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

Accepted Answer

$$\begin{aligned}
W _ { 1 } & = \left[ ( .16 ) ^ { 2 } - .60 \times .10 \times .16 ( 016 ) \right] \div \left[ .10 ^ { 2 } + .16 ^ { 2 } - 2 ( 60 ) ( .10 ) ( 16 ) \right] \
& = 016 \div .0164 = 9756
\end{aligned}$$

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

Accepted Answer

The minimum portfolio variance for a two stock portfolio when r_1.2 = 1 is E(?₂) ¸ [E(?₁) - E(?₂)]. This is because when r_1.2 = 1, the two stocks are perfectly correlated and the portfolio variance is minimized when the weights are equal.

Deck 29: Portfolio Variance and Stock Weight Calculations