## Qaunt Question

naresh.thkr
Good Student
Posts: 25
Joined: Sat Aug 11, 2012 7:02 pm

### Qaunt Question

Hi All,

Plz help in solving below question:

Consider two stocks A and B. Assume their annual returns are jointly normally distributed, the marginal distribution of each stock has mean 2% and standard deviation 10%, and the correlation is 0.9. What is the expected annual return of stock A if the annual return of stock B is 3%?

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

### Re: Qaunt Question

Hi Naresh,

The first step, is to find the Beta of Stock A with respect to Stock B.
Beta (A) = correlation * std(A)/std(B) = 0.9*10%/10% = 0.9

Now, Return A = Avg A + Beta(A)*[(Return(B) - Avg B]
Return A = 2% + 0.9*(3%-2%)
= 2.9%

Hope this helps!

vandana.jain
Finance Junkie
Posts: 41
Joined: Tue Jul 24, 2012 4:56 pm

### Re: Qaunt Question

Hi,
I dont understand this part:how this equation is derived
Return A = Avg A + Beta(A)*[(Return(B) - Avg B]

plz explain....

vandana.jain
Finance Junkie
Posts: 41
Joined: Tue Jul 24, 2012 4:56 pm

### Re: Qaunt Question

Hi pristine,

plz explain....

vandana.jain
Finance Junkie
Posts: 41
Joined: Tue Jul 24, 2012 4:56 pm

### Re: Qaunt Question

I dont understand this part:how this equation is derived
Return A = Avg A + Beta(A)*[(Return(B) - Avg B]

plz explain....

shreyas
Finance Junkie
Posts: 83
Joined: Thu Jul 19, 2012 6:49 pm

### Re: Qaunt Question

We are trying to take out return for stock A. The equation used is OLS where A is the dependent variable and B is the independent variable. So we are using the regression equation to derive the returns for Stock A.

naresh.thkr
Good Student
Posts: 25
Joined: Sat Aug 11, 2012 7:02 pm

### Re: Qaunt Question

Hi,

This is question of Joint probability:

Hope below equation will solve your problem:

E[ra | rb = x] = μa + (ρabσaσb/σ2a)(x – μb) = 0.02 + 0.9 * (0.03 – 0.02) = 0.029

Thanks
Naresh

Posts: 1
Joined: Thu May 12, 2016 4:15 am

### Re: Qaunt Question

The explaination is not sufficient .
i have not seen any equation like this in my book.

edupristine
Finance Junkie
Posts: 981
Joined: Wed Apr 09, 2014 6:28 am

### Re: Qaunt Question

the explanation is given below
slope or beta(A with respect to B) is
Slope (A regressed on B) = Beta (A with respect to B) = Covariance(A,B) /Variance(A,B) = correlation(A,B)*StdDev(A)*StdDev(B)/Variance(B) = correlation(A,B)*StdDev(A)/StdDev(B).
Slope (A regressed on B) = 0.9*10%/10% = 0.9
A(i) = intercept + slope*B(i) = 0.2% + 0.9*3%; i.e., this is the regression
A(i) = E[A|B] = A(i) = intercept + slope*B(i) = 0.2% + 0.9*3%
so the calculation is E[A|B=3%] = 0.2% + 0.9*3% = 2.9%