Math 5440: Week 6 Assignment
Due Date: March 3, 2023 at 10am
Exercise Stock Returns vs. Price Impact Increments
This assignment assumes that the exercises in Week 5 Assignment have
yielded a functioning script.
1. Wrap the script from Week 5 into a function of dt, the date.
2. Loop over values of dt and aggregate variances and covariances into
a single table across dates, stocks, halflives, and prediction horizons.
The following exercises concern about the regression r = λ∆I + �,
where � is assumed to be Gaussian and i.i.d:
3. Compute λ = E[r∆I]/E[(∆I)2] and in-sample R2 by stock, halflife,
and prediction horizon; that is, run a regression using the data across
all dates for each (stock, halflife, prediction horizon) pair. Plot the
corresponding distribution; cf. page 36 of Lecture 5.
4. Compute λ = E[r∆I]/E[(∆I)2] and out-of-sample R2 by month,
halflife, and prediction horizon; that is run a regression using the
data across all stocks for each (month, halflife, prediction horizon)
pair and calculate the model R2 in the next month. Plot the corre-
sponding timeseries; cf. page 37 of Lecture 5.