Question: Assume that security returns are generated by the single-index model: R i = i + i R m + e i , where R i

  1. Assume that security returns are generated by the single-index model:

Ri=i + iRm + ei,

where Ri is the return for security i, and Rm is the markets return. The risk-free rate is 3%. The standard deviation of market returns m =0.20. Suppose also that there are three securities, X, Y, and Z, characterized by the following data:

Security

i

E(Ri)

ei

A

0.4

0.09

0.20

B

0.8

0.15

0.10

C

1.4

0.18

0.23

  1. Calculate the variance of returns of securities X, Y, and Z.

VarA =4.64%

VarB = 3.56%

VarC = 13.13%

  1. Calculate the covariance of securities X and Y.

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