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

Ri=ai + Bi Rm + Ei

where Ri is the excess return for security i and Rm is the market's excess return. Suppose also that there are three securities A, B, C characterized by the following data:

Security                   Beta                         Expected Return                      o^2 (Ei)

A                               0.8                                    0.10                                    0.05

B                               1.0                                    0.12                                      0.01

C                               1.2                                   0.14                                    0.10

A) If o^2 M= 0.04 calculate the variance (e.g. the total risk) of returns of securities A,B, and C.

B) B.) Now assume there are an infinite number of assets with the return characteristics identical to those of A, B, and C, respectively. If one forms a well-diversified portfolio of type A securities, what will be the variance of the portfolio's return? Similarly, what will the variance of the portfolio's return for portfolios formed only from type B? type C?

C) Listed below are the characteristic lines and correlation's (correlation of each fund with the market) for three mutual funds:

R₁=-0.5 + 1.25R_m                   p=0.8

R₂=1.25+0.95R_{m             Â} Â Â Â Â Â Â Â Â Â Â Â Â  p=0.75

R₃=0.75+1.35R_m                     p=0.7

Which fund has the most non-diversifiable risk?