Project Abstract - Fuqua School of Business · Web viewUsing the CFO Survey we are able to glean real market sentiment directly from those who invest, raise, and distribute capital

Information in the Expectations of Volatility:

A two-part study into both qualitative and quantitative measures

FINANCE 663: International Finance

Prepared for: Prof. Cam Harvey

March 3, 2014

Compiled by Chatvaari

Whit Graham / Josh Kaehler / Matt Seitz

Assistance from – Brooks Hopple

Project Abstract

Can expectations about future volatility have implications for investors? In our paper, we examine two measures of expected volatility; the first, quantitative data based on the term structure of variance swaps and the second, a more qualitative measure based on the variation in the expectations of CFOs. We study the relationship between expected volatility and both US and global equity market performance and realized volatility. Based on our findings, we find significance in the variables used to predict realized volatility in the market with moderate levels of predictive power. We noticed that generally short-term expectations were much more robust in forecasting realized volatility than longer-term expectations. Using several ex-ante portfolios, we track returns based on actions signaled by the various models constructed in this research. Successful trading strategies do materialize with the majority of value accumulation occurring during periods of market turmoil. Our research indicates opportunities exist to preempt large market events by tracking implied volatility measures and trading accordingly.

Introduction to Research Interest and Topics Discussed

Measures of Volatility

In the most basic sense, volatility is a measure of variation over time. When applied to financial markets, volatility represents the changes in prices of various instruments in a given period. Two representations of volatility are often cited – realized volatility and implied volatility. In the case of realized volatility, the measure is backward looking and indicates the actual variation between a set of dates. The realized volatility (value expressed in percent) can be computed from a series of daily logarithmic returns of a given number of trading days (N) using the equation below[footnoteRef:1]: [1: JP Morgan – Equity Derivatives. “Just what you need to know about Variance Swaps.” May 2005.]

Implied volatility, on the other hand can be gleaned through the use of various marketable indices or derivatives. The Market Volatility Index (or VIX, for short) computed by the Chicago Board Options Exchange (CBOE) is a well-known measure of implied 30-day volatility in one particular index - the S&P 500[footnoteRef:2]. Using options prices, the CBOE computes a VIX index value (again in percent terms) that represents short-term market sentiment at a point in time. [2: http://www.cboe.com/micro/VIX/vixintro.aspx]

The Variance Swap

One segment of our research examines the term structure of variance swaps, another derivative instrument used to measure implied volatility. The variance swap allows parties to trade on various pre-tenses, including volatility trades, forward volatility trades, spreads on indices, and dispersion trades. There are documented advantages (and disadvantages) of the variance swap over a standard options strategy. Though much research has already been dedicated to these aspects of mispricing, replication, and the sensitivity of variance swaps. The focus of this paper will be on the term structure of variance swaps and the information therein.

The term structure for variance swaps is composed of several spot rates at a particular point in time for various expiration lengths. Similar to the VIX, the spot rate (quoted in percentage terms) represents the implied volatility for underlying security for a given duration. On the expiration date, trades are settled using realized volatility (as calculated above) and comparing against the agreed upon rate at the beginning of the period. When the realized volatility exceeds the implied volatility, the long investor is compensated (by the short investor) an amount equal to the difference in the squares of realized volatility and implied volatility, scaled by a notional amount. The spot rates are set in the market by this buying and selling activity, thereby creating a useful measure of market sentiment to analyze.

The data used for this study includes spot rates for variance swaps on the S&P 500 from January 1996 to December 2013 at durations of 1-month, 2-month, 3-month, 6-month, 12-month, and 24-month. By analyzing realized returns ex-post, we are able to gain insight into the predictive power of the term structure ex-ante. By tracking changes in both the swap spot rates and the spreads between durations along the term structure, we can construct portfolios and evaluate various trading strategies in an effort to prove if foretelling information exists in the data.

The Duke University/CFO Magazine Survey

An additional area of interest revolves around a distinctly more qualitative measure of volatility. The CFO Survey, conducted quarterly in a joint effort by Duke University and CFO Magazine, aims to capture the sentiment of chief financial officers throughout the world. Sentiment, as described in previous sections, is more or less an indirect contextual measure implied by numerical market expectations. Using the CFO Survey we are able to glean real market sentiment directly from those who invest, raise, and distribute capital for businesses globally. Questions range from ranking external risks, to qualifying demographic information, to more contemporary issues such as the Affordable Care Act, as was the case in the latest quarterly release.

By aggregating the hundreds of responses from a wide range of companies, the CFO Survey captures not only average estimates for various measures but also relative spreads in opinion between managers. Our study will carefully consider the disagreement or dispersion statistics and look for signals in the variation of CFO sentiment about future market volatility. While the CFO survey has roots as early as 1996, the data used in our research starts in 2000 and runs through Q4 of 2013. A deep dive into over a decade of information from company financial leadership will potentially yield predictive forecasts around which trading strategies can be constructed.

Analysis of Variance Swap Data

Key Questions

We focused our research on the information in variance swaps around three key questions:

1) How well do variance swaps predict future realized volatility?

2) Can variance swaps and trailing volatility data predict changes in implied volatility?

3) Can information in the term structure of variance swaps predict future short term returns in the S&P 500?

In the next section of our paper, we examine each of these questions, present key findings, and examine our findings in the context of a potential trading strategy.

Using Variance Swaps to Predict Future Realized Volatility

We began with a very basic question to gain a better understanding of the purpose and effectiveness of variance swaps. With variance swaps intended to act as a hedge against future realized volatility, we wanted to test their effectiveness. From there, we extended this question to examine the potential for signals in the shape of the term structure, in addition to using spot rates to predict future realized volatility. Finally, we wanted to determine if the predictive power of S&P 500 variance swaps might extend to foreign equity markets.

Methodology

We used a dataset of daily variance swap prices for the time period from December 1995 to December 2013. Our data provided variance swap rates, quoted in percentage points of standard deviation, for 1 month, 2 month, 3 month, 6 month, 12 month, and 24 month timeframes. We obtained daily adjusted close prices for the S&P 500 index over that same timeframe, calculated the log daily returns subsequently the future realized volatility for each of the time frames listed above using the same methodology used for variance swap payoffs (for several regressions we halted the data in December 2011 in order to have a 24 month timeframe to examine variance swap rates against realized volatility). For each point in time, we also calculated the difference between the various swap rates, which we will refer to as the “spread.” For example, the difference between the 3 month swap rate and the 1 month swap rate provides the 3m vs. 1m spread.

We then ran a series of regressions, beginning with using the current swap rate to predict realized volatility over the same timeframe as the swap duration (for instance using the 3 month variance swap rate on January 1 to predict realized volatility over the first three months of that year).

Next, in addition to using the current swap rates, we ran a series of multiple regressions also taking into account the “spread” or difference between the swap rates for different durations. We began by using each swap rate at a given duration paired with the spread of the similar duration variance swap over the one month variance swap to predict realized volatility for the swap’s duration (for instance using the 2 month swap rate plus the 2m vs 1m spread to predict 2m realized volatility). Next, we examined several regressions that paired a short term swap rate with the spread of a longer maturity variance swap over the 1 month swap in order to predict realized volatility over the same timeframe as the short term swap.

Finally, we extended our analysis to international markets by obtaining adjusted close prices for the FTSE and DAX indices. We then used the same S&P variance swap data discussed above, but instead of running regressions to predict the realized volatility of the S&P 500, we attempted to predict the volatility of the FTSE and DAX indices.

Discussion of Results

Our results argue that information in variance swap rates is reasonably accurate at predicting future realized volatility, especially in the short term. All of the simple regressions generate a negative intercept coefficient, and a coefficient for the swap rate that is positive but less than 1. This makes intuitive sense in that variance swaps on average overestimate future volatility due to the volatility risk premium. The table below shows the results of our simple regressions using swap rates at a given date to predict future realized volatility. As can be observed from the results, the variance swap rates produce fairly high r-squared values for one month and two month periods, but show significantly less “explanatory power” with r-squared values that drop off significantly after three months and fall to 2.3% for 24 months, despite T-stats that remain highly significant, even when predicting realized volatility over the long time periods. Based on these results, it seems reasonable to conclude that variance swaps are reasonably good predictors of short term realized volatility, but not particularly good at predicting volatility in the longer term. (Details of these regression outputs can be found in Appendix 1)

Variance Swap Duration

T-stat - swap rate coefficient

Regression R-squared

1 month

74.8

58.3%

2 month

57.7

45.4%

3 months

48.2

36.8%

6 months

35.0

23.4%

12 months

27.9

16.2%

24 months

9.7

2.3%

Table 1 – S&P 500 Simple Regression Summary

We also find that the spread or difference between variance swap rates of various lengths, is statistically significant when predicting future realized volatility. The form of these regression equations took the form of a positive intercept, a positive swap rate coefficient and a negative spread coefficient. This suggests that there would be a correction downward for spreads that were higher than “normal” in predicting future realized volatility. When we re-ran the regressions discussed above, adding a “spread” coefficient was significant for each of the time periods out to 12 months, and the r-squared of each regression was higher than that calculated for the simple regressions. Although there was an increase in r-squared and we obtained significant t-stats, the r-squared values increased only slightly, and the vast majority of the r-squared was generated by the simple regression. While we also tried regressions that included a short term swap rate with a longer term spread over the one month variance swap, we found that matching the duration of the swap rate with the spread generated the best results statistically. The table below summarizes some of our key regression outputs. (Details of these regressions can be found in Appendix 2)


T-stat - “spread” coefficient



2 month

-18.4

48.2

49.7%

3 months

-17.5

39.5

41.3%

6 months

-13.5

28.4

26.8%

12 months

-9.0

23.3

17.9%

Table 2 – S&P 500 Multiple Regression Summary

Finally, we found that the patterns identified above for using S&P variance swaps to predict future volatility generally held true when predicting future volatility for the FTSE and DAX indices. As with the S&P 500, using variance swaps to predict volatility over shorter time horizons generated regressions with much higher T-stats and r-squared values, however t-stats remained significant even over longer time periods. Similar to our findings with the S&P 500, adding spread coefficients for regressions predicting international volatility results in slightly higher r-squared values and significant T-stats. Although far from telling the whole story, it seems reasonable to conclude that due to the integration of global markets, especially for the UK, Germany and the United States, there is value in using variance swaps to predict future volatility in global equity markets. The summary of key regressions for the FTSE and DAX analyses are included below. (Details of these regressions can be found in Appendix 3)




1 month

71.9

53.4%

2 month

52.5

40.8%

3 months

44.3

32.9%

12 months

28.5

16.9%

Table 3 - FTSE Simple Regression Summary





2 month

-13.9

44.1

43.5%

3 months

-13.6

36.7

35.9%

12 months

-13.1

22.9

20.3%

Table 4 - FTSE Multiple Regression Summary




1 month

71.9

53.4%

2 month

55.2

43.2%

3 months

47.4

35.9%

12 months

26.6

15.0%

Table 5 - DAX Simple Regression Summary





2 month

-13.2

46.8

45.6%

3 months

-15.6

39.1

39.6%

12 months

-17.2

20.0

20.8%

Table 6 - DAX Multiple Regression Summary

Implications of Results

Variance swaps are good predictors of short term realized volatility up to about 3 months. After 6 months, we find that predictive power diminishes significantly. Looking at the term structure of variance swaps by examining the “spread” over the one month swap rate displays statistically significant results, but does not explain much of the changes in volatility beyond a simple regression using the variance swap rate. It appears that there is value in examining information in S&P 500 variance swaps in order to make predictions about volatility in global markets, at least for places like the UK and Germany that are integrated with the US/global equity markets.

Using Variance Swaps to Predict Changes in Implied Volatility

Having found that variance swaps are reasonably good at predicting future realized volatility, the next question we chose to examine was whether or not variance swaps, perhaps coupled with other indicators, could predict changes in implied volatility. If so, this could have implications for developing a trading strategy based on the VIX with trading that capitalizes on predicted changes in implied volatility.

Methodology

We began with the variance swap and S&P 500 data we compiled to examine our last question. In addition to the calculations already performed, for each data point we also calculated 1 month trailing volatility, which we consider as an input to our analysis. We then converted our daily data to monthly data, focusing on the period from February 1996 through December 2011, a period of 15 years and 10 months. We made this monthly conversion in order to test a possible trading strategy if we found one in the data. Next, we pulled VIX spot prices for the same time period as our measure of implied volatility. For each point in our dataset, we then calculated the actual 30 day change in implied volatility starting from that day’s close. We then ran a series of regressions, attempting to predict the one month change in implied volatility based on variance swap rates, trailing volatility, the term structure of variance swaps, or some combination of these variables. Our results are summarized in the next section.


We found that variance swaps may have some predictive power with respect to changes in implied volatility, but overall, our findings do not necessarily suggest actionable information. We began with a series of simple regressions, and were encouraged when we found statistically significant results for each of our simple regressions using the 1, 2, and 3 month variance swap rates to predict the change in realized volatility. (Summarized below, full results in Appendix 4) Surprisingly, the 3 month swap rate performed slightly better than the 1 or 2 month in terms of r-squared. We also performed a simple regression using 1 month trailing volatility to predict the one month change in implied volatility, and found an r-squared of 4.4% and a t-stat of -2.9.

VARIANCE SWAP Duration



1 month

-2.7

3.7%

2 month

-2.9

4.2%

3 months

-2.9

4.2%

Table 7 - Change in Implied Volatility - Simple Regression Summary

Despite the statistically significant results, examining these simple regression results further shows potential issues with the time period and trusting such a naïve prediction. For each of our simple regressions, our output shows a significant positive intercept, coupled with a negative slope coefficient for the variance swap rate. This effectively results in a forecast predicting that “on average implied volatility is going to increase, unless the variance swap rate increases above a certain level, then implied volatility is going to go down.” It is likely that the significant increases in volatility during the financial crisis in our sample resulted in the upward bias for the VIX over the regression period. However, our findings led us to examine additional factors to see if we could improve on our simple regressions.

We next ran additional regressions using 1 month trailing volatility, variance swap rates for various durations, as well as the variance swap spread over the 1 month rate for various maturities, to see if we could find a multiple regression that improved upon our simple regression results. Ultimately, we did not find any statistically significant combinations (all coefficients with T-stats of at least 2.0). Despite their obvious shortcomings, our simple regressions were the best we could do for predicting realized volatility. As a result, we are left to conclude that using information obtained from variance swaps and trailing volatility is not particularly effective at predicting short term changes in realized volatility.

Using Variance Swaps to Predict Short-Term Equity Returns

Finally, we wanted to determine if information in variance swaps and other volatility indicators might be used to predict future equity returns. If so, we would examine a long/short strategy based on the S&P 500 index and possibly international indices.

Methodology

We used the same data set described in the last section, but this time focused our analysis around a different series of regressions. For this analysis we attempted to predict future 1 month returns on the S&P 500 index by using a given set of volatility parameters at a particular date. Our possible variables included 30 day trailing volatility, variance swap rates of different durations, and spreads between different durations of variance swaps. Our results are summarized below.


We conclude that variance swaps and trailing volatility are not good predictors of future S&P 500 returns, at least for the time period we examined. Despite running dozens of simple and multiple regressions, we could not find a single result with T-stats greater than two. Based on our data, it was not possible to find a signal in variance swap data that predicts short term S&P returns. Because we did not find any significant results for the S&P 500, we elected not to extend the analysis to the FTSE and DAX because it is unlikely we would have found a significant relationship. (Regression outputs are included in Appendix 5)

Implications and Possible Trading Strategies

Based on our results, we were skeptical of the viability of any trading strategies based on our variance swap data, but we decided to examine a VIX trading strategy based on the best of our simple regressions for predicting changes in implied volatility- using the 3 month variance swap rate plus an intercept to predict the change in implied volatility. Both the regression and our strategy were simple: when our regression predicted that implied volatility would increase over the coming month, we would go long the VIX, otherwise, we would short the VIX. The next month, we would re-examine the three month variance swap rate and take the appropriate action. As we discussed earlier, due to using the swap rate and an intercept, our strategy boiled down to this: if the 3 month variance swap rate was less than 27.5, go long VIX, otherwise, short the VIX. Ultimately, our strategy resulted in a long VIX position in 154 out of 190 months that we sampled.

Despite our skepticism, our strategy was extremely profitable! Over the course of 15.8 years from February 1996 to November 2011, following our proposed strategy results in an annualized return of 52.5%, compared to an annualized return of just 4.2% for the S&P 500 for the similar period. Despite the high returns, our strategy was also extremely volatile, with an annualized standard deviation of 70.2%. (We did enjoy positive skew of 1.67).

The extreme volatility of the centered around the financial crisis of 2008-2009 likely accounts for much of our strategy’s abnormally high returns. By constantly predicting that volatility was going to increase, we were sure to realize gains on the massive increases in the VIX during this timeframe. And, at the height of the crisis, once three month variance swap rates were high enough, our strategy would eventually call for changing to a short position on the VIX and we would then gain on the back end of the crisis as well. The graph below summaries the strategy’s monthly returns over time, with a spike in returns during the 2008 financial crisis on a long VIX position, followed by additional gains in 2009 on a short position as volatility stabilized from its highs.

Figure 1 - VIX Trading Strategy Returns

We are left to conclude that while this trading strategy was successful, it is likely that it worked because the presence of the financial crisis was known ex-post when we ran the regression, and it is unlikely that such a huge spike in volatility could have been foreseen ex-ante. While it was not part of our analysis for this paper, it is likely that the most robust strategies that can be constructed based on our findings would rely on using variance swap term structure to predict future realized volatility, where we have noted significant explanatory power in our research. Such a strategy would most likely center around an options trading strategy, or perhaps even trading variance swaps directly. (Trading strategy data included in Appendix 6)

Analysis of Duke/CFO Magazine Survey Data

Key Questions

The analysis of the CFO Survey was conducted with the intention of answering the following questions:

1) Can information about volatility contained in CFO forecasts be useful in predicting future realized volatility?

2) Can information about volatility contained in CFO responses to questions about sentiment be useful in predicting future realized volatility?

We examine the two questions above by analyzing data and running pertinent regressions in order to understand potential relationships. Again, we present key findings and apply our findings to the construction of a trading strategy.

Information About Volatility in CFO Survey Forecasts

The Duke/CFO Magazine Survey requests information in three forms. Responses can be organized into short-term forecasts, long-term forecasts, and sentiment of the respondent. Our analysis first hoped to establish whether or not the forecasts, either short of long-term, of U.S. CFOs served as indicators for movements in the market. Initial indications suggested that CFOs could not effectively forecast market returns, which is to be expected as they are not investing professionals. However, we were interested to learn if their anticipations of market uncertainty could be related to what is eventually realized. Our hypothesis being that the combination of the CFOs concerns at the micro level, their company and its industry, might reveal information that the market has not currently priced in.

Methodology

The following research looks closely at two factors from both the one year and ten year forecasts that CFOs provided from 2000-2013. The items are the average of individual standard deviations of market return, and disagreement between CFO risk projections. The standard deviation metric is computed by asking CFOs their opinion on the likelihood of the market outperforming and underperforming their expectation. It is the belief of the authors that CFOs reporting a high standard deviation, or a significant change in standard deviation could be an indicator of future volatility. Disagreement amongst CEOs is measured by the standard deviation of risk premium forecasts given by respondents. Disagreement amongst CEOs on how risky the market is could reveal that the business environment has become murky, or other information that has yet to be priced in.

Although the forecasts were for either one or ten years, our analysis sought to find the predictive ability this information would have on the actual volatility over different periods. As a result, we compared the factors from the forecasts to the annualized realized volatility over the following one month, two month, three month, six month, one year, and two year periods beginning with the quarter the survey was completed. By using different period lengths we hoped to determine whether CFOs viewpoints revealed more about what would happen in the short term or over a longer time horizon.

Discussion of Results – CFO Standard Deviation Forecasts

After testing the CFO standard deviation forecasts, we found that short-term forecasts had the best explanatory power. We also found that the relationship between the forecast and realized volatility was only statistically significant on a shorter horizon. The adjusted r-squared of the one year forecast on one month realized volatility was greater than .2 with a t-stat of 3.815. Moving out to the two month horizon the explanatory power nearly halves, although the relationships is still comfortably significant. The relationship is not significant from the six month horizon on, suggesting that CFOs’ opinion on volatility can be informative in the near-term, but provides little value beyond that. Even the short-term value is limited in how informative it is as its explanatory value is relatively low, especially compared to what was observed in the variance swap analysis.

Volatility Period

T-Stat - coefficient

REgression Adj. R-Squared

1 month

3.815

0.201

2 month

2.796

0.114

3 month

2.385

0.081

6 month

1.729

0.037

12 month

1.390

0.018

24 month

0.183

-0.021

Table 8 - Realized Volatility vs 1Y Standard Deviation Forecasts - Regression Summary

Unfortunately, despite its limited value the first of the relationships we studied using standard deviation forecasts proved to be the most significant. We decided to research the impact a change in the one year forecast might have on realized volatility, with the assumption being that a large move in the managers’ view of risk could have a relationship with the observed volatility. Some of the detected trends mirrored prior analysis.

The three shorter horizons all showed significant relationships, but r-squareds dropped across the board indicating that the change in the one year forecast is a worse predictor of realized volatility than the average response itself.

Volatility Period

T-STAT Coefficient


1 month

3.030

0.134

2 month

2.226

0.069

3 month

2.094

0.061

6 month

1.431

0.020

12 month

1.180

0.007

24 month

0.891

-0.004

Table 9 - Realized Volatility v Change in 1Y Standard Deviation Forecasts - Regression Summary

The next step we took in our research was to look at the change in the forecast on the change in the realized volatility, beginning with the short horizons because of the results we had already observed. This proved to add little value. One month volatility versus the one year forecast yielded a t-stat of 1.565 with an adjusted r-squared of .027. On the two month horizon the t-Stat was .309 with an r-squared of -.017.

After completing our research on the one year standard deviation forecast we turned our attention to the ten year forecast. We theorized that there were two cases in which the ten year could “outperform” the one year in terms of usefulness. First, the ten year could be a better predictor of the longer horizons that the one year forecasts failed to explain. We thought it possible that respondents subconsciously allowed near-term bias and information affect their one year forecasts, but would trend towards a more historical average for the ten year response. The second case would be that despite the mismatch of horizons, the ten year forecast would provide better information on realized volatility no matter the period. The thinking being that asking CFOs to take a long term view might cause them to evaluate more factors that could cause an “outperform” or “underperform” environment, so the quality of information going into the response would be better.

The results ultimately disproved both of these cases. The ten year forecasts proved to have little to no value as a predictor realized volatility. As was observed with the one year forecasts, t-stats were higher on the shorter horizon, but the greatest was only slightly greater than one. It seems that contrary to our theory, instead of financial managers using better information in responding to the ten year forecast question, they may have used less. It is possible that the ten year horizon was longer than the average CFO is accustomed to considering, and as a result the information contained was worse.

Volatility Period

t-stat Coefficient

Regression Adj. R-Squared

1 month

1.002

0.000

2 month

0.439

-0.018

3 month

0.595

-0.015

6 month

0.284

-0.021

12 month

0.067

-0.024

24 month

-0.261

-0.024

Table 10 - Realized Volatility vs 10Y Standard Deviation Forecasts - Regression Summary

Our research on volatility forecasts from CFOs was not as informative as we had originally hoped. One item we noticed that could have affected the quality of data, and has been studied at length by Harvey, was the consistent “undershooting” of volatility by managers. However, we still expected the directionality to be more instructive. The information contained in short term volatility forecasts on short horizon realized volatility is likely the one area worthy of further study. Complete regression outputs for this section can be found in Appendix 7.

Discussion of Results – Disagreement of CFO Forecasts

A number of the trends we observed in the standard deviation analysis persisted when we looked at the impact of respondent disagreement. The sign of the relationship was what we expected. The larger the disagreement on the market risk premium at the time of the survey, the higher the realized volatility going forward.

Again, the one year forecast produced more attractive results than the ten year. In fact, the t-stat on the regression with one month volatility as the dependent variable was the largest we saw with any forecasting data we studied. Between three and six months statistical significance is lost, just as was observed in the prior section. Somewhat surprisingly, the disagreement regressions generally possessed stronger r-squareds than their standard deviation counterparts. This suggests that disagreement on the value received for risk-taking provides more information on volatility than responses relating to the “size” of the “tails”.

Volatility Period

T-Stat Coefficient

regression Adj. R-Squared

1 month

4.454

0.259

2 month

3.204

0.149

3 month

2.733

0.109

6 month

1.745

0.038

12 month

1.193

0.008

24 month

1.119

0.005

Table 11 - Realized Volatility v 1Y Disagreement - Regression Summary

The ten-year disagreement regressions contained less explanatory power than the one year. Both t-stats and r-squareds reduced, but interestingly the one month, two month, and three month were much closer to equal in terms of effectiveness compared to prior tests. The ten year regressions were another example of statistical significance being lost somewhere between three month volatility and six month volatility.

Volatility Period

T-Stat Coefficient

Adj. R-Square

1 month

2.230

0.068

2 month

2.201

0.068

3 month

2.128

0.062

6 month

1.693

0.035

12 month

1.364

0.017

24 month

1.131

0.006

Table 12 - Realized Volatility vs 10Y Disagreement - Regression Summary

The results of tests done on the disagreement of respondents’ market risk premium forecasts returned slightly better explanatory power, which is interesting. However, the explanatory power remained low, and the relationship between disagreement and realized volatility seemed to only exist on short horizons. Complete regression outputs for this section can be found in Appendix 8.

Information About Volatility in CFO Responses to Sentiment Questions

Methodology

The second section of our research on the CFO survey examines their confidence in the business environment in which they operate on a daily basis. The two items considered are optimism diffusion on the economy and own firm optimism diffusion. In both cases, optimism diffusion is computed based on the responses to a question that asks participants if they are “more optimistic”, “less optimistic”, or “no change”. The diffusion is the percent of respondents that answer “less” subtracted from the percent that respond “more”. Therefore, a highly positive number reflects collective improvement in optimism about either their individual firms or the broader economy, depending on the question. Our research analyzes the relationship between this metric and future volatility of the S&P 500.

Discussion of Results – Economic Optimism Diffusion

We expected a negative relationship between economic optimism diffusion and realized volatility. As anticipated, the more optimistic CFOs were at the time of the survey, the lower the observed volatility in future periods. Unlike prior tests on the CFO data, the relationship was significant on all of the time periods tested. Additionally, in this case the two year horizon proved to have the strongest relationship after registering the worst in each prior test. We are at this point unable to explain the “U-shape” of the results when viewed across the different horizons. The one month performs better than the two, three, and six, as was the trend in other tests, however the largest r-squareds occur in the two longest periods. Our initial theory was that maybe optimism about the economy is decided by longer term items like political cycles. We also considered the impact of the Fed minutes, which have been important in recent years, are released almost monthly, and often contain the long-term view of the Federal Reserve. Complete regression outputs for this section can be found in Appendix 9

Volatility Period

T-Stat Coefficient


1 month

-2.965

0.140

2 month

-2.509

0.099

3 month

-2.425

0.094

6 month

-2.076

0.067

12 month

-3.052

0.153

24 month

-3.467

0.193

Table 13 - Realized Volatility vs Economic Optimism Diffusion

Discussion of Results - Own Firm Optimism Diffusion

Own firm optimism diffusion also has a negative relationship with realized volatility, as expected. One result we did not expect was that results of these regressions contain the same “U-shape” referenced above. In this case, the one month has the strongest relationship, in fact it is the strongest of all the CFO data we measured. The group’s belief was that we would see decidedly stronger relationships between company optimism and short horizon volatility. We felt this way because most publicly traded, there are both public and non-public companies in the survey, firms are thought to be primarily concerned with short-term, quarter-to-quarter, results. We believed that for many CFOs, whether or not the company would meet or exceed earnings expectations would drive “optimism”. It is still possible that it has, given that one month volatility has the largest t-stat and r-squared, but the result of the two year data is unexpected.

Ultimately, the team decided to pursue a trading strategy based on the information contained in this section of our research. The results were not only strongest, but given the fact that these CFOs know their company better than any other item about which they were asked, they may be indirectly revealing information to the public that is not easily accessible and could, as a collection, be very valuable. Complete regression outputs for this section can be found in Appendix 10.

Volatility Period

T-Stat Coefficient

regression Adj. R-Squared

1 month

-4.880

0.332

2 month

-4.015

0.247

3 month

-3.866

0.233

6 month

-3.597

0.213

12 month

-3.751

0.237

24 month

-4.262

0.311

Table 14 - Realized Volatility vs Own-Firm Optimism Diffusion - Regression Summary

Other Considerations and Research with the CFO Survey

In addition to the research already mentioned, our team decided to examine both multivariable regressions, and the impact of the aforementioned independent variables on volatility in international markets.

Our multivariable analysis focused in on the shorter time horizons, as we had already seen that our prior tests had more success explaining these periods. For the one, two, and three month horizons, we began by trying regressions with three or more independent variables. We dropped variables until we reached a regression in which all independent variables had t-stats greater than two. In each case this occurred at the two variable threshold. Depending on the horizon, we found the variables to be two of the following three: Average of the 1 year Standard Deviation Forecast, Optimism Diffusion of the Economy, and 1 year Disagreement. For each time horizon, the r-squared of the multivariable regression was less than the strongest single variable regression. Because of this, we did not believe that the combination of factors provided more effective insight into future observed volatility.

The regression outputs of the successful multivariable regressions can be found in Appendix 11.

In order to broaden the scope of the work we had completed, we wanted to take our research beyond a U.S. centric focus. Initially, we hoped to use responses from international CFOs, but ran into issues that we believe could cloud any results. For example, we were interested in European countries, but the responses were grouped into “Europe” rather than individual countries, and given the complex differences between many European nations we thought it would be difficult to interpret any results. Instead we chose to look more closely at the U.S. responses to see if the sentiment of American managers had any impact or relationship with volatility in international markets. To measure this we repeated our prior tests, substituting the FTSE for the S&P 500.

We focused our analysis on those tests which had been most successful in predicting S&P 500 volatility. As such, we began with a look at the impacts of one year standard deviation forecasts on a one to three month horizon. The patterns observed were similar to what was seen on the U.S. volatility data, but with a somewhat weaker relationship across all horizons, as we expected. Both the one month and two month have statistically significant t-stats, but the three month does not.

Complete regression outputs for this section can be found in Appendix 12.

Volatility Period

T-Stat Coefficient

Adj. R-Square

1 month

3.148

.142

2 month

2.055

.057

3 month

1.785

.040

Table 15 – FTSE Realized Volatility vs One Year Standard Deviation Forecast - Regression Summary

This same trend persisted in the research done on the disagreement of responses. The significance of the relationships was less on the FTSE data, however as was observed on the U.S. data, one year disagreement appeared to be a stronger independent variable than the standard deviation forecast. The ten year disagreement performed slightly worse than the one year data, similar to what was detected in the U.S. research.


Volatility Period

T-Stat Coefficient

Adj. R-Square

1 month

3.477

.170

2 month

2.548

.092

3 month

2.244

.070

Table 16 – FTSE Realized Volatility vs One Year Disagreement - Regression Summary

Volatility Period

T-Stat Coefficient

Adj. R-Square

1 month

1.858

.043

2 month

1.608

.029

3 month

1.678

.033

Table 17 – FTSE Realized Volatility vs Ten Year Disagreement - Regression Summary

We compared realized FTSE volatility to economic optimism diffusion of U.S. CFOs as a next step. Just like in the U.S. data we saw a significant relationship across all of the tested time horizons. The unique “U-shape” of strength across the time horizon persisted as well. This was the most interesting international test as we found that CFO optimism about the economy had a stronger relationship with realized volatility on the FTSE than it did with S&P 500 volatility. For example, the two year time period, the strongest for both tests, returned a t-stat of -3.89 and an r-squared of .261 in our FTSE analysis, compared to -3.467 and .193 respectively for the U.S. data. Our initial theory is that this result indicates the impact of globalization. Perhaps CFO optimism is impacted more by global events that impact business partners abroad than is reflected in U.S. markets. However, one would expect that U.S. markets would easily understand these impacts and properly reflect their effects through market volatility. This likely requires further research into other markets, and over a longer time period as this sample captures a period of significant turmoil in Europe which might in some way account for this result.


Volatility Period

T-Stat Coefficient

Adj. R-Square

1 month

-3.161

.158

2 month

-2.698

.116

3 month

-2.669

.113

6 month

-2.142

.070

12 month

-2.932

.147

24 month

-3.890

.261

Table 18 – FTSE Realized Volatility vs Economic Optimism Diffusion - Regression Summary

Surprisingly, the relationship between own firm optimism and realized volatility in the FTSE is also, in many ways, stronger than that between the S&P and the same metric. It is possible that the factors mentioned above are impacting these results, but further research should be done to better understand this interesting difference during this time period. As was observed in the U.S. data, it appears that own firm optimism diffusion is the best indicator of FTSE volatility. However, in this case the 24 month horizon does not follow the pattern exhibited in prior tests, and performs the worst of any horizon. It is not immediately clear what accounts for this unexpected result.


Volatility Period

T-Stat Coefficient

Adj. R-Square

1 month

-4.927

.341

2 month

-4.510

.301

3 month

-4.397

.294

6 month

-4.030

.262

12 month

-4.112

.280

24 month

-3.521

.236

Table 19 – FTSE Realized Volatility vs Own Firm Optimism Diffusion - Regression Summary

Implications and Possible Trading Strategies

Based on our results, we decided to test a potential trading strategy using information contained in the own firm optimism diffusion data as that proved to be strongest metric across most tests. We were unsure of how successful any strategies would be because we did not find the data to be as effective as expected in predicting realized volatility in the market. We also appreciated that taking advantage of a realized volatility prediction was not as easy as one might hope. Ultimately, we pursued strategies trading the VIX, which is based on 30 day implied volatility, and variance swaps which payout based on observed volatility.

Our first thought was to test the relationship of own firm optimism diffusion and implied volatility, since we believed this would be effective given our prior tests on realized volatility. Unexpectedly, the regressions were not useful. The results of these regressions can be found in Appendix 16. Since this approach did not work we looked elsewhere to develop strategies.

Difference Between Implied Volatility and Projected Volatility Trading Strategies

The next strategy attempted was to use our one month volatility projection, based on the results of the own firm optimism diffusion, as a signal of whether or not to go long the VIX. Said differently, if our one month projection was greater than the VIX, a measure of 30 day implied volatility, we would go long the VIX. The relationship between implied volatility and realized can be somewhat problematic, but the thinking of our strategy would be that the market is potentially over or underestimating future volatility based on the difference between the two data points. This strategy would be implemented quarterly as responses to the survey became available. Our projections of 1 month volatility were based on the equation below:

1month realized vol = 21.448 - 28.7014 Optimism diffusion firm

We adjusted this strategy into three different approaches. The first was a Long VIX or Cash strategy. When our projection indicated implied volatility was too low we bought the VIX, if not we stayed in cash. The results of this strategy are below:

The strategy outperforms a hold strategy for both the VIX and S&P 500 over this period, however the annualized return over annualized standard deviation is only slightly greater than what is achieved with an S&P hold strategy (0.26). Because of this fact we wanted to adjust our strategy to be more active to see if we would find better results. The first adjustment we made was to go short the VIX in periods where our prediction suggested that implied volatility was too high, instead of remaining in cash. The results of that strategy are below:

Involving the short VIX aspect made the strategy a negative return as the strategy captured many more poor quarterly returns as evidenced by the difference in skew between the two strategies and the worst quarterly return being almost four times the worst quarterly return for the initial strategy. Our next iteration involved being long the S&P in times where the projection indicated implied volatility was too high. We believed that these were times where the S&P would be good value for the investor, and a chance to capture upside over the quarter. The results from this approach are below:

This version of the strategy is the best performer. The return/risk metric has crept to .39, an appreciable difference from the .26 of the S&P hold strategy. Again, this strategy benefits from eliminating some of the larger negative returns that the middle strategy faced.

Despite the apparent success of these strategies from 2002 to 2013, the large gains are made in the mid to late 2000s when our “signal” was correct, see the 159% quarterly gain. Looking closer at the results we saw that only the third version has positive total returns from mid-2002 to the end of 2006, and even in that case the returns are only 16%. Knowing what we know about the competitiveness of this industry, we doubt that someone implementing this strategy in 2002 would have lasted to experience the “wins” that make the strategy as a whole appear successful. Because of this we pursued other approaches to improve our results.

VIX Projection Trading Strategies

To take our initial volatility projection one step further, we looked to see if there was a relationship between our one month projection and the realized VIX price one quarter into the future. We found that, in fact, there was a relationship. The regression showing these results is located in Appendix 17. The way this works is as follows. For example, in September 2013 we have an own firm optimism diffusion from the CFOS and develop a volatility projection for one month out using this information. Using that one month projection we can also project a one quarter out price for the VIX. Using that prediction of the future VIX level we can implement a strategy.

Our first iteration was to use the VIX prices to develop an expected quarterly return for the VIX. If the expected return was positive, we went long, if it was negative, short. Very similar to the second iteration of our first strategy.

This strategy performed similarly to the final of our “difference” strategies. In this case we see a slightly greater annualized return combined with higher risk leading to roughly the same return/risk measure. However, it is worth noting that this strategy provides a slightly better total return in the early 2000s, 33% over the same period as discussed above, albeit with greater risk.

One consideration that we decided was important was the degree to which our signals suggested we should go long or short. In fact, some of our large gains or losses were the result of going long or short in periods in which the projections only suggested a slight change in the VIX. As a result, for our next test of this trading strategy we decided we would only “trade” in those quarters in which our projection suggested an absolute return of greater than 10%. If it was less than this threshold we would move into a cash position. While we recognize this is a somewhat arbitrary threshold we wanted to see the impacts of considering magnitude of trading signals in our strategy.

This small consideration created important improvements in our strategy. We actually decreased the standard deviation while increasing returns. Additionally, this strategy achieved a 67% total return between 2002 and 2006, the best of the strategies we studied, and a return that we believe to be significant enough to indicate that this strategy could be effective even without the significant swings that were experienced in the late 2000s.

Variance Swap Trading Strategies

Our team also decided to pursue a strategy using variance swaps because the payout for effectively predicting volatility was so straightforward. We went back to our own firm optimism equation to predict one month volatility each quarter, and used that information to “trade” one month variance swaps at that point in time. Our primary attempt was to go long the swap when our projection was higher than the swap market and vice versa. Because of the “risk premium” priced into variance swaps, we ended up selling more than we bought. As expected, this strategy had positive returns that appeared attractive, however our team believed that this was natural as we were simply collecting risk premium most quarters. Because we were exposing ourselves to asymmetric risk, we did not ultimately find this to be a strategy that captured much risk adjusted return.

Areas for Further Study

After completing our research we identified items that, if we had a greater amount of time, we believe to be worthy of additional research. These items primarily involve building out the research we have already done or finding explanations for trends that we observed.

The first, and potentially most obvious, area for further study is the combination of variance swap and CFO data. We think it would be interesting to use the best performing metrics from both data sets as independent variables in the same volatility tests. By doing this we could potentially discover if the data within each category is giving us overlapping or entirely different information about the market.

From a trading strategy perspective, we would have liked to have done further research on attempting to implement a trading strategy in international markets. We were unsure about the development of a liquid volatility measure that could be used, and therefore focused on U.S. trades for this paper. To improve our U.S. strategies we believe it would be worthwhile to test more complex strategies with “profit-taking” triggers to take advantage of fast price moves. This could potentially reduce exposure to the volatility of volatility and make the strategies more attractive.

The final area to consider further is the length of horizons tested. We noticed trends sometimes changing between a six month observation and one year observation. Future research could look more closely at the tipping point between the two. As time passes the length of volatility observations could be taken beyond two years for further testing as well. Ultimately, some of this will depend on the size of the sample. One of the potential limitations of our findings is that our data still comes from a relatively small sample. Continuing to study this data as years pass could give clarity to or raise new questions about our findings. Running our trading strategies through less turbulent times might reveal more information about their true effectiveness. We consider this paper a small piece of what there is to be learned from the data we have studied.

APPENDIXAppendix 1 - Regression Output for Predicting S&P 500 Realized Volatility Using Variance Swap Rates

1m variance swap rate vs. 1m realized volatility






Appendix 2 - Regressions Output for Predicting S&P 500 Realized Volatility Using Variance Swap Rates & Spreads

2m variance swap rate & 2m vs 1m spread vs. 2m realized volatility




Appendix 3 - Regressions Output for Predicting FTSE & DAX Realized Volatility Using Variance Swaps Rates and Spreads

1m variance swap rate vs. 1m FTSE realized volatility




2m variance swap rate & 2m vs 1m spread vs. 2m FTSE realized volatility



1m variance swap rate vs. 1m DAX realized volatility




2m variance swap rate & 2m vs 1m spread vs. 2m DAX realized volatility



Appendix 4 - Regression Output for Predicting 1M Change in Implied Volatility Using Variance Swap Rates

1m variance swap rate vs. 1m change implied volatility



1m trailing volatility vs. 1m change implied volatility

1m variance swap rate & 1m trailing volatility vs. 1m change implied volatility

1m variance swap rate & 2m vs 1m spread vs. 1m change implied volatility

2m variance swap rate & 2m vs. 1m spread vs. 1m change implied volatility

Appendix 5 - Regression Output for Predicting 1M Returns on S&P 500 Using Variance Swap Rates & Trailing Volatility

1m trailing volatility & 1m variance swap rate vs. 1m S&P 500 Return

1m variance swap rate & 2m vs 1m spread vs. 1m S&P 500 Return

1m trailing volatility & 2m vs 1m spread vs. 1m S&P 500 Return

1m trailing volatility & 12m vs. 1m spread vs. 1m S&P 500 Return

Appendix 6 - VIX Trading Strategy Summary Statistics

Appendix 7 - Regression Output for CFO Standard Deviation Forecasts

Change in 1 Year SD Forecast vs. Change in 1 month realized volatility

Change in 1 Year SD Forecast vs. Change in 2 month realized volatility

Change in 1 Year SD Forecast vs. 1 month realized volatility






1 Year SD Forecast vs. 1 month realized volatility












APPENDIX 8 - Regression Output for Disagreement of CFO Forecasts

1 Year Disagreement of Forecasts v. 1 month realized volatility












APPENDIX 9 - Regression Output for Economic Optimism Diffusion

Economic Optimism Diffusion v. 1 month realized volatility






APPENDIX 10 - Regression Output for Own Firm Optimism Diffusion

Own Firm Optimism Diffusion v. 1 month realized volatility






APPENDIX 11 - Regression Output for Multivariate Analyses

Multivariable v. 1 month realized volatility



APPENDIX 12 - Regression Output for FTSE 1 year Standard Deviation Forecasts

1 Year Standard Deviation v. 1 month realized volatility FTSE



APPENDIX 13 - Regression Output for FTSE 1 year and 10 year Disagreement

1 Year Disagreement v. 1 month realized volatility FTSE






APPENDIX 14 - Regression Output for FTSE Economic Optimism Diffusion

Economic Optimism Diffusion v. 1 month realized volatility FTSE






APPENDIX 15 - Regression Output for FTSE Own Firm Optimism Diffusion

Own Firm Optimism Diffusion v. 1 month realized volatility FTSE






APPENDIX 16 - Regression Outputs for Using Own Firm Optimism Diffusion to Explain Changes in VIX

Optimism Diffusion and Optimism Diffusion Lagged v. Next Quarter VIX Change

Nominal Change in Optimism Diffusion v. Next Quarter VIX Change

Optimism Diffusion v. Next Quarter VIX Change

APPENDIX 17 - Regression Output for 1 Month Volatility Projection versus VIX Price

Total Return (Log %)35096.035125.035156.035186.035217.035247.035278.035309.035339.035370.035400.035431.035462.035490.035521.035551.035582.035612.035643.035674.035704.035735.035765.035796.035827.035855.035886.035916.035947.035977.036008.036039.036069.036100.036130.036161.036192.036220.036251.036281.036312.036342.036373.036404.036434.036465.036495.036526.036557.036586.036617.036647.036678.036708.036739.036770.036800.036831.036861.036892.036923.036951.036982.037012.037043.037073.037104.037135.037165.037196.037226.037257.037288.037316.037347.037377.037408.037438.037469.037500.037530.037561.037591.037622.037653.037681.037712.037742.037773.037803.037834.037865.037895.037926.037956.037987.038018.038047.038078.038108.038139.038169.038200.038231.038261.038292.038322.038353.038384.038412.038443.038473.038504.038534.038565.038596.038626.038657.038687.038718.038749.038777.038808.038838.038869.038899.038930.038961.038991.039022.039052.039083.039114.039142.039173.039203.039234.039264.039295.039326.039356.039387.039417.039448.039479.039508.039539.039569.039600.039630.039661.039692.039722.039753.039783.039814.039845.039873.039904.039934.039965.039995.040026.040057.040087.040118.040148.040179.040210.040238.040269.040299.040330.040360.040391.040422.040452.040483.040513.040544.040575.040603.040634.040664.040695.040725.040756.040787.040817.040848.00.3470355731225290.4421014807950520.2946687595741060.2906405431473040.1067222579072710.5066842930580850.3661353851235620.361316565422950.4459497360592150.3853313849108410.5461720766245270.4390043179674730.5439548126523120.5000508843304450.4302308575645840.3812848594194450.5497166765659540.5851387720303190.7607912066160030.5808719112711531.7056141133762562.4057274262704252.1438491159074561.8348327096791511.5337885281203032.1156720391603291.8237027723327252.3332540999149991.6280584230604472.3084335481416524.9071547383754973.7736546515161655.4677091886112525.9380880386920715.785266716253926.2937449345481336.1092266311804547.6904469358243988.872284687749758.99829709700702311.6011595644096814.7690488403785914.762649064063516.4674623950219514.4775870158858914.5756794641531515.7527888433604116.8624821214462515.483757488618217.6013566484314519.3381119586567716.5718772563974314.4814839870764415.5114701274653612.5305672480056814.8769976207345619.4309249888596923.9496262734633223.3776370248358919.5280585896290325.6125524098237826.1432870732675623.1484271866919521.5917517151531318.9443625609457422.0207752539772527.4512596888892135.8998681037278935.9112851421263144.0566724235673737.6923270411052133.2866040881054134.049610902566131.8897400904340134.2252101555849635.1910060471887448.10601471167665.9298134856668873.7367822576079657.5941868251283362.7117330367016666.6257644177959371.666957765304464.8115843912190866.3740024999615170.1713222493687387.1610913476841578.5042356896438778.7084068136541978.8312871941480470.6750303820230182.3707948673343563.6153336584513666.3042947485856472.4848918811331667.7892434103016258.7304073869365867.8719725064053767.6651497661459360.9144747745934756.7361973358172357.1920094200473857.6478215042774951.4722963693535765.9587656415202152.37770069886450.690356266594648.862330123231248.9037784441981457.1105459956526662.1421191762556649.1095197904315147.8121859447245450.723790018620455.3052846643094451.408873330125361.6532252478427446.4223738576264349.9242039556539951.274307125977947.8062705690764247.9331499553045452.8737226022404661.380099855225854.9788361648479660.328495584271549.163041903148349.2469265886050844.2977301466556641.9364236229377341.568186713650141.1631261134337163.6964747928730658.8708211736827857.1532156482082955.1731653744721170.33728278776857105.2367298201088111.475388647736784.82382093565535110.6575607576548114.3137325015504103.5739751675625120.7705844173394118.2865050516235115.320073501733995.830819564053690.44563097601036121.8335873177481118.1459827936212108.0103918780805245.632712278156102.584500107781287.67552714185908124.5772827806623116.320576437833795.88628335176142108.4072938647507123.364109345788141.8954185570868160.0665403576218165.1037090492026164.5269600594484169.5240003631299154.9266151180371186.3253274487464184.2743202139061209.3991588406997178.3841433940627161.7124083641887169.5751455506334247.0882048892885265.7960380098087341.7915010582508395.9087976082982392.7521349232594381.0270713499889372.8020267538143305.601662393578336.3481952983988401.0241397174906338.4530337262391286.7547268656338310.7505447669714280.4272677349927418.5695749596678563.2731984453353438.7855223584007627.4551493850608760.4844821280594Monthly Return (%)35096.035125.035156.035186.035217.035247.035278.035309.035339.035370.035400.035431.035462.035490.035521.035551.035582.035612.035643.035674.035704.035735.035765.035796.035827.035855.035886.035916.035947.035977.036008.036039.036069.036100.036130.036161.036192.036220.036251.036281.036312.036342.036373.036404.036434.036465.036495.036526.036557.036586.036617.036647.036678.036708.036739.036770.036800.036831.036861.036892.036923.036951.036982.037012.037043.037073.037104.037135.037165.037196.037226.037257.037288.037316.037347.037377.037408.037438.037469.037500.037530.037561.037591.037622.037653.037681.037712.037742.037773.037803.037834.037865.037895.037926.037956.037987.038018.038047.038078.038108.038139.038169.038200.038231.038261.038292.038322.038353.038384.038412.038443.038473.038504.038534.038565.038596.038626.038657.038687.038718.038749.038777.038808.038838.038869.038899.038930.038961.038991.039022.039052.039083.039114.039142.039173.039203.039234.039264.039295.039326.039356.039387.039417.039448.039479.039508.039539.039569.039600.039630.039661.039692.039722.039753.039783.039814.039845.039873.039904.039934.039965.039995.040026.040057.040087.040118.040148.040179.040210.040238.040269.040299.040330.040360.040391.040422.040452.040483.040513.040544.040575.040603.040634.040664.040695.040725.040756.040787.040817.040848.00.3470355731225290.0705741626794259-0.102234636871508-0.00311138767890478-0.142501555693840.361393323657475-0.0932835820895521-0.003527336860670320.0621700879765395-0.04192286193404140.11610268378063-0.06931166347992360.0729327170005136-0.028436018957346-0.0465451055662187-0.03422244589833920.1219385096404380.0228571428571430.110812023328847-0.1021809369951540.7114695340501790.258763180393274-0.0768935024990388-0.0982923781757602-0.1061946902654870.229649595687332-0.09370988446726570.180455015511892-0.2115637319316690.2588888888888890.785483870967742-0.1918859649122810.3548758049678010.0727272727272727-0.02202643171806150.0749385749385749-0.02529815684857240.2224180472329930.1359927470534910.0127642600717990.2603305785123970.251396648044693-0.0004058441558442720.108155255124291-0.1139189731247490.006337709370755960.07557354925775980.0662393162393162-0.0771855010660980.1284658040665430.0933671313899449-0.136012364760433-0.1189624329159210.0665301944728762-0.1805352798053530.1734169994295490.2868254739912490.221169686985173-0.0229257641921397-0.1579143389199260.2963988919667590.0199430199430199-0.110335195530726-0.0644628099173554-0.1171838814265860.1542497376705140.2358949416342410.2969502407704650.0003094059405939460.220674713710925-0.141252006420546-0.1138655462184870.0222537878787878-0.0616232464929860.07100907634810460.0274177467597210.3568568568568570.3629656953153820.116644113667118-0.2159926470588230.08733880422039850.06143344709897610.0745454545454545-0.09433962264150940.02374077638755210.05636179547755640.238716502115656-0.09819360815192220.0025680534155110.00154162384378203-0.1021686746987950.163177670424047-0.2249644043663980.0416149068322980.0918306499701848-0.0638995084653195-0.1316897173782320.153047091412742-0.00300300300300288-0.0983129726585224-0.06748466257668710.007894736842105450.00783289817232363-0.1052984574111340.276078431372549-0.202827289489859-0.0316114109483423-0.03536493604213690.0008312551953448890.1644518272425250.0865862313697658-0.206401045068583-0.02588996763754040.05964912280701760.0885761589403973-0.06920152091254750.195469798657718-0.2430976430976430.07384341637010680.0265120132560066-0.06634304207119750.002599653379549580.1009657594381040.157894736842105-0.1026170798898070.095565749235474-0.1820598006644520.00167224080267539-0.0984974958263773-0.052128583840139-0.00857632933104619-0.009515570934256040.534432589718719-0.0745891276864727-0.0286885245901638-0.03404885270170240.2699530516431920.4892174984596430.0587241233629065-0.2369546621043630.3010089686098660.0327445066781559-0.09313511149978150.164444444444444-0.0203996669442131-0.0248681235870384-0.167548500881834-0.0556144067796610.343241727425687-0.0300211416490486-0.08506867523260971.262469733656174-0.580005023863351-0.1439305393220910.416143628667348-0.06575-0.1741748438893840.1292340884573890.136707663197730.1490084985835690.1271637816245010.0312738367658277-0.003472222222222130.030188679245283-0.08560311284046690.201368523949169-0.01094890510948910.135608856088561-0.147410358565737-0.09293873312564910.04832291074474140.4544217687074830.07540799099606080.2848447961046860.157872340425532-0.00795311845960663-0.0297777777777779-0.0215300045808519-0.1797752808988760.1002816901408450.19171866137266-0.155640171346978-0.1522988505747130.0833898305084746-0.09726775956284150.4908632640201640.344885883347422-0.2206159648020110.4290037243947860.211676732815646

29

Regression Statistics

R SquareAdj.RSqrStd.Err.Reg.# Cases# Missingt(2.5%,46)

0.2010.16710.2344902.013

Summary Table

VariableCoeffStd.Err.t-Stat.P-valueLower95%Upper95%

Intercept-0.6578.652-0.0760.940-18.07216.757

Avg_1_yr_SD_Forecast3.4171.5592.1910.0340.2786.556

Optimism_diffusion__economy-9.4113.847-2.4460.018-17.153-1.668



0.1920.15710.0724902.013

Summary Table


Intercept6.9085.3771.2850.205-3.91617.732

_1YrDisagree2.4001.1052.1720.0350.1764.624




0.1580.1428.8185502.006

Summary Table


Intercept-3.2636.594-0.4950.623-16.4899.962

Average_of_individual_standard_deviations3.6271.1523.1480.0031.3165.938



0.0750.0579.8815402.007

Summary Table


Intercept2.4517.3890.3320.741-12.37617.278

Average_of_individual_standard_deviations2.6531.2912.0550.0450.0625.244



0.0580.0409.1225402.007

Summary Table


Intercept5.4686.8210.8020.426-8.22019.156

Average_of_individual_standard_deviations2.1281.1921.7850.080-0.2644.520



0.1860.1708.6015502.006

Summary Table


Intercept2.4424.3670.5590.578-6.31811.201

Disagreement__standard_deviation_of_risk_premium_estimates3.1260.8993.4770.0011.3224.929



0.1090.0929.6045502.006

Summary Table


Intercept5.2564.8761.0780.286-4.52515.036




0.0870.0708.9625502.006

Summary Table


Intercept7.4774.5501.6430.106-1.65016.603




0.0610.0439.3085502.006

Summary Table


Intercept-0.5669.620-0.0590.953-19.86218.730

Disagreement__standard_deviation_of_risk_premium_estimates6.4573.4761.8580.069-0.51513.428



0.0460.0299.9785502.006

Summary Table


Intercept0.81910.3120.0790.937-19.86521.502




0.0510.0339.1525402.007

Summary Table


Intercept1.6749.4760.1770.860-17.34120.689




0.1750.1588.6654902.012

Summary Table


Intercept17.4781.25813.8880.00014.94620.009




0.1340.1169.9814902.012

Summary Table


Intercept18.0971.45012.4840.00015.18121.013




0.1320.1139.2184902.012

Summary Table


Intercept18.2511.33913.6330.00015.55820.944




0.0890.0708.7794902.012

Summary Table


Intercept18.3661.27514.4050.00015.80120.931




0.1670.1477.6624502.017

Summary Table


Intercept19.1711.15816.5600.00016.83621.505




0.2800.2615.9934102.023

Summary Table


Intercept19.6270.95320.5950.00017.70021.555




0.3560.3417.7414602.015

Summary Table


Intercept21.2791.48314.3510.00018.29124.267

Optimism_diffusion__firm-26.8285.445-4.9270.000-37.801-15.855



0.3160.3018.6264602.015

Summary Table


Intercept21.8121.65213.2010.00018.48225.142




0.3100.2948.0614502.017

Summary Table


Intercept21.8531.55914.0130.00018.70824.998




0.2790.2627.6354402.018

Summary Table


Intercept21.4891.48814.4430.00018.48724.492




0.2970.2806.8524202.021

Summary Table


Intercept21.3651.35615.7580.00018.62424.105




0.2560.2366.2153802.028

Summary Table


Intercept21.5251.31516.3640.00018.85724.192




0.021-0.0240.4004602.017

Summary Table


Intercept0.0250.0800.3120.756-0.1370.187

Optimism_diffusion__firm0.3480.3620.9610.342-0.3821.079

Optimism_diffusion__firm__1Lag-0.2350.360-0.6540.516-0.9600.490



0.018-0.0040.3964602.015

Summary Table


Intercept0.0450.0580.7730.444-0.0730.163

Nominal_Change_OptDiffusion0.2910.3230.8990.374-0.3610.942



0.011-0.0110.3974602.015

Summary Table


Intercept0.0110.0770.1410.888-0.1440.166

Optimism_diffusion__firm0.1970.2770.7110.481-0.3620.756



0.1780.1609.0984602.015

Summary Table


Intercept9.8993.8492.5720.0142.14317.656

_1_moVol_Projection_1_Fwd0.6840.2213.0900.0030.2381.130

Long VIX and Cash Strategy

Total Return500%

Annualized Return16%

Standard Deviation55%

Return/Risk0.30

Skew 4.37

Best Quarterly Return159.89%

Worst Quarerly Return-25.83%

VIX Hold Strategy Total Return-35%

VIX Hold Strategy Ann. Return-4%

S&P Hold Strategy Total Return72%

S&P Hold Strategy Ann. Return5%

Long and Short VIX Strategy

Total Return-87%

Annualized Return-16%


Return/Risk(0.20)

Skew0.58


Worst Quarterly Return-96.79%

Long VIX and Long S&P Difference Strategy

Total Return954%



Return/Risk0.39

Skew3.88



LONG/SHORT VIX Projection Strategy

Total Return1826%



Return/Risk0.40

Skew 1.45



VIX Hold Strategy Total Return-35%

VIX Hold Strategy Ann. Return-4%



LONG/SHORT/CASH VIX Projection

Total Return12006%



Return/Risk0.79

Skew 2.42



LONG/SHORT VarSwap Strategy

Total Return1039%



Return/Risk0.40


Multiple R0.763706908

R Square0.583248241

Adjusted R Square0.583144079

Standard Error6.724571568

Observations4003

CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%

Intercept-2.1139111670.291403783-7.254234.83E-13-2.685224918-1.542597416-2.685224918-1.542597416

SPX Index vs 1m0.9330028260.01246839974.829400.9085578190.9574478340.9085578190.957447834



R Square0.454368768



Observations4003


Intercept-0.1831221740.3436254-0.5329122180.594123944-0.8568193840.490575036-0.8568193840.490575036

SPX Index vs 2m0.8369037810.01449895357.7216717700.8084777570.8653298050.8084777570.865329805



R Square0.368236317



Observations4003


Intercept1.4790422060.376011693.9335005958.51368E-050.7418498252.2162345870.7418498252.216234587

SPX Index vs 3m0.7621085270.01578143848.2914511700.7311681180.7930489370.7311681180.793048937



R Square0.234985347



Observations4003


Intercept4.8050461730.42378943211.338286912.36743E-293.9741828015.6359095463.9741828015.635909546

SPX Index vs 6m0.6202467960.01769272535.056599744.9693E-2350.5855591980.6549343940.5855591980.654934394



R Square0.162399426



Observations4003


Intercept7.73 0.44 17.71 0.00 6.87 8.58 6.87 8.58

SPX Index vs 12m0.51 0.02 27.85 0.00 0.47 0.54 0.47 0.54



R Square0.023065273



Observations4003


Intercept15.713616210.4398536835.724644167.4189E-24314.8512579616.5759744614.8512579616.57597446

SPX Index vs 24m0.177263530.0182384789.7192063364.37419E-220.1415059530.2130211070.1415059530.213021107



R Square0.497009968



Observations4003


Intercept3.25 0.388.570.002.503.992.503.99

SPX Index vs 2m0.73 0.0248.190.000.700.760.700.76

2m vs 1m spread(1.81) 0.10-18.410.00-2.00-1.62-2.00-1.62



R Square0.41330551



Observations4003


Intercept4.9339676210.41252600311.960379682.03379E-324.1251867845.7427484574.1251867845.742748457

SPX Index vs 3m0.651317850.01647091139.543522255.8928

Documents

Project Abstract - Fuqua School of Business · Web viewUsing the CFO Survey we are able to glean real market sentiment directly from those who invest, raise, and distribute capital