## Quant 1

niharikatayal
Posts: 4
Joined: Sat Feb 21, 2015 9:21 am

### Quant 1

Under online document Quantitative Analysis I, Pg 51, Question 2
You are given the following information about the returns of stock P and stock Q:
• Variance of return of stock P = 100.0
• Variance of return of stock Q = 225.0
• 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,
as measured by standard deviation of return, can be reduced by this strategy?

I am getting an answer D however actual answer mentioned is B. Can anyone help

edupristine
Finance Junkie
Posts: 722
Joined: Wed Apr 09, 2014 6:28 am

### Quant 1

The portfolio with 100% invested in Stock P has a variance of return equal to 100 and a standard deviation of return equal to 10.
Moving the portfolio to 75% (USD 3 million/USD 4 million) Stock P and 25% (USD 1 million/USD 4 million) Stock Q changes the variance to:
Variance = (0.75)^2 (100) + (0.25)^2 (225) + 2(0.75)(0.25)(53.2) = 56.25 + 14.06 + 19.95 = 90.26
Therefore, Standard deviation = (90.26) ^0.5 = 9.5
Hence, the percentage of risk reduced = (10-9.5)/10 = 5.0%.

niharikatayal
Posts: 4
Joined: Sat Feb 21, 2015 9:21 am

Thanks