MISCELLANY
Xiaoyang Zhuang
Economics 201FS
Duke University
March 16, 2010
Price Series
ONE-MINUTE PRICE DATA
Alcoa.
DuPont .
The world’s leading producer of aluminum.
A diversified scientific company.
April 9, 1997 – December 30, 2010
3404 data points
Aligned
Returns Series
*
^
FIVE-MINUTE RETURNS DATA (OVERNIGHT RETURNS EXCLUDED)
(*) October 10, 2008, 9:40 - 9:50: Standard & Poor’s revised the firm’s outlook from “stable”
to “negative” after markets closed on October 9.
[$11.76 11.82 12.43 12.54 13.09 $13.00 12.53 12.40 12.29 12.25 $12.04]
DuPont. (^)May 6, 2010, 14:40 – 14:50: Flash crash.
[$36.60 $34.10 $35.44]
Alcoa.
Contents
1.
Separating Market Microstructure Noise from the Price Process
2.
Using Overnight Returns to Predict (Next-Day) Price Reversal
Contents
1.
Separating Market Microstructure Noise from the Price Process
2.
Using Overnight Returns to Predict (Next-Day) Price Reversal
Volatility Series
ANNUALIZED, DAILY, ONE- AND FIVE-MINUTE REALIZED VOLATILITY DATA
where t the day index, M is the number of intervals per day, and ∆ is the sampling interval size.
Market Microstructure Noise
MOTIVATING QUESTION
Given one-minute stock price data, is it possible to disentangle actual volatility from market
microstructure noise?
THE IDEA
•(*) The difference between realized volatilities calculated using x- and y-minute (x < y) returns data
should be due to finite sample considerations and microstructure noise:
where RVolt,x-minute is the realized volatility on day t calculated using x-minute returns data; A is the
difference due to finite sample considerations; and εmicrostructure is the difference due to microstructure
noise.
•The Percent of RVolt,xmin Not Accounted for by RVolt,(x+6)min seems to stabilize when x ≥ ~6 (as
we will see).
•Could the stabilized value serve as an estimator of finite sample considerations as the sampling
frequency changes?
(RVolt,1min - RVolt,6min)/ (RVolt,1min)
Percent of RVolt,1min Not Accounted for by RVolt,6min
SAMPLE STATISTICS: AA
mean(Percent) = 6.30
median(Percent) = 6.95
std(Percent) = 13.12
range(Percent) = [-57.40
50.55]
SAMPLE STATISTICS: DD
mean(Percent) = 8.00
median(Percent) = 8.24
std(Percent) = 13.73
range(Percent) = [-50.40
78.56]
(RVolt,6min - RVolt,11min)/ (RVolt,6min)
Percent of RVolt,6min Not Accounted for by RVolt,11min
SAMPLE STATISTICS: AA
mean(Percent) = 2.59
median(Percent) = 2.68
std(Percent) = 12.55
range(Percent) = [-62.97
52.65]
SAMPLE STATISTICS: DD
mean(Percent) = 3.62
median(Percent) = 3.55
std(Percent) = 12.56
range(Percent) = [-51.31
45.26]
(RVolt,11min - RVolt,16min)/ (RVolt,11min)
Percent of RVolt,11min Not Accounted for by RVolt,16min
SAMPLE STATISTICS: AA
mean(Percent) = -0.79
median(Percent) = -0.45
std(Percent) = 14.76
range(Percent) = [-56.30
53.01]
SAMPLE STATISTICS: DD
mean(Percent) = -0.28
median(Percent) = 0.22
std(Percent) = 14.82
range(Percent) = [-85.91
59.17]
(RVolt,16min - RVolt,21min)/ (RVolt,16min)
Percent of RVolt,16min Not Accounted for by RVolt,21min
SAMPLE STATISTICS: AA
mean(Percent) = 0.82
median(Percent) = 1.16
std(Percent) = 16.03
range(Percent) = [-71.70
57.39]
SAMPLE STATISTICS: DD
mean(Percent) = 1.16
median(Percent) = 1.79
std(Percent) = 16.15
range(Percent) = [-78.41
49.66]
Can the mean of stable Percent values (i.e. x ≥ ~6)
serve as an estimator of finite sample considerations?
Contents
1.
Separating Market Microstructure Noise from the Price Process
2.
Using Overnight Returns to Predict (Next-Day) Price Reversal
Overnight Returns and (Next-Day) Price Reversal
MOTIVATING QUESTION
Given that a stock loses value in afterhours trading, how will the stock perform in the first 15 minutes
after the market opens the following morning?
PROCEDURE
Define t as the day index.
1. For each stock, consider every case in which the overnight return is negative:
i.e. [pricet,15:59 pricet+1,9:35] = [x y], where x > y
2. Compute a = max([pricet+1,9:36
pricet+1,9:37
...
pricet+1,9:50]).
3. Plot each (negative) overnight return against its corresponding Price Reversal, where
Price Reversal = log(a) – log(pricet+1,9:35)
Overnight Returns and (Next-Day) Price Reversal
SAMPLE STATISTICS: AA
mean(Reversal) = 0.4281%
median(Reversal) = 0.2552%
% of Reversal data points exceeding 0: 74.8
SAMPLE STATISTICS: DD
mean(Reversal) = 0.3441%
median(Reversal) = 0.2309%
% of Reversal data points exceeding 0: 77.0