SEC Follow Up Exhibits Part C SEC_OEA_FCIC_001760-2501

Reg SHO Pilot Report 2/12/2007
distribution of returns or return reversals. Essentially, this method estimates the likelihood of
observing a particular number of reversals under the null hypothesis that the distribution of
reversals in the pilot sample is the same as the distribution in the control sample. This is
implemented as follows. For a given “threshold” level of the reversals measure, we count the
number of reversals in the pilot sample that exceed that threshold. We then select from the
control sample (with replacement) a random sample of reversals equal in size to the pilot sample.
Within this randomized sample, we count the number of reversals exceeding the threshold, and
observe whether the number is higher or lower than the number observed in the pilot sample. We
repeat the process 1,000 times and observe the frequency with which the number of reversals in
the randomized control sample equals or exceeds the number in the pilot sample. We report the
significance based on a two-tailed test—for example, the number of reversals in the pilot sample
would be deemed significant at the five percent level if a number that high occurs 2.5% of the
time or less in randomized control samples.
D. Autoregression Methodology for Measuring Reversals
As an alternative approach to measuring the impact of the pilot on price reversals, we
employ a new methodology. Similar in spirit to autoregression, this methodology involves
measuring the extent to which positive and negative price movements reverse in subsequent
periods. Specifically, we use intraday returns to estimate a model of the form:
5
∑
5
−
n Rt
− n + ∑
n=
1 n=
1
R = α β R .
t
In this equation, Rt represents the stock return in period t, and the regressors are the positive and
negative components of lagged returns:
−
R t = min( 0,
Rt
)
n
+
t −n
+
R t = max( 0,
Rt
) .
Prepared by the Office of Economic Analysis 32