Market Sentiment and Volatility

This week we are discussing one-way analysis of variance of the mean (ANOVA). Our objectives here are to discuss and ask questions about concepts in which are unclear to us. Well the whole thing seems a bit foggy to me so I figured I’d try a hands-on experiment. I’m just not smart enough to know the right questions to ask so I’ll fumble through this.

Market Sentiment and Market Volatility

I am trying to see if stock market volatility has an effect on individuals market outlook, i.e. sentiment towards future economic prospects. Before I start to build my market model, I first want to see if there is as statistical significance when comparing the means of the variables in the model.

My null hypothesis H0 is that stock market volatility has no effect on investor sentiment.

The alternative hypothesis H1 is that stock market volatility does have an affect on investor sentiment.

To measure economic sentiment, I am using the American Association of Individual Investors (AAII) market survey. “The AAII Sentiment Survey measures the percentage of individual investors who are bullish, bearish, and neutral on the stock market short term; individuals are polled from the AAII Web site on a weekly basis.” (Investors, n.d.).

To measure market volatility, I am using the closing weekly price of the CBOE Volatility Index (VIX). “The VIX Index is a calculation designed to produce a measure of constant, 30-day expected volatility of the U.S. stock market, derived from real-time, mid-quote prices of S&P 500® Index (SPXSM) call and put options. On a global basis, it is one of the most recognized measures of volatility -- widely reported by financial media and closely followed by a variety of market participants as a daily market indicator.” (CBOE VIX, n.d.).

The higher the VIX price, the more expected market volatility.

Data Preparation

I took 5 years’ worth of weekly survey results and created a ratio of bullish (positive view)/bearish (negative view). So, the higher (lower) the ratio, the more positive (negative) individuals are about the market prospects. I then uploaded the data on SPSS and calculated the mean, standard deviation and other statistical measures.

Figure 1: Statistical features of the Percent Bullish to Bearish Ratio. Source SPSS.

The data indicated that the mean score for the ratio is 1.13. Any ratio above 1.13 is considered bullish and below it bearish. The standard deviation for the ratio is .46. I used 1 standard deviation as my level of extreme bullishness and bearishness. Any score >= 1.59 is considered bullish (positive) and any number <= .67 is considered bearish (negative). We find the skewness is 1.23 and kurtosis of 3.66. This indicates a leftward bias to the data.

Survey’s that are >=1.59 (bullish) were coded as group “1” in SPSS and the corresponding VIX price level was recorded. The survey results that were <=.67 (bearish) were coded as group “2” in SPSS. A one-way ANOVA test was conducted.

Figure 2: Statistical Descriptives of the Percent Bullish to Bearish Ratio. Source SPSS.

There is a total of 79 observations. 39 (49.4%) are bullish and 40 (50.6%) are bearish. The mean VIX price for bullish sentiment is 13.18. The mean VIX price for bearish sentiment is 23.39. The standard deviation of the VIX price is 2.33 and 11.41 for bullish and bearish sentiment, respectively.

The figure below represents our ANOVA test.

Figure 3: Volatility ANOVA test. Source SPSS.

The ANOVA test of variance of means. The F value is the variation between sample means / variation within the samples. The F value is 30.042 which is statistically significant on an F Table for alpha=.01. The p value is < .01.

The test for homogeneity of variance has a p value < .01 as well. This means the variance within each group is statistically different from each other. Both measures of robustness are exhibiting p values < .01.

Based upon the statistically significant variance of the means, I can reject the null hypothesis and continue to work on building a model that incorporates investor sentiment and market volatility.

Figure 4: Mean plots of investor sentiment and volatility. Source SPSS.

Joseph S. Kalinowski, CFA

References

CBOE VIX. (n.d.). Retrieved July 27, 2020, from http://www.cboe.com/vix

Green, S. B., & Salkind, N. J. (2011). Using SPSS for Windows and Macintosh:

Analyzing and Understanding Data (7th ed.). Upper Saddle River, NJ: Prentice Hall.

Investors, A. (n.d.). Retrieved July 27, 2020, from https://www.aaii.com/sentimentsurvey