Question 2
a.
Security E:
E(Re) = 0.45 * 8.00 + 0.40 * 10.00 + 0.15 * 14.00
= 9.7%

σe2 = 0.45 (8 - 9.7)2 + 0.4 (10 - 9.7)2 + 0.15 (14 – 9.7)2
= 4.11 σe = 2.027313

Security F:
E(Rf) = 0.45 * 4.00 + 0.40 * 7.00 + 0.15 * 9.00
= 5.95%

σf2 = 0.45 (4 - 5.95)2 + 0.40 (7 – 5.95)2 + 0.15 (9 – 5.95)2
= 3.5475 σf = 1.883481

Security R:
E(Rr) = 0.45 * 2.00 + 0.4 * 7.00 + 0.15 * 10.00
= 5.2%

σr2 = 0.45 (2 - 5.2)2 + 0.40 (7 – 5.2)2 + 0.15 (10 – 5.2)2
= 9.36 σr = 3.059412

b. Coefficient of correlation between Security E and itself: ρee = 1

Coefficient of correlation between Securities E and F:
COVef = 0.45(8 – 9.7)(4 – 5.95) + 0.4(10 – 9.7)(7 – 5.95) + 0.15(14 – 9.7)(9 – 5.95)
= 3.585

ρef = 3.585 / (2.027313 * 1.883481) = 0.9389

Coefficient of correlation between Securities R and F:
COVrf = 0.45(2 – 5.2)(4 – 5.95) + 0.4(7 – 5.2)(7 – 5.95) + 0.15(10 – 5.2)(9 – 5.95) = 5.76

ρrf = 5.76 / (3.059412 * 1.883481) = 0.9996

c.
Expected return and standard deviation for portfolio consisting of 55% Security R and 45% Security F:
E(Rp) = 0.45[(4 * 0.45) + (2 * 0.55)] + 0.40[(7 * 0.45) * (7 * 0.55)] + 0.15[(9 * 0.45) + (10 * 0.55)] = 5.5375%

σp2 = (0.45)(1.883481) + (0.55)(3.059412) + 2(0.45)(0.55)(0.9996)(1.883481)(3.059412) = 5.281462571 σp = 2.319798

She should invest 55% in Security R and 45% in Security F because this portfolio gives her a higher return at a lower risk than Security R by itself.

d.
Security E: βe = (0.8 * 2.027313 * 4.5) / 4.52 = 0.3604

E(Re) = 3.03 + 0.3604(12 – 3.03) = 6.2628

Security F: βf = (0.7 * 1.883481 * 4.5) / 4.52 = 0.2930

E(Rf) = 3.03 + 0.2930(12 – 3.03) = 5.658

βr = (0.55 * 3.059412 * 4.5) / 4.52 = 0.3739

E(Rr) = 3.03 + 0.3739(12 – 3.03) = 6.3839

Bev should invest in Stocks E and F because the required return is less than the