Python for Finance

Chapter 8
The covariance between them is negative. When its value is positive, Roll's model
would fail. In a real world, it could occur for many cases. Usually, practitioners
adopt two approaches: when the spread is negative, we just ignore those cases or use
other methods to estimate spread. The second approach is to add a negative sign in
front of a positive covariance.
Estimating Amihud's illiquidity
According to Amihud (2002), liquidity reflects the impact of order flow on price. His
illiquidity measure is defined as follows:
Here, illiq(t) is the Amihud's illiquidity measure for month t, Ri is the daily return at
day i, Pi is the closing price at i, and Vi is the daily dollar trading volume at i. Since
the illiquidity is the reciprocal of liquidity, the lower the illiquidity value, the higher
the liquidity of the underlying security. First, let's look at an item-by-item division:
>>>x=np.array([1,2,3],dtype='float')
>>>y=np.array([2,2,4],dtype='float')
>>>np.divide(x,y)
array([ 0.5 , 1. , 0.75])
>>>
In the following code, we estimate Amihud's illiquidity for IBM based on trading
data in October 2013. The value is 1.21*10-11. It seems that this value is quite small.
Actually, the absolute value is not important; the relative value matters. If we
estimate the illiquidity for WMT over the same period, we would find a value of
1.52*10-11. Since 1.21 is less than 1.52, we conclude that IBM is more liquid than
WMT. This correlation is represented in the following code:
import numpy as np
import statsmodels.api as sm
from matplotlib.finance import quotes_historical_yahoo_ochl as getData
begdate=(2013,10,1)
enddate=(2013,10,30)
ticker='IBM'
# or WMT
data= getData(ticker, begdate, enddate,asobject=True, adjusted=True)
p=np.array(data.aclose)
dollar_vol=np.array(data.volume*p)
ret=np.array((p[1:] - p[:-1])/p[1:])
illiq=np.mean(np.divide(abs(ret),dollar_vol[1:]))
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