Option Volume, Market Sentiment, and Future Performance and Volatility
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A thesis presented to: The Honors Tutorial College, Ohio University
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In partial fulfillment of the requirements for graduation from the Honors Tutorial College with the degree of Bachelor of Business Administration
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Natalie Clark April 2018
This thesis has been approved by The Honors Tutorial College and the College of Business Finance Department
______Dr. Andy Fodor Chair, Finance Department Thesis Adviser
______Dr. Raymond Frost Honors Tutorial College, DOS Business Administration
______Cary Roberts Frith Interim Dean Honors Tutorial College
Acknowledgements
The opportunity to be involved with both the College of Business and the Honors
Tutorial College has been an exceptional one, and I am very grateful for the incredible experiences that both communities have provided. I would like to thank my thesis advisor, Dr. Andy Fodor, for his continuous support throughout the past few years and his flexibility throughout a few topic changes. This thesis would not have been possible without the support I received along the way. Dr. Fodor has been an incredible advisor by providing critical feedback to my thesis, but he has also been an even better mentor by providing advice throughout my academic career and helping me to start my professional career. Additionally, I would like to thank the Fixed Income Management Group, the student organization where I found my passion for financial markets. The group has given me several opportunities to gain hands-on experience in the finance industry, and I am happy that I was able to pair this passion with my thesis research throughout my senior year.
I would also like to thank Dr. Raymond Frost for his continuous encouragement throughout my academic career and supporting all of the decisions I have made regarding my class choices. I truly believe that because of Dr. Frost, I was able to get as much as I could out of the Honors Tutorial College Business Administration Program. He provided me with countless pieces of advice throughout my four years here and numerous opportunities to work within my areas of study and outside of the College of Business.
Lastly, I would like to thank The Honors Tutorial faculty and staff. I could not imagine a better academic experience with such an outstanding group of professionals while fostering a challenging and nurturing environment. Technical Crash Course
What is SPY? What is VIX?
SPY is the ticker, or market-accepted abbreviation, for the S&P 500. The S&P
500 is a market index that is composed of 505 common stocks that are traded on
American stock exchanges. These 505 companies’ stocks cover a large majority of the
American equity market by capitalization, making it a strong gauge of overall economic performance.
The S&P 500 is one of three major equity, or stock, indices. The other two are the
Dow Jones Industrial Average (DJIA) and the NASDAQ. An index is a collection of securities in various proportions, similar to a general investment portfolio. The S&P 500 was created in 1957 as another index to compare to the Dow Jones Industrial Average.
The S&P 500 includes some companies that the Dow Jones does not, which can be interpreted as being more useful as a perspective of the actual American economy. The
Dow Jones Industrial Average was created in 1896 by Charles H. Dow and is based on different stock prices as the weightings. This means that if a stock has a higher price, it makes a larger impact on the index as a whole. Indices do not have to be reflective of the entire market but can act as a benchmark for an entire industry or group of industries. The
NASDAQ is known as an index for technology stocks, which can provide an insight into the technology sector’s overall performance. S&P 500 options, then, are observed in the market to forecast future market performance.
The VIX, or the Chicago Board of Exchange (CBOE) Volatility Index shows the market’s expectation of 30-day volatility, or standard deviation (stability) of the S&P
500’s returns. The VIX is known as the “fear gauge” of the equity markets. With respect to financial markets, standard deviation is a common measure of volatility as it serves to measure the average deviation of a daily or monthly return relative to the average return over a given period of time. The VIX is determined by using the price of several options from the S&P 500. With this being said, using VIX options is the market’s forecast for future market stability.
What is market sentiment?
Market sentiment is defined as the overall “tone” of the market. Market sentiment can be analyzed by prices in different markets in different asset classes (i.e. rising prices in major market indices would indicate a bullish market sentiment). Some indices, including the VIX, can be used as a measure of market sentiment. When prices in other asset classes fall, the levels on the VIX tend to be higher as the “fear” heightens on this index.
What is an option?
An option is a derivative. A derivative is a (synthetic) contract that is written to be based off of the price movements of an actual (underlying) security, such as a stock. They can be used to bet on the outcome of the underlying asset. Options that do not have any special or unusual features are known as vanilla options, and options that have special or unusual features embedded in it, are known as exotic options. Investors who have superior information or are skilled at predicting performance can profit more from using an option instead of just investing in the underlying. This is due to the concept of leverage, which includes the combination of options’ high sensitivity to the movement of the underlying asset and the small initial investment as opposed to buying the asset itself.
Given the ability of leverage to magnify returns, it is reasonable to expect, and past literature has shown, that informed or skilled investors should prefer to invest in option markets when available.
There are two different styles of options: European and American. The difference between these two option styles is the time that the investor is allowed to exercise, or redeem, the option. American options can be exercised at any time from creation to expiration, whereas European options can only be exercised at the time of expiration.
Because of the restriction in European options, the two styles tend to be priced differently in the market, even if they have other similar characteristics.
There are also different classifications for options based on the relative position between the underlying price and the strike price. When an option is classified as “in the money,” it would result in a positive payout if the investor were to exercise the option.
When an option is classified as “at the money,” the underlying asset’s price is equal to the strike price, causing the investor to make exactly $0. When an option is out of the money at maturity, the investor will not exercise the option because it would be a loss on the option in addition to the premium that was paid.
Call Option Payout Diagram $25
$20
$15
$10
$5
$- $- $5 $10 $15 $20 $25 $30 $35 $40
Payout Diagram of a call option, where the price of the option is not included in this. The dot at $20 on the horizontal axis signifies the strike price. When the price of the underlying asset is at $20 as well, the payout would be $0, and the option would be classified as “at the money.” Any underlying asset price that is on dotted line to the left of the dot would be considered as “out of the money” because it would result in a loss for the investor. Any underlying asset price that is on the solid line to the right of the dot would be considered as “in the money” because it would result in a positive payout.
What kinds of options are discussed in this paper?
The two options that are discussed are the vanilla call option and the vanilla put option. These two securities can be used to provide leverage in the financial markets and as a result can give an investor increased upside relative to the underlying assets.
When an investor wants to purchase a call option, he or she is hoping that the stock price rises above the option’s strike price, or the price at which the option contract can be redeemed. The call option allows the investor the right but not the obligation to purchase the underlying security at the strike price. For call options, the return is positively correlated with the underlying asset price. However, investors can choose to invest in options with a variety of strike prices, as call options with higher strike prices with respect to the underlying asset are cheaper. This means they represent greater magnification of returns, but also greater risk.
The profit from the call option when the underlying exceeds the strike price is the difference between the underlying price and the strike price minus the price of the option, or the price that was paid to purchase this optionality. If the price of the underlying falls below the strike price, the investor loses the price of the option, resulting in a 100% loss.
If more calls are being bought, this is a bullish, or positive sentiment.
Call Option Profit Diagram $20
$15
$10
$5
$0 $0 $5 $10 $15 $20 $25 $30 $35 $40 -$5
-$10
Profit Diagram of a call option, where the option price is $5.00, and the strike price is $20.00. The break-even profit for this option, where the investor would have no profit and no loss, is at $25. Underlying Asset Return and Call Option Return 350% 300% 250% 200% 150% 100% 50% 0% $0 $5 $10 $15 $20 $25 $30 $35 $40 -50% -100% -150%
Underlying Return Call Return
This chart illustrates the power of leverage with a call option. The strike price is $20, and the price of the option is $5. The dashed line shows the return of the underlying asset at different prices and the dotted line shows the return of the call option. As the two lines converge, the difference in return is similar, but as the price of the stock exceeds the strike price, the slope of the line, or change in price as a function of underlying asset price, on the option is significantly greater relative to the underlying.
When an investor wants to purchase a put option, he or she is hoping that the stock price falls below the option’s strike price, or the price at which the option contract can be redeemed. The put option allows the investor the right but not the obligation to sell the underlying security at the strike price. For put options, the return is negatively correlated with the underlying asset price. However, investors can choose to invest in options with a variety of strike prices, as put options with lower strike prices with respect to the underlying asset are cheaper. This means they represent greater magnification of returns, but also greater risk.
The profit from the put option when the strike price exceeds the underlying price is the difference between the strike price and the underlying price minus the price of the option, or the price that was paid to purchase this optionality. If the price of the underlying rises above the strike price, the investor loses the price of the option, resulting in a 100% loss. If more puts are being bought, this is a bearish, or negative sentiment.
Put Option Profit $20
$15
$10
$5
$0 $0 $5 $10 $15 $20 $25 $30 $35 $40 -$5
-$10
Profit Diagram of a put option, where the option price is $5.00, and the strike price is $20.00. The break-even profit for this option, where the investor would have no profit and no loss, is at $15.
In this paper, we are focusing on the purchase of these securities instead of the sale of them. The purpose of analyzing option purchases instead of option sales is because the majority of investors who want to make a purchase on a put or call option are investing in an opinion about the underlying security. However, the sale of the option is typically taking place on the broker-side, or at firms that are charging a premium price for the option to take on this opposing risk of the investment.
How are these options priced?
The Black-Scholes Model, a pricing model developed in 1973 by Fisher Black,
Robert Merton, and Myron Scholes to calculate the fair price of an option. Some assumptions that are made in this model are that the options are all European, there are no dividends paid out during the life of the option, the risk-free rate and volatility of the option are known and constant, and no transaction costs are included. The major components of the pricing model are as follows: the current underlying price, the option strike price, the time to expiration, the risk-free interest rates, and implied volatility. Each of these components has different effects on the price of an option.
The current underlying price is the price of the asset that the options is derived from. The strike price is the predetermined price that the call (put) buyer has the right, but not the obligation to buy (sell) the option at on – or before for American options – the day of expiration. The time to expiration is expressed as a percentage of time and shows how much time is remaining for the option contract. The risk-free rate is an interest rate used to reflect the cost of borrowing.
Volatility is a statistical metric for analyzing the standard deviation, or price movement from the average price, over a given period of time. Volatility is observed in two different ways: the realized volatility and the implied volatility. Realized volatility is the historical price movement of a security whereas implied volatility is the predicted price movement of a security. In the Black-Sholes model, every variable is known and easily observable except for implied volatility. We would also be able to use the Black-
Sholes model to find the implied volatility of the option by obtaining the currently traded option price. The implied volatility is a unique measure of sentiment because it is market- based, where we would be obtaining a metric based on what other participants are investing in the market.
These factors affect the price of options in different ways and can have different impacts on different types of options. Below is a chart for calls and puts, and their variables’ relationship to price. Call Put with an increase in… Underlying Price Positive Negative Strike Price Negative Positive Time to Expiration Positive Positive Risk Free Rate Positive Negative Volatility Positive Positive
This table shows the relationship between call and put options and the variables involved in the Black- Sholes pricing model.
Call options have a positive relationship between the underlying price, the time to expiration, the risk-free rate, and the volatility. If the underlying price increases, the price of the call will increase because the option is closer to being in the money. In conjunction with this, a higher risk-free rate implies higher expected returns for the underlying, which would put upward pressure on a call option. If the time to expiration is increased, the option has a longer timeline to be in the money. If the volatility of a call option is high, this is positive because there is a higher probability of large underlying price movements for the option to be in the money or closer to the money, resulting in a greater price. Call options have a negative relationship with the strike price because with an increased strike price, it is further away from being in the money, creating a higher price target expectation for the underlying.
Put options have a positive relationship between the strike price, the time to expiration, and the volatility. If the strike price increases, the price of the put will increase because the option is closer to being in the money. This is because the option will be classified as in the money if the underlying price falls below the strike price. If the time to expiration is increased, the option has a longer timeline to be in the money. If the volatility of a put option is high, this is positive because there is a higher probability of large underlying price movements for the option to be in the money or closer to the money, resulting in a greater price. Put options have a negative relationship with an increased underlying price and the risk-free rate. An increased underlying price would result in the option getting further away from being below the strike price or in the money. Higher risk-free rates imply higher expected returns for the underlying, which would put downward pressure on a put option.
How did we use this to find our conclusion?
We used data from 2007 to 2015 on both SPY and VIX options and the indices’ respective returns to find if market returns could predict market volatility, vice versa, or both. There has been strong evidence in previous research that demonstrates the predictive power that options have on stocks. As mentioned previously, the attractiveness of options for investors is present when there is either insider information or above- average confidence in the investment thesis from the investors’ perspective. A lead-lag relationship has been observed from options to stocks, primarily because of the ability to utilize leverage and capitalize on these positions, which then compress as the underlying catches up to the option. This is due to the stock market moving towards the option market’s opinion, and relative returns between the option and the stock become similar.
We used a call-put ratio to determine when market or volatility sentiment was bullish, neutral, or bearish, and separated these measures of sentiment out into terciles.
We calculated call/put volume ratios for SPY and VIX options separately for each calendar month as shown in the equation below:
퐶푎푙푙 푉표푙푢푚푒푗 퐶푃푉푅푆푃푌 = 퐶푎푙푙 푉표푙푢푚푒푗 + 푃푢푡 푉표푙푢푚푒푗
For S&P options, the call option volume was divided into separate terciles with an equal number of observations in each. These terciles were defined by the top tier, middle tier, and bottom tier of volume of call options relative to total option trading. The purchase of a call option represents a bullish sentiment, due to the positive correlation between the underlying asset and the option’s price, making it a strong indicator for future market sentiment.
For VIX options, the call option volume was divided into separate terciles with an equal number of observations in each. We used the same call-put volume ratio equation for the VIX as we did for SPY. These terciles were defined by the top tier, middle tier, and bottom tier of volume of call options relative to total option trading. The purchase of a call option represents a bullish sentiment, due to the positive correlation between the underlying asset and the option’s price, making it a strong indicator for future volatility sentiment.
We tested the significant predictability levels in these different sentiment terciles for both predicting market return and market volatility.
How does this apply to the paper?
We used this metric to determine that investors concerned with future market returns should more closely follow market volatility sentiment when market sentiment is bearish or neutral. Investors concerned with future market volatility should follow market volatility sentiment when market sentiment is bullish.
Investors concerned with future market volatility should more closely follow market sentiment when market volatility sentiment is bearish or neutral. Investors concerned with future market returns should follow market sentiment when market volatility sentiment is bullish.
We also used economic indicators to test the robustness of our results. We performed this test using a multivariate regression, and even with these variables introduced to the test, we found consistent results as previously stated.
Personal Journey
I started my academic college career in the Honors Tutorial College as both a
Chemistry and a Business Administration major. After a week in both majors, I found my passion for business and the career paths that it had to offer. I enjoyed the challenging and competitive environment that Business Administration had to offer with the ability to integrate quantitative analysis and constant interactions with others in the form of group projects. I was able to experience this during my first two classes in the College of
Business in Dr. Raymond Frost’s Management Information Systems class and Dr. Janna
Chimeli’s Quantitative Business Analysis class. In both classes, they had fun lectures and
I was able to explore new concepts via the Team-Based Learning method. I chose to major in management information systems and finance within the Business
Administration area of study.
Given my new excitement for business, I was eager to get involved in the College of Business to learn more with other students and gain some hands-on experience in the majors that I chose. In the second semester of my freshman year, I was introduced to the
Fixed Income Management Group. The Fixed Income Management Group, an organization that manages a $2.8 million portfolio of Ohio University’s working capital through fixed income vehicles such as corporate bonds, mortgage-backed securities, and
Treasuries. I started in the group as an analyst and soon advanced to leading my own team to pitch investments to the group as a head analyst. As I continued to learn about the basics of Fixed Income, I was curious about the mechanics of financial markets and the macroeconomic environment. This curiosity persisted, and I became interested in researching further into the subject. In January of my sophomore year, I joined the executive board of the Fixed Income Management Group as the Vice President of
Operations.
During the second semester of my sophomore year, I had a Research Methods tutorial with Dr. Katie Hartman. This tutorial was very impactful on my college career primarily because it not only taught me how to read and write academic papers, but also pushed me to introduce myself to my now-thesis advisor, Dr. Andy Fodor. Dr. Hartman gave us an assignment that included an interview with a potential thesis advisor and I was very fortunate to have met Dr. Fodor in this way. Dr. Fodor has done prior research studies in asset pricing, which takes a lot of account into macroeconomic factors. We began to discuss different areas of interest and found several overlaps of interest, and this led to the continuation of our tutorials for the next two years.
The summer after my sophomore year, I wanted to experiment with my interest in information systems and interned at The Wendy’s Corporation as a systems analyst in the
IT group. I enjoyed working in the IT department and learning about the different ways that the company’s systems interacted, but I learned quickly that I wanted to lean more towards the financial aspects of the business. Along with my opportunity at Wendy’s, I was invited to attend diversity conference at Bank of America Merrill-Lynch and a sales and trading workshop at UBS. I was able to have these incredible opportunities because of the education in the classroom, my hands-on experience in the Fixed Income
Management Group, and the academic research done with Dr. Fodor. These two events reconfirmed my desire for an investments-driven role by introducing me to the work environment of the trading floor of both banks and allowing me to network with junior and senior employees to learn more about what to expect in a career in finance. In my junior year, I continued to work with Dr. Fodor on different research topics, and we decided to work with options and their components to predict future performance.
I was eager to start my thesis research, and we made the decision to start the research process early. We determined that a publishable paper was the most ideal route for a thesis, and we began exploring different types of data and performed some analysis using
SAS. We initially were going to look at options and their predictability for asset bubbles, but we switched topics in my senior year to observe market performance and volatility predictability, as this topic proves more likely to lead to a publishable thesis.
I used this new knowledge to continue my interests and discuss my passion for financial markets to find an internship in the sales and trading division at Bank of
America Merrill-Lynch. I had the opportunity to actually work with the securities that I had been studying and analyzing for my thesis and it was interesting to interact with industry professionals about my research and their personal experiences. The ability to network with salespeople and traders about the market’s mechanics made me even more excited to return to school and continue my thesis research and see how it could discover some new patterns in the market.
The thesis has complemented my academic career by developing my technical skills as well as my organizational skills and self-discipline. I have been able to learn about financial markets in increased depth and breadth while working with new software to transform the data into useable information. Being able to effectively communicate this information to a new audience was also very important when writing a publishable paper. I have also learned how to consult my advisor for different problems and collaborate with him to find new solutions. I have become incredibly self-disciplined and learned how to structure milestones and my own research path to get to the end goal.
I’m excited to continue with this interest as I finish my thesis and go on to work full-time at Bank of America Merrill-Lynch as a commodity options trader. I am very grateful for the opportunities that HTC has provided me, and I am excited to pursue my interests in the same industry that my thesis encompasses.
Table of Contents Abstract ...... 1
1. Introduction ...... 2
2. Literature Review ...... 3
2.1 Advantages of Trading Options ...... 3
2.2 The Beginning of Options and Predictability ...... 4
2.2 Using Option Volume as an indicator ...... 4
2.3 Market Volatility ...... 5
2.4 Using Economic Data for Prediction ...... 8
2.5 Varying market states and their effect on investor decisions...... 9
3. Data and Methodology ...... 10
4. Conclusion ...... 24
5. Bibliography ...... 27
6. Index of Figures and Tables ...... 30
Abstract
In this paper, we examine the relationship between market (SPY) and market volatility (VIX) options and future market performance and volatility forecasting. We find higher relative call volume for SPY options predicts higher returns, absolute value of returns, and volatility. Higher relative VIX call volume is associated with lower future returns and volatility. The main contribution of this paper is examining the power of SPY and VIX option volumes to jointly predict future returns and volatility. When SPY call volumes are at low and moderate (high) levels, VIX option volumes predict future returns
(volatility). When VIX call volumes are at low and moderate (high) levels, VIX option volumes predict volatility (future returns and volatility). We also show our results are robust to controlling for a variety of macroeconomic indicators.
1 1. Introduction
In this paper, we provide statistically significant evidence suggesting index options on both the market (SPY) and market volatility (VIX) have predictive power for future market performance and volatility. We used 20-day returns as a measure of market performance and absolute value of returns and their standard deviations to measure volatility.
We found that when SPY call volume is relatively high, returns, absolute value of returns, and volatility of returns are all higher. This is evidence that when options traders are bullish on market performance, the market actually shows greater returns. This supports previous studies on the lead-lag relationship between options on the stock market. Conversely, when VIX call volume is relatively high, returns on the S&P 500 are lower and volatility is lower.
We also performed double-sorts with SPY call ratios and VIX call ratios. We first sorted by SPY (VIX) call volume ratios into terciles and then sorted those terciles into
VIX (SPY) call volume ratio terciles. When SPY call ratios are in the low or middle terciles and VIX call ratios are relatively high, returns are significantly lower. However, within the high SPY tercile, return differences are insignificant across VIX terciles, but standard deviations and absolute values of returns are lower when VIX call ratios are higher.
Within the low VIX tercile, higher SPY call volume ratios predict higher market volatility. Within the high VIX tercile, when SPY call volume ratios are relatively high, returns and standard deviation of returns are higher. However, within the middle VIX
2 tercile, the only significant relationship is a positive relationship between SPY call volume and absolute returns.
We also show our results are robust to controlling for a variety of macroeconomic indicators via univariate regression analysis. When controlling for these indicators, results are consistent with previous tests.
2. Literature Review
In our study, we use market option volumes to predict returns and volatility in the market. We classify market returns as daily returns on the S&P 500 and volatility as absolute values and standard deviations. We use option volumes on SPY and VIX respectively as measures of market sentiment and market volatility sentiment. The S&P
500 is a widely accepted index that measures market performance by tracking the returns of more than 500 different companies that represent more than 80% of overall market capitalization. The VIX is an index that uses implied volatilities from S&P 500 options to provide a forward-looking measure of market volatility.
2.1 Advantages of Trading Options
Black (1975) writes that the major attraction that options for investors is the typically lower cost in relation to purchasing the underlying security, allowing for use of financial leverage. Manaster and Rendleman (1982) point out that options may provide an attractive alternative when there is low availability of short selling of the underlying asset and there are no margin requirements for some option positions. Additionally,
Chan, Chung, and Fong (2002) show that if an informed investor has inside information about volatility, he or she can turn to the option market to benefit from this knowledge.
3 2.2 The Beginning of Options and Predictability
Many past works have provided evidence of the connectedness of stock and option markets. Manaster and Rendleman Jr. (1982) demonstrate the lead-lag relationship between stock and option returns in equilibrium. Easley, O’Hara, and Srinivas (1998) further explore this concept by building a model that shows a lead-lag relationship from option prices to both negative and positive stock price movements. Anthony (1988) shows the relation between stock and option prices via trading volume data using call/put option ratios, documenting a positive relationship between this measure and future stock returns. Easley, O’Hara, and Srinivas (1998) also provide evidence that informed traders will go to the option market to capitalize on leverage. This is observed from trades in a multimarket environment that experiences both positive and negative news and can provide information about future stock price changes.
Chang, Chung, and Fong (2002) take a similar approach and use a sample of 60 stocks with options listed on the CBOE and have comparable results to Easley, O’Hara, and Srinivas (1998), reaffirming option-predictability exists for underlying assets. This was achieved by demonstrating the positive (negative) relationship between call (put) volume and future stock prices. Chakravarty, Gulen, and Mayhew (2004) use 5 years of historical stock and option data for 60 firms and find that on average 17% of option activity contributes to stock price movement and is significant for price discovery.
2.2 Using Option Volume as an indicator
Cao, Chen, and Griffin (2005) examine the asymmetry present in stock and option volume, finding option markets have predictive power prior to takeovers. Easley, O’Hara, and Srinivas (1998) show that using not only option volume, but directional volume, is
4 more effective when predicting future market activity. By using a directional analysis, we can observe overall market sentiment (bullish/bearish). Instead of simply using a ratio of put and call volumes, Cao, Chen, and Griffin (2005) also consider if trades are buyer- initiated or seller-initiated. Roll, Schwartz, and Subrahmanyam (2009) use O/S
(option/stock) trading volume ratio as a variable for predicting future market performance. The authors chose to use O/S volume as it provides further insight to the importance of institutional behavior, delta, and trading costs. Cremers, Fodor, and
Weinbaum (2012) find option volume has predictive power for stock returns ahead of news events and this predictive power varies based upon if news events are expected or unexpected.
2.3 Market Volatility
When pricing options using the Black-Scholes model, the only unknown variable is volatility over the remaining life of the option. Whaley (2000) states that there is statistically significant evidence of a negative relationship between two volatility index
(VIX and VXN) levels and returns of two stock indices (NASDAQ100 and S&P100).
Poon and Granger (2003) summarize several works examining forecasting implied volatility. Cremers and Weinbaum (2010) further investigate the relationship of implied volatility, resulting in a one-to-one correlation between implied volatility and the option price. This shows implied volatility can be a useful variable when analyzing option data.
Skinner (1989) demonstrates the significance of option trading on individual stocks, showing differential pricing and trading characteristics. Market volatility prediction was further investigated using the prices of call options on the S&P100 in
5 Blair, Poon, and Taylor (2000), using a GARCH model. Similar conclusions were reached in Martens and Zein’s tests (2002) when using a long memory model.
In 1992, Day and Lewis tested different methods to predict future market returns using volatility. Giot (2003) used NASDAQ100, S&P100, VIX, and VXN data to perform OLS regressions and reconfirm the relationship between market performance and volatility performance, and also analyze the asymmetry between these market indicators. Giot took three different time periods involving different combinations of volatility levels and market sentiment to further explore this relationship in different market states.
Ofek et al. (2004) used implied volatility as a variable to determine mispricing between options and underlying assets to predict future stock returns. In a more recent study, Lin and Lu (2015a) found option implied volatilities have greater predictive ability during upcoming analyst-related news.
There have been several studies that aim to predict market volatility. These studies primarily use two distinct methods. The first is ARCH/GARCH models, which forecast future stock market return volatility using lagged returns (Donaldson and
Kamstra, 2004). The second is using option market volume, as shown in Chordia, Kurov,
Muravyev, and Subrahmanyam (2017) where order flow is observed to determine future stock returns.
In 2010, Xing, Zhang, and Zhao performed another study that analyzed the predictive power of option volatility smiles on future equity returns, resulting in evidence of persistent predictability for at least 6 months. They accomplish this by developing
6 trading strategies with the volatility smile (skew) and then performing a Fama-MacBeth regression to determine if this variable can predict the next week’s returns.
Chung, Tsai, Wang, and Weng (2011) used S&P 500 options as well as VIX options to predict future S&P 500 returns. Moreover, the addition of VIX option data significantly improved the predictability of future market performance within the S&P.
Using regression analysis, there is similar, but not identical predictability of future market returns from the S&P 500 and the VIX. Adding VIX was discovered to be most effective in times of more extreme market levels.
Fernandes, Medieros, and Scharth (2014) conduct a time series analysis of the
CBOE’s VIX. As expected, VIX level and S&P 500 returns have a negative relationship along with a positive contemporaneous link with S&P 500 volume. This is consistent with Whaley’s (2000) description of VIX as a gauge for negative sentiment or “fear.” In this sense, if VIX is high, it translates to more negative sentiment in the market.
Conversely, lower levels of VIX signal more complacency or sometimes even optimism in the market (Fernandes, Medieros, and Scharth, 2014). These higher (lower) levels of
VIX tend to result in an undervaluation (overvaluation) in the S&P500, occasionally resulting in a rally (correction) shortly following.
Carr and Wu (2016), found a significant relationship between expected risk premium from a stock’s volatility surface and the stock’s future value. Carr and Wu define option realized volatility as “zero realized profit” volatility while performing analysis using delta hedging. Option expected volatility is then determined by finding the volatility level where “zero expected profit” is reached.
7 Many past works demonstrate that market volatility can also be predicted by different variables from options, namely option volume and option volatility.
2.4 Using Economic Data for Prediction
Later in our paper we use economic indicators in a multivariate regression to predict various returns and standard deviations of returns. Bakshi, Panayotov, and
Skoulakis (2011) find stock index variances can be useful in predicting future returns and other economic variables, similar to the ones we use in our regressions.
Mayhew and Stivers (2003) used equity index options and found that these securities’ implied volatilities provide trustworthy information about future firm-level volatility. This was done in comparison to a time series approach. In the same year,
Nofsinger and Prucyk (2003) analyzed 21 different macroeconomic news announcements on S&P100 stock-index option volume and volatility. They found that when bad news is reported, option volume increases are delayed, but there is an immediate reaction for option volatility.
In Conrad and Loch (2014), similar macroeconomic variables are used to predict future market volatility. Smith and Rajan (2017) used a regression analysis similar to ours to predict major stock market moves and/or stock market volatility using Fed bank variables and macroeconomic indicators including money supply, CPI, PPI, and GDP.
This observation is further tested for robustness by controlling for macroeconomic data, similar to our study. The study concludes that net buying of put options predicts index returns. The results show that market-makers have superior information about future market performance. This is further supported by Hendershott, Livdan, and
Schürhoff (2015), who discovered that institutional trading predicts macroeconomic
8 news, leading to greater knowledge about broad markets. However, previous literature suggests these institutions that function as market makers do not typically take a highly levered “side” of the markets, but instead hedge out their risk (Chordia, Kurov,
Muravyev, and Subrahmanyam, 2017). Additionally, Cooper, Gutierrez, and Hameed
(2004) utilize economic indicators as a robustness test when observing market ups and downs in equities.
2.5 Varying market states and their effect on investor decisions
Past research has shown that investors behave differently in different market states.
Kim and Zumwalt (1979) have an extension of Fabozzi and Francis’s model on beta coefficient adjustments during bull and bear markets. They show a large amount of companies that have a significantly different market beta when the market is in differing cycles. They also demonstrate that investors require a discount when taking on downside risk and are willing to pay a premium for upside variation, showing that investors make different decisions during different cycles and are sensitive to different market states when pricing risk.
Tang and Shum (2003) incorporate skewness and kurtosis in a study for predicting returns during both bullish markets and bearish markets. They also find that total risk can be positively and significantly related during up markets and negatively and significantly related during down markets. Gutierrez, and Hameed (2004) find that during different business cycles, momentum has different predictive power on future returns. They show that there are higher future returns after a positive market rather than a negative one. In our paper, we acknowledge this research by analyzing the variables into different terciles of bullish, bearish, and neutral market sentiment.
9
3. Data and Methodology
We collect option trading volume for all SPY and VIX options with 90 or less days to expiration from OptionMetrics from January 2008 to December 2015. SPY, the
SPDR S&P 500 ETF Trust, is a major exchange-traded fund that tracks the performance of the S&P 500 Index. VIX, the CBOE Volatility Index, is an index used to gauge the 30- day market expectation for S&P 500 volatility and is constructed using implied volatilities from S&P 500 index options. Daily S&P 500 return data is collected from
CRSP for the period December 2007 through January 2016. We calculate 20-day buy- and-hold returns beginning on the first day of each month in the sample period as shown in equation (1).
20 퐵퐻푅푡 = ∑푖=1(1 + 푅푒푡푖) − 1 (1) where 푅푒푡푡 is the daily return on the S&P 500. Absolute value of 20-day returns (|BHRt|) is the absolute value of BHRt. Standard deviation of 20-day returns (푆푇퐷푡) is calculated as shown in equation (2)
1 푆푇퐷 = √ ∑20 (푅푒푡 − 푅푒푡̂ )2 (2) 푡 20 푖=1 푖 where 푅푒푡̂ is the mean of returns for days 1 through 20.
We calculate call/put volume ratios for SPY and VIX options separately for each calendar month as shown in equation (3).
퐶푎푙푙 푉표푙푢푚푒푗 퐶푃푉푅푆푃푌 = (3) 퐶푎푙푙 푉표푙푢푚푒푗+푃푢푡 푉표푙푢푚푒푗 where 퐶푎푙푙 푉표푙푢푚푒푗 is the sum of volume for all call options in our sample for SPY in month j and 푃푢푡 푉표푙푢푚푒푗 is the sum of volume for all put options for SPY in month j.
CPVRVIX is calculated in the same way using all VIX options in month j.
10 We also use multiple regression to determine the robustness of the relationship between the VIX and S&P 500 option volumes and return, absolute return, and standard deviation of returns. We included the following variables which have been shown to predict S&P 500 returns and volatility: CPI (Consumer Price Index) Data, SPX (S&P
500) daily and monthly pricing, U.S. historical Treasury rates, Bloomberg Barclays
Aggregate Bond Index Returns, and various S&P 500 Valuation metrics including price to earnings, price to book, enterprise value to sales, enterprise value to earnings before interest and taxes (EBIT), and enterprise value to earnings before interest, taxes, depreciation, and amortization (EBITDA). All T-stats are shown in parentheses.
Table 1: S&P 500 Returns by SPY Volume Ratio
In Table 1, we analyzed raw returns, absolute value of returns, and standard deviation of returns on the S&P 500 after dividing months into terciles based on the SPY volume ratio, presented in equation 3. The SPY volume ratio is an indicator of option market sentiment where a higher (lower) SPY volume ratio implies a bullish (bearish) outlook. Given this, we expect future S&P 500 returns to be higher (lower) for the higher
(lower) SPY volume ratio terciles.
The 20-day average return for the highest SPY volume ratio tercile was 71 basis points, where the average return for the lowest tercile was 16 basis points. The difference of 54 basis points was significant at the five percent level. This annualized difference of
6.68% is also economically significant. The finding of bullish (bearish) option market sentiment predicting strong (weak) future returns is consistent with our expectations and findings in existing literature.
11 While our main point of focus after dividing months only by SPY volume ratio is raw returns, we also explore future volatility in Table 1. To the degree that large price movements, in either direction, contribute to higher volatility, we expect higher absolute value of returns and standard deviations for the highest and lowest SPY volume terciles relative to the middle tercile. However, for both measures the lowest (highest) values are observed for the lowest (highest) SPY tercile. The high minus low tercile absolute value of returns difference is .0082, and the standard deviation difference is .0017. Both of these differences are significant at the one percent level. This implies future returns are more volatile following bullish option market sentiment relative to bearish option market sentiment. This is contrary to our expectations and is further explored in later tables.
Overall, findings in Table 1 suggest trading volume in index options is informative for future returns and volatility.
Table 1: SPY Tercile Ret[1,20] AbsRet[1,20] StdRet[1,20] Low 0.002 0.033 0.011 2 0.007 0.035 0.011 High 0.007 0.041 0.013 High-Low 0.005 0.008 0.002 t-stat (1.99) (4.33) (3.74)
Table 1: SPY Returns and Volatility by SPY Volume Ratio In this table, we sort months into terciles based on SPY volume ratios. After dividing months into terciles, we calculate means for the BHRt, |BHRt|, and STDt. We also present differences of means, and T-statistics for each variable between the highest and lowest SPY volume ratio terciles.
Table 2: SPY Returns by VIX Volume Ratio
In Table 2, we performed analysis similar to Table 1, but sorted months into terciles based on VIX volume ratios. The VIX volume ratio is an indicator of option market volatility sentiment where a higher (lower) VIX volume ratio should imply a
12 higher (lower) future volatility. Given this, we expect future S&P 500 returns to be more
(less) volatile for the highest (lowest) VIX volume ratio tercile. The results for future absolute value of returns are consistent in sign with our expectations. The highest
(lowest) VIX volume ratio tercile has an absolute value of return of 3.84% (3.56%).
However, this difference is statistically insignificant. For standard deviation of returns, the value for the highest (lowest) tercile is 1.13% (1.22%). This is somewhat counterintuitive but will be addressed below.
While volatility is the main focus of this table, we also analyze raw returns across
VIX volume ratio terciles. Interestingly, we find a significant difference in raw returns between the high and low VIX volume ratio terciles. The highest (lowest) tercile has a raw return of 5 (95) basis points. The 20-day absolute value average return for the difference between the highest and lowest VIX volume ratio tercile was 89 basis points, and is significant at the one percent level. This annualized difference of 11.22% is also economically significant. This is consistent with the notion that high volatility is typically paired with poor returns. This sends a signal of poor returns which are larger in magnitude than in the low VIX tercile, but slightly more consistent. We later explore the findings in Table 2 between VIX volume ratio and S&P 500 returns while considering other variables shown to predict future returns and return volatility in previous works.
13 Table 2: VIX Tercile Ret[1,20] AbsRet[1,20] StdRet[1,20] Low 0.010 0.036 0.012 2 0.005 0.035 0.011 High 0.001 0.038 0.011 High-Low -0.009 0.003 -0.001 t-stat (3.29) (1.51) (2.07)
Table 2: SPY Returns and Volatility by VIX Volume Ratio In this table, we sort months into terciles based on VIX volume ratios. After dividing months into terciles, we calculate means for the BHRt, |BHRt|, and STDt. We also present differences of means, and T-statistics for each variable between the highest and lowest SPY volume ratio terciles.
Table 3: S&P 500 Returns by SPY Volume Ratio/VIX Volume Ratio
Panel A and Panel B show that when market sentiment is bearish or neutral
(lowest or middle SPY volume ratio tercile), a higher VIX volume ratio predicts poor future returns. In both cases, differences between high and low VIX volume ratio tercile returns are negative, economically significant, and statistically significant at the 1% level.
In the low and middle SPY volume terciles, respectively, annualized high minus low return differences are 16.9% and 15.1%. This is consistent with Table 2 where evidence is presented that bullish volatility sentiment is associated with poor returns. Future volatility as measured through absolute value of returns or return standard deviation did not differ significantly across VIX volume ratio terciles when market sentiment was bearish or neutral.
Panel C shows that when market sentiment is bullish (high SPY volume ratio tercile), a higher VIX volume ratio predicts lower future standard deviations. In this case, the difference between high and low VIX volume ratio tercile standard deviations of returns are negative, economically significant, and statistically significant at the 1% level.
Differences for absolute value of returns and raw returns did not differ significantly
14 across VIX volume ratio terciles when market sentiment was bullish. This is consistent with Table 2 findings and will be further explored.
In total, the results from Table 3 suggest for bearish and neutral expectations for future market returns, bullish volatility signals suggest relatively lower future returns.
This is consistent with the general finding for volatility sentiment and returns in Table 2.
When market expectations for future returns are bullish, volatility sentiment has less importance in predicting future returns. For the standard deviation of returns, predictive power is strong in the highest SPY tercile. This is not the case when market sentiment is bearish for future returns or is neutral. However, when market sentiment for future returns is bullish, we observe a negative relationship between volatility sentiment and standard deviation of returns.
Table 3, Panel A, Difference across VIX terciles Low SPY Terciles Ret[1,20] AbsRet[1,20] StdRet[1,20] VIX 1 0.007 0.032 0.011 VIX 2 0.004 0.032 0.010 VIX 3 -0.006 0.035 0.012 High-Low -0.013 0.003 0.001 t-stat (3.16) (1.17) (0.87)
Table 3, Panel B, Difference across VIX terciles Middle SPY Tercile Ret[1,20] AbsRet[1,20] StdRet[1,20] VIX 1 0.013 0.035 0.011 VIX 2 0.007 0.034 0.010 VIX 3 0.001 0.036 0.011 High-Low -0.012 0.000 0.000 t-stat (2.73) (0.15) (0.02)
15 Table 3, Panel C, Difference across VIX terciles High SPY Tercile Ret[1,20] AbsRet[1,20] StdRet[1,20] VIX 1 0.009 0.040 0.015 VIX 2 0.006 0.038 0.012 VIX 3 0.007 0.045 0.011 High-Low -0.002 0.005 -0.003 t-stat (0.34) (1.24) (3.83)
Table 3: S&P 500 Returns and Volatility by SPY Volume Ratio/VIX Volume Ratio In Table 3, we first sort months into terciles based on SPY volume ratios, and then further sort the within SPY volume ratio terciles based on VIX volume ratios. After dividing months into terciles, we calculate means for the BHRt, |BHRt|, and STDt within each of the nine groups and present differences of means, and T-statistics for each variable between the highest and lowest VIX volume ratio terciles within SPY volume ratio terciles. Results for the low SPY volume ratio tercile are presented in Panel A, the middle tercile in Panel B, and the highest volume ratio tercile in Panel C.
Table 4: S&P 500 Returns by VIX Volume Ratio/SPY Volume Ratio
Panel A shows that when volatility sentiment is bearish (lowest VIX volume ratio tercile), a higher SPY volume ratio predicts more volatile future returns. For absolute value of returns and standard deviations, differences between high and low SPY volume ratio terciles are positive, economically significant, and statistically significant at the 1% level. Surprisingly, future market performance as measured through raw returns did not differ significantly across SPY volume ratio terciles when volatility sentiment was bearish, as was the case in Table 1. Panel B is mostly consistent with the results in Panel
A, where the predictive nature of the SPY ratio is similar for the middle VIX tercile and low VIX tercile. The only exception is differences across SPY terciles for standard deviation and absolute value of returns have slightly lower magnitudes and significance levels.
Panel C shows that when volatility sentiment is bullish (high VIX volume ratio tercile), a higher SPY volume ratio predicts higher raw returns and higher absolute values of returns. In this case, the difference between high and low SPY volume ratio tercile
16 returns is positive, economically significant, and statistically significant at the 5% level with an annualized high minus low return difference of 16.08%. Future market performance as measured through standard deviation of returns did not differ significantly across VIX volume ratio terciles when volatility sentiment was bullish.
Table 4, Panel A: Difference across SPY terciles Low VIX Tercile Ret[1,20] AbsRet[1,20] StdRet[1,20] SPY 1 0.007 0.032 0.011 SPY 2 0.013 0.035 0.011 SPY 3 0.009 0.040 0.015 High-Low 0.001 0.009 0.004 t-stat (0.29) (3.00) (4.72) Table 4, Panel B: Difference across SPY terciles Middle VIX Tercile Ret[1,20] AbsRet[1,20] StdRet[1,20] SPY 1 0.004 0.032 0.010 SPY 2 0.007 0.034 0.010 SPY 3 0.006 0.038 0.012 High-Low 0.003 0.006 0.001 t-stat (0.58) (2.05) (1.69) Table 4, Panel C: Difference across SPY terciles High VIX Tercile Ret[1,20] AbsRet[1,20] StdRet[1,20] SPY 1 -0.006 0.035 0.012 SPY 2 0.001 0.036 0.011 SPY 3 0.007 0.045 0.011 High-Low 0.013 0.010 0.000 t-stat (2.34) (2.56) (0.10)
Table 4: S&P 500 Returns by VIX Volume Ratio/SPY Volume Ratio In Table 4, we first sort months into terciles based on VIX volume ratios (volume of calls divided by volume of both calls and puts on VIX), and then further sort the within VIX volume ratio terciles based on SPY volume ratios (volume of calls divided by volume of both calls and puts on SPY). After dividing months into terciles, we calculate means for the BHRt, |BHRt|, and STDt within each of the nine groups and present differences of means, and T-statistics for each variable between the highest and lowest SPY volume ratio terciles within VIX volume ratio terciles.
Table 5: OLS Single and Double Regressions
17 In Table 5, we performed OLS regressions that reiterate the results in Tables 3 and 4. In Panel A, we show that coefficients of absolute return and standard deviation of return for SPY ratio are positive and significant. In Panel B, we find return and standard deviation of return coefficients are negative and significant. In Panel C, we included both
SPY ratio and VIX ratio as independent variables. We determined that absolute return and standard deviation again have significant and positive relationships with SPY ratio and that return and standard deviation of return is significant and negative for VIX ratio.
This is consistent with the results from Panels A and B from Table 5. The signs and significance levels of the coefficients are consistent with the results from Tables 1 and 2.
Table 5, Panel A: Single Regression SPY Tercile Ret[1,20] AbsRet[1,20] StdRet[1,20] Intercept -0.007 0.016 0.007 (1.04) (3.76) (7.12) SPY Ratio 0.031 0.053 0.011 (1.89) (4.76) (4.29)
Table 5, Panel B: Single Regression VIX Tercile Ret[1,20] AbsRet[1,20] StdRet[1,20] Intercept 0.024 0.034 0.015 (4.07) (8.31) (15.23) VIX Ratio -0.028 0.004 -0.005 (3.26) (0.60) (3.29)
Table 5, Panel C: Double Regression Ret[1,20] AbsRet[1,20] StdRet[1,20] Intercept 0.013 0.012 0.010 (1.47) (2.00) (7.18) SPY Ratio 0.027 0.054 0.011 (1.68) (4.81) (4.08) VIX Ratio -0.027 0.006 -0.004 (3.13) (0.93) (3.01)
18 Table 5: OLS Regressions In Table 5, we present the results for OLS regressions within the period of January 2008 to December 2015 where the independent variable is standard return, absolute value of return, standard deviation of return. Standard return was calculated from a 20-day buy-and-hold return calculation. The second variable, absolute value of return, was calculated by taking the absolute value of the standard return. Standard deviation of return was calculated using a 20-day buy and hold return and subtracting it from the mean of the 20-days of returns. The dependent variables are SPY ratio (Panel A), the call to total volume traded ratio for the same time period as above for SPY, VIX ratio (Panel B), the call to total volume traded ratio for the same time period as above for VIX, and SPY ratio and VIX ratio (Panel C).
Table 6: VIX Tercile Regressions
In Table 6, we test for the robustness of the relationship between VIX and future returns and future volatility within SPY volume terciles using regression analysis. In
Panel A, we find a negative and significant relationship between VIX and future returns within the lowest SPY volume tercile. This is consistent with Table 3, Panel A. For absolute returns and standard deviation of returns, the coefficient of VIX volume ratio is insignificant. This is also consistent with Table 3, Panel A. The signs and significance of
VIX volume ratio coefficients in Panel B, middle SPY volume tercile, are consistent with
Panel A and also Table 3, Panel B.
In Panel C, the highest SPY tercile, we find results consistent with Table 3 Panel
C. For returns and absolute returns, the coefficient of the VIX volume ratio is insignificant. For standard deviation of returns, the coefficient is negative and significant.
19 Table 6, Panel A: S&P Tercile Regressions SPY Ratio 0 Ret[1,20] AbsRet[1,20] StdRet[1,20] Intercept 0.028 0.027 0.010 (2.88) (4.12) (6.58) VIX Ratio -0.038 0.009 0.001 (2.75) (0.96) (0.27)
Table 6, Panel B: S&P Tercile Regressions SPY Ratio 1 Ret[1,20] AbsRet[1,20] StdRet[1,20] Intercept 0.030 0.038 0.012 (3.11) (5.85) (7.42) VIX Ratio -0.035 -0.005 -0.001 (2.46) (0.54) (0.46)
Table 6, Panel C: S&P Tercile Regressions SPY Ratio 2 Ret[1,20] AbsRet[1,20] StdRet[1,20] Intercept 0.014 0.033 0.020 (1.24) (4.19) (11.33) VIX Ratio -0.010 0.013 -0.011 (0.62) (1.08) (4.23)
Table 6: S&P Tercile Regressions In Table 6, we present OLS regressions divided into terciles. in Panel A, Panel B, Panel C we present regressions for the lowest, middle, and highest SPY ratio tercile where the independent variables are standard return, absolute value of return, and standard deviation of return, and the dependent variable is VIX ratio. We present the results for OLS regressions divided into terciles within the period of January 2008 to December 2015 where the independent variables are standard return, absolute value of return, standard deviation of return. Standard return was calculated from a 20-day buy-and-hold return calculation. The second variable, absolute value of return, was calculated by taking the absolute value of the standard return. Standard deviation of return was calculated using a 20-day buy and hold return and subtracting it from the mean of the 20-days of returns. The dependent variable is the VIX ratio, the call to total volume traded ratio for the same time period as above for VIX.
Table 7: SPY Tercile Regressions
In Table 7, we test for the robustness of the relationship between SPY and future returns and future volatility within VIX volume terciles using regression analysis. In
Panel A, we find a positive and significant relationship between the SPY and absolute returns and standard deviation of returns within the lowest VIX volume tercile. For future returns, the coefficient of the SPY volume ratio is insignificant. These findings are
20 consistent with Table 4, Panel A. The signs and 10% significance of SPY volume ratio coefficients in Panel B, middle VIX volume tercile, are consistent with Table 4, Panel B.
In Panel C, the highest VIX tercile, we find results consistent with Table 4 Panel
C. For returns and absolute returns, the coefficient of the SPY volume ratio is positive and significant. For standard deviation of returns, the coefficient is insignificant.
Table 7, Panel A: VIX Tercile Regressions VIX Ratio 0 Ret[1,20] AbsRet[1,20] StdRet[1,20] Intercept 0.017 0.010 0.002 (1.61) (1.52) (0.93) SPY Ratio -0.019 0.066 0.028 (0.71) (3.80) (5.81)
Table 7, Panel B: VIX Tercile Regressions VIX Ratio 1 Ret[1,20] AbsRet[1,20] StdRet[1,20] Intercept -0.002 0.020 0.008 (0.14) (2.74) (4.19) SPY Ratio 0.018 0.039 0.009 (0.65) (2.06) (1.83)
Table 7, Panel C: VIX Tercile Regressions VIX Ratio 2 Ret[1,20] AbsRet[1,20] StdRet[1,20] Intercept -0.029 0.018 0.011 (2.60) (2.27) (7.06) SPY Ratio 0.078 0.053 0.000 (2.70) (2.55) (0.02)
Table 7: VIX Tercile Regressions In Table 7, we present OLS regressions divided into terciles. in Panel A, Panel B, Panel C we present regressions for the lowest, middle, and highest VIX ratio tercile where the independent variables are standard return, absolute value of return, and standard deviation of return, and the dependent variable is SPY ratio. We present the results for OLS regressions divided into terciles within the period of January 2008 to December 2015 where the independent variables are standard return, absolute value of return, standard deviation of return. Standard return was calculated from a 20-day buy-and-hold return calculation. The second variable, absolute value of return, was calculated by taking the absolute value of the standard return. Standard deviation of return was calculated using a 20-day buy and hold return and subtracting it from the mean of the 20-days of returns. The dependent variable is the SPY ratio, the call to total volume traded ratio for the same time period as above for SPY.
21 Table 8: Multivariate Regressions
In Table 8, we present the results of multivariate regressions where we control for lagged returns, CPI, the one-year Treasury Bill, and returns on the Bloomberg Barclays
Aggregate Index. Some coefficients may be scaled for aesthetic purposes. These control variables are consistent with past works studying market returns and volatility such as
Conrad Loch (2014). Our main variables of interest again are the SPY ratio and the VIX ratio. Generally, our results are consistent with those presented in prior tables. In Table
8, Panel A, the coefficient of SPY ratio is positive and significant for future returns and absolute value of returns. It is also positive for standard deviation of returns but is not significant. In Table 8, Panel B, the coefficient of the VIX ratio is positive and significant for absolute value of returns and standard deviation of returns. It is also positive for future returns but is insignificant. In Panel C, when both SPY ratio and VIX ratio are included in the regressions, the results are consistent with those of Panels A and B.
Our results from Tables 1 through 4 are generally consistent with regression analysis performed in Tables 1 through 7. With a few exceptions, these relationships persist in our robustness test.
22 Table 8, Panel A: Multivariate Regression SPY Ret[1,20] AbsRet[1,20] StdRet[1,20] Intercept 0.148 0.248 0.080 (4.69) (11.87) (19.23) SPY Ratio 0.047 0.033 0.003 (3.04) (3.20) (1.37) LRet20 -0.054 -0.172 -0.060 (2.51) (12.03) (20.87) CPI -0.649 -0.992 -0.311 (4.89) (11.32) (17.79) One-Year Treasury -0.031 0.003 0.002 (14.61) (2.14) (7.49) AGG 0.711 0.526 0.115 (1.67) (1.87) (2.05)
Table 8, Panel B: Multivariate Regression VIX Ret[1,20] AbsRet[1,20] StdRet[1,20] Intercept 0.175 0.269 0.080 (5.70) (13.30) (19.99) VIX Ratio 0.175 0.010 -0.004 (0.12) (1.70) (3.76) LRet20 -0.055 -0.172 -0.060 (2.54) (12.05) (20.93) CPI -0.069 -0.106 -0.030 (5.01) (11.66) (16.36) One-Year Treasury -0.031 0.002 0.002 (13.99) (1.69) (8.30) AGG 0.631 0.452 0.119 (1.48) (1.61) (2.13)
23 Table 8, Panel C: Multivariate Regression SPY and VIX Ret[1,20] AbsRet[1,20] StdRet[1,20] Intercept 0.149 0.251 0.079 (4.70) (11.98) (18.98) SPY Ratio 0.048 0.034 0.002 (3.05) (3.31) (1.15) VIX Ratio 0.003 0.011 -0.004 (0.32) (1.91) (3.69) LRet20 -0.054 -0.172 -0.059 (2.51) (12.04) (20.92) CPI -0.066 -0.104 -0.029 (4.80) (11.43) (16.25) One-Year Treasury -0.031 0.002 0.002 (14.14) (1.54) (8.23) AGG 0.706 0.506 0.123 (1.66) (1.80) (2.19)
Table 8: Multivariate Regression In Table 8, we ran regressions for the BHRt, |BHRt|, and STDt with different macroeconomic variables within the same timeframe as shown in the table. The macroeconomic indicators include the monthly CPI data, the one-year treasury bill rate, and monthly returns on the Bloomberg Barclays Aggregate Index. We present the intercepts for each of these values in the regression along with their respective T-values. Some coefficients were scaled for aesthetic purposes.
4. Conclusion
In this paper, we find statistically significant evidence suggesting index options on both the market (S&P 500) and market volatility (VIX) have predictive power for future market performance and volatility.
We demonstrated this using several analyses. We first divided months into terciles based on SPY and VIX volume ratios and used these terciles as metrics for market and volatility sentiment. After this, we analyzed raw returns, absolute returns, and standard deviations of returns across terciles. We tested these relationships individually for SPY and VIX volumes as well as jointly and demonstrated the robustness of these results using regression analysis.
24 We find that higher SPY Ratios generally imply higher raw returns, absolute returns, and standard deviations of returns. When dividing the sample into terciles, we find the relationship between SPY terciles and future returns is strongest within the high
VIX tercile while results of absolute returns and standard deviation of returns is consistent across all terciles.
This implies that more bullish sentiment with respect to future returns is associated with greater future returns and higher volatility, though these relationships vary based on volatility sentiment.
A higher VIX ratio generally predicts poorer future returns. There is mixed evidence relative to volatility where a weak positive relationship between VIX ratio and absolute value of return exists and a negative relationship between standard deviation of returns and volatility sentiment is observed. The return relationship with volatility sentiment is driven by the lowest SPY terciles, while the standard deviation relationship is driven by the highest SPY tercile. This implies stronger volatility sentiment is associated with weaker but more consistent returns. Again, these relationships vary based on SPY ratio tercile.
Moving forward, this study could have further modifications to either provide additional support for this research or lead to new practical implications. The compilation and analysis of additional variables in multivariate regressions would provide more macroeconomic evidence from both the United States and the world.
Some examples of this could include international inflation data and government bills, notes, and bond yields, manufacturing data, currency price action, and commodity data. The incorporation of this data would also require international market indices to be
25 measured for “future market performance.” Moreover, a process that could be introduced to our study would be utilizing the time series (GARCH/ARCH) models as a different methodology.
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29 6. Index of Figures and Tables
Equation 1: Buy and Hold Return Calculation...... 10
Equation 2: Standard Deviation Calculation ...... 10
Equation 3: Call-Put Volume Ratio Calculation ...... 10
Table 1: SPY Tercile ...... 12
Table 2: VIX Tercile...... 14
Table 3, Panel A: Difference across VIX terciles ...... 15
Table 3, Panel B: Difference Across VIX terciles...... 15
Table 3, Panel C: Difference Across VIX terciles ...... 16
Table 4, Panel A: Difference across SPY terciles...... 17
Table 4, Panel B: Difference Across SPY terciles ...... 17
Table 4, Panel C: Difference Across SPY terciles ...... 17
Table 5, Panel A: Single Regression SPY Tercile...... 18
Table 5, Panel B: Single Regression VIX Tercile ...... 18
Table 5, Panel C: Double Regression...... 18
Table 6, Panel A: S&P Tercile Regressions ...... 20
Table 6, Panel B: S&P Tercile Regressions ...... 20
Table 7, Panel A: VIX Tercile Regressions ...... 21
Table 7, Panel B: VIX Tercile Regressions ...... 21
Table 7, Panel C: VIX Tercile Regressions ...... 21
Table 8, Panel A: Multivariate Regression...... 23
Table 8, Panel B: Multivariate Regression ...... 23
Table 8, Panel C: Multivariate Regression ...... 24
30