Implied Options Volatility to Improve RIsk Forecasting
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Transcript of Implied Options Volatility to Improve RIsk Forecasting
© 2015 MSCI Inc. All rights reserved. Please refer to the disclaimer at the end of this document.
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
• Introduction
• Implied Volatility
• Barra Equity Model
• Implied Volatility Adjustment
• Common Factors
• Specific Risk
• Empirical Results
AGENDA
2
• 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
IMPLIED VOLATILITY
3
FUNDAMENTAL COMMON SOURCES OF EQUITY RETURNS
4
• 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:
• 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)
Observed exposure
or “sensitivity” of
asset k to factor n
Estimated/derived
return of factor n
Asset k
return
Observed exposures of
asset k to Common Factors
Specific return of
asset k
COMMON FACTORS IN BARRA US TRADING MODEL
5
85 Common Factors
1 US Market Factor
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
60 GICS Based
Industry Factors
ESTIMATING FACTOR COVARIANCE
6
• 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
COMMON FACTORS VS SPECIFIC COVARIANCE MATRIX
7
Stock Specific Risk
…
…
0
2
1
24 Risk Indices (Style) 60 Industries
…
…
Covar
Siz/Gro
Covar Gr/OilGasDr
2
Size
2
Growth
2
OilGasDr
2
Banks
2
2
0
0
0 0
0
0
… …
2
N
Common Factor Covariance Matrix for US Trading Model
Covariance terms
are all zeroes
Covariance terms
are all zeroes
Volatility of the residual (stock
specific) is on the diagonal
LITERATURE REVIEW AND NEW RESEARCH
8
• 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
INFORMATION CONTENT OF IMPLIED VOLATILITY
9
EWMA VRA VRA + VIX
R2 17.68% 23.35% 27.07%
Adjusted R2 17.66% 23.31% 27.03%
CV R2 17.52% 23.16% 26.80%
Coefficient: Intercept 0.0004 -0.0001 -0.0030
Coefficient: EWMA 0.72
Coefficient: VRA 0.78 0.13
Coefficient: VIX 0.91
T-Stat: Intercept 1.53 -0.27 -9.86
T-Stat: EWMA 32.25
T-Stat: VRA 38.41 2.91
T-Stat: VIX 15.73
• Volatility Regime Adjustment (VRA) improves accuracy as compared to the standard EWMA estimator
• VIX provides additional informational content not captured by VRA
Daily Regression, 30-Jun-1995 to 30-Sep-2014
EWMA:
VRA:
VRA + VIX:
IMPLIED VOLATILITY BIAS
10
1997 2000 2002 2005 2007 2010 2012
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
Bias VRA
Bias VIX
• VIX exhibits extended periods of over- and underforecasting risk
• This may be attributed to time-varying
risk premium
1.5 Year Rolling Bias Statistic (30-Jun-1995 to 30-Sep-2014)
Bias Statistic
COMBINING IMPLIED VOLATILITY AND MODEL FORECAST
VRA Market Factor Risk Forecast
VIX
Adjusted Market Factor Risk Forecast
VRA Factor Covariance Matrix
Adjusted (Scaled) Covariance Matrix
VRA Stock Specific Risk Forecast
Stock Implied Volatility
Adjusted Stock Specific Risk Forecast
Adjusted Portfolio Risk Forecast
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 returns as a function of market returns
3. Given factor covariance matrix , calculate beta for factor as
4. Adjust covariance matrix as
13
FACTOR VOLATILITY Q-STATISTICS
14
Cumulative Q-Like Differences in BPS (IVOL - VRA)
• Market volatility Q-Statistic improves considerably
• Significant improvement for factors
correlated with market
• Q-Like is defined following Patton 2007
2007 2010 2012
-400
-350
-300
-250
-200
-150
-100
-50
0
Country
Size
Residual Volatility
Bounce
Beta
Patton, Andrew 2007 Evaluating Volatility and Correlation Forecasts
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
4. Remove market-wide effects
5. Apply to the latest specific risk forecast
SPECIFIC RISK ADJUSTMENT
15
1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.51
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
SPECIFIC RISK – EMPIRICAL RESULTS
16
• Bias Statistics by cap-decile
• Q – Statistics by cap-decile
Equally Weighted 1 2 3 4 5 6 7 8 9 10 Total
VRA 1.12 1.06 1.04 1.06 1.05 1.04 1.03 1.03 1.03 1.01 1.07
IVOL 1.07 1.01 1.00 1.01 1.00 0.99 0.99 0.99 0.99 0.98 1.02
Cap Weighted 1 2 3 4 5 6 7 8 9 10 Total
VRA 1.10 1.05 1.04 1.06 1.05 1.04 1.03 1.03 1.03 1.00 1.02
IVOL 1.05 1.01 1.00 1.01 1.00 0.99 0.99 0.99 0.99 0.97 0.98
Equally Weighted 1 2 3 4 5 6 7 8 9 10 Total
VRA 2.9684 2.8558 2.8656 2.9312 2.8882 2.8638 2.8245 2.8270 2.7775 2.6689 2.8470
IVOL 2.9359 2.8315 2.8395 2.8851 2.8514 2.8347 2.7981 2.8010 2.7435 2.6458 2.8166
Diff -0.0325 -0.0243 -0.0261 -0.0461 -0.0368 -0.0290 -0.0264 -0.0261 -0.0340 -0.0231 -0.0304
Cap Weighted 1 2 3 4 5 6 7 8 9 10 Total
VRA 2.9241 2.8557 2.8647 2.9280 2.8880 2.8622 2.8260 2.8224 2.7719 2.6444 2.6974
IVOL 2.8946 2.8325 2.8392 2.8829 2.8514 2.8337 2.7987 2.7961 2.7384 2.6232 2.6730
Diff -0.0295 -0.0232 -0.0254 -0.0451 -0.0366 -0.0286 -0.0274 -0.0263 -0.0335 -0.0212 -0.0244
SPECIFIC RISK – EMPIRICAL RESULTS
17
After Shrinkage / Filtering Before Shrinkage / Filtering
2007 2010 2012
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
1
2
3
4
5
6
7
8
9
10
Total
2007 2010 2012
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
1
2
3
4
5
6
7
8
9
10
ENHANCEMENTS: IMPACT ON MODEL RESULTS
18
• Factor volatility adjustment improves forecasts for long portfolios and betas
• Specific risk adjustment helps on active portfolios
2007 2010 2012
-250
-200
-150
-100
-50
0
Style Quint Long
Random Active
Style Quint Active
Bias Statistic Q Statistic Q-Stat Difference
VRA IVOL VRA IVOL vs VRA
Market 1.00 0.99 2.5655 2.5250 -0.0405
Random Long 1.00 0.99 2.5010 2.4656 -0.0354
Random Active 1.01 0.99 2.4298 2.4217 -0.0081
Industries Long 1.01 0.99 2.4356 2.4129 -0.0227
Industries Active 1.02 1.01 2.4699 2.4630 -0.0069
Style Quintile Long 1.01 1.00 2.4018 2.3761 -0.0257
Style Quintile Active 1.03 1.02 2.3271 2.3217 -0.0053
Style Characteristic 0.98 0.97 2.4549 2.4533 -0.0016
Min-Vol 0.96 0.95 2.3592 2.3442 -0.0150
Average 1.00 0.99 2.4383 2.4204 -0.0179
2007 2010 2012
-2.5
-2
-1.5
-1
-0.5
0
x 10-4
1
2
3
4
5
6
7
8
9
10
Cumulative Diff SOSQ of Beta Residuals Cumulative Diff of Q-Statistic
INFORMATION DECAY OF IMPLIED VOLATILITY
19
Total VS VRA
VRA 2.8470
IVOL L0 2.8064 -0.0406
IVOL L1 2.8166 -0.0304
IVOL L2 2.8170 -0.0300
IVOL L3 2.8188 -0.0283
IVOL L6 2.8248 -0.0223
IVOL L11 2.8305 -0.0165
IVOL L21 2.8431 -0.0039
Market Factor Volatility Adjustment
Specific Risk Adjustment
ENRON CORPORATION
20
• During 2001, a series of
irregular accounting procedures were revealed to the public
• Enron filed for bankruptcy on Dec 2, 2001
Oct Nov Dec
0
0.2
0.4
0.6
0.8
1
1.2
VRA
IVOL
Cum Ret
QLIKE
VRA 15.78
IVOL 12.94
Risk Forecast Accuracy:
(01-Sep-2001 to 30-Dec-2001)
RECENT EXAMPLES: BRITISH PETROLEUM
21
• 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
QLIKE
VRA 3.06
IVOL 2.88
Risk Forecast Accuracy:
NAVIDEA BIOPHARMACEUTICALS
22
(01-Jul-2012 to 30-Oct-2012)
Feb Mar Apr
0.5
0.6
0.7
0.8
0.9
1
1.1
VRA
IVOL
Cum Ret
(01-Jan-2013 to 30-Apr-2013)
• 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
Aug Sep Oct
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
VRA
IVOL
Cum Ret
• 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
SUMMARY
23
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