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EMPLOYING IMPLIED VOLATILITY TO
IMPROVE SHORT-TERM RISK
FORECASTS OF EQUITY MODELS
"Successful investing is anticipating the anticipations of others." - John Maynard Keynes
Igor Mashtaler
Nicolas Meng
March 24, 2015
© 2015 MSCI Inc. All rights reserved.
Please refer to the disclaimer at the end of this document.
AGENDA
•
•
•
Introduction
•
Implied Volatility
•
Barra Equity Model
Implied Volatility Adjustment
•
Common Factors
•
Specific Risk
Empirical Results
2
IMPLIED VOLATILITY
•
•
VIX
•
Represents the square root of the S&P 500 par variance swap rate for a 30 day term
•
Can be statically replicated using a weighted average of the next-term puts and calls
•
Introduced in 1993 by the Chicago Board Options Exchange (CBOE)
•
Revised in 2003 jointly by CBOE and Goldman Sachs
•
Futures contract trading commenced in 2004, options in 2006
OptionMetrics Ivy DB Stock-level implied volatilities
•
Calculated using modified Cox-Ross-Rubinstein binomial tree algorithm
•
Used to construct standardized stock-level implied volatility surfaces
•
Go back to Jan 2, 1996
3
FUNDAMENTAL COMMON SOURCES OF EQUITY RETURNS
• Asset returns can be attributed to different common fundamental factors such as styles,
industries, countries or currencies, to which the stock is exposed over time:
Asset k
return
Specific return of
asset k
Observed exposures of
asset k to Common Factors
Observed exposure
or “sensitivity” of
asset k to factor n
Estimated/derived
return of factor n
• Descriptors used in Barra’s style factors are derived from:
• Company fundamentals such as Assets, Earnings, etc…
• Market information such as stock price, trading volume
• What constitutes a suitable descriptor?
• Used in fundamental equity research, or fund management
• Describes an asset attribute valid across all assets
• Data availability for a majority of assets across the universe
• Adds explanatory power to the model (higher R-Squared)
4
COMMON FACTORS IN BARRA US TRADING MODEL
1 US Market Factor
85 Common Factors
60 GICS Based
Industry Factors
24 Style Factors
Beta
Size
Mid Capitalization
Value
Growth
Leverage
Liquidity
Short-Term Reversal
One-Day Reversal
Momentum
Residual Volatility
Earnings Yield
Dividend Yield
Earnings Quality
Long-Term Reversal
Management Quality
Profitability
Prospect
Sentiment
Short Interest
Industry Momentum
Regional Momentum
Seasonality
Downside Risk
5
ESTIMATING FACTOR COVARIANCE
•
From the times series of f1 and f2, we can calculate the volatility of f1 and f2 as well as their
correlation. Combined, they yield the Factor Covariance Matrix
•
Common Factor Covariance Matrix:
f1
f2
6
COMMON FACTORS VS SPECIFIC COVARIANCE MATRIX
Volatility of the residual (stock
specific) is on the diagonal
Common Factor Covariance Matrix for US Trading Model
24 Risk Indices (Style)
60 Industries
2
 Size
Covar
Siz/Gro
2
 Growth
…
Covar
Gr/OilGasDr
Stock Specific Risk
 12
0
0
 22
…
…
2
 OilGasDr
Covariance terms
are all zeroes
…
0
…

2
Banks
Covariance terms
are all zeroes
0
…
0
0
0
 N2
7
LITERATURE REVIEW AND NEW RESEARCH
•
Canina, Linda, and Stephen Figlewski. "The informational content of implied volatility."
Review of Financial studies 6.3 (1993): 659-681.
•
Christensen, Bent J., and Nagpurnanand R. Prabhala. "The relation between implied and
realized volatility." Journal of Financial Economics 50.2 (1998): 125-150.
•
Ederington, Louis, and Wei Guan. "Is implied volatility an informationally efficient and
effective predictor of future volatility?." Journal of Risk 4 (2002): 29-46.
•
DiBartolomeo, D., and S. Warrick. "Making covariance based portfolio risk models sensitive
to the rate at which markets reflect new information." Ch12 in Linear Factor models Edited.
Knight, J. and Satchell, S. Elsevier Finance (2005).
New Contributions:
•
Improve daily portfolio risk forecasts by combining a fundamental equity model
and information from option markets
•
Leverage CBOE VIX Index for portfolio common risk forecasts
•
Utilize stock level implied volatilities to capture event risk
8
INFORMATION CONTENT OF IMPLIED VOLATILITY
EWMA
R2
17.68%
Adjusted R2
17.66%
CV R2
17.52%
Coefficient: Intercept 0.0004
Coefficient: EWMA
0.72
Coefficient: VRA
Coefficient: VIX
T-Stat: Intercept
1.53
T-Stat: EWMA
T-Stat: VRA
VRA
23.35%
23.31%
23.16%
-0.0001
VRA + VIX
27.07%
27.03%
26.80%
-0.0030
0.78
-0.27
0.13
0.91
-9.86
38.41
2.91
•
Volatility Regime Adjustment (VRA)
improves accuracy as compared to the
standard EWMA estimator
•
VIX provides additional informational
content not captured by VRA
32.25
T-Stat: VIX
15.73
Daily Regression, 30-Jun-1995 to 30-Sep-2014
EWMA:
VRA:
VRA + VIX:
9
IMPLIED VOLATILITY BIAS
1.2
•
VIX exhibits extended periods of overand underforecasting risk
•
This may be attributed to time-varying
risk premium
1.15
1.1
1.05
1
0.95
Bias Statistic
0.9
0.85
Bias VRA
Bias VIX
0.8
1997
2000
2002
2005
2007
2010
2012
1.5 Year Rolling Bias Statistic (30-Jun-1995 to 30-Sep-2014)
10
COMBINING IMPLIED VOLATILITY AND MODEL FORECAST
VRA Market Factor
Risk Forecast
Adjusted
Market Factor
Risk Forecast
VIX
Adjusted (Scaled)
Covariance Matrix
VRA Factor
Covariance Matrix
VRA Stock Specific
Risk Forecast
Adjusted
Portfolio Risk
Forecast
Adjusted Stock Specific Risk Forecast
Stock
Implied Volatility
11
MARKET FACTOR VOLATILITY ADJUSTMENT
1.
Start with VIX level
and VRA model volatility forecast
for the market factor
2.
Calculate adjustment factor
3.
Apply to the latest level of VIX to obtain adjusted volatility forecast
12
COVARIANCE MATRIX SCALING
1.
Start with covariance matrix
that corresponds to the unadjusted
market factor VRA volatility forecast
2.
Model factor
3.
Given factor covariance matrix
4.
Adjust covariance matrix
returns as a function of market returns
, calculate beta for factor
as
as
13
FACTOR VOLATILITY Q-STATISTICS
0
•
Market volatility Q-Statistic improves
considerably
•
Significant improvement for factors
correlated with market
•
Q-Like is defined following Patton 2007
-50
-100
-150
-200
-250
Country
Size
-300
Residual Volatility
Bounce
-350
Beta
-400
2007
2010
2012
Cumulative Q-Like Differences in BPS (IVOL - VRA)
Patton, Andrew 2007 Evaluating Volatility and Correlation Forecasts
14
SPECIFIC RISK ADJUSTMENT
1.
Start with stock
implied volatility
and VRA total risk forecast
2.
Calculate implied to total volatility adjustment factor
3.
Adjust the most recent implied to total volatility ratio
1.5
1.45
4.
Remove market-wide effects
1.4
1.35
1.3
1.25
1.2
5.
Apply to the latest specific risk forecast
1.15
1.1
1.05
1
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
15
1.5
SPECIFIC RISK – EMPIRICAL RESULTS
•
Bias Statistics by cap-decile
Equally Weighted
VRA
IVOL
1
1.12
1.07
2
1.06
1.01
3
1.04
1.00
4
1.06
1.01
5
1.05
1.00
6
1.04
0.99
7
1.03
0.99
8
1.03
0.99
9
1.03
0.99
10
1.01
0.98
Total
1.07
1.02
Cap Weighted
VRA
IVOL
1
1.10
1.05
2
1.05
1.01
3
1.04
1.00
4
1.06
1.01
5
1.05
1.00
6
1.04
0.99
7
1.03
0.99
8
1.03
0.99
9
1.03
0.99
10
1.00
0.97
Total
1.02
0.98
•
Q – Statistics by cap-decile
Equally Weighted
VRA
IVOL
Diff
1
2
3
4
5
6
7
8
9
10
Total
2.9684 2.8558 2.8656 2.9312 2.8882 2.8638 2.8245 2.8270 2.7775 2.6689 2.8470
2.9359 2.8315 2.8395 2.8851 2.8514 2.8347 2.7981 2.8010 2.7435 2.6458 2.8166
-0.0325 -0.0243 -0.0261 -0.0461 -0.0368 -0.0290 -0.0264 -0.0261 -0.0340 -0.0231 -0.0304
Cap Weighted
VRA
IVOL
Diff
1
2
3
4
5
6
7
8
9
10
Total
2.9241 2.8557 2.8647 2.9280 2.8880 2.8622 2.8260 2.8224 2.7719 2.6444 2.6974
2.8946 2.8325 2.8392 2.8829 2.8514 2.8337 2.7987 2.7961 2.7384 2.6232 2.6730
-0.0295 -0.0232 -0.0254 -0.0451 -0.0366 -0.0286 -0.0274 -0.0263 -0.0335 -0.0212 -0.0244
16
SPECIFIC RISK – EMPIRICAL RESULTS
0
0
-50
-50
-100
-100
-150
-150
1
-200
1
-200
2
3
-250
3
-250
4
5
-300
6
7
8
-350
9
-400
4
5
-300
6
7
-350
2
8
9
10
-400
10
Total
-450
-450
2007
2010
2012
Before Shrinkage / Filtering
2007
2010
2012
After Shrinkage / Filtering
17
ENHANCEMENTS: IMPACT ON MODEL RESULTS
Bias Statistic
VRA
IVOL
1.00
0.99
1.00
0.99
1.01
0.99
1.01
0.99
1.02
1.01
1.01
1.00
1.03
1.02
0.98
0.97
0.96
0.95
1.00
0.99
Market
Random Long
Random Active
Industries Long
Industries Active
Style Quintile Long
Style Quintile Active
Style Characteristic
Min-Vol
Average
Q Statistic
Q-Stat Difference
VRA
IVOL
vs VRA
2.5655 2.5250
-0.0405
2.5010 2.4656
-0.0354
2.4298 2.4217
-0.0081
2.4356 2.4129
-0.0227
2.4699 2.4630
-0.0069
2.4018 2.3761
-0.0257
2.3271 2.3217
-0.0053
2.4549 2.4533
-0.0016
2.3592 2.3442
-0.0150
2.4383 2.4204
-0.0179
•
•
Factor volatility adjustment improves
forecasts for long portfolios and betas
Specific risk adjustment helps on
active portfolios
-4
x 10
0
0
-50
-0.5
-100
-1
1
2
-150
3
-1.5
4
5
-200
6
-2
Style Quint Long
7
8
-2.5
-250
9
Random Active
Style Quint Active
10
2007
2010
2012
Cumulative Diff SOSQ of Beta Residuals
2007
2010
2012
Cumulative Diff of Q-Statistic
18
INFORMATION DECAY OF IMPLIED VOLATILITY
Market Factor Volatility Adjustment
Specific Risk Adjustment
VRA
IVOL L0
IVOL L1
IVOL L2
IVOL L3
IVOL L6
IVOL L11
IVOL L21
Total
VS VRA
2.8470
2.8064 -0.0406
2.8166 -0.0304
2.8170 -0.0300
2.8188 -0.0283
2.8248 -0.0223
2.8305 -0.0165
2.8431 -0.0039
19
ENRON CORPORATION
•
VRA
1.2
IVOL
Cum Ret
1
•
0.8
During 2001, a series of
irregular accounting
procedures were revealed
to the public
Enron filed for bankruptcy
on Dec 2, 2001
0.6
Risk Forecast Accuracy:
0.4
VRA
IVOL
0.2
QLIKE
15.78
12.94
0
Oct
Nov
Dec
(01-Sep-2001 to 30-Dec-2001)
20
RECENT EXAMPLES: BRITISH PETROLEUM
•
Deepwater Horizon oil spill
began on April 20, 2012
•
It was capped on July 15,
2012
•
During this time, the
adjusted risk forecast was
significantly higher
Risk Forecast Accuracy:
VRA
IVOL
QLIKE
3.06
2.88
21
NAVIDEA BIOPHARMACEUTICALS
1.2
VRA
IVOL
1.1
Cum Ret
•
Navidea produces solutions
in medical diagnostics field,
such as diagnostic agents or
medical imaging
•
FDA approval for a
“radiocative imaging agent”
got denied in early
September 2012
•
Subsequent improved filing
passed FDA approval on
March 14, 2013
•
The adjusted risk forecast
significantly increased prior
to these significant events
1
0.9
0.8
0.7
0.6
0.5
0.4
Aug
Sep
Oct
(01-Jul-2012 to 30-Oct-2012)
1.1
1
VRA
0.9
IVOL
Cum Ret
0.8
0.7
0.6
0.5
Feb
Mar
Apr
(01-Jan-2013 to 30-Apr-2013)
22
SUMMARY
•
VIX and stock-level implied volatilities provide additional information that can be
leveraged in combination with the fundamental risk model
•
VIX improves market factor volatility forecast
•
Factor covariance matrix can be scaled to match the market factor
•
Stock specific implied volatilities capture changes in volatility anticipated by market
participants
23
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