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.diff(p) cov_=sp.cov(d[:-1...