

In [1]:

    
# from __future__ import division,unicode_literals
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.dates as dts
import pandas as pd
import Quandl
from lxml import etree
import requests

Covered interest parity

Covered interest parity is a no-arbitrage condition in foreign exchange markets. In terms of US dollars and British pounds, the covered interest parity condition can be expressed as: $$ 1+i_{\$} = (1+i_{\unicode{xA3}}) \cdot \frac{F_{\$/\unicode{xA3}}}{E_{\$/\unicode{xA3}}} $$ Where $i_{\$}$ is the risk-free interest rate on dollars, $i{\unicode{xA3}}$ is the risk-free intrest rate on pounds, $E{\$/\unicode{xA3}}$ is the current spot rate in terms of dollars per pound, and $F_{\$/\unicode{xA3}}$ is the forward exchagne rate. The left-side of the equation is the risk-free return on dollars and the right-side is the risk-free return on pounds expressed in dollars. Equilibrium requires equality between the two returns because otherwise a person could earn risk-free profit by borrowing on one currency and saving in another.

Historical data on forward exchange rates is not readily available for many countries. This program uses data from Quandl and from the Federal Reserve Bank of New York to obtain interest, spot exchange, and forward exchange rate data for the purposes of evaluating the covered interest parity condition. All intrest rates used below are 6-month Libor rates and all forward rates are for transactions to be executed in 6-months and all exchange rates are expressed in terms of US dollars per unit of foreign currency.

Yen (daily)
Euro (daily)
Pound (monthly)
Swiss franc (monthly)

Note: since the interest rates are expressed in annualized terms, the interest rate terms in the covered interest parity condition must be divided by 2: $$ 1+\frac{i_{\$}}{2} = \left(1+\frac{i_{\unicode{xA3}}}{2} \right) \cdot \frac{F_{\$/\unicode{xA3}}}{E_{\$/\unicode{xA3}}} $$

Daily CIP data from FRBNY



In [2]:

    
def downloadXml(url,fileName):

    u = requests.get(url)

    with open(fileName, 'wb') as f:
        for chunk in u.iter_content(chunk_size=1024): 
            if chunk: # filter out keep-alive new chunks
                f.write(chunk)
                f.flush()
    f.close()



In [3]:

    
downloadXml(url='https://www.newyorkfed.org/medialibrary/media/xml/data/fx/EUR10.xml',fileName = 'euroSpot.xml')
downloadXml(url='https://www.newyorkfed.org/medialibrary/media/xml/data/fx/EUR10Forward6.xml',fileName = 'euroForward.xml')
downloadXml(url='https://www.newyorkfed.org/medialibrary/media/xml/data/fx/JPY10.xml',fileName='yenSpot.xml')
downloadXml(url='https://www.newyorkfed.org/medialibrary/media/xml/data/fx/JPY10Forward6.xml',fileName='yenForward.xml')



In [4]:

    
tree = etree.parse('euroSpot.xml')
root = tree.getroot()



In [5]:

    
def getDataFromXml(fileName,columnName):
    
    tree = etree.parse(fileName)
    root = tree.getroot()
    dates=[]
    values=[]
    y = root[1][0]
    for i, vals in enumerate(y):
        if i>0:
            try:
                float(vals.getchildren()[1].text)
                dates.append(vals.getchildren()[0].text)
                values.append(float(vals.getchildren()[1].text))
#                 print(i)
            except:
                print('missing value:',vals.getchildren()[0].text)
    
    frame = pd.DataFrame({columnName:values},index=pd.to_datetime(dates))
    return frame



In [6]:

    
euroSpotFrame = getDataFromXml('euroSpot.xml','euro spot')
euroForwardFrame = getDataFromXml('euroForward.xml','euro forward')
yenSpotFrame = getDataFromXml('yenSpot.xml','yen spot')
yenForwardFrame = getDataFromXml('yenForward.xml','yen forward')

euroRates = pd.concat([euroSpotFrame,euroForwardFrame],axis=1).dropna()
yenRates = pd.concat([1/yenSpotFrame,1/yenForwardFrame],axis=1).dropna()
rates = pd.concat([yenRates,euroRates],axis=1).dropna()









    



missing value: 2003-12-30
missing value: 2003-12-30



In [7]:

    
yenLibor = Quandl.get('FRED/JPY6MTD156N', collapse='daily',authtoken="QqLL1AFCjc31_MVo4qsU")
euroLibor = Quandl.get('FRED/EUR6MTD156N', collapse='daily',authtoken="QqLL1AFCjc31_MVo4qsU")
dollarLibor=Quandl.get('FRED/USD6MTD156N', collapse='daily',authtoken="QqLL1AFCjc31_MVo4qsU")

euroLibor.columns = ['euro interest']
yenLibor.columns = ['yen interest']
dollarLibor.columns = ['dollar interest']



In [8]:

    
yenFrame = pd.concat([yenRates,yenLibor,dollarLibor],axis=1).dropna()
euroFrame = pd.concat([euroRates,euroLibor,dollarLibor],axis=1).dropna()

fullFrame = pd.concat([euroRates,euroLibor,yenRates,yenLibor,dollarLibor],axis=1).dropna()
fullFrame[['euro spot', 'euro forward', 'euro interest', 'yen spot', 'yen forward','yen interest', 'dollar interest']].to_csv('cipEuroYenDaily.csv')



In [9]:

    
iEuro = 200*(1+euroFrame['euro interest']/200)*euroFrame['euro forward']/euroFrame['euro spot'] - 200


fig = plt.figure()
ax = fig.add_subplot(2,1,1)
ax.plot_date(euroFrame.index,euroFrame['dollar interest'],'-',lw=3,alpha = 0.6,label='dollar interest')
ax.plot_date(euroFrame.index,iEuro,'-',lw=3,alpha = 0.6,label='euro interest')
ax.set_ylabel('Percent')
ax.grid()

ax.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3,ncol=4, mode="expand", borderaxespad=0.)

ax = fig.add_subplot(2,1,2)
ax.plot_date(euroFrame.index,euroFrame['dollar interest']-iEuro,'-r',lw=3,alpha = 0.6)
ax.set_title('Interest on dollars less interest on euros')
ax.set_ylabel('Percent')
ax.grid()

plt.tight_layout()



In [10]:

    
iyen = 200*(1+yenFrame['yen interest']/200)*yenFrame['yen forward']/yenFrame['yen spot'] - 200


fig = plt.figure()
ax = fig.add_subplot(2,1,1)
ax.plot_date(yenFrame.index,yenFrame['dollar interest'],'-',lw=3,alpha = 0.6,label='dollar interest')
ax.plot_date(yenFrame.index,iyen,'-',lw=3,alpha = 0.6,label='yen interest')
ax.set_ylabel('Percent')
ax.grid()

ax.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3,ncol=4, mode="expand", borderaxespad=0.)

ax = fig.add_subplot(2,1,2)
ax.plot_date(yenFrame.index,yenFrame['dollar interest']-iyen,'-r',lw=3,alpha = 0.6)
ax.set_title('Interest on dollars less interest on yen')
ax.set_ylabel('Percent')
ax.grid()

plt.tight_layout()

Monthly CIP data from Quandl



In [11]:

    
# 3. Forward rate and interest rate arbitrage

# 3.1 dollar-pound data
poundForward = Quandl.get('BOE/XUMADS6', collapse='monthly',trim_start='1994-01-31',authtoken="QqLL1AFCjc31_MVo4qsU")
poundLibor = Quandl.get('BOE/IUMAVSMA', collapse='monthly',trim_start='1994-01-31',authtoken="QqLL1AFCjc31_MVo4qsU")
poundSpot = Quandl.get('BOE/XUMAUSS', collapse='monthly',trim_start='1994-01-31',authtoken="QqLL1AFCjc31_MVo4qsU")
dollarLibor = Quandl.get('BCB/3841', collapse='monthly',trim_start='1994-01-31',authtoken="QqLL1AFCjc31_MVo4qsU")



In [12]:

    
poundForward.columns = ['pound forward']
poundSpot.columns = ['pound spot']
poundLibor.columns = ['pound interest']
dollarLibor.columns = ['dollar interest']

poundFrame = pd.concat([poundForward,poundSpot,poundLibor,dollarLibor],axis=1).dropna()



In [13]:

    
# 3.3 dollar-Swiss franc data
francForward = Quandl.get('SNB/G3_M1_M', collapse='monthly',trim_start='1994-01-31',authtoken="QqLL1AFCjc31_MVo4qsU")
dollarLibor = Quandl.get('BCB/3841', collapse='monthly',trim_start='1994-01-31',authtoken="QqLL1AFCjc31_MVo4qsU")
francSpot = Quandl.get('BOE/XUMASFD', collapse='monthly',trim_start='1994-01-31',authtoken="QqLL1AFCjc31_MVo4qsU")
francLibor = Quandl.get('BCB/3843', collapse='monthly',trim_start='1994-01-31',authtoken="QqLL1AFCjc31_MVo4qsU")



In [14]:

    
francForward = pd.DataFrame({'franc forward':1/francForward['6-month forward rate'].values},index = francForward['6-month forward rate'].index)
francForward
francSpot = 1/francSpot

francForward.columns = ['franc forward']
francSpot.columns = ['franc spot']
francLibor.columns = ['franc interest']
dollarLibor.columns = ['dollar interest']

francFrame = pd.concat([francForward,francSpot,francLibor,dollarLibor],axis=1).dropna()



In [15]:

    
fullFrame = pd.concat([poundForward,poundLibor,poundSpot,francForward,francSpot,francLibor,dollarLibor],axis=1).dropna()
fullFrame[['pound spot', 'pound forward', 'pound interest', 'franc spot', 'franc forward','franc interest', 'dollar interest']].to_csv('cipPoundFrancMonthly.csv')



In [16]:

    
ipound = 200*(1+poundFrame['pound interest']/200)*poundFrame['pound forward']/poundFrame['pound spot'] - 200


fig = plt.figure()
ax = fig.add_subplot(2,1,1)
ax.plot_date(poundFrame.index,poundFrame['dollar interest'],'-',lw=3,alpha = 0.6,label='dollar interest')
ax.plot_date(poundFrame.index,ipound,'-',lw=3,alpha = 0.6,label='pound interest')
ax.set_ylabel('Percent')
ax.grid()

ax.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3,ncol=4, mode="expand", borderaxespad=0.)

ax = fig.add_subplot(2,1,2)
ax.plot_date(poundFrame.index,poundFrame['dollar interest']-ipound,'-r',lw=3,alpha = 0.6)
ax.set_title('Interest on dollars less interest on pounds')
ax.set_ylabel('Percent')
ax.grid()

plt.tight_layout()



In [17]:

    
ifranc = 200*(1+francFrame['franc interest']/200)*francFrame['franc forward']/francFrame['franc spot'] - 200


fig = plt.figure()
ax = fig.add_subplot(2,1,1)
ax.plot_date(francFrame.index,francFrame['dollar interest'],'-',lw=3,alpha = 0.6,label='dollar interest')
ax.plot_date(francFrame.index,ifranc,'-',lw=3,alpha = 0.6,label='franc interest')
ax.set_ylabel('Percent')
ax.grid()

ax.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3,ncol=4, mode="expand", borderaxespad=0.)

ax = fig.add_subplot(2,1,2)
ax.plot_date(francFrame.index,francFrame['dollar interest']-ifranc,'-r',lw=3,alpha = 0.6)
ax.set_title('Interest on dollars less interest on francs')
ax.set_ylabel('Percent')
ax.grid()

plt.tight_layout()