HelloCan you show how this is done, the second picture is the solution. There is a equation with two unknown variables and i have to solve for that in order to recieve. I have tried to do this myself but i cant get the correct answer. So if you can show me how to solve thisRP_1 =10% and RP_2 = 5% 4.PortfolioBeta on FBeta on F2Expected ReturnA1.52.031%B2.2-0.227%Equation 10.11 applies here:E(r, ) = r+ Bpi [E(rı)-r]+ Br2 [E(r2)-r]We need to find the risk premium (RP) for each of the two factors:RP1= [E(ri) – r;] and RP2= [E(r2)-r;]In order to do so, we solve the following system of two equations with two unknowns:.31 = .06 + (1.5 × RP1) + (2.0 × RP;).27 = .06 + (2.2 x RP1) + [(-0.2) × RP2]The solution to this set of equations isRP1 = 10% and RP;= 5%Thus, the expected return-beta relationship isE(rp) = 6% + (Bp1 × 10%) + (Bp2 x 5%) 4. Suppose that there are two independent economic factors, F, and F2. The risk-free rate is 6%,and all stocks have independent firm-specific components with a standard deviation of 45%.Portfolios A and B are both well-diversified with the following properties:PortfolioBeta on F,Beta on F2Expected ReturnA1.52.031%B2.2-0.227%What is the expected return-beta relationship in this economy?

Let us assume RP1=PRP2=Q expected return =rf+beta on F1×RP1+beta on F2×RP2=rf+beta on F1×P+beta on…

Answered: Portfolio Beta on F, Beta on F2…

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Hello

Can you show how this is done, the second picture is the solution. There is a equation with two unknown variables and i have to solve for that in order to recieve. I have tried to do this myself but i cant get the correct answer. So if you can show me how to solve this

RP_1 =10% and RP_2 = 5%

4.
Portfolio
Beta on F
Beta on F2
Expected Return
A
1.5
2.0
31%
B
2.2
-0.2
27%
Equation 10.11 applies here:
E(r, ) = r+ Bpi [E(rı)-r]+ Br2 [E(r2)-r]
We need to find the risk premium (RP) for each of the two factors:
RP1= [E(ri) – r;] and RP2= [E(r2)-r;]
In order to do so, we solve the following system of two equations with two unknowns:
.31 = .06 + (1.5 × RP1) + (2.0 × RP;)
.27 = .06 + (2.2 x RP1) + [(-0.2) × RP2]
The solution to this set of equations is
RP1 = 10% and RP;= 5%
Thus, the expected return-beta relationship is
E(rp) = 6% + (Bp1 × 10%) + (Bp2 x 5%)

4. Suppose that there are two independent economic factors, F, and F2. The risk-free rate is 6%,
and all stocks have independent firm-specific components with a standard deviation of 45%.
Portfolios A and B are both well-diversified with the following properties:
Portfolio
Beta on F,
Beta on F2
Expected Return
A
1.5
2.0
31%
B
2.2
-0.2
27%
What is the expected return-beta relationship in this economy?

Expert Solution

Step 1

Let us assume

$R P_{1} = P R P_{2} = Q$

$\begin{array}{rcl} e x p e c t e d r e t u r n & = & r_{f} + b e t a o n F_{1} \times R P_{1} + b e t a o n F_{2} \times R P_{2} \\ = & r_{f} + b e t a o n F_{1} \times P + b e t a o n F_{2} \times Q \end{array}$

substituting values in expected return formula:

$\begin{array}{rcl} e x p e c t e d r e t u r n o f A & = & r_{f} + b e t a o n F_{1} \times R P_{1} + b e t a o n F_{2} \times R P_{2} \\ 31 % & = & 6 % + 1.5 \times P + 2.0 \times Q \\ 31 % - 6 % & = & 1.5 P + 2 Q \\ 25 % & = & 1.5 P + 2 Q \end{array}$

25%=1.5 P +2 Q................................(1)

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Portfolio Beta on F, Beta on F2 Expected Return A 1.5 2.0 31% B 2.2 -0.2 27% Equation 10.11 applies here: E(r, ) = rg+ Bpi [E(rı)-r]+ Br2 [E(r2)-r] We need to find the risk premium (RP) for each of the two factors: RP1 = [E(r1) – r] and RP2= [E(r2) – r]