
2011-09-21 $1,202.09 $1,203.63 $1,206.30 $1,166.21 $1,166.76 -2.94%
2011-09-22 $1,166.76 $1,164.55 $1,164.55 $1,114.22 $1,129.56 -3.19%
2011-11-09 $1,275.92 $1,275.18 $1,275.18 $1,226.64 $1,229.10 -3.67%
2015-08-21 $2,035.73 $2,034.08 $2,034.08 $1,970.89 $1,970.89 -3.19%
2015-08-24 $1,970.89 $1,965.15 $1,965.15 $1,867.01 $1,893.21 -3.94%
2015-09-01 $1,972.18 $1,970.09 $1,970.09 $1,903.07 $1,913.85 -2.96%
2016-06-24 $2,113.32 $2,103.81 $2,103.81 $2,032.57 $2,037.41 -3.59%
2018-02-05 $2,762.13 $2,741.06 $2,763.39 $2,638.17 $2,648.94 -4.10%
2018-02-08 $2,681.66 $2,685.01 $2,685.27 $2,580.56 $2,581.00 -3.75%
2018-10-10 $2,880.34 $2,873.90 $2,874.02 $2,784.86 $2,785.68 -3.29%
2018-10-24 $2,740.69 $2,737.87 $2,742.59 $2,651.89 $2,656.10 -3.09%
2018-12-04 $2,790.37 $2,782.43 $2,785.93 $2,697.18 $2,700.06 -3.24%
2019-08-05 $2,932.05 $2,898.07 $2,898.07 $2,822.12 $2,844.74 -2.98%

The nearly 3% drop in the S&P 500's value on Monday, 5 August 2019 pales in comparison to the worst ever single day decline of 20.47% that was recorded back on Monday, 19 October 1987, which earned that day the title of "Black Monday", the single worst day ever recorded in U.S. stock market history.

Note that many of these relatively rare large one-day declines have tended to be clustered together in time. Whether that happens now in 2019 will depend on the flow of new information that might cause investors to shift their attention to other points of time in the future, where an additional 3% drop from its current level would coincide with investors shifting their attention to the current quarter of 2019-Q3. And as you can see from our first chart, any news that might fix the attention of investors on 2020-Q2 would coincide with a much, much larger crash in stock prices.

That assumes, of course, that there is no erosion in the expectations in the S&P 500's dividends per share at these future points of time, which would amplify the indicated potential declines.

The S&P 500’s Bear Market Rallies

Stock Market Chaos!

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 0.034% for the index, where the variation in the percentage change is well-described by a normal distribution.

S&P 500 Daily Volatility (Percent Change Between Closing Value and Previous Trading Day's Closing Value), 3 January 1950 - 4 January 2019

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:

  • 1955: 2 between 6 June 1955 and 6 July 1955.
  • 1962: 3 between 29 May 1962 and 24 October 1962.
  • 1974-1975: 8 between 12 July 1974 and 27 January 1975.
  • 1982: 5 between 17 August 1982 and 30 November 1982.
  • 1987: 3 between 20 October 1987 and 29 October 1987.
  • 1990-1991: 3 between 27 August 1990 and 21 August 1991.
  • 1997: 2 between 2 September 1997 and 28 October 1997.
  • 1998: 5 between 1 September 1998 and 15 October 1998.
  • 2000-2003: 25 between 16 March 2000 and 17 March 2003.
  • 2008-2009: 29 between 11 March 2008 and 15 July 2009.
  • 2010: 5 between 10 May 2010 and 1 September 2010.
  • 2011: 8 between 9 August 2011 and 20 December 2011.
  • 2018-2019: 2 between 26 December 2018 and 4 January 2019 (at this writing).

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.

References

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.