Deck 29: Portfolio Variance and Stock Weight Calculations

Question 1

Exhibit 7A.1
$$\mathrm { W } _ { 1 } = \left[ \mathrm { E } \left( \sigma _ { 2 } \right) ^ { 2 } - r _ { 1.2 } \mathrm { E } \left( \sigma _ { 1 } \right) \mathrm { E } \left( \sigma _ { 2 } \right) \right] \div \left[ \mathrm { E } \left( \sigma _ { 1 } \right) ^ { 2 } + \mathrm { E } \left( \sigma _ { 2 } \right) ^ { 2 } - 2 r _ { 1.2 } \mathrm { E } \left( \sigma _ { 1 } \right) \mathrm { E } \left( \sigma _ { 2 } \right) \right]$$

-Refer to Exhibit 7A.1.What weight of security 1 gives the minimum portfolio variance when r_1.2 = .60,E(?₁)= .10 and E(?₂)= .16?

A) .0244
B) .3679
C) .5697
D) .6309
E) .9756

Answer 1

.9756

Question 2

Exhibit 7A.1
$$\mathrm { W } _ { 1 } = \left[ \mathrm { E } \left( \sigma _ { 2 } \right) ^ { 2 } - r _ { 1.2 } \mathrm { E } \left( \sigma _ { 1 } \right) \mathrm { E } \left( \sigma _ { 2 } \right) \right] \div \left[ \mathrm { E } \left( \sigma _ { 1 } \right) ^ { 2 } + \mathrm { E } \left( \sigma _ { 2 } \right) ^ { 2 } - 2 r _ { 1.2 } \mathrm { E } \left( \sigma _ { 1 } \right) \mathrm { E } \left( \sigma _ { 2 } \right) \right]$$

-Refer to Exhibit 7A.1.Show the minimum portfolio variance for a two stock portfolio when r_1.2 = 1.

A) E(?₂) ¸ [E(?₁) - E(?₂)]
B) E(?₂) ¸ [E(?₁) + E(?₂)]
C) E(?₁) ¸ [E(?₁) - E(?₂)]
D) E(?₁) ¸ [E(?₁) + E(?₂)]
E) None of the above

Answer 2

E(?₂) ¸ [E(?₁) - E(?₂)]