Answered: There are only shares of A and B…

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter8: Analysis Of Risk And Return

Section: Chapter Questions

Problem 3P

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Question

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

State	Probability	Ra	Ra²	Ra²p	Rb	Rb²	Rb²_p
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

$E x p e c t e d r e t u r n = R_{1} P_{1} + R_{2} P_{2} + R_{3} P_{3}$

Variance(X) = Σx²p − μ²

Mean(μ) Ra=0.165; μ²=0.027225

$V a r (R a) = 0.03675 - 0.027225 = 0.009525 o r 0.95 %$

S.D.= $\sqrt{V a r i a n c e} = 0.097596$

Mean(μ) Rb=0.05; μ²=0.0025

$V a r (R b) = 0.019 - 0.0025 = 0.0165 o r 1.65 %$

S.D.= $\sqrt{V a r i a n c e} = 0.12845$

Step 2

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

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

Mean(μ) Ra=0.165; μ²=0.027225

$V a r (R a) = 0.03675 - 0.027225 = 0.009525 o r 0.95 %$

S.D.= $\sqrt{V a r i a n c e} = 0.097596$

Mean(μ) Rb=0.05; μ²=0.0025

$V a r (R b) = 0.019 - 0.0025 = 0.0165 o r 1.65 %$

S.D.= $\sqrt{V a r i a n c e} = 0.12845$

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