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Bates Research  |  10-24-14

Volatility Returns to the Market

Volatility has been on the rise recently, and many pundits have warned that this could be a negative turn of events for equity investors, who have largely enjoyed a bull rally since the bottom of the credit crisis. Here at Bates Research, we decided to investigate whether or not this widely held “truth” holds up.

For purposes of our analysis, we used the CBOE VIX Index, which measures market expectations for volatility using option prices for S&P 500 contracts. This metric gained widespread popularity as a measure of market fear during the credit crisis. The chart below shows the dramatic increase in volatility during the crisis and the gradual decline thereafter. We also used the S&P 500 as our gauge of market returns during periods of increasing volatility.

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For our analysis we used daily VIX values from 01/04/99 to 10/22/14, a total of 3,977 observations. We segmented our relevant population into instances wherein the VIX had increased by 10% or more over a five-trading-day (one week) period. Using rolling weekly periods, we found 644 observations in which the five-day change in the value of the VIX met or exceeded the 10% threshold, or about 16.2% of the time. Since we are looking at a rolling five-day period, the value of the five-day change in VIX level could still be above 10% even if the index itself had started to reverse directions back down to a lower level. To make sure we were using only relevant changes in the Index, we isolated instances in which the overall trend of the change in VIX level was positive -- that is, where the VIX level had increased 10% or more over the preceding five days and was continuing to increase compared to the previous day’s value. 465 observations met these criteria, or about 72% of our sample (11.7% of our original population). Having identified instances in which the VIX level had increased by 10% or more and was continuing on an upward trend, we turned our attention to the pattern of returns to the S&P 500.

Presumably, according to popular wisdom, a rising VIX should lead to a fall in market values. For each date whereon the VIX level had risen 10% or more over the past week, we calculated the change in value of the S&P 500 over the subsequent five-trading-day (one week) period. Our results show that large moves in the VIX were more likely to be associated with positive S&P 500 returns over the next five days, rather than negative returns.

Out of 465 observations, the S&P 500 posted a positive return about 61% of the time (282 observations). The average increase in value was 2.09%. To further refine our analysis, we next looked at the number of positive returns versus negative returns when we segmented our results by the change in VIX over the previous five days. The chart below shows our results (we have omitted five observations, three positive and two negative, associated with VIX movements in excess of 55% for graphical clarity).

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When the VIX level increased by 10% but not by more than 15%, the S&P 500 moved up 110 times (compared to down 80 times) over the next week. For any given band of VIX movement, this pattern repeats (a 15-20% move in the VIX corresponds to 66 positive returns versus 45 negative returns for example), though as the magnitude of the VIX movement increases, the gap between positive movements and negative movements narrows. For VIX movements greater than 35% but less than 40% we find five instances of positive S&P 500 returns and five instances of negative S&P 500 returns over the next week. As the change in volatility increases, the likelihood that a negative return will occur also increases.

If we look at the average returns themselves, we can see that the positive returns average a higher rate than the negative ones. As seen in the chart below, this is true in all bands except for VIX level changes greater than 30% but less than 35%.

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The relatively stable averages do hide some impressive volatility, especially for downward movements. The next chart shows the maximum and minimum observed value in each band for positive and negative S&P 500 movements respectively.

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Should investors fear rising volatility? Not necessarily. On October 9th the one-week move in the VIX was an increase of about 29%. Over the next five days the S&P 500 fell 3.41%. Based on our historical analysis, there was a 40% chance of a downward movement, with 3.41% exceeding the average decline of about 1%, but within the minimum decline observed of 6.61%. By October 14th, the last day we experienced an upward trending VIX, the five-day change in VIX level had hit about 51%. There was a 75% chance of a positive return for the S&P 500 over the next five days, given the change in VIX. The average positive movement given that level was 4.4% in our historical analysis, compared with a 1.40% appreciation over the next five days this time. The five day appreciation of the S&P 500 on the very next day was 4.23%. An upward trending VIX may not signal an impending decline in the market after all.