12_Correlation from PDF_sol - Corr(r A r...

BM 410 HW #12
For problems 1-4 below:
A) Calculate the correlation.
B) If the return on stock A is independent from the return on the index fund, verify that
joint probabilities are the product of the unconditional probabilities.
C) If the returns on stock A and the index fund perfectly linear dependent , find the
constants m and b in the equation r
A
=mr
I
+b, where r
I
represents the return on the index
fund, and r
A
represents the return on stock A.
1.
2.
3.
4.
1

#1 Solution
A)
Since correlation by definition is Cov(r
I
,r
A
)/( σ
I
* σ
A
), the correlation must also be zero.
B)
In this case, the stock and the index fund are independent.
C)
The stock and index fund are not perfectly linear dependent.
#2 Solution
E[r
A
]=.47*25+.53*(-15)=3.8
E[r
I
]=.47*10+.53*(-2)=3.64
stdev[r
A
]=sqrt(0.47*(25-3.8)^2+0.53*(-15-3.8)^2)=19.96
stdev[r
I
]=sqrt(0.47*(10-3.64)^2+0.53*(-2-3.64)^2)=5.99