## mock test 1

Good Student
Posts: 29
Joined: Thu Oct 04, 2012 2:09 am

### mock test 1

John, a quantitative analyst at an Indian company IC Inc. needs to estimate the correlation of the sales of IC with its British counterpart BC Corp. John knows that the sale of both the companies depend only on the GDP of their respective country and therefore regressed the sales with the GDP and estimated:

SIC = 3 + a*GDP INDIA
SBC = 5 + b*GDP BRITAIN

He has knows the following information from a public source:

Covariance(SIC, GDP INDIA )=36
Correlation(SIC, GDP INDIA )= 0.5
Correlation(SBC, GDP BRITAIN )=0.3
Covariance(SBC, GDP BRITAIN )=25
Covariance(GDPINDIA, GDP BRITAIN )=16
Variance(GDPINDIA)=16
Variance(GDP BRITAIN )=9

Calculate the covariance of the sales between IC Inc. and BC Corp.
a. 100
b. 2.4
c. 240
d. 16
how to calculate?

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content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### Re: mock test 1

We need Cov(SIC,SBC) which is equivalent to Cov(3 + a*GDPINDIA,5 + b*GDPBritain).
From the properties of covariance we know Cov(m+aX,n+bY) = a*b*Cov(X,Y), which implies:
Cov(3 + a*GDPINDIA,5 + b*GDPBritain) = a*b*Cov(GDPINDIA,GDPBritain)=a*b*16.
Here values of variable a,b is not given, so we need to calculate from the information given.
As a,b are the slope coefficients of the regression lines, we know:
a= Covariance(SIC, GDPINDIA)/ Variance(GDPINDIA)
=36/16
Similarly b=25/9.
Putting these values we get:
Cov(3 + a*GDPINDIA,5 + b*GDPBritain) = a*b*Cov(GDPINDIA,GDPBritain)=a*b*16 = 36/16*25/9*16=100

Let me know if this needs further clarification, and at which step..

Good Student
Posts: 29
Joined: Thu Oct 04, 2012 2:09 am

### Re: mock test 1

Thank u so much.. Very lucid explanation. Each point is very well explained