## Quants

anbu.edu
Finance Junkie
Posts: 205
Joined: Mon Feb 04, 2013 3:35 pm

### Quants

You are given the following information about the returns of stock P and stock Q:
1. Variance of return of stock P=100.0
2. Variance of return of stock Q=225.0
3. Covariance between the return of stock P and the return of stock Q=53.2
At the end of 1999, you are holding USD 4 million in stock P. you are considering a strategy of shifting USD 1 million into stock Q and keeping USD 3 million in stock P. What percentage of risk is reduced?
a. 9.50% Incorrect
b. 5.00% Correct
c. 7.40% Incorrect
d. 0.50% Incorrect
sportfolio= Sqrt(w2 sa2+ (1-w)2 sb2+ 2w(1-w) *sa *sb *correlation(a,b))
=SQRT(( 0.75)2*100 + (0.25)2*225 + 2*(0.75)*(0.25)*53.2) = 9.50;
Incorrect

SD before is SQRT of 100 =10

Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

### Quants

Yes, The calculation detail is.
Variance = (0.75)2 (100) + (0.25)2 (225) + 2(0.75)(0.25)(53.2) = 56.25 + 14.06 + 19.95 = 90.26

Standard deviation = (90.26) 0.5 = 9.50

Hence, the percentage of risk reduced = (10-9.5)/10 = 5.0%