The document is a final project report analyzing the correlation between the S&P 500 index and the CBOE Volatility Index (VIX). It provides an introduction to the topic, surveys relevant literature on investor sentiment and volatility, outlines the model and hypothesis that increases in short-term rolling correlations between the two indices indicate trend reversals in the S&P 500. Empirical analysis is presented calculating rolling correlations on historical S&P 500 and VIX data from 1990 to 2015. The analysis finds the correlations are noisy in the short-term but provide some informational value on slightly larger time frames.

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Team - Ryan Hendricks, Joyce Meng, Haoxiang Ju (James)
ECO 9723 - FINAL PROJECT
The Correlation Between S&P 500 and VIX Indices
Instructor – Sebastiano Manzan

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1. Introduction
2. Survey of Literature
3. Model and Hypothesis
4. Data
5. Empirical Application
6. Conclusion
Table of Contents

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Introduction
“The speculator’s chief enemies are always boring from within. It is
inseparable from human nature to hope and to fear.”
“All through time, people have basically acted and reacted the same
way in the market as a result of: greed, fear, ignorance, and hope. That
is why the numerical (technical) formations and patterns recur on a
constant basis.”
-Jesse Livermore ~ Circa 1929

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“Up on Escalators, Down in Elevators”
• Tail Risk, Outliers, Skew? Or Panic?
• Sentiment (Emotion) - a psychological, or “human”, component of financial markets
• Potential link between behavioral and quantitative finance?
• Bulls & Bears
• Defined by, and differ only in, expectations of future market returns
• Both have views of where they think the market is headed
• These expectations are often factored into their investment decisions
• Volatility is the derivative of these expectations and sentiment
• Can we quantify investor sentiment and these associated expectations?
• The CBOE Volatility Index® (VIX®)
• Often referred to as “the fear index”

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• Introduced in 1993 as a means to gauge the market’s short-term expected
volatility.
• Originally calculated using at-the-money (ATM) S&P 100® Index (OEX®)
option prices.
• The VIX quickly gained in popularity and in 2003 during the tech bubble
crisis.
• The VIX was changed to include option prices over a wider range of strike
prices and options of the S&P 500® Index (SPX) were used instead.
• In 2014, the VIX weekly SPX options were added to the index calculation.
The CBOE Volatility Index® (VIX®)

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Calculation of the VIX

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 Investor Sentiment
 Overall optimism or pessimism about the market
 Propensity to speculation
 Graham (1973), Malkeil (1990) and Brown (1991)
 1961 – High demand for growth stocks
 High investor sentiment
 Malkeil (1990), Brown (1991), Siegel (1998)
 Early 1970 – Bearish market
 Low investor sentiment
 “The New Trading for a Living”
 “Chart patterns reflect swings of mass psychology in the financial markets. Each trading session is a battle
between bulls, who make money when prices rise and bears, who profit when they fall.”
 “Market is set up in a manner where most traders lose money and winners’ proceeds will be drained by the
market.”
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Survey of Literature

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 Correlation
 Rolling Correlations – n returns
 Hypothesis
 Increase in short-term rolling correlation between SPX and VIX is an indicator of a trend reversal
for SPX.
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Model and Hypothesis

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Data
• Historical data for S&P 500 and VIX from December 11, 1990 and December 12, 2015.

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Empirical Application
• VIX is NOT the inverse of SPX

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Empirical Application
• Correlations & Rolling Statistic Calculations

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SPX – 06/01/2015 to 12/11/2015 via Quantmod
• Rolling Correlations
between SPX/VIX
• 2 day
• 3 day
• 5 day

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Rolling Correlations vs SPX Returns (blue line)
Limitations:
• Very Noisy
• Short-Term Indicator; not so
useful for Investors.
But Some Market Participants
ONLY care about very short
time frames. Intraday SPY
option % returns October 2015.

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Rolling Correlation Period = 3
Slightly larger
rolling
correlation
period has
informational
value on
slightly larger
time frames.

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Standard Dev = Volatility = Higher Option Premium
Figure 2: Rolling Standard
Deviations of SPX daily returns
with (n) = 2, 3, 5, from top to
bottom respectively. The green
and blue lines represent the 2-
day and 3-day Rolling
Correlations between VIX and
SPX as overlays. Clearly, these
sudden changes in the short-
term correlation are not just
random noise.

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Periods with/without Volatility Clustering

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Conclusion

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Conclusion