Estimating Roll's spread

Liquidity is defined as how quickly we can dispose of our asset without losing its intrinsic value. Usually, we use spread to represent liquidity. However, we need high-frequency data to estimate spread. Later in the chapter, we show how to estimate spread directly by using high-frequency data. To measure spread indirectly based on daily observations, Roll (1984) shows that we can estimate it based on the serial covariance in price changes, as follows:

Here, S is the Roll spread, Pt is the closing price of a stock on day,

is Pt-Pt-1, and

, t is the average share price in the estimation period. The following Python code estimates Roll's spread for IBM, using one year's daily price data from Yahoo! Finance:

from matplotlib.finance import quotes_historical_yahoo_ochl as getData
import scipy as sp 
ticker='IBM' 
begdate=(2013,9,1) 
enddate=(2013,11,11) 
data= getData(ticker, begdate, enddate,asobject=True, adjusted=True) 
p=data.aclose 
d=sp...