P1.T1.402. Question 1

[Ekin4112]

Hi,

" Answers:

402.1. C. No, there is no arbitrage opportunity because all three portfolios plot on the SML; and Security C has the highest volatility
All three portfolios lie on the SML because for each: (excess return)/beta = 0.10; for example, for Security A, (10% - 1%)/0.90 = 0.10.
The variance of each security is given by beta^2*20%^2+sigma[e(i)]^2, such that Security C has the highest variance (and therefore volatility) given by 1.30^2*20%^2+10%^2 = 0.776 "

How did you derive this variance formula from and also where did you get 1.3 from?

Thanks

 

[PaulHugan]

Hi,

" Answers:

402.1. C. No, there is no arbitrage opportunity because all three portfolios plot on the SML; and Security C has the highest volatility
All three portfolios lie on the SML because for each: (excess return)/beta = 0.10; for example, for Security A, (10% - 1%)/0.90 = 0.10.
The variance of each security is given by beta^2*20%^2+sigma[e(i)]^2, such that Security C has the highest variance (and therefore volatility) given by 1.30^2*20%^2+10%^2 = 0.776 "

How did you derive this variance formula from and also where did you get 1.3 from?

Thanks

Hi.

The variance was derived from The Market Model. The market model is the linear regression model used to derive the Beta for common stocks.

The linear regression model is: R(i) = Alpha(i) + Beta(i) * R(m) + Epsilon(i)
Here Epsilon(i) is the regression error attributed to firm-specific surprises, used to compute idiosyncratic risk.

With this model:

Expected return for Asset i: E( R(i) ) = Alpha(i) + Beta(i) * E( R(m) )
Variance of Asset i: Variance(i) = ( Beta(i)^2 ) * ( Variance(m) ) + Variance(epsilon)
Covariance between assets i and j: Covariance(i,j) = Beta(i) * Beta(j) * ( Variance(m) )

Hope this helps.