Question

6. You have been provided with the following data on three firms and the market: 6.4 Pim [i] 0.90 1.10 Security Firm A Firm B Firm C The Market The risk-free asset σι 0.12 ii] 0.24 0.10 0.01 0.4 0.75 [iv] 0 v] [vi]

find the missing values (i-vi) in the table.

Answer 1

$\beta$_i = $\rho$_i,M * [$\sigma$_i / $\sigma$_M]

i). 0.90 = $\rho$_A,M * [0.12 / 0.10]

0.90 = $\rho$_A,M * 1.2

$\rho$_A,M = 0.90 / 1.2 = 0.75

ii). 1.10 = 0.4 * [$\sigma$_B / 0.10]

1.10 = 4 * $\sigma$_B

$\sigma$_B = 1.1 / 4 = 0.275, or 27.50%

iii). $\beta$_C = 0.75 * [0.24 / 0.10]

= 0.75 * 2.4 = 1.8

iv). Correlation of market with itself is 1.0

v). Beta of Market is 1.0

vi). $\beta$_RF = 0 * [0.01 / 0.10] = 0