There are only shares of A and B companies in the market. Currently, the market value of A and B shares is $200 million and $300 million, respectively. In addition, the risk-free interest rate (Rf) is 5 per cent. The probability and rate of return for the future state of the two entities are given as follows: (Value values with a decimal place or higher to the fifth decimal place.) 1) Obtain the expected return and variance of Entity A and B, respectively. 2) When forming a market portfolio with two shares, obtain the expected return rate and variance and standard deviation of the market portfolio. 3) Calculate the beta of share A, and calculate the required yield of share A. state probability Ra Rb 1 0.3 0.30 0.20 2 0.4 0.15 -0.10 3 0.3 0.05 0.10

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
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Chapter1: Investments: Background And Issues
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There are only shares of A and B companies in the market. Currently, the market value of A and B shares is $200 million and $300 million, respectively. In addition, the risk-free interest rate (Rf) is 5 per cent. The probability and rate of return for the future state of the two entities are given as follows: (Value values with a decimal place or higher to the fifth decimal place.)

1) Obtain the expected return and variance of Entity A and B, respectively.

2) When forming a market portfolio with two shares, obtain the expected return rate and variance and standard deviation of the market portfolio.

3) Calculate the beta of share A, and calculate the required yield of share A.

state probability Ra Rb
1 0.3 0.30 0.20
2 0.4 0.15 -0.10
3 0.3 0.05 0.10
Expert Solution
Step 1

1.

State Probability Ra Ra2 Ra2p Rb Rb2 Rb2p
1 0.3 0.30 0.09 0.027 0.20 0.04 0.012
2 0.4 0.15 0.0225 0.009 -0.10 0.01 0.004
3 0.3 0.05 0.0025 0.00075 0.10 0.01 0.003
        0.03675     0.019

Expected return=R1P1+R2P2+R3P3

Variance(X) = Σx2p − μ2

 

Mean(μ) Ra=0.165; μ2=0.027225

Var(Ra) = 0.03675-0.027225=0.009525 or 0.95%

S.D.=Variance=0.097596

Mean(μ) Rb=0.05; μ2=0.0025

Var(Rb) =0.019-0.0025=0.0165 or 1.65%

S.D.=Variance=0.12845

Step 2

Expected return of Entity A=0.3×0.30+0.4×0.15+0.3×0.05=0.09+0.06+0.015=0.165=16.5%

Expected return of Entity B=0.3×0.20+0.4×-0.10+0.3×0.10=0.06-0.04+0.03=0.05=5%

 

Mean(μ) Ra=0.165; μ2=0.027225

Var(Ra) = 0.03675-0.027225=0.009525 or 0.95%

S.D.=Variance=0.097596

 

Mean(μ) Rb=0.05; μ2=0.0025

Var(Rb) =0.019-0.0025=0.0165 or 1.65%

S.D.=Variance=0.12845

 

 

 

 

 

 

 

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