Stock price clustering Data

Stock price clustering Data

The dataset for this exercise is in the Excel file”Clustering data”. This file contains two worksheets
Named Eurotunnel and L’Oreal with daily market data: ´
• The dates in format dd/mm/yyyy are reported in column A. There is 1 observation per day;
• open (column B) reports the opening price;
• close (column C) reports the closing price;
• low (column D) reports the lowest price of the day;
• high (column E) reports the highest price of the day;
• nb trades (column F) reports the number of traded shares in thousands.
Step 1
The tick size for a stock corresponds to the minimum price increment between two adjacent prices on
the allowed price grid. The tick size is equal to 0.01 (euro) for the Eurotonnel stock and 0.05 (euro) for
the L’Oreal stock. ´
1. For both stocks and at each date, compute the equivalent in number of ticks of the opening price.
2. Compute the proportion of even and odd numbers of ticks and compare the two stocks. Hint: Use
the ISEVEN Excel function, which returns TRUE for an even number and FALSE otherwise.
3. Repeat steps 1 and 2 using the closing price. Are the results comparable with those obtained with
opening prices? Give a plausible explanation for the differences you may find.
Step 2
We will now investigate more precisely the determinants of the probability of observing even-tick closing
prices using logistic regression.
1. Let denote Y the random variable that takes on the value y = 1 when the closing price corresponds
to an even number of ticks and value y = 0 otherwise. We assume that Y has the following
conditional distribution:
P(Y = 1|x) = F(x