Option-Implied Volatility Measures
and Stock Return Predictability
Xi Fu - University of Liverpool
Eser Arisoy - Université Paris-Dauphine
Mark Shackleton - Lancaster University
Mehmet Umutlu - Yasar University
The New Financial Reality Seminar No. 4: Volatility
Kent Business School
Relevant Literature
Outperformance of option-implied information
• Christensen and Prabhala (1998), Kang, Kim and Yoon (2010), Muzzioli
(2011), Poon and Granger (2005), Szakmary, Ors, Kim and Davidson
(2003), Taylor, Yadav and Zhang (2010), and Yu, Lui and Wang (2010)
show that option-implied volatility performs better than historical
volatility in future volatility prediction.
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
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Relevant Literature
Option-implied volatility measures and stock returns
• An, Ang, Bali and Cakici (2014): Changes in call (put) implied volatilities;
• Bali and Hovakimian (2009): Call-put implied volatility spread, and realizedimplied volatility spread;
• Baltussen, Grient, Groot, Hennink and Zhou (2012): Out-of-the-money
volatility skew, at-the-money volatility skew, realized-implied volatility
spread, and weekly change in at-the-money volatility skew;
• Cremers and Weinbaum (2010): Call-put implied volatility spread;
• Doran and Krieger (2010): Call-put implied volatility spread, implied
volatility skew, “above-minus-below”, and “out-minus-at” of calls/puts;
• Xing, Zhang and Zhao (2010): Implied volatility skew.
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Research Questions
• Whether some of the option-implied volatility measures capture the
same or different information contained in volatility curve;
• Which measures are important for investors in predicting stock
returns;
• Whether predictive ability of each measure is sensitive to the length
of investment horizons.
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Data
• Compustat: Financial statement data;
• CRSP: Monthly and daily stock return data;
• OptionMetrics: Option implied volatility data;
• Kenneth French’s data library: Fama-French three-factor data.
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Data Filters
• Only ordinary common shares (CRSP share codes 10 and 11) are
retained. Closed-end funds and REITs (SIC codes 6720-6730 and 6798)
are excluded.
• Stock options with days-to-maturity greater than 30 but less than 91
days are kept.
• This study deletes options:
•
•
•
•
with zero open interest;
with zero best bid prices;
with missing implied volatility;
whose bid-ask spread exceeds 50% of the average of the bid and ask prices.
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Option-Implied Volatility Measures
• Call-put implied volatility spread:
𝐶𝑃𝐼𝑉 = 𝐼𝑉𝐴𝑇𝑀,𝑐𝑎𝑙𝑙 − 𝐼𝑉𝐴𝑇𝑀,𝑝𝑢𝑡
• 𝐶𝑃𝐼𝑉 does not necessarily point out the existence of arbitrage
opportunity due to various reasons.
• It is expected that 𝐶𝑃𝐼𝑉 is positively correlated with future stock
returns.
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
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Option-Implied Volatility Measures
• Implied volatility skew:
𝐼𝑉𝑆𝐾𝐸𝑊 = 𝐼𝑉𝑂𝑇𝑀,𝑝𝑢𝑡 − 𝐼𝑉𝐴𝑇𝑀,𝑐𝑎𝑙𝑙
• 𝐼𝑉𝑆𝐾𝐸𝑊 captures negative jump risk.
• 𝐼𝑉𝑆𝐾𝐸𝑊 is expected to be negatively related to future returns on
underlying stocks.
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
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Option-Implied Volatility Measures
• Above-Minus-Below:
𝐼𝑉𝐼𝑇𝑀,𝑝𝑢𝑡 + 𝐼𝑉𝑂𝑇𝑀,𝑐𝑎𝑙𝑙 − (𝐼𝑉𝐼𝑇𝑀,𝑐𝑎𝑙𝑙 + 𝐼𝑉𝑂𝑇𝑀,𝑝𝑢𝑡 )
𝐴𝑀𝐵 =
2
• 𝐴𝑀𝐵 captures how skewed the volatility curve is by investigating
both tails of the implied volatility curve.
• 𝐴𝑀𝐵 is expected to be positively related to subsequent stock returns.
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
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Option-Implied Volatility Measures
• Out-Minus-At:
𝐶𝑂𝑀𝐴 = 𝐼𝑉𝑂𝑇𝑀,𝑐𝑎𝑙𝑙 − 𝐼𝑉𝐴𝑇𝑀,𝑐𝑎𝑙𝑙
𝑃𝑂𝑀𝐴 = 𝐼𝑉𝑂𝑇𝑀,𝑝𝑢𝑡 − 𝐼𝑉𝐴𝑇𝑀,𝑝𝑢𝑡
• Both 𝐶𝑂𝑀𝐴 and 𝑃𝑂𝑀𝐴 capture the volatility curve asymmetry by
using out-of-the-money and at-the-money options.
• It is expected that 𝐶𝑂𝑀𝐴 is positively related to future underlying
stock returns, whereas 𝑃𝑂𝑀𝐴 is negatively related to underlying
stock returns.
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
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Option-Implied Volatility Measures
• Realized-implied volatility spread:
𝑅𝑉𝐼𝑉 = 𝑅𝑉 − 𝐼𝑉𝐴𝑇𝑀
• 𝑅𝑉𝐼𝑉 is related to the volatility risk premium, which has been widely
tested in empirical literature.
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
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Option-Implied Volatility Measures
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
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Results
Table 1 Summary Statistics
CPIV
IVSKEW
AMB
COMA
POMA
RVIV
CPIV
IVSKEW
AMB
COMA
POMA
RVIV
Mean
-0.0075
0.0676
-0.0821
-0.0184
0.0574
-0.0195
Mean
-0.0104
0.0727
-0.0841
-0.0230
0.0623
-0.0053
Panel A: Full Sample
5 Pct
25 Pct
Median
75th Pct
-0.0677
-0.0189
-0.0047
0.0083
-0.0036
0.0341
0.0572
0.0878
-0.2408
-0.1283
-0.0739
-0.0286
-0.0735
-0.0359
-0.0187
-0.0020
-0.0026
0.0289
0.0497
0.0763
-0.2332
-0.1030
-0.0393
0.0350
Panel B: Intersection Sample (Sample Size=68095)
5th Pct
25th Pct
Median
-0.0692
-0.0168
-0.0046
-0.0027
0.0359
0.0608
-0.2427
-0.1298
-0.0755
-0.0764
-0.0386
-0.0215
-0.0018
0.0307
0.0532
-0.2429
-0.1039
-0.0335
th
th
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
95th Pct
0.0466
0.1703
0.0478
0.0367
0.1429
0.2619
75th Pct
0.0052
0.0956
-0.0303
-0.0057
0.0831
0.0599
Sample Size
233576
128106
71898
118683
123421
288666
95th Pct
0.0300
0.1851
0.0447
0.0256
0.1556
0.3282
13
Results
Table 1 Summary Statistics
IVSKEW
AMB
COMA
POMA
RVIV
ln( size)
B / M Ratio
Momentum
Stock Volume
Market Beta
Bid  Ask Spread
OptionVolume
CPIV
-0.6241
-0.2976
-0.1811
0.0437
0.0049
0.1203
0.0031
-0.0263
0.0307
0.0022
-0.0264
0.0141
Panel C: Correlation Table for the Intersection Sample
COMA
IVSKEW
AMB
-0.3333
-0.2803
0.7534
0.0646
0.0832
0.1547
0.0121
0.1249
0.0378
-0.0979
0.1089
0.6548
-0.6767
-0.0287
-0.1510
-0.1295
-0.0359
-0.1044
-0.0558
0.1669
-0.0709
-0.5108
-0.0243
-0.0415
-0.1287
0.0253
-0.0499
-0.0747
0.1180
0.0152
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
POMA
RVIV
0.0868
0.2077
0.2004
-0.0066
0.1856
0.0502
-0.1474
0.1511
0.0431
0.0581
0.1474
0.0770
0.2475
0.0441
0.0355
14
Results
Table 2 Results for Portfolio Level Analysis
CPIV
IVSKEW
AMB
COMA
POMA
RVIV
Return
Alpha
Return
Alpha
Return
Alpha
Return
Alpha
Return
Alpha
Return
Alpha
1
0.0039
-0.0071
0.0113
0.0012
0.0078
-0.0028
0.0084
-0.0032
0.0060
-0.0043
0.0124
0.0019
Panel A: Equally-Weighted Portfolios
2
3
4
0.0079
0.0098
0.0109
-0.0020
0.0002
0.0013
0.0093
0.0081
0.0069
-0.0004
-0.0016
-0.0034
0.0091
0.0089
0.0078
-0.0018
-0.0016
-0.0025
0.0105
0.0104
0.0095
0.0001
0.0002
-0.0008
0.0088
0.0092
0.0097
-0.0008
-0.0008
-0.0004
0.0108
0.0091
0.0090
0.0010
-0.0006
-0.0011
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0.0156
0.0049
0.0019
-0.0093
0.0043
-0.0070
0.0077
-0.0031
0.0061
-0.0048
0.0077
-0.0036
5-1
0.0118***
0.0120***
-0.0094***
-0.0105***
-0.0035
-0.0042*
-0.0007
0.0001
0.0001
-0.0005
-0.0047***
-0.0055***
p-value
(0.0000)
(0.0000)
(0.0000)
(0.0000)
(0.1721)
(0.0768)
(0.7427)
(0.9382)
(0.9699)
(0.7754)
(0.0049)
(0.0010)
15
Results
Table 2 Results for Portfolio Level Analysis
CPIV
IVSKEW
AMB
COMA
POMA
RVIV
Return
Alpha
Return
Alpha
Return
Alpha
Return
Alpha
Return
Alpha
Return
Alpha
1
0.0037
-0.0056
0.0134
0.0056
0.0086
0.0004
0.0092
-0.0004
0.0074
-0.0006
0.0121
0.0034
Panel B: Value-Weighted Portfolios
2
3
4
0.0062
0.0096
0.0103
-0.0018
0.0021
0.0028
0.0119
0.0095
0.0067
0.0044
0.0022
-0.0009
0.0096
0.0067
0.0116
0.0014
-0.0014
0.0037
0.0115
0.0097
0.0079
0.0034
0.0018
0.0002
0.0107
0.0090
0.0106
0.0029
0.0013
0.0028
0.0113
0.0089
0.0069
0.0036
0.0016
-0.0008
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
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0.0133
0.0051
0.0056
-0.0029
0.0044
-0.0045
0.0040
-0.0039
0.0073
-0.0006
0.0064
-0.0029
5-1
0.0096***
0.0108***
-0.0078***
-0.0085***
-0.0041
-0.0050
-0.0052
-0.0034
-0.0001
0.0001
-0.0057**
-0.0062***
p-value
(0.0002)
(0.0002)
(0.0003)
(0.0001)
(0.3461)
(0.2078)
(0.1261)
(0.2756)
(0.9706)
(0.9721)
(0.0199)
(0.0057)
16
Results
Table 3 Firm-Level Cross-Sectional Regression Results Over One-Week
Intercept
P-value
CPIV
P-value
IVSKEW
P-value
AMB
P-value
COMA
P-value
POMA
P-value
RVIV
P-value
…
I
0.0052
0.5971
0.0721***
0.0000
II
0.0032
0.7463
III
0.0043
0.6683
IV
0.0037
0.7116
V
0.0029
0.7727
VI
0.0016
0.8688
VII
0.0025
0.8002
0.0675***
0.0000
-0.0392***
0.0000
-0.0130*
0.0528
-0.0081
0.6530
-0.0155
0.1604
…
…
…
…
…
-0.0045
0.1595
…
-0.0240**
0.0127
0.0362*
0.0916
-0.0397***
0.0012
-0.0060*
0.0597
…
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
VIII
0.0018
0.8521
-0.0518***
0.0000
-0.0324***
0.0001
0.0403*
0.0578
-0.0059*
0.0624
…
IX
0.0028
0.7707
0.0777***
0.0000
X
0.0018
0.8502
-0.0405***
0.0000
0.0143
0.4602
-0.0208*
0.0536
-0.0061*
0.0545
…
-0.0033
0.8523
-0.0058*
0.0659
…
17
Results
Table 4 Firm-Level Cross-Sectional Regression Results Over One-Month
Intercept
P-value
CPIV
P-value
IVSKEW
P-value
AMB
P-value
COMA
P-value
POMA
P-value
RVIV
P-value
…
I
0.0260
0.1419
0.1051***
0.0002
II
0.0219
0.2273
III
0.0245
0.1712
IV
0.0234
0.1946
V
0.0224
0.2228
VI
0.0234
0.1824
VII
0.0245
0.1716
0.1224***
0.0000
-0.0762***
0.0000
0.0029
0.8076
0.0182
0.6092
-0.0503**
0.0308
…
…
…
…
…
0.0041
0.5087
…
-0.0078
0.6630
0.0406
0.2866
-0.0528*
0.0645
0.0009
0.8707
…
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
VIII
0.0216
0.2205
-0.0895***
0.0000
-0.0248**
0.0490
0.0405
0.2937
0.0008
0.8977
…
IX
0.0235
0.1914
0.1215***
0.0000
X
0.0212
0.2289
-0.0814***
0.0000
0.0357
0.2849
-0.0503**
0.0171
0.0003
0.9650
…
0.0084
0.7963
0.0006
0.9149
…
18
Results
Table 5 Firm-Level Cross-Sectional Regression Results Over One-Quarter
Intercept
P-value
CPIV
P-value
IVSKEW
P-value
AMB
P-value
COMA
P-value
POMA
P-value
RVIV
P-value
…
I
0.0445
0.3726
0.1356***
0.0076
II
0.0385
0.4458
III
0.0425
0.4019
IV
0.0413
0.4147
V
0.0413
0.4246
VI
0.0415
0.4098
VII
0.0427
0.4022
0.1712***
0.0004
-0.1322***
0.0007
0.0029
0.9005
0.1007
0.1332
-0.0764
0.1393
…
…
…
…
…
0.0140
0.1814
…
-0.0348
0.1980
0.1606**
0.0236
-0.0957
0.1033
0.0046
0.6255
…
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
VIII
0.0374
0.4571
-0.1440***
0.0001
-0.0472**
0.0315
0.1424**
0.0495
0.0042
0.6580
…
IX
0.0423
0.4068
0.1731***
0.0003
X
0.0366
0.4676
-0.1374***
0.0002
0.1351**
0.0491
-0.0778
0.1077
0.0041
0.6622
…
0.0855
0.1964
0.0046
0.6339
…
19
Results
Table 6 Firm-Level Cross-Sectional Regression Results Over One-Week (Before Crisis)
Intercept
P-value
CPIV
P-value
IVSKEW
P-value
AMB
P-value
COMA
P-value
POMA
P-value
RVIV
P-value
…
I
0.0083
0.5246
0.0886***
0.0000
II
0.0070
0.5911
III
0.0057
0.6679
IV
0.0053
0.6900
V
0.0043
0.7438
VI
0.0038
0.7705
VII
0.0073
0.5774
0.0895***
0.0000
-0.0437***
0.0001
-0.0145
0.1198
-0.0028
0.9021
-0.0133
0.3468
…
…
…
…
…
-0.0061
0.1249
…
-0.0265*
0.0529
0.0594**
0.0259
-0.0365**
0.0260
-0.0083**
0.0319
…
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
VIII
0.0060
0.6419
-0.0618***
0.0000
-0.0414***
0.0004
0.0608**
0.0238
-0.0080**
0.0372
…
IX
0.0066
0.6049
0.0993***
0.0000
X
0.0058
0.6510
-0.0458***
0.0000
0.0360
0.1291
-0.0162
0.2413
-0.0082**
0.0322
…
0.0074
0.7458
-0.0076**
0.0447
…
20
Results
Table 6 Firm-Level Cross-Sectional Regression Results Over One-Week (After Crisis)
Intercept
P-value
CPIV
P-value
IVSKEW
P-value
AMB
P-value
COMA
P-value
POMA
P-value
RVIV
P-value
…
I
-0.0012
0.9344
0.0377**
0.0258
II
-0.0048
0.7378
III
0.0013
0.9245
IV
0.0004
0.9774
V
-0.0001
0.9954
VI
-0.0029
0.8391
VII
-0.0074
0.6014
0.0216
0.2653
-0.0299**
0.0237
-0.0098
0.1660
-0.0191
0.5131
-0.0202
0.2527
…
…
…
…
…
-0.0011
0.8432
…
-0.0188**
0.0274
-0.0121
0.7126
-0.0463***
0.0059
-0.0014
0.8177
…
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
VIII
-0.0069
0.6116
-0.0311**
0.0162
-0.0138*
0.0820
-0.0022
0.9441
-0.0016
0.7871
…
IX
-0.0051
0.7215
0.0329*
0.0924
X
-0.0064
0.6396
-0.0295**
0.0192
-0.0310
0.3123
-0.0303*
0.0552
-0.0017
0.7727
…
-0.0256
0.3333
-0.0019
0.7518
…
21
Discussion
Put-Call Parity
• Due to the existence of frictions in the market, Finucane (1991)
proposes a measure of deviation from put-call parity
𝐸𝑡 ≡ 𝐶𝑡𝑏 − 𝑃𝑡𝑎 + 𝐾 − 𝑆𝑡 + 𝐷𝑡
• The bounds for this measure can be written as:
𝐾 𝑒 −𝑟 𝑇−𝑡 − 1 − 𝐵𝐴𝐶𝑡 − 𝐵𝐴𝑃𝑡 ≤ 𝐸𝑡 ≤ 0
• Among stocks whose 𝐸𝑡 locates within the lower and upper bounds,
𝐶𝑃𝐼𝑉 is still significantly and positively related to future stock returns.
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
22
Discussion
Information Spillover
• Bollen and Whaley (2004): a positive relation between option
expensiveness which can be measured by implied volatility and enduser demand.
• Bali and Hovakimian (2009): there is significant volatility spillover
effect and information spills over from individual equity options to
individual stocks.
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
23
Discussion
Informed Trading
• Bali and Hovakimian (2009): Informed investors, who know that stock
prices will change but are not sure about the direction, are more
likely to trade in the options market.
• Cremers and Weinbaum (2010): 𝐶𝑃𝐼𝑉 tends to predict returns to a
greater extent in firms that face a more asymmetric information
environment.
• Xing, Zhang and Zhao (2010): Informed traders trade in the options
market and the stock market is slow to incorporate information from
the options market.
• Lin and Lu (2015): Predictability of option-implied volatilities is driven
by insiders’ information about upcoming analyst-related news.
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
24
Discussion
Delta-Hedge Trading Strategy
• Doran and Krieger (2010): The predictive power of option-implied
volatility measures on stock returns could be due to trading activities
of delta-hedge traders.
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
25
Discussion
Constraints on Short Sale
• Figlewski and Webb (1993): Call-put implied volatility spread if closely
correlated with short interest, which is a proxy for constraints on
short sale.
• Ofek, Richardson and Whitelaw (2004): For stocks that are difficult or
expensive to short, a deviation from put-call parity is more likely to be
observed.
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
26
Conclusion
• Portfolio level analysis
• 𝐶𝑃𝐼𝑉: positively related to stock returns;
• 𝐼𝑉𝑆𝐾𝐸𝑊: negatively related to stock returns;
• 𝑅𝑉𝐼𝑉: negatively related to stock returns.
• Firm-level cross-sectional regressions
• One-week horizon: 𝐼𝑉𝑆𝐾𝐸𝑊
• One-month horizon:𝐼𝑉𝑆𝐾𝐸𝑊
• One-quarter horizon: 𝐼𝑉𝑆𝐾𝐸𝑊 & 𝐶𝑂𝑀𝐴
The New Financial Reality Seminar No. 4: Volatility - Xi Fu
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