Question

In: Finance

The expected returns on Able Ltd, Blume Ltd and Cosmo Ltd can be explained fully by...

  1. The expected returns on Able Ltd, Blume Ltd and Cosmo Ltd can be explained fully by the Capital Asset Pricing Model. The standard deviation of returns on the market portfolio is 25%. The returns, standard deviation of returns and betas estimated for the companies are as follows:

Company

Expected return

Standard

deviation

Beta

Able Ltd

24%

31%

1.2

Blume Ltd

14%

42%

0.5

Cosmo Ltd

18%

35%

0.78

Using this information determine the correlation coefficient between Cosmo Ltd and the Market Index. You will need to use the data above to, firstly, calculate the expected return on the market portfolio and the risk-free rate of interest.

Solutions

Expert Solution

Sol:

Given,

Standard deviation on Market portfolio (SM) = 25%

Under capital pricing model,

Required return (RR) = Rf + Beta * ( RM - Rf)

where , Rf = Risk free rate

RM = Expected market return on portfolio

Calculating market return on portfolio and risk free rate of interest

ERA = Rf + Beta A * ( RM - Rf)

or, 24 = Rf + 1.2 * ( RM - Rf) ...................(1)

ERB = Rf + Beta B * (RM - Rf)

or, 14 = Rf + 0.5 * ( RM - Rf)....................(2)

Solving equation (1) & (2) , we get

24 = Rf + 1.2 * (RM - Rf )

14 = Rf +0.5 * (RM - Rf)

- - -

10 = 0 + 0.7 * (RM - Rf)

RM - Rf = 10/0.7 = 14.29 %

Putting the value of (RM - Rf ) = 14.29 % in equation (1)

24 = Rf  + 1.2 * 14.29

Rf = 24 -17.15 = 6.85 %

RM - Rf  = 14.29

RM - 6.85 =14.29

RM  = 14.29+6.85 = 21.14 %

Hence, the expected return on market portfolio (RM) is 21.14 % and the risk free rate of interest (Rf) is 6.85 %.

Determination of correlation coefficient between Cosmo ltd. and the market index

Beta C = Beta cosmo

Standard deviation cosmo = SD (C) = 0.35

Standard deviation on market portfolio = SD ( M) = 0.25

Correlation coefficient between cosmo and market index = r c,m = ?

Beta (C) = SD (C) * r c,m

SD ( M)

or, 0.78 = 0.35 * r c,m   

0.25

or, 0.78* 0.25 = r c,m

0.35

rc,m = 0.557 = 0.56

Hence, the correlation coefficient between Cosmo ltd. and the Market Index is 0.56.

  

jeff jeffy answered 6 months ago
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