**Update 30/7/2017:** Changed regression equation to reflect correct log values.

Given the recent talk on complacency versus the VIX (VXX), we thought it would be interesting to test this theory. We hypothesize that the VIX and complacency are related and that high levels of complacency do indicate low levels of the VIX.

**Definition of Complacent**

In Latin, complacent from the verb complacere, meant pleasing. According to Dictionary.com, complacent is defined as “pleased, especially with oneself or one's merits, advantages, situation”. Given this context, it seems to us that complacent is a feeling or a type of sentiment. We will make several critical assumptions, one being that sentiment is a measure complacency, and secondly neutral sentiment equals complacent, in other words neither bullish or bearish on any particular situation.

**The Data**

While we can choose from several sentiment databases, to make things simple, we will use the American Association of Individual Investors Sentiment Survey (AAII Sentiment Survey), as our measure of sentiment, specifically the measurement of neutral sentiment. The AAII provides sentiment survey data starting in June of 1987. The Chicago Board Options Exchange (CBOE) provides monthly VIX data as early as January 1990 and ending in 2016.

**Our Hypothesis**

Our null hypothesis is that low levels of neutral sentiment tend to indicate low levels of the VIX, and our alternative hypothesis is that high levels of neutral sentiment tend to indicate low levels of the VIX. More casually we will test if values of neutral sentiment relate to values of the VIX.

**Correlation Analysis**

Let’s begin with studying the relationship between volatility and neutral sentiment. There are several ways we can examine this relationship. Two useful methods are scatter plots and correlation analysis. Below we’ve created a scatter plot of the CBOE Volatility Index and the AAII Neutral Sentiment Survey from January 1990 through December 2016.

Source: CBOE Volatility Index vs. AAII Sentiment (Jan 1990 - Dec 2016)

Looking at the chart above, we see a somewhat negative relationship, but how strong is it? We can express this relationship within a single number using correlation analysis. If we compute the correlation coefficient for the entire dataset, we result in a correlation of -0.275846396.

As you may have already noticed, there are some limitations to correlation analysis. One limitation is that correlation only measures linear relationships. For example, two variables may still have a non-linear relation but a small correlation coefficient.

Correlation may also be an unreliable measure when outliers are present. You’ll notice the data point at the top of the chart, it’s not hard to figure that one out, it’s the year 2008 in the month of October, where the VIX hit a high of 59.89. Neutral sentiment on this date was 0.2229. Should we include or exclude this outlier? Is this noise or news? It depends on how one wants to analyze the data but we would consider this an important data point. We also find another outlier near the far bottom left. In November 2006 the VIX was near historical lows of around 10.91 and neutral sentiment was also near historical lows at 0.1229. Removing this data point would most likely increase the negative correlation coefficient. We are not sure that would be wise, but we should try to explain this low neutral sentiment value. One theory may be bullish sentiment had overpowered both bearish and neutral sentiment, pushing neutral sentiment down but also volatility along with it. We would have to test this theory specifically, but that will have be put aside for future research.

Another important question is the time period used in our analysis. For example, if you believe the current low interest rate environment and quantitative easing justify a different time period to measure, we can specifically examine the 2008 to 2016 period. These next plots break down our original scatter plot into different time periods. We’ve decided to highlight prior and post the great recession.

Source: CBOE Volatility Index vs. AAII Sentiment (Jan 2008 - Dec 2016)

Source: CBOE Volatility Index vs. AAII Sentiment (Jan 1990 - Dec 2007)

An interesting insight to point out is the correlation between the VIX and neutral sentiment prior and post 2008. The correlation of the data from 2008 through 2016 is -0.5391, while the correlation from 1990 through 2007 is only -0.0949.

Unfortunately another issue with correlation is that of spurious correlations. Is it neutral sentiment that has a relationship with volatility or something else? For example, that something else could be lower interest rates or quantitative easing that is pushing volatility down, again this will require further examination.

Yet another way to measure the correlation between the VIX and neutral sentiment is to compute the percentage changes of each monthly value. Below we have plotted and computed the correlation between 1990-2016.

Source: CBOE Volatility Index (%) vs. AAII Sentiment (%) (Jan 1990 - Dec 2016)

We find the correlation of the changes to be even lower at -0.1179373845. Again it should be noted correlation may not be a reliable measure when outliers are present.

**Linear Regression**

We can also use linear regression, another powerful tool in examining the relationship between two variables as a straight line. Linear regression allows us to use one variable to make a prediction, test hypotheses about the relation between two variables, and quantify the strength of the relationship between those two variables.

We will use a log regression model, this is appropriate when one believes that proportional changes in the dependent variable (in this case the log of the CBOE VIX Index) bears a constant relationship to changes in the independent variable (AAII Neutral Sentiment). We can plot the log of the VIX to Neutral Sentiment below.

Source: Log of CBOE Volatility Index vs. AAII Sentiment (Jan 1990 - Dec 2016)

Overall Fit | |||||

R-square | 0.075 | ||||

Adj R-square | 0.073 | ||||

Residual SD | 0.323 | ||||

Sample SD | 0.336 | ||||

N observed | 324 | ||||

N missing | 0 | ||||

Coefficients | |||||

Estimate | Std. Error | t value | Pr(>|t|) | ||

(Intercept) | 3.282 | 0.073 | 45.146 | < 0.0001 | |

Neutral | -1.192 | 0.233 | -5.126 | < 0.0001 | |

ANOVA Table | |||||

Df | Sum Sq | Mean Sq | F value | Pr(>F) | |

Model | 1 | 2.743 | 2.743 | 26.272 | < 0.0001 |

Residual | 322 | 33.624 | 0.104 | ||

Total | 323 | 36.367 | 0.113 |

*All results reported above are hypothetical results, subject to peer review, do not indicate future returns and do not reflect management or trading fees.

**The regression analyses above require further testing specifically for heteroskedasticity and therefore may be subject to bias and inconsistency.

We find that AAII Neutral Sentiment can only explain about 7.5% of the variation in the log of the CBOE VIX Index, as represented by the R-square number presented below. The coefficient of -1.192, with a t value of -5.126 looks to be statistically significant. Therefore we may reject the null hypothesis that low levels of neutral sentiment indicate low levels of the VIX and instead accept our alternative hypothesis, high levels of neutral sentiment indicate low levels of the VIX.

We can also specifically examine the regression of the VIX and neutral sentiment within the current quantitative easing regime from 2008 through 2016.

Source: Log of CBOE Volatility Index vs. AAII Sentiment (Jan 2008 - Dec 2016)

We fine that neutral sentiment explains about 35% of the variation in the CBOE VIX Index. The coefficient of -2.710 with a t value of -7.587 also looks to be statistically significant.

Overall Fit | |||||

R-square | 0.352 | ||||

Adj R-square | 0.346 | ||||

Residual SD | 0.293 | ||||

Sample SD | 0.363 | ||||

N observed | 108 | ||||

N missing | 0 | ||||

Coefficients | |||||

Estimate | Std. Error | t value | Pr(>|t|) | ||

(Intercept) | 3.810 | 0.113 | 33.822 | < 0.0001 | |

Neutral | -2.710 | 0.357 | -7.587 | < 0.0001 | |

ANOVA Table | |||||

Df | Sum Sq | Mean Sq | F value | Pr(>F) | |

Model | 1 | 4.958 | 4.958 | 57.558 | < 0.0001 |

Residual | 106 | 9.131 | 0.086 | ||

Total | 107 | 14.089 | 0.132 |

*All results reported above are hypothetical results, subject to peer review, do not indicate future returns and do not reflect management or trading fees.

**The regression analyses above require further testing specifically for heteroskedasticity and therefore may be subject to bias and inconsistency.

As a reminder AAII neutral sentiment on July 20 2017 is 0.38. Using the first regression model and the value computed, we use the equation y = -1.192(0.38) + 3.282, and find the model predicts the natural log of the VIX index will be 2.829. We take the antilogarithm of 2.829 by raising e to that power which equals 16.9323. We currently stand at a VIX value of less than 10. We can look at this in different ways, but one perspective may be that the VIX is not correctly pricing in the current level of neutral sentiment. Depending on the perspective, one could take a long or short position on volatility using either (UVXY) or (SVXY).

In conclusion, we first set out to find if there was any relationship between the VIX and neutral sentiment. We found, although weak, a correlation coefficient of -0.275846396 signifying a negative relationship between the VIX and neutral sentiment. We also used linear regression to measure the relationship between the VIX and neutral sentiment. We found a coefficient of -1.192, with a t value of -5.126 that looked to be statistically significant. Therefore this allowed us to reject our null hypothesis, that low levels of neutral sentiment indicate low levels of the VIX and instead accept our alternative hypothesis, high levels of neutral sentiment indicate low levels of the VIX. Taking into account the assumptions of linear regression, our model predicted that the current neutral sentiment value of 0.38 should justify a VIX value of around 17. To make any real predictions of the direction of the VIX or neutral sentiment, will require further analysis in future research, but it seems we can be confident that there is a relationship here. Given our analysis at current levels of neutral sentiment and the VIX, we are more likely complacent.

**Disclosure:** I/we have no positions in any stocks mentioned, but may initiate a long position in UVXY over the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.