We examine how close the VIX’s estimate of volatility has been to realized volatility over various time periods.
Over the last several weeks, the CBOE S&P 500 Volatility Index VIX has dropped from above 40 during the final week of October to its current level of around 23, signaling that the level of expected volatility has dropped significantly.
The VIX calculates the implied volatility of near-term S&P 500 SPX options based on their market values to arrive at an expected level of volatility for the index over the subsequent 30 days, which is expressed as an annualized figure. For example, if the current level of the VIX is 40 the expected level of annualized volatility over the next 30 days is 40%. While the VIX calculation is based on observable market data, it is forward-looking, and therefore it is only an estimate of future volatility. If the SPX options used in the VIX calculation are mispriced, then it would be reasonable to expect that the VIX would not accurately estimate realized volatility. Given the large recent decline in the VIX, we were curious how close the VIX’s estimate of volatility has been to realized volatility over various time periods.
In order to analyze this, we compared the daily level of the VIX since the beginning of 2004 (prior to this time the VIX was calculated using a different methodology) to the realized volatility of the S&P 500 SPX over four subsequent time periods – one week (five trading days), one month (21 trading days), two months (42 trading days) and three months (63 trading days). The table below shows the annualized realized volatility of daily returns for each of these four intervals subtracted from the closing value of the VIX the day before the period began. For example, the first VIX value in our study was from 1/2/2004, which we compared to the annualized realized daily volatility of SPX over the subsequent five trading days to arrive at our first “VIX – 1WK” value. We then did the same for the next daily VIX value and averaged the results by year (the yearly classification is based on the date of the VIX reading).
Our results show that, on average, the VIX’s expected volatility overestimated realized volatility over every interval – one week, one month, two months, and three months. However, it also revealed something else interesting, in 2008 and 2020, two incredibly volatile years for the market, on average, the VIX underestimated realized volatility over most time periods. One practical implication of this may be that many investors are buying options at the wrong time. Volatility is one of the primary determinants of options prices, thus when expected volatility (and the VIX) are high, options are expensive and as a result many investors are hesitant to buy options during these periods. Based on our results, however, it appears that during these highly-volatile periods the implied volatility of SPX options (which underlie the VIX calculation) was lower than the subsequent realized volatility and thus the options were relatively cheap compared to the level of the realized volatility.
