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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

• 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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