Qaunt Question

naresh.thkr
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Qaunt Question

Postby naresh.thkr » Wed Sep 19, 2012 7:39 pm

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%?

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content.pristine
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Re: Qaunt Question

Postby content.pristine » Thu Sep 20, 2012 12:30 pm

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! 8-)

vandana.jain
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Re: Qaunt Question

Postby vandana.jain » Fri Oct 05, 2012 7:40 am

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
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Posts: 41
Joined: Tue Jul 24, 2012 4:56 pm

Re: Qaunt Question

Postby vandana.jain » Tue Oct 09, 2012 8:38 am

Hi pristine,

plz explain....

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

Re: Qaunt Question

Postby vandana.jain » Thu Oct 11, 2012 9:06 am

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

plz explain....

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shreyas
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Re: Qaunt Question

Postby shreyas » Mon Oct 15, 2012 12:05 pm

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

Postby naresh.thkr » Tue Oct 16, 2012 9:06 pm

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

aditya.dhatrak
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Re: Qaunt Question

Postby aditya.dhatrak » Fri May 20, 2016 10:22 am

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

edupristine
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Re: Qaunt Question

Postby edupristine » Sat May 21, 2016 10:03 am

Hi Aditya

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%


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