Does Option Trading Have a Pervasive Impact on Underlying Stock Prices

1
Does Option Trading Have a Pervasive Impact on
Underlying Stock Prices?

• Neil Pearson, Allen Poteshman, and Joshua White
• 9 March 2007

2
Introduction Do Equity Options Impact
Underlying Stock Prices?

• Major concern of investors, regulators, exchange
  officials from opening of CBOE in 1973
• Basis for severe limits on available contracts in
  early years
• Evidence from previous research
• Price level change upon option introduction No
• Price changes at option expiration Yes
• Pervasive changes (not just at introduction or
  expiration) No

3
Does option introduction change price level of
underlying stock?

• Early papers Option introduction increases
  stock price. Conrad (1989) and Detemple and
  Jorion (1990)
• More recent papers Post 1990, option
  introduction decreases stock price. Sorescu
  (2002) and Ho and Liu (1997)
• Current Price level effects vanish when
  benchmarked against matched firms that do not
  have options introduced. Mayhew and Mihov
  (2004)
• Bottom line No evidence that option
  introduction changes price level

4
Do options change the prices of underlying stocks
at expiration?

• Early studies do not find much evidence of
  expiration effects. CBOE (1976), Klemonsky
  (1978), Cinar and Vu (1987)
• Ni, Pearson, and Poteshman (2005) produce strong
  evidence that the prices of optioned stocks
  cluster at strike prices on expiration dates

5
Stock Prices Altered at Expiration(from Ni,
Pearson, Poteshman (2005))
Percentage of optioned stocks closing with 0.125
of a strike price

• Rebalancing by delta hedgers with net purchased
  option positions
• Manipulation by proprietary traders who sell
  option during exp. week

6
Do options produce pervasive changes (not just at
intro. or expir.) on underlying stocks?

• Early papers Option introduction decreases
  underlying stock volatility. Bansal, Pruitt,
  and Wei (1989), Conrad (1989), and Skinner
  (1989)
• Current papers Volatility effects vanish when
  benchmarked against matched firms that do not
  have options introduced. Lamoureux and Pankkath
  (1994), Freund, McCann, and Wbb (1994), and
  Bollen (1998)
• Exchanges tend to introduce options after
  underlying stock volatility increases
• Bottom line No convincing evidence that option
  introduction changes volatility level

7
This paper Do options produce pervasive changes
in stocks?

• Re-examines whether option trading changes
  volatility of underlying stocks
• Point of departure
• Ni et. al. (2005) find that re-hedging of option
  positions just before expiration produces
  measurable stock price changes
• Does re-hedging away from stock expiration also
  lead to stock price changes?
• Unlike previous literature, we ask whether
  volatility of underlying stocks changes
  conditional on the option positions of likely
  delta hedgers
• In particular, we test the theoretical prediction
  that the volatility of underlying stocks is
  negatively related to the gamma of the option
  positions of delta hedgers.
• (Gamma Change in delta per dollar change in
  underlying stock price
• Delta Change in option price per dollar
  change in underlying stock)

8
Overall Approach

• Existing theoretical literature gamma of
  delta-hedgers positions negatively impacts
  volatility of underlying stock
• Empirical strategy using unique CBOE dataset,
  identify position gammas of likely delta-hedgers
  (option market makers or market makers plus firm
  proprietary traders)
• See whether gamma of likely delta-hedgers
  positions significantly predicts future
  volatility, even on days that are not close to
  expiration.

9
Findings

• There is a negative relationship between the
  gamma of the option positions of likely
  delta-hedgers and the volatility of the
  underlying stock
• Robust to controls for stock volatility
  persistence, information trading, stock size,
  subperiods, definition of likely delta-hedgers,
  exclusion of expiration week
• Effect is an economically significant determinant
  of volatility for equities
• One std. dev. shock to gamma alters variability
  of underlying stock by 12 of its average value
• Stock volume from hedge re-balancing is
  positively related to total stock volume
• One std. dev. shock to stock volume from hedge
  re-balancing accounts for 14 of average total
  stock volume

10
Outline

• Mechanism by which hedge re-balancing impacts
  underlying stock prices
• Data
• Empirical results
• Conclusion

11
Mechanism Hedge rebalancing and demand

• Mechanism for option-underlying relationship
• Market participants hedge option positions,
  creating demand for the underlying, which
  influences underlying prices
• Delta hedging of purchased (written) options
  requires selling (buying) when underlying price
  rises, buying (selling) when underlying price
  decreases
• If some, but not all option market participants
  are delta hedgers, possible influence of hedging
  demand on underlying price
• Existing theoretical models
• Frey and Stremme (1997), Sircar and Papanicolaou
  (1998), Schönbucher and Wilmott (2000), and
  others

12
Hedge rebalancing and demand
Current underlying price 20
delta 0
13
Hedge rebalancing and demand
Movement in underlying
delta .5 Net sale of .5 shares induced in hedge
position
delta 0
14
Hedge rebalancing and demand

• When delta-hedgers are long options
• Sell shares in response to price increases
• Buy shares in response to price decreases
• Potentially decreases volatility of underlying
  stock
• When delta-hedgers are short options
• Buy shares in response to price increases
• Sell shares in response to price decreases
• Potentially increases volatility of underlying
  stock
• Measure of option hedge rebalancing in response
  to stock price movements
• G ??/?S

15
Gamma and hedge rebalancing
Option delta changes rapidly with price large
hedge rebalancing effect
Small hedge rebalancing effect
16
Empirical predictions

• If we can identify the option positions of
  delta-hedgers, then
• When hedgers have
• large positive gamma ? stabilizing influence on
  the price ? lower future volatility
• large negative gamma ? destabilizing influence on
  the price ? higher future volatility

17
Empirical strategy

• For each optionable stock and each date, need to
  compute aggregate net (purchased - written) gamma
  of delta hedgers
• Aggregate across different options on the same
  underlying stock
• Can we identify the delta hedgers?

18
Option market participants

• Option market participants identified in CBOE
  dataset
• Firm proprietary traders
• E.g., Goldman Sachs
• Public customers
• E.g., Retail-level
• Market makers
• Identified as residual

Possible delta hedgers
Likely delta hedgers Cox and Rubinstein (1985),
Hull (2003), McDonald (2006)
19
Data

• CBOE dataset
• Proprietary dataset including daily purchased and
  written open interest by public customers and
  firm proprietary traders
• 1990 2001
• Every option series trading at CBOE covered
• CRSP
• Underlying stock prices, volume

20
Variable construction

• Variables constructed from raw CBOE data on open
  interest for public and non-public participants
• netDelta and netGamma aggregate delta and gamma
  of option market participants
• netDeltaVolume Absolute changes in netDelta
  (induced volume)

21
Variable construction

(Sum over all Ns,t options on same underlying, s)
The units of D, G, S, and M are shares,
(shares)2/, /share, and shares, respectively,
implying that the ratio (S/M)?G(t, S) is
dimensionless.
22
Hedger gamma and underlying volatility

• Key prediction volatility decreasing in gamma of
  delta hedgers
• Positive gamma ? stabilizing hedging trades ?
  lower vol
• Negative gamma ? destabilizing hedging trades ?
  higher vol

23
Market maker gamma and absolute returns
Mean absolute next day return
24
Hedger gamma and underlying volatility

• Key prediction Volatility decreasing in gamma
  of delta hedgers
• Potential difficulty Common causation
• Investor has private information that volatility
  will increase
• Market maker writes options and has negative
  gamma
• Future volatility is higher

25
Hedger gamma and underlying volatility
Identification strategy

• Common causation Plausible?
• Lakonishok, Lee, Pearson and Poteshman
  (forthcoming RFS) find that pure volatility plays
  (straddles, strangles, butterflies) on individual
  equity options are rarely traded
• Ni, Pan, and Poteshman (2006) detect volatility
  information trading

26
Hedger gamma and underlying volatility
Identification strategy

• Strategy Identify change in gamma that does not
  result from investors buying or selling options
  on the basis of volatility information
• Gamma changes over time for two reasons
• New positions
• Stock price movements

Potentially related to private volatility
information
Plausibly exogenous source of gamma variation
27
Hedger gamma and underlying volatility
specification

• Decompose current (time t) market maker gamma
  into three pieces

Change in gamma due to stock price movement
Change in gamma due to new positions
Gamma of old positions held at t - t
28
Gamma of market maker positions at t - t (example)
Purchased options with K 30
Purchased options with K 40
Written options with K 25
29
Hedger gamma and underlying volatility
specification
Change in gamma due to new positions
Change in gamma due to underlying price movement
Old gamma, t days prior
30
Hedger gamma and underlying volatility
specification

• LHS variable Absolute returns
• Controls Multiple lags of prior absolute
  returns to capture volatility persistence
• Coefficients are average of OLS
  equation-by-equation
• Standard errors for this average are constructed
  by clustering by date, and are heteroskedasticity
  robust
• Lag for gamma change calculation t 5

31
Table 2 Hedger gamma and underlying volatility
32
Cross-section of b coefficient estimates

• 73 of b coefficient estimates for individual
  stocks are less than 0

33
Hedger gamma and underlying volatility

• Changes in gamma induced by stock price movements
  significantly affect volatility
• Causality plausible, because movements of the
  stock price from regions of high to low gamma, or
  vice versa, are unrelated to private volatility
  information.
• Other sources of gamma are also strong predictors
  of volatility harder to make causal link

34
Hedger gamma and underlying volatility

• Economic significance is high!
• Absolute returns in our sample have mean of 310
  bp and std. dev. of 320 bp
• One std. dev. shock to gamma induces
• 37 bp ( -0.000543 x 6.772) change in absolute
  return
• 12 of one std. dev. of absolute return
• 12 of average daily absolute return

35
Table 3 Hedger gamma and large returns
Unconditional probability r gt 3 is 0.28. A
one-standard-deviation change in gamma reduces
this probability from 0.28 to 0.25, an 11
reduction. A one std.dev. change in gamma reduces
Probr gt 0.05 by 18.5, from 0.139 to 0.113.
36
Table 1 Descriptive statistics
37
Hedger gamma and underlying volatility a
pervasive effect

• We know from Ni, Pearson and Poteshman (2005)
  that optionable stocks tend to pin at expiration
• Is the gamma-conditional delta-hedging effect
  solely near expiration, or is it pervasive?
• Regression with expiration week omitted gives
  similar point estimates and significance
• Results present in two major subperiods

38
Table 4 Gamma and underlying volatility
pervasive effect

• Expiration week omitted

39
Table 5 Gamma and underlying volatility
pervasive effect

• Subperiods

40
Table 6 Gamma and underlying volatility
pervasive effect

• Large versus not large (large among largest
  250 on 31 Dec. of previous year)

41
Table 7 Different definition of old
positions t 10 days
42
Table 8 Option gammas from OptionMetrics
43
Delta hedging volume and underlying volume

• Regression of underlying volume on
  deltaHedgeVolume and controls
• Coefficients are average of OLS
  equation-by-equation
• Standard errors for this average are constructed
  by clustering by date, and are heteroskedasticity
  robust

44
Table X Delta hedging volume and underlying
volume
Cofficient estimate of 4.132 implies that one
standard deviation change in deltaHedgeVolume
results in 134,732 change in daily trading
volume, equal to about 14 of average daily
volume. There also 9 lags of aboslute return on
RHS.
45
Delta hedging volume and underlying volume

• Volume is higher during periods of high hedging
  activity
• Coefficients gt 1
• Measure of delta hedge volume is based on net
  positions of market makers
• Assume hedge rebalancing only once per day
• Identified option hedgers are not only option
  hedgers
• Potential multiple-counting of volume on NASDAQ

46
Conclusion

• Significant negative relation between stock
  return volatility and gammas of likely
  delta-hedgers
• Strong argument for causality based on
  identification from gamma changes induced by
  stock price movements
• Economically significant and pervasive effect
• Additional support from volume relationship
  high underlying volume associated with high
  induced delta-hedging volume