presentation for qwafafew, june 8, 2011

Presentation for QWAFAFEW, June 8, 2011

The Impact of the Federal Reserve's Interest Rate Target Announcement on Stock Prices: A Closer Look at How the

Market Impounds New Information

Justin Birru

and

Stephen Figlewski*

New York University Stern School of Business

The Classic Event Study Market Response Plot

Price

TimeNews release

Figlewski QWAFAFEW Presentation June 2011 2

The Classic Event Study Market Response Plot, with Information Leakage

Price

TimeNews release

3Figlewski QWAFAFEW Presentation June 2011

Figure 1: Intraday Behavior of the Forward Value of the S&P Index on Dec. 11, 2007


Date Target Rate Change S&P 500 Index

Change

Fed Funds Futures

"Surprise" 5/3/2005 3 0.25 -0.99 0 6/30/2005 3.25 0.25 -8.52 0 8/9/2005 3.5 0.25 8.25 0 9/20/2005 3.75 0.25 -9.68 0.014 11/1/2005 4 0.25 -4.25 0.225

12/13/2005 4.25 0.25 7.00 0 1/31/2006 4.5 0.25 -5.11 0 3/28/2006 4.75 0.25 -8.38 0 5/10/2006 5 0.25 -2.29 -0.007 6/29/2006 5.25 0.25 26.87 -0.015 8/8/2006 5.25 0 -4.29 -0.039 9/20/2006 5.25 0 7.54 0

10/25/2006 5.25 0 4.84 0 12/12/2006 5.25 0 -1.48 0 1/31/2007 5.25 0 9.42 0 3/21/2007 5.25 0 24.10 0 5/9/2007 5.25 0 4.86 0 6/28/2007 5.25 0 -0.63 0 8/7/2007 5.25 0 9.04 0.025 9/18/2007 4.75 -0.5 43.13 -0.138

10/31/2007 4.5 -0.25 18.36 -0.020 12/11/2007 4.25 -0.25 -38.31 0.007 1/30/2008 3 -0.5 -6.49 -0.095 3/18/2008 2.25 -0.75 54.14 0.155 4/30/2008 2 -0.25 -5.35 -0.055 6/25/2008 2 0 7.68 -0.025 8/5/2008 2 0 35.87 -0.006 9/16/2008 2 0 20.90 0.056

10/29/2008 1 -0.5 -10.42 -0.060 12/16/2008 0.125* -0.875 44.61 -0.110

Table 1: Federal Reserve Interest Rate Target Announcements


Hypotheses and Questions about the Impact of the Fed Announcement

Is the market's response to the announcement unbiased?

Does the information in the announcement all enter the market at the moment of the public announcement?

• Information leakage beforehand?

• Sluggish adjustment or overshooting afterward?

The mean of the Risk Neutral Density (RND) and the forward value of the spot S&P index are tied together by arbitrage. Do they behave identically on announcement day?

• Is one a better prediction of the announcement than the other?

The RND reveals the market's risk neutral expectation for the future value of the index and also the variance around that expectation, a direct measure of uncertainty.

• How much uncertainty does a Fed announcement resolve on average?

• Does it matter if the announcement is viewed as positive or negative by the market?


Hypotheses and Questions about Informational Efficiency

Information flow within a time interval can be proxied by the standard deviation of price change over the interval or by volatility within the interval. What is information flow like over an announcement day?

• How much information does the announcement itself convey?

• How is the day's price change distributed within the day?

• Is there a distinct period of re-equilibration after the announcement?

• How does an announcement day compare to a regular day?

Information flow is assumed to be serially independent, so price changes in an efficient

market should have zero autocorrelation.

• Does this hold for the forward index level?

• Does it hold for the RND mean?


Answers Using the Risk Neutral Density for the S&P 500

We address these questions by exploring the behavior of the risk neutral probability density for the market portfolio on days when the Federal Reserve announces its interest rate target.

Data sample:

• Option Price Reporting Authority (OPRA) National Best Bid and Offer data provides a continuous synchronized record of price movements in the markets for all equity and equity index options and their underlyings

• S&P 500 index calls and puts, with maturities in March, June, September, and December, 28 announcement days 2005 – 2008

• Puts and calls are combined to cover the range of traded exercise prices: Out of the money puts for low X; out of the money calls for high X; a weighted combination of calls and puts for X in the middle range.

• Options with bid prices less than $0.50 were discarded


The Risk Neutral Probability Distribution for the S&P 500 Index

The market price of a risky asset depends on the market's assessment of the probability distribution for its future payoff together with the market's risk aversion. Neither of these can be observed directly, but the two can be combined and expressed as the "Risk Neutral Probability Density" (RND).

Breeden and Litzenberger (Journal of Business, 1978) showed how the risk neutral probability distribution for ST, the value of the underlying asset on option expiration day can be extracted from a set of market option prices.

Two major problems in constructing a complete risk neutral density from a set of market option prices:

1. How to smooth and interpolate option prices to limit pricing noise and produce a smooth density

2. How to extend the distribution to the tails beyond the range of traded strike prices.

But one terrific advantage is that unlike implied volatility, the risk neutral density is model-free.


Extracting the Risk Neutral Density from Options Prices in Theory

The value of a call option is the expected value under the risk neutral distribution of its payoff on the expiration date T, discounted back to the present.

Taking the partial derivative in (1) with respect to X,

( ) ( )

rTT T TX

Ce S X f S dS

X X

( ) 1 ( )

rT rT

T TX

Ce f S dS e F X

X

( ) 1

rT C

F X eX

( ) ( ) rT

T T TXC e S X f S dS


Extracting the Risk Neutral Density from Options Prices in Theory

We will use three options with sequential strike prices Xn-1, Xn, and Xn+1 in order to obtain an approximation to F(X) centered on Xn.

Taking the derivative with respect to X a second time yields the risk neutral density function at X.

which is approximated by

1 1

1 1

( ) 1

rT n nn

n n

C CF X e

X X

2

2( )

rT C

f X eX

1 1

2

2( )

( )

rT n n nn

C C Cf X e

X


Extracting the Risk Neutral Density, a more intuitive approach

Consider a call option that allows you to buy a share of some underlying stock for a price of 101 one month from now. If the stock price in one month is above 101, you will exercise the option. The market price for this option is 5.00 .

There is a second call option that allows you to buy 1 share of the same stock for a price of 100 in one month. The market price for Option 2 is 5.70.

For every stock price above 101, the second option pays 1 more than the first option.

The market values that extra 1 that option 2 pays if the stock price is above 101 as being worth 5.70 – 5.00 = 0.70. So (roughly speaking) the market is saying the probability the stock price will be above 101 is 70%.

12

Stock price in 1 month

90 95 100 101 105 110

Option 1 value

0 0 0 0 4 9

Option 2 value

0 0 0 1 5 10

Figlewski QWAFAFEW Presentation June 2011

Calls Puts Strike price

Best bid Best offer

Average price

Implied volatility

Best bid

Best offer

Average price

Implied volatility

500 - - - - 0.00 0.05 0.025 0.593

550 - - - - 0.00 0.05 0.025 0.530

600 - - - - 0.00 0.05 0.025 0.473

700 - - - - 0.00 0.10 0.050 0.392

750 - - - - 0.00 0.15 0.075 0.356

800 - - - - 0.10 0.20 0.150 0.331

825 - - - - 0.00 0.25 0.125 0.301

850 - - - - 0.00 0.50 0.250 0.300

900 - - - - 0.00 0.50 0.250 0.253

925 - - - - 0.20 0.70 0.450 0.248

950 - - - - 0.50 1.00 0.750 0.241

975 - - - - 0.85 1.35 1.100 0.230

995 - - - - 1.30 1.80 1.550 0.222

1005 - - - - 1.50 2.00 1.750 0.217

1025 - - - - 2.05 2.75 2.400 0.208

1050 134.50 136.50 135.500 0.118 3.00 3.50 3.250 0.193

1075 111.10 113.10 112.100 0.140 4.50 5.30 4.900 0.183

1100 88.60 90.60 89.600 0.143 6.80 7.80 7.300 0.172

1125 67.50 69.50 68.500 0.141 10.10 11.50 10.800 0.161

1150 48.20 50.20 49.200 0.135 15.60 17.20 16.400 0.152

1170 34.80 36.80 35.800 0.131 21.70 23.70 22.700 0.146

1175 31.50 33.50 32.500 0.129 23.50 25.50 24.500 0.144

1180 28.70 30.70 29.700 0.128 25.60 27.60 26.600 0.142

1190 23.30 25.30 24.300 0.126 30.30 32.30 31.300 0.141

1200 18.60 20.20 19.400 0.123 35.60 37.60 36.600 0.139

1205 16.60 18.20 17.400 0.123 38.40 40.40 39.400 0.139

1210 14.50 16.10 15.300 0.121 41.40 43.40 42.400 0.138

1215 12.90 14.50 13.700 0.122 44.60 46.60 45.600 0.138

1220 11.10 12.70 11.900 0.120 47.70 49.70 48.700 0.136

1225 9.90 10.90 10.400 0.119 51.40 53.40 52.400 0.137

1250 4.80 5.30 5.050 0.117 70.70 72.70 71.700 0.139

1275 1.80 2.30 2.050 0.114 92.80 94.80 93.800 0.147

1300 0.75 1.00 0.875 0.115 116.40 118.40 117.400 0.161

1325 0.10 0.60 0.350 0.116 140.80 142.80 141.800 0.179

1350 0.15 0.50 0.325 0.132 165.50 167.50 166.500 0.198

1400 0.00 0.50 0.250 0.157 - - - -

1500 0.00 0.50 0.250 0.213 - - - -

S&P 500 Index Options PricesJan. 5, 2005

S&P close 1183.74

Option expiration 3/18/05

At the money


Extracting the Risk Neutral Density from Options Prices in Practice

Obtaining a well-behaved risk neutral density from market option prices is a nontrivial exercise. Here are the main steps we follow.

1. Use bid and ask quotes, rather than transactions prices. Eliminate options too far in or out of the money.

2. Construct a smooth curve in strike-implied volatility space

3. Interpolate the IVs using a 4th degree smoothing spline

4. Fit the spline to the bid-ask spread

5. Use out of the money calls, out of the money puts, and a blend of the two at the money

6. Convert the interpolated IV curve back to option prices and extract the middle portion of the risk neutral density

7. Append tails to the Risk Neutral Density from a Generalized Extreme Value distribution


Calls Puts Strike price

Best bid Best offer

Average price

Implied volatility

Best bid

Best offer

Average price

Implied volatility

500 - - - - 0.00 0.05 0.025 0.593

550 - - - - 0.00 0.05 0.025 0.530

600 - - - - 0.00 0.05 0.025 0.473

700 - - - - 0.00 0.10 0.050 0.392

750 - - - - 0.00 0.15 0.075 0.356

800 - - - - 0.10 0.20 0.150 0.331

825 - - - - 0.00 0.25 0.125 0.301

850 - - - - 0.00 0.50 0.250 0.300

900 - - - - 0.00 0.50 0.250 0.253

925 - - - - 0.20 0.70 0.450 0.248

950 - - - - 0.50 1.00 0.750 0.241

975 - - - - 0.85 1.35 1.100 0.230

995 - - - - 1.30 1.80 1.550 0.222

1005 - - - - 1.50 2.00 1.750 0.217

1025 - - - - 2.05 2.75 2.400 0.208

1050 134.50 136.50 135.500 0.118 3.00 3.50 3.250 0.193

1075 111.10 113.10 112.100 0.140 4.50 5.30 4.900 0.183

1100 88.60 90.60 89.600 0.143 6.80 7.80 7.300 0.172

1125 67.50 69.50 68.500 0.141 10.10 11.50 10.800 0.161

1150 48.20 50.20 49.200 0.135 15.60 17.20 16.400 0.152

1170 34.80 36.80 35.800 0.131 21.70 23.70 22.700 0.146

1175 31.50 33.50 32.500 0.129 23.50 25.50 24.500 0.144

1180 28.70 30.70 29.700 0.128 25.60 27.60 26.600 0.142

1190 23.30 25.30 24.300 0.126 30.30 32.30 31.300 0.141

1200 18.60 20.20 19.400 0.123 35.60 37.60 36.600 0.139

1205 16.60 18.20 17.400 0.123 38.40 40.40 39.400 0.139

1210 14.50 16.10 15.300 0.121 41.40 43.40 42.400 0.138

1215 12.90 14.50 13.700 0.122 44.60 46.60 45.600 0.138

1220 11.10 12.70 11.900 0.120 47.70 49.70 48.700 0.136

1225 9.90 10.90 10.400 0.119 51.40 53.40 52.400 0.137

1250 4.80 5.30 5.050 0.117 70.70 72.70 71.700 0.139

1275 1.80 2.30 2.050 0.114 92.80 94.80 93.800 0.147

1300 0.75 1.00 0.875 0.115 116.40 118.40 117.400 0.161

1325 0.10 0.60 0.350 0.116 140.80 142.80 141.800 0.179

1350 0.15 0.50 0.325 0.132 165.50 167.50 166.500 0.198

1400 0.00 0.50 0.250 0.157 - - - -

1500 0.00 0.50 0.250 0.213 - - - -

S&P 500 Index Options PricesJan. 5, 2005

S&P close 1183.74

Option expiration 3/18/05

At the money

15

Not used

Blended

Figlewski QWAFAFEW Presentation June 2011

Figure 2: Risk Neutral Density from Raw Options Prices

-0.005

0

0.005

0.01

0.015

0.02

0.025

800 900 1000 1100 1200 1300 1400

S&P 500 Index

Pro

ba

bil

ity

Density from put prices Density from call prices


Figure 3: Market Option Prices with Cubic Spline Interpolation

0

20

40

60

80

100

120

140

160

180

500 600 700 800 900 1000 1100 1200 1300 1400 1500

S&P 500 Index

Op

tion

pri

ce

Spline interpolated call price Spline interpolated put price Market call prices Market put prices


Figure 4: Densities from Option Prices with Cubic Spline Interpolation

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

800 900 1000 1100 1200 1300 1400

S&P 500 Index

De

nsi

ty

Density from interpolated put prices Density from interpolated call prices


Figure 5: Implied Volatilities with Spline and 4th degree Polynomial Interpolation

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

500 600 700 800 900 1000 1100 1200 1300 1400 1500

S&P 500 Index

Impl

ied

vola

tility

4th degree polynomial call IV 4th degree polynomial put IV Call IVs Put IVs Call spline IVs Put spline IVs


Figure 6: Densities from Interpolated Implied Volatilities

-0.004

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

800 900 1000 1100 1200 1300 1400

S&P 500 Index

De

nsi

ty

Calls w. 4th deg poly Puts w. 4th deg poly Calls w. spline IVs Puts w. spline IVs


4th Degree Smoothing Spline with Bid-Ask Spread Adjustment


Empirical Risk Neutral Density January 5, 2005with IV Interpolation using 4th Degree Polynomial

0.000

0.002

0.004

0.006

0.008

0.010

0.012

800 900 1000 1100 1200 1300 1400

S&P 500 Index

De

nsi

ty


The Generalized Extreme Value (GEV) Distribution

We complete the risk neutral density by adding tails from a GEV density.

The GEV distribution has three parameters:

μ = location

σ = scale

ξ = tail shape

If ξ > 0, the GEV is a Fréchet distribution, that has a heavier tail than the normal distribution;

ξ = 0, the GEV is a Gumbel distribution with tails like the normal;

ξ < 0, the density is a Weibull, with a finite tail that does not extend to infinity.

1/

GEVx

F (x ; , , ) exp 1


Figure 9: Risk Neutral Density and Fitted GEV Tail Functions

0.000

0.002

0.004

0.006

0.008

0.010

0.012

800 900 1000 1100 1200 1300 1400

S&P 500 Index

De

nsi

ty

Empirical RND Left tail GEV function Right tail GEV function Attachment points

2% 5%92%

95%

95%

98%


95%

98%

Figure 10: Full Estimated Risk Neutral Density Function for Jan. 5, 2005

0.000

0.002

0.004

0.006

0.008

0.010

0.012

800 900 1000 1100 1200 1300 1400

S&P 500 Index

De

nsi

ty

Empirical RND Left tail GEV function Right tail GEV function


The Risk Neutral Density in a Black-Scholes World

An Aside: The RND under Black-Scholes Assumptions

Risk neutral valuation was first developed in the context of the Black-Scholes model. The returns process is modeled as:

The empirical distribution of the date T asset price is lognormal.

Risk neutralization simply replaces the empirical drift μ with the riskless rate r:

The risk neutral distribution is still lognormal with the same volatility. It is simply shifted to the left, and only the mean changes.

Is the curve on the previous slide lognormal? No! It can't be, because it is skewed to the left while the lognormal is skewed to the right.

dSdt dz

S

dSr dt dz

S


Figure 2: Initial Impact of the Fed Announcement on the Risk Neutral Density, Dec. 11, 2007


Figure 3: Re-equilibration of the Stock Market after the Fed Announcement, Dec. 11, 2007


Information Flow and the Resolution of Uncertainty

New information entering the market will produce a change in the market price. The size of the price move measures the flow of new information during a given time interval.

We estimate the rate of information flow over different periods of the day by the standard deviation of interval price changes across announcement dates.

The RND mean is the market's expectation for the level of the S&P index on option expiration day, and the RND variance is the market's uncertainty about S(T), given S(t). The risk neutral variance measures how much new information the market anticipates will arrive over the time remaining to expiration.

If there are T days to expiration, on average 1/T of the uncertainty should be resolved each day and the RND variance is should fall by the fraction 1/T per day. Research shows that this relationship holds very closely in the data.

We look at the change in RND variance to measure how much the market's uncertainty is resolved by the information contained in the Fed's announcement


Full day:

Close date t-1 to Close date t

Overnight: Close date t-1 to 10:00 AM

date t

Pre-announcement: 10:00 AM to 2:14

PM

Announcement impact:

2:14 PM to 2:24 PM

Re-equilibration:

2:24 PM to Close date t

Change in Forward S&P

mean 5.70 2.12 2.79 -0.63 1.42 std dev 17.93 8.46 4.96 7.61 12.03

Change in RND mean

mean 4.02 0.52 2.70 -0.66 1.45 std dev 20.07 9.31 4.95 7.47 12.23

RND variance Relative change

mean -4.97 -3.51 -1.16 -0.43 0.13 std dev 9.10 5.50 2.18 3.04 4.65

Market Up after Announcement change in S&P forward 18.37 3.94 3.36 1.99 9.07

change in RND mean 18.36 4.13 3.12 1.93 9.17 change in RND variance -7.50 -4.00 -1.29 -1.39 -0.82

Market Down after Announcement

change in S&P forward -6.97 0.30 2.21 -3.25 -6.23 change in RND mean -10.32 -3.08 2.28 -3.25 -6.27

change in RND variance -2.45 -3.03 -1.02 0.52 1.08

Excerpt from Table 2Levels and Changes of Key Variables on Fed Announcement Days


Impact Re-Equilibration

Full Re-Equil

From 2:14 P.M. 2:24 P.M. 2:36 P.M. 2:48 P.M. 3:00 P.M. 3:12 P.M. 3:24 P.M. 3:36 P.M. 3:48 P.M. 2:24 P.M.

To 2:24 P.M. 2:36 P.M. 2:48 P.M. 3:00 P.M. 3:12 P.M. 3:24 P.M. 3:36 P.M. 3:48 P.M. 4:00 P.M. 4:00 P.M.

Announcement Days

Std dev of change over full interval

S&P forward 7.61 3.72 5.69 4.89 2.84 5.51 3.01 3.94 8.61 12.03 RND mean 7.47 3.83 5.88 5.21 2.89 5.57 3.04 4.22 8.44 12.23

Interval std dev relative to full trading day


Std dev of 1-minute changes in interval


Interval 1-minute std dev relative to full day


Autocorrelation of 1-minute changes

S&P forward 0.17 0.14 0.03 -0.02 0.03 0.05 -0.02 0.12 0.12 0.06 RND mean 0.10 0.08 -0.01 -0.07 -0.03 -0.06 -0.13 -0.05 -0.01 -0.06

Non-Announcement Days

Std dev of change over full interval


Interval std dev relative to full trading day


Std dev of 1-minute changes in interval


Interval 1-minute std dev relative to full day


Autocorrelation of 1-minute changes

S&P forward 0.08 0.00 0.06 0.03 0.12 0.03 0.06 -0.05 0.20 0.04 RND mean -0.22 -0.18 -0.12 -0.19 -0.26 -0.25 -0.16 -0.14 -0.06 -0.24

Table 6: Volatility of the Forward S&P Index and the RND Mean during the Re-Equilibration Period, by Sub-Intervals


Variance Diminishes Gradually During Re-equilibration

To explore the time decay of volatility further, we regress the log of the absolute price change in each minute relative to the volatility within the impact period, as a function of the number of minutes since the end of the impact period.

is a minute within date t, with 0 representing 2:24 P.M.

Ft,impact is the standard deviation of 1-minute changes in the index forward during the

impact period on date t.

t-statistics are shown in parentheses. NOBS = 2649

(15) log( | Ft,τ | / Ft,impact) = -0.562 + -0.276 log( - 0) R2 = 0.027

(-4.84) (-8.82)


Variance Diminishes Gradually During Re-equilibration

Running this regression with the absolute change in the RND mean gives

log( | RNDmeant, | / RNDt,impact) = -0.749 + -0.183 log( - 0)

(-7.99) (-7.23) R2 = 0.019

The RND variance also shrinks consistently during the re-equilibration period

log( RNDvart, / RNDvart,impact) = -0.012 + -0.0061 log( - 0)

(-2.92) (-5.39) R2 = 0.010


The Evolution of the RND on December 11, 2007

Movie Time

On December 11, 2007 the Federal Reserve announced that it was lowering its interest rate target by 25 basis points. Normally a cut in the Fed funds rate causes the stock market to rise, but this time the market was clearly disappointed that the cut was not larger. Although the market had drifted higher during the day before the announcement, the S&P index fell 27 points (-1.74%) in the next 10 minutes, and a further 18 points by the end of the day.

This video shows how the Risk Neutral probability density behaved minute by minute during the course of that day. The density is for the level of the stock market on option expiration day, March 21, 2008. The vertical green line shows the current forward level of the S&P index in the market at the same time.


Table 8: Autocorrelation in Intraday Index Option Mid-Quote Changes on Non-Announcement Days

Trading

Day

Pre- Announce-

ment Impact Re-equilibration subintervals

Full Re-equili-bration

10:00 AM 10:00 AM 2:14 PM 2:24 PM 2:36 PM 2:48 PM 3:00 PM 3:12 PM 3:24 PM 3:36 PM 3:48 PM 2:24 PM 4:00 PM 2:14 PM 2:24 PM 2:36 PM 2:48 PM 3:00 PM 3:12 PM 3:24 PM 3:36 PM 3:48 PM 4:00 PM 4:00 PM

Calls All -0.347 -0.362 -0.386 -0.323 -0.394 -0.298 -0.313 -0.248 -0.316 -0.300 -0.314 -0.307

0-5% -0.419 -0.436 -0.443 -0.353 -0.465 -0.365 -0.386 -0.290 -0.372 -0.408 -0.370 -0.372 5-15% -0.354 -0.375 -0.372 -0.295 -0.380 -0.286 -0.333 -0.214 -0.311 -0.303 -0.305 -0.297

15-25% -0.299 -0.309 -0.357 -0.293 -0.367 -0.267 -0.259 -0.227 -0.290 -0.232 -0.261 -0.268 25-35% -0.280 -0.292 -0.331 -0.279 -0.314 -0.225 -0.225 -0.221 -0.257 -0.212 -0.258 -0.242 35-45% -0.296 -0.312 -0.343 -0.305 -0.339 -0.248 -0.242 -0.227 -0.282 -0.219 -0.252 -0.260 45-55% -0.271 -0.279 -0.327 -0.298 -0.311 -0.232 -0.242 -0.198 -0.254 -0.199 -0.281 -0.247 55-65% -0.257 -0.270 -0.314 -0.292 -0.309 -0.211 -0.243 -0.198 -0.251 -0.204 -0.281 -0.244 65-75% -0.331 -0.349 -0.390 -0.382 -0.421 -0.285 -0.275 -0.209 -0.304 -0.263 -0.373 -0.303 75-85% -0.431 -0.445 -0.485 -0.495 -0.495 -0.408 -0.417 -0.365 -0.408 -0.428 -0.519 -0.419 85-95% -0.544 -0.548 -0.597 -0.612 -0.580 -0.613 -0.591 -0.570 -0.596 -0.536 -0.570 -0.544

95-100% -0.675 -0.664 -0.731 -0.735 -0.767 -0.807 -0.762 -0.773 -0.714 -0.768 -0.802 -0.717

Puts All -0.287 -0.302 -0.330 -0.286 -0.318 -0.231 -0.246 -0.198 -0.274 -0.211 -0.266 -0.249

0-5% -0.519 -0.525 -0.570 -0.530 -0.466 -0.553 -0.594 -0.473 -0.535 -0.568 -0.593 -0.545 5-15% -0.428 -0.447 -0.391 -0.420 -0.421 -0.332 -0.420 -0.297 -0.404 -0.352 -0.405 -0.379

15-25% -0.335 -0.361 -0.332 -0.290 -0.354 -0.273 -0.257 -0.226 -0.267 -0.226 -0.302 -0.272 25-35% -0.279 -0.292 -0.308 -0.289 -0.300 -0.230 -0.232 -0.203 -0.253 -0.174 -0.239 -0.234 35-45% -0.286 -0.303 -0.340 -0.288 -0.318 -0.218 -0.227 -0.231 -0.276 -0.199 -0.249 -0.246 45-55% -0.264 -0.278 -0.335 -0.274 -0.290 -0.214 -0.211 -0.190 -0.257 -0.196 -0.266 -0.230 55-65% -0.229 -0.246 -0.286 -0.243 -0.248 -0.158 -0.208 -0.127 -0.228 -0.162 -0.221 -0.192 65-75% -0.236 -0.246 -0.303 -0.246 -0.287 -0.176 -0.213 -0.149 -0.250 -0.164 -0.236 -0.209 75-85% -0.248 -0.259 -0.335 -0.261 -0.312 -0.213 -0.223 -0.146 -0.251 -0.200 -0.232 -0.224 85-95% -0.251 -0.268 -0.306 -0.238 -0.288 -0.190 -0.220 -0.112 -0.252 -0.183 -0.240 -0.209

95-100% -0.267 -0.278 -0.325 -0.281 -0.314 -0.217 -0.216 -0.180 -0.268 -0.192 -0.239 -0.232


Simulation of Option Quotes when Stock Price Follows a Diffusion and Tick Sizes are Different


Conclusions about the Impact of the Fed Announcement

Is the market's response to the announcement unbiased?

Does the information in the announcement all enter the market at the moment of the public announcement?

• Information leakage beforehand?

• Sluggish adjustment or overshooting afterward?

The mean of the Risk Neutral Density (RND) and the forward value of the spot S&P index are tied together by arbitrage. Do they behave identically on announcement day? Is one a better prediction of the announcement than the other?

The RND reveals the market's risk neutral expectation for the future value of the index and also the variance around that expectation, a direct measure of uncertainty.

• How much uncertainty does a Fed announcement resolve on average?

• Does it matter if the announcement is viewed as positive or negative by the market?

YES, IT APPEARS TO BE

MAYBE SOME LEAKAGE

THERE IS A LOT OF FURTHER ADJUSTMENT DURING RE-EQUILIBRATIONAFTER THE ANNOUNCEMENT, BUT NO APPARENT BIAS

NOT QUITE IDENTICAL BUT NEITHER SHOWS PREDICTIVE ABILITY

ABOUT THE SAME AS ON 5 ORDINARY DAYS

YES. MUCH LESS UNCERTAINTY IS RESOLVED WHEN THE MARKET FALLS AFTER THE ANNOUNCEMENT


Conclusions about the Impact of the Fed Announcement, p.2

Information flow within a time interval can be proxied by the standard deviation of price change over the interval or by volatility within the interval. What is information flow like over an announcement day?

• How much information does the announcement itself convey?

STANDARD DEVIATION OVER 10 MINUTES ~ 30-40% OF FULL DAY PRICE CHANGE

• How much of the day's price change occurs before the market opens?

SURPRISINGLY, ABOUT HALF

• How much during trading hours before the announcement?

IN TOTAL ABOUT 1/3 LESS THAN IN THE 10 MINUTES OF IMPACT

• How much in the re-equilibration period following the initial impact of the announcement?

A LOT! 60 – 70% OF FULL DAY MOVE

• Is there a time pattern of diminishing volatility during re-equilibration? YES, AND VOLATILITY DROPS MORE FOR THE FORWARD THAN THE RND

• How does an announcement day compare to a regular day?THE TIME PATTERN IS MUCH DIFFERENT


presentation for qwafafew, june 8, 2011

Documents

announcement day

public announcement

announcement unbiased

efficient market

forward value

forward index leve

regular day

spot sp index