1. finance
2. investing
3. stocks

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
CONTACT US
AMERICAS
EUROPE, MIDDLE EAST
& AFRICA
ASIA PACIFIC
Americas
1 888 588 4567 *
Cape Town
+ 27 21 673 0100
China North
10800 852 1032 *
Atlanta
+ 1 404 551 3212
Frankfurt
+ 49 69 133 859 00
China South
10800 152 1032 *
Boston
+ 1 617 532 0920
Geneva
+ 41 22 817 9777
Hong Kong
+ 852 2844 9333
Chicago
+ 1 312 675 0545
London
+ 44 20 7618 2222
Mumbai
+ 91 22 6784 9160
Monterrey
+ 52 81 1253 4020
Milan
+ 39 02 5849 0415
Seoul
00798 8521 3392 *
New York
+ 1 212 804 3901
Paris
0800 91 59 17 *
Singapore
800 852 3749 *
San Francisco
+ 1 415 836 8800
Sydney
+ 61 2 9033 9333
Sao Paulo
+ 55 11 3706 1360
Taipei
008 0112 7513 *
Toronto
+ 1 416 628 1007
Tokyo
81 3 5290 1555
* = toll free
msci.com
[email protected]
24
NOTICE AND DISCLAIMER
This document and all of the information contained in it, including without limitation all text, data, graphs, charts (collectively, the “Information”) is the property of MSCI Inc. or its subsidiaries (collectively, “MSCI”), or MSCI’s licensors, direct or indirect
suppliers or any third party involved in making or compiling any Information (collectively, with MSCI, the “Information Providers”) and is provided for informational purposes only. The Information may not be modified, reverse-engineered, reproduced
or redisseminated in whole or in part without prior written permission from MSCI.
The Information may not be used to create derivative works or to verify or correct other data or information. For example (but without limitation), the Information may not be used to create indexes, databases, risk models, analytics, software, or in
connection with the issuing, offering, sponsoring, managing or marketing of any securities, portfolios, financial products or other investment vehicles utilizing or based on, linked to, tracking or otherwise derived from the Information or any other MSCI
data, information, products or services.
The user of the Information assumes the entire risk of any use it may make or permit to be made of the Information. NONE OF THE INFORMATION PROVIDERS MAKES ANY EXPRESS OR IMPLIED WARRANTIES OR REPRESENTATIONS WITH RESPECT TO
THE INFORMATION (OR THE RESULTS TO BE OBTAINED BY THE USE THEREOF), AND TO THE MAXIMUM EXTENT PERMITTED BY APPLICABLE LAW, EACH INFORMATION PROVIDER EXPRESSLY DISCLAIMS ALL IMPLIED WARRANTIES (INCLUDING, WITHOUT
LIMITATION, ANY IMPLIED WARRANTIES OF ORIGINALITY, ACCURACY, TIMELINESS, NON-INFRINGEMENT, COMPLETENESS, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE) WITH RESPECT TO ANY OF THE INFORMATION.
Without limiting any of the foregoing and to the maximum extent permitted by applicable law, in no event shall any Information Provider have any liability regarding any of the Information for any direct, indirect, special, punitive, consequential
(including lost profits) or any other damages even if notified of the possibility of such damages. The foregoing shall not exclude or limit any liability that may not by applicable law be excluded or limited, including without limitation (as applicable), any
liability for death or personal injury to the extent that such injury results from the negligence or willful default of itself, its servants, agents or sub-contractors.
Information containing any historical information, data or analysis should not be taken as an indication or guarantee of any future performance, analysis, forecast or prediction. Past performance does not guarantee future results.
The Information should not be relied on and is not a substitute for the skill, judgment and experience of the user, its management, employees, advisors and/or clients when making investment and other business decisions. All Information is impersonal
and not tailored to the needs of any person, entity or group of persons.
None of the Information constitutes an offer to sell (or a solicitation of an offer to buy), any security, financial product or other investment vehicle or any trading strategy.
It is not possible to invest directly in an index. Exposure to an asset class or trading strategy or other category represented by an index is only available through third party investable instruments (if any) based on that index. MSCI does not issue,
sponsor, endorse, market, offer, review or otherwise express any opinion regarding any fund, ETF, derivative or other security, investment, financial product or trading strategy that is based on, linked to or seeks to provide an investment return related
to the performance of any MSCI index (collectively, “Index Linked Investments”). MSCI makes no assurance that any Index Linked Investments will accurately track index performance or provide positive investment returns. MSCI Inc. is not an
investment adviser or fiduciary and MSCI makes no representation regarding the advisability of investing in any Index Linked Investments.
Index returns do not represent the results of actual trading of investible assets/securities. MSCI maintains and calculates indexes, but does not manage actual assets. Index returns do not reflect payment of any sales charges or fees an investor may pay
to purchase the securities underlying the index or Index Linked Investments. The imposition of these fees and charges would cause the performance of an Index Linked Investment to be different than the MSCI index performance.
The Information may contain back tested data. Back-tested performance is not actual performance, but is hypothetical. There are frequently material differences between back tested performance results and actual results subsequently achieved by
any investment strategy.
Constituents of MSCI equity indexes are listed companies, which are included in or excluded from the indexes according to the application of the relevant index methodologies. Accordingly, constituents in MSCI equity indexes may include MSCI Inc.,
clients of MSCI or suppliers to MSCI. Inclusion of a security within an MSCI index is not a recommendation by MSCI to buy, sell, or hold such security, nor is it considered to be investment advice.
Data and information produced by various affiliates of MSCI Inc., including MSCI ESG Research Inc. and Barra LLC, may be used in calculating certain MSCI indexes. More information can be found in the relevant index methodologies on www.msci.com.
MSCI receives compensation in connection with licensing its indexes to third parties. MSCI Inc.’s revenue includes fees based on assets in Index Linked Investments. Information can be found in MSCI Inc.’s company filings on the Investor Relations
section of www.msci.com.
MSCI ESG Research Inc. is a Registered Investment Adviser under the Investment Advisers Act of 1940 and a subsidiary of MSCI Inc. Except with respect to any applicable products or services from MSCI ESG Research, neither MSCI nor any of its products
or services recommends, endorses, approves or otherwise expresses any opinion regarding any issuer, securities, financial products or instruments or trading strategies and MSCI’s products or services are not intended to constitute investment advice or
a recommendation to make (or refrain from making) any kind of investment decision and may not be relied on as such. Issuers mentioned or included in any MSCI ESG Research materials may include MSCI Inc., clients of MSCI or suppliers to MSCI, and
may also purchase research or other products or services from MSCI ESG Research. MSCI ESG Research materials, including materials utilized in any MSCI ESG Indexes or other products, have not been submitted to, nor received approval from, the
United States Securities and Exchange Commission or any other regulatory body.
Any use of or access to products, services or information of MSCI requires a license from MSCI. MSCI, Barra, RiskMetrics, IPD, FEA, InvestorForce, and other MSCI brands and product names are the trademarks, service marks, or registered trademarks of
MSCI or its subsidiaries in the United States and other jurisdictions. The Global Industry Classification Standard (GICS) was developed by and is the exclusive property of MSCI and Standard & Poor’s. “Global Industry Classification Standard (GICS)” is a
service mark of MSCI and Standard & Poor’s.
25