20 Years of VIX: Fear, Greed and Implications for Traditional Asset Classes

20 years of VIX:
Fear, Greed and Implications for Traditional Asset Classes

The Abstract
In this article, I investigate the statistical properties and relationships of VIX with
equities, commodities, real estate and bonds. I find that different VIX states result in
very different risk adjusted performance for all asset classes, not just equities, and that
significant deviations from normality are observed for each state as well as the full
sample. Additionally, I demonstrate that correlations among asset classes are unstable
and non-linear, leading to highly concentrated diversification benefits at the times of
market stress, which a broad set of exposures is likely to negate. Based on empirical
data, practical recommendations for investment analysis and risk management are
included throughout the article. A companion article on alternative investment strategies
called “20 Years of VIX: Fear, Greed and Implications for Alternative Investment
Strategies” is available at http://ssrn.com/abstract=1597904

Mikhail Munenzon, CFA, CAIA
mikhailmunenzon@gmail.com

Introduction

Whaley (1993) introduced the VIX index. In the same year, the Chicago Board

Options Exchange (CBOE) introduced the CBOE Volatility Index and it quickly became

the benchmark for stock market volatility and, more broadly, investor sentiment. The

first VIX was a weighted measure of the implied volatility with 30 days to expiration

of eight S&P 100 at-the-money put and call options. Ten years later, it expanded to use

options based on a broader index, the SP 500, which allows for a more accurate view of

investors' expectations on future market volatility. On March 26, 2004, the first ever

trading in futures on the VIX index began on the CBOE. Based on the methodology for

SP 500, the index has historical information going back to the start of 1990.

Why should an investor care about volatility? Black (1975) suggested that the

informed investors would try to take advantage of their views through the options market

because of the leverage such instruments provided. Therefore, clues from the options

market may have implications for the performance characteristics of a security (for

example, see Bali and Hovakimian (2009) and Doran and Krieger (2010)). Moreover,

starting with the work of Engle (1982) and Bollerslev(1986), evidence emerged

documenting the clustering behavior of volatility1 and its resulting predictability.

Consequently, if different volatility states are associated with different performance

characteristics of a security, an investor’s investment and risk management policies will

need to be flexible enough to incorporate that such information.

In this article, I investigate the statistical characteristics of the VIX index and its

relationship not just with SP 500 but also with other traditional asset classes, which can

1
High volatility is like to be followed by high volatility; low volatility is likely to be followed by low
volatility.

2

be useful to practitioners. This article is structured as follows. After an overview of data,

I will present key empirical results; concluding remarks follow.

Data and Methods

I used data for the following asset classes: equities – SP 500 Total Return Index;

bonds - JPM Morgan Aggregate Bond Total Return Index; commodities – SP GSCI

Commodities Index; real estate – FTSE EPRA/NAREIT US Total Return Index2.

The daily data for the indices was downloaded via Bloomberg. The full historical time

horizon for this analysis is 1/2/1990 to 1/29/2010. Based on the level of VIX, I divided

the full historical sample into 6 groups to evaluate any differences in results as compared

to the full sample, assuming one remains invested only when VIX is in that particular

state. Such classification is broadly consistent with Figure 1 and practitioners’ views on

what constitutes low, medium and high volatility and provides a practical way of judging

any changes in performance and other characteristics of asset classes, given a VIX state.

Key Empirical Results

Figure 1 shows the historical level of VIX and cumulative return graphs for the

asset classes and VIX. Though the starting and ending points for VIX are relatively

comparable, the range of results is very high; one also finds that there are extended

periods of high and low volatility. The figure also suggests that crashes don’t just happen

– they are generally preceded by periods of increasing turbulence, which ultimately push

markets over the edge.

2
Some investors consider commodities and real estate alternative asset classes, as compared to stocks and
bonds. However, for the purposes of this analysis, I consider all such asset classes to be traditional
ingredients in an investment program.

3

Table 1 presents key statistical information on VIX and the asset classes for the

full historical period. For all the asset classes, cumulative returns are strongly positive,

especially real estate3. However, the peaks and troughs for each asset class are very large

– evidence of fat tails of distributions, as seen in high kurtosis. Moreover, the assumption

that returns follow a normal distribution, one of the fundamental assumptions of classical

finance, can be strongly rejected for all the indices4. Not only do we not observe

normality, but we also find serial correlation across all time series5, which is inconsistent

with a random walk model. In classical finance, correlation6, a linear measure of

dependency, plays a key role in portfolio risk measurement and optimization. In Table 4,

one can see that in the full sample, correlations among asset classes are relatively low

(particularly, between SP500 and SP GSCI indices) and all asset classes have very low

correlation with VIX. Finally, because of fat tails, historical VaR significantly

understates realistic losses one can experience in adverse scenarios, as measured by

historical CVaR7.

Which states dominated historically? The first state (VIX below 20%) accounted

for over 50% of all days in the historical sample due to extended periods of calm in the

90s and, to a lesser extent, in the middle of this decade (Table 5). The first 3 states (VIX

3
Secular decline in long term interest rates and the subsequent real estate bubble, which is still being
resolved, also played key roles.
4
For a normal distribution, skewness should be 0 and kurtosis should be 3.
5
Positive returns are likely to be followed by positive returns and negative returns are likely to be followed
by negative returns
6
Throughout the paper, correlation refers to what is more formally known as Pearson product-moment
correlation coefficient, which is used extensively by practitioners and academics to model dependence.
7
VaR(a) is defined as the probability of a loss less than or equal to quantity Q, with the confidence level of
a. Thus, it stops at the start of extreme events and does not analyze the tail. CVaR(a) is defined as the
average loss once Q is exceeded, with the confidence level of a. Historical based measures are evaluated
based on historical data and thus fully incorporate all features of a distribution of a return series. If one
assumes a normal distribution of returns, one can find VaR of a a return series via an analytical formula
with just its mean and volatility. However, such a measure will understate the realistic extent of losses
even more than the historical VaR. For example, for SP 500, the normal VaR(95%) in the full sample is
0.01%.. For more detail, the reader is referred to Alexander (2008).

4

at up to 30%) accounted for over 90% of all days. However, as seen in the historical VIX

chart, the last decade was far more volatile than the decade of the 90s. In addition, once

in a particular state, VIX is very likely to remain in that state for a period of time, as

transitions occur gradually.

How similar are risk/return properties of asset classes in various states and

relative to the full historical sample? Very dissimilar (Tables 2 and 3). In fact, they are

so dissimilar that if one relies on the average figures from this long data sample, one may

face the risk of drowning in a pool that is on average only a foot deep by ignoring the full

spectrum of information for investment analysis and risk management. Only bonds

provide cumulatively positive returns across all the states. Unsurprisingly, equities are

extremely sensitive to different levels of VIX even if extreme changes in returns across

states may be surprising, going from the cumulative return feast in state 1 to famine in

state 6 and meaningful gains or losses in the intermediate states. It is worth noting that in

the full sample, the percentage of positive days is close to 50% for all assets, suggesting

that it is the magnitude of returns (or losses) that drove performance, rather than the

frequency of positive days. However, the percentage of positive days for equities drops

very quickly as VIX rises (again, only the bond market continues to deliver positive

returns in over 50% of days in each of the states). The picture for commodities and real

estate is a little more mixed than that for equities. While one loses money in those asset

classes in states 3, 4 (SP GSCI is actually very slightly positive on a cumulative basis)

and 6, one makes money in state 5. As with equities, the percentage of positive days for

commodities and equities drops as VIX rises (with the exception of commodities in state

4). Finally, it is interesting to observe that normal distribution remains a very poor

5

descriptor of return frequencies for all the asset classes in all the states. Similarly, serial

correlation generally remains present as well.

How consistent are cumulative returns for asset classes in various states (Figures

2-4)? They are very consistent at the extreme states 1 and 6. In state 1, all are positive,

especially equities and real estate. In state 6, all asset classes, except fixed income, drop

very sharply and fixed income produces a return. Also, equities and fixed income exhibit

a generally consistent pattern of returns in each state – with the exception of state 2,

equities do not appear to respond well to rising volatility and bonds show a generally

steady, upward pattern. However, the picture is mixed for the intermediate states for

commodities and real estate, with both having up and down periods in the same state.

For example, in state 3, SP GSCI is significantly down on a cumulative basis in the first

half of that state but then has a period of positive returns in the second half; this situation

is repeated in state 4 for real estate. In state 5, cumulatively positive returns for real

estate and commodities are almost entirely due to the period in early 2009, as the

extraordinary volatility of the 2008 crash began to subside. These results suggest that

other factors may be driving such divergent performances, such as interest rates or the

prior volatility state.

Given the prior discussion of returns in different states, it is not surprising to find

how unstable correlations are across states (Table 4). For example, in state 6, equities,

commodities and real estate are almost perfectly synchronized while VIX and bonds have

significant negative correlation; all asset classes are also closely synchronized in state 1.

In state 3, however, such correlations for equities, commodities and real estate are quite

different. Such behavior suggests that not only are dependencies among asset classes

6

time varying, but that they are also non-linear. Therefore, correlation may not be an

appropriate means of evaluating dependence among asset classes8. Moreover, while at

the points of extreme stress, diversification can provide protection at the asset class level,

such benefits are limited only to bonds, and this result is consistent across the full sample.

Finally, given the non-synchronized relationship of VIX with asset classes, it should play

a useful role in an investment program by helping investors minimize potential losses and

thus enhance portfolio performance.

Conclusions

The level of VIX seems to have important and different implications for return

expectations for all asset classes, not just equities. This is particularly true for the

extreme levels of VIX. Though the historical range for VIX is very broad, it exhibits

clustering, which make it useful for forecasting. I further present evidence that during the

historical period used in the article, several important assumptions of classical finance –

normal distribution, randomness of data (no serial correlation) and the use of correlation

to describe dependence – find limited support in empirical data. Therefore, a practitioner

should generate value by incorporating more realistic assumptions to model markets for

investment analysis and risk management, such as non-normal distributions which can

incorporate skews and fat tails of returns and copulas which can capture non-linearity of

dependencies, particularly in the tails. Further, I demonstrate that only bonds

consistently provided downside protection at times of market stress in the full sample.

8
Correlation will correctly describe dependence structure only in very particular cases, such as multivariate
normal distributions. Also, at extremes, correlation should be zero for a multivariate normal distribution,
which is not empirically supported. For a more detailed critique on the use of correlations to model
dependence, see Embrechts et al (2002).

7

Consequently, while diversification can add value at the asset class level, its benefits are

highly concentrated when they are needed most, which a broad set of exposures is likely

to minimize significantly. Also, given the performance characteristics of VIX and its

relationship with other assets, its inclusion in an investment program should provide

valuable benefits in risk management.

The analytical framework presented in this article can be refined further by adding

more factors deemed important, such as inflation or information about the prior VIX

state; it can also be extended to sectors within an asset class and alternative investment

strategies. Finally, while we do not know which volatility states will dominate in the

future or how long they may last, greater awareness of the current investment

environment, its implications for risk adjusted performance and flexible investment

policies to position portfolios appropriately should help investors produce more

consistent results.

References

Alexander, C. 2008. Value at Risk Models John Wiley & Sons.

Bali, T. and A. Hovakimian. 2009. “Volatility Spreads and Expected stock Returns.”

Management Science, vol. 55, no. 11 (November): 1797-1812.

Black, F. 1975. “Fact and Fantasy in the Use of Options.” Financial Analysts Journal,

vol. 31, no. 4 (July/August): 36-41.

Bollerslev, T. 1986. “Generalized Autoregressive Conditional Heteroskedasticity.”

Journal of Econometrics 31: 307-327.

8

Doran J. and K. Krieger. 2010. “Implications for Asset Returns in the Implied Volatility

Skew.” Financial Analysts Journal, vol. 66, no, 1 (January/February): 65-76.

Engle, R. 1982. “Autoregressive Conditional Heteroskedasticity with Estimates of the

Variance of UK inflation.” Econometrica 50: 987-1007.

Embrechts, P, A. McNeil, and D. Straumann. 2002. “Correlation and dependence in risk

management: Properties and Pitfalls.” In M. Dempster (e.d), Risk Management: Value at

Risk and Beyond. Cambridge University Press.

Whaley, R. 1993. “Derivatives on Market Volatility: Hedging Tools Long Overdue.”

Journal of Derivatives, 1 (Fall): 71-84.

9

Cumulative Return VIX

0
2
4
6
8
10
12
14
16
18
20
Figure 1

0
10
20
30
40
50
60
70
80
90
1/2/1990 1/2/1990
1/2/1991 1/2/1991
1/2/1992 1/2/1992
1/2/1993 1/2/1993

SP 500 Total Return
1/2/1994 1/2/1994

1/2/1995 1/2/1995

1/2/1996 1/2/1996

1/2/1997 1/2/1997

FTSE EPRA/NAREIT US Total Return
1/2/1998 1/2/1998

1/2/1999 1/2/1999

1/2/2000 1/2/2000
Date

Date
1/2/2001 1/2/2001

1/2/2002

SP GSCI
1/2/2002
Historical VIX (1/2/1990-1/29/2010)

1/2/2003 1/2/2003

1/2/2004 1/2/2004
Cumulative Return - Full Historical Sample

1/2/2005
1/2/2005

1/2/2006
1/2/2006

1/2/2007
1/2/2007

1/2/2008
1/2/2008
1/2/2009
1/2/2009

JP Morgan US Aggregate Bond Total Return
1/2/2010
1/2/2010

Cumulative Return Cumulative Return

0
2
4
6
8
10
12
14
16
18
20

0.5
1
1.5
2
2.5
3
Figure 2
'1/3/1990'
'1/5/1990'
'4/4/1991'
'4/17/1990'
'8/22/1991'
'12/21/1990' '1/17/1992'
'4/8/1992' '6/3/1992'

SP 500 Total Return
'10/21/1992'

SP 500 Total Return
'4/1/1997'
'3/5/1993'
'8/8/1997'
'7/20/1993'
'12/5/1997' '12/2/1993'
'4/16/1998' '4/21/1994'

'11/24/1998' '9/5/1994'

'1/18/1995'
'4/28/1999'
'6/2/1995'
'9/9/1999' '10/17/1995'
'12/14/1999' '2/29/1996'

'3/8/2000' '7/19/1996'

Date

Date
'12/11/1996'
'7/6/2000'
'2/19/1998'

SP GSCI
'1/30/2001' SP GSCI
'8/28/2000'
'6/15/2001' '7/18/2003'

'11/21/2001' '12/19/2003'
'5/11/2004'
Cumulative Return - State 1 of VIX (<=20)

'2/12/2002'
'9/23/2004'
'1/3/2003'
Cumulative Return - State 2 of VIX (>20 and <=25)

'2/7/2005'
'8/5/2003' '6/22/2005'

'10/30/2007' '11/4/2005'
'3/21/2006'
'4/4/2008'
'8/8/2006'
'8/1/2008'
'12/21/2006'

'9/22/2009' '5/7/2007'
'12/18/2009' '5/16/2008'


0.5
0.7
0.9
1.1
1.3
Figure 3

0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
'8/7/1990' '1/5/1990'

'10/11/1990' '2/21/1990'

'11/2/1990' '4/17/1990'

'10/29/1997' '11/16/1990'

SP 500 Total Return
'8/4/1998' '12/21/1990'

SP 500 Total Return
'9/25/1998' '2/21/1991'

'10/27/1998' '4/8/1992'

'2/10/1999' '1/9/1997'

'3/21/2001' '4/1/1997'

'9/11/2001' '6/19/1997'

'10/5/2001' '8/8/1997'

'10/29/2001' '9/18/1997'

'7/29/2002' '12/5/1997'

Date

Date
'9/26/2002' '2/5/1998'

SP GSCI
'10/29/2002' '4/16/1998'
'6/3/1998'

SP GSCI
'12/5/2002'
'2/4/2003' '11/24/1998'

'2/18/2003' '3/18/1999'


'3/5/2003' '4/28/1999'

'3/19/2003' '7/23/1999'

'9/16/2008' '9/9/1999'

'5/7/2009' '11/3/1999'

'5/25/2009' '12/14/1999'


'6/18/2009' '1/25/2000'


0
0.2
0.4
0.6
0.8
1
1.2
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
Figure 4

'8/31/1998'
'8/6/1990'
'9/30/1998'
'10/30/1997'
'10/9/1998'
'11/12/1997'
'7/22/2002'
'10/7/2002' '9/2/1998'

SP 500 Total Return

SP 500 Total Return
'10/7/2008' '9/16/1998'

'10/16/2008' '9/29/1998'
'10/27/2008' '9/26/2001'
'11/5/2008'

'7/15/2002'

'11/14/2008'
'7/24/2002'
'11/25/2008'
'8/8/2002'
'12/4/2008'

Date
'9/4/2002'
Date

'12/15/2008'
'9/12/2002'
'12/24/2008'
SP GSCI

'9/20/2002'

SP GSCI
'1/9/2009'
'1/20/2009' '10/2/2002'
Cumulative Return - State 6 of VIX (>40)

'1/30/2009' '10/14/2002'
Cumulative Return - State 5 of Vix (>35 and <=40)

'2/10/2009' '9/30/2008'
'2/19/2009' '1/5/2009'
'3/2/2009'
'4/9/2009'
'3/11/2009'
'4/16/2009'
'3/20/2009'
'4/24/2009'

'3/31/2009'

'5/1/2009'

Table 1
1/2/1990-1/31/2010 SPX GSCI NAREIT JPMAGG VIX
daily data
Arithmetic avg return 0.0357% 0.0253% 0.0554% 0.0264% 0.1763%
Compounded avg return 0.0291% 0.0158% 0.0426% 0.0261% 0.0068%
max 11.6% 7.8% 18.4% 1.3% 64.2%
min -9.0% -16.9% -19.5% -1.5% -25.9%
vol 1.2% 1.4% 1.6% 0.3% 5.9%
VaR (95%) -1.7% -2.1% -1.7% -0.4% -8.2%
VaR (99%) -3.1% -3.7% -5.2% -0.7% -12.4%
CVaR(95%) -2.7% -3.2% -3.8% -0.5% -11.2%
CVaR(99%) -4.6% -5.2% -8.0% -0.8% -15.8%
Skewness 0.00 -0.40 0.47 -0.14 1.23
Kurtosis 12.71 10.74 33.85 4.77 10.91
Number of days 5,238 5,238 5,238 5,238 5,238
Normality at 95% confidence level? No No No No No
p-values 0.1% 0.1% 0.1% 0.1% 0.1%
No serial correlation at 95% confidence level? No No No No No
p-values 0.0% 0.0% 0.0% 0.0% 0.0%
Cumulative Return 358.7% 129.2% 833.0% 292.9% 42.8%
% of days with positive returns 51.7% 49.3% 51.9% 53.0% 45.8%

Notes:
Jarque-Bera test was used to evaluate normality of a time series; null hypothesis is stated in the question.
Ljung-Box test with 20 lags was used to evaluate serial correlation of a time series;
null hypothesis is stated in the question.
SPX - SP500 Total Return
GSCI - SP GSCI
NAREIT - FTSE EPRA/NAREIT US Total Return
JPMAGG - JPM Morgan Aggregate Bond Total Return
VIX - VIX Index

Table 2
State 1 - VIX <=20 SPX GSCI NAREIT JPMAGG VIX
daily
Arithmetic avg return 0.0983% 0.0411% 0.1004% 0.0254% -0.1932%
Compounded avg return 0.0962% 0.0351% 0.0976% 0.0252% -0.3318%
max 2.9% 6.8% 3.6% 1.0% 64.2%
min -3.5% -4.6% -4.8% -1.1% -25.9%
vol 0.7% 1.1% 0.7% 0.2% 5.3%
VaR (95%) -1.0% -1.8% -1.1% -0.3% -8.0%
VaR (99%) -1.6% -2.8% -2.0% -0.6% -12.1%
CVaR(95%) -1.4% -2.4% -1.7% -0.5% -10.8%
CVaR(99%) -1.9% -3.4% -2.8% -0.7% -15.3%
Skewness 0.02 0.18 -0.33 -0.04 1.25
Kurtosis 4.16 5.06 7.03 4.77 13.94
Number of days 2,945 2,945 2,945 2,945 2,945
p-values 0.1% 0.1% 0.1% 0.1% 0.1%
No serial correlation at 95% confidence level? Yes Yes No No No
p-values 49.5% 13.0% 1.1% 0.9% 0.0%
Cumulative Return 1595.7% 181.1% 1669.5% 109.9% -100.0%


State 2 - VIX >20 & <=25 SPX GSCI NAREIT JPMAGG VIX
daily
Compounded avg return 0.0402% 0.0398% 0.0729% 0.0228% 0.2832%
max 4.8% 6.2% 6.5% 0.8% 51.7%
min -3.7% -5.5% -6.7% -1.5% -23.1%
vol 1.1% 1.3% 1.1% 0.3% 6.1%
VaR (95%) -1.7% -2.1% -1.5% -0.4% -7.8%
VaR (99%) -2.5% -3.2% -3.1% -0.7% -11.7%
CVaR(95%) -2.2% -2.8% -2.5% -0.6% -10.5%
CVaR(99%) -2.8% -3.9% -3.9% -0.8% -14.5%
Skewness 0.24 -0.04 0.58 -0.27 1.51
Kurtosis 3.78 4.22 9.21 4.53 12.41
Number of days 1,210 1,210 1,210 1,210 1,210
p-values 0.1% 0.1% 0.1% 0.1% 0.1%
No serial correlation at 95% confidence level? Yes Yes No Yes No
p-values 9.4% 22.4% 0.0% 40.9% 0.0%
Cumulative Return 62.7% 61.9% 141.4% 31.8% 2961.5%

daily
Arithmetic avg return -0.0776% -0.0227% -0.0296% 0.0230% 0.4789%
Compounded avg return -0.0872% -0.0373% -0.0392% 0.0226% 0.2802%
max 5.0% 5.9% 8.8% 0.9% 40.7%
min -3.8% -16.9% -7.0% -0.9% -20.0%
vol 1.4% 1.7% 1.4% 0.3% 6.4%
VaR (95%) -2.3% -2.8% -2.1% -0.5% -9.5%
VaR (99%) -2.9% -4.7% -4.3% -0.8% -12.6%
CVaR(95%) -2.7% -4.1% -3.5% -0.6% -11.8%
CVaR(99%) -3.2% -7.1% -5.5% -0.8% -15.0%
Skewness 0.27 -1.76 0.20 -0.36 0.72
Kurtosis 3.23 19.72 9.96 3.68 6.01
Number of days 590 590 590 590 590
p-values 1.9% 0.1% 0.1% 0.1% 0.1%
No serial correlation at 95% confidence level? Yes Yes No Yes Yes
p-values 11.0% 12.8% 0.0% 84.1% 56.6%
Cumulative Return -40.2% -19.8% -20.7% 14.3% 421.0%

Notes:
GSCI - SP GSCI
VIX - VIX Index

Table 3
daily
Arithmetic avg return -0.1244% 0.0223% 0.0049% 0.0447% 1.4675%
Compounded avg return -0.1412% 0.0080% -0.0186% 0.0443% 1.2604%
max 5.4% 5.1% 10.9% 0.8% 34.3%
min -6.9% -4.3% -8.9% -0.7% -14.4%
vol 1.8% 1.7% 2.2% 0.3% 6.6%
VaR (95%) -2.9% -3.1% -3.4% -0.5% -8.1%
VaR (99%) -4.9% -4.0% -7.2% -0.7% -12.1%
CVaR(95%) -4.1% -3.6% -5.5% -0.6% -10.1%
CVaR(99%) -5.8% -4.2% -8.2% -0.7% -13.4%
Skewness 0.04 0.11 0.59 -0.15 1.00
Kurtosis 4.09 3.42 10.43 3.23 5.82
Number of days 235 235 235 235 235
Normality at 95% confidence level? No Yes No Yes No
p-values 1.0% 28.9% 0.1% 47.3% 0.1%
No serial correlation at 95% confidence level? Yes Yes No No Yes
p-values 49.6% 6.1% 0.0% 0.6% 21.7%
Cumulative Return -28.2% 1.9% -4.3% 11.0% 1798.1%

daily
Compounded avg return -0.0061% 0.3565% 0.3527% 0.0259% 0.3153%
max 5.7% 7.8% 13.6% 0.7% 24.9%
min -4.7% -8.8% -11.2% -1.1% -17.6%
vol 2.1% 2.1% 3.4% 0.3% 8.0%
VaR (95%) -3.5% -2.5% -4.2% -0.4% -11.4%
VaR (99%) -4.5% -7.0% -9.8% -1.0% -16.7%
CVaR(95%) -4.0% -4.1% -6.8% -0.6% -13.4%
CVaR(99%) -4.5% -7.0% -9.8% -1.0% -16.7%
Skewness 0.29 0.09 0.61 -0.94 0.78
Kurtosis 3.09 7.89 6.32 5.81 4.09
Number of days 100 100 100 100 100
Normality at 95% confidence level? Yes No No No No
p-values 40.0% 0.1% 0.1% 0.1% 0.6%
No serial correlation at 95% confidence level? Yes Yes Yes Yes Yes
p-values 84.1% 27.8% 65.3% 35.0% 81.3%
Cumulative Return -0.6% 42.7% 42.2% 2.6% 37.0%

State 6 - VIX>40 SPX GSCI NAREIT JPMAGG VIX
daily
Arithmetic avg return -0.5372% -0.4839% -0.7983% 0.0562% 1.5559%
Compounded avg return -0.5940% -0.5300% -1.0065% 0.0555% 1.1540%
max 11.6% 7.5% 18.4% 1.3% 34.5%
min -9.0% -8.1% -19.5% -1.0% -24.7%
vol 3.4% 3.0% 6.5% 0.4% 9.2%
VaR (95%) -5.9% -5.9% -10.0% -0.5% -10.9%
VaR (99%) -8.9% -7.6% -15.0% -1.0% -21.1%
CVaR(95%) -7.5% -6.7% -13.0% -0.8% -16.0%
CVaR(99%) -9.0% -7.9% -17.3% -1.0% -23.0%
Skewness 0.41 0.12 0.49 0.12 0.66
Kurtosis 4.22 3.25 3.64 4.36 4.77
Number of days 158 158 158 158 158
Normality at 95% confidence level? No Yes No No No
p-values 0.7% 50.0% 1.9% 0.9% 0.1%
No serial correlation at 95% confidence level? Yes Yes Yes No No
p-values 62.0% 33.2% 30.2% 0.6% 1.9%
Cumulative Return -61.0% -56.8% -79.8% 9.2% 512.8%

Notes:
GSCI - SP GSCI
VIX - VIX Index

Table 4
Correlation matrices

Full sample
SPX GSCI NAREIT JPMAGG VIX
SPX 1
GSCI 0.614909 1
NAREIT 0.828916 0.846607 1
JPMAGG 0.822595 0.770811 0.864026 1
VIX 0.155275 0.061055 -0.029318 0.276768 1

State 1 - VIX <=20 State 4 - VIX >30 & <=35
SPX GSCI NAREIT JPMAGG VIX SPX GSCI NAREIT JPMAGG VIX
SPX 1 SPX 1
GSCI 0.898321 1 GSCI -0.288855 1
NAREIT 0.974663 0.929054 1 NAREIT 0.308306 -0.536519 1
JPMAGG 0.910627 0.728673 0.883676 1 JPMAGG -0.71221 0.149066 0.116173 1
VIX -0.465434 -0.284836 -0.447933 -0.673159 1 VIX -0.739751 -0.118798 0.32146 0.842166 1

State 2 - VIX >20 & <=25 State 5 - VIX >35 & <=40
SPX 1 SPX 1
GSCI 0.786621 1 GSCI 0.291233 1
NAREIT 0.727929 0.711477 1 NAREIT 0.555915 0.720048 1
JPMAGG 0.838083 0.81479 0.914554 1 JPMAGG -0.364912 0.019158 0.28198 1
VIX -0.357736 0.011339 -0.171163 -0.151194 1 VIX -0.717426 -0.173092 -0.557295 -0.219695 1

State 3 - VIX >25 & <=30 State 6 - VIX>40
SPX 1 SPX 1
GSCI -0.168537 1 GSCI 0.947808 1
NAREIT 0.086168 -0.305081 1 NAREIT 0.9922 0.960259 1
JPMAGG -0.682311 0.032938 -0.248043 1 JPMAGG -0.668409 -0.811675 -0.693375 1
VIX -0.901783 0.206418 -0.433721 0.729271 1 VIX -0.839971 -0.708645 -0.822588 0.232618 1

Table 5
Transition probability matrix for VIX
Next day State
Current State 1 2 3 4 5 6
1 95.9% 4.1% 0.0% 0.0% 0.0% 0.0%
2 9.9% 82.0% 7.9% 0.2% 0.0% 0.0%
3 0.0% 16.3% 75.1% 8.5% 0.2% 0.0%
4 0.0% 0.4% 22.1% 68.5% 8.1% 0.9%
5 0.0% 0.0% 0.0% 22.0% 64.0% 14.0%
6 0.0% 0.0% 0.0% 0.0% 10.1% 89.9%

Average Maximum % of all days
VIX State Duration Duration in State
1 24.3 578 56.2%
2 5.6 37 23.1%
3 4.0 16 11.3%
4 3.2 25 4.5%
5 2.8 10 1.9%
6 9.9 64 3.0%

Notes:
Based on daily data.

20 Years of VIX: Fear, Greed and Implications for Traditional Asset Classes

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20 Years of VIX: Fear, Greed and Implications for Traditional Asset Classes