Consider a value-weighted market index that includes the following two companies.On Day 1 you form a portfolio to mimic the index.(In other words,to earn the same return as the index.)

What is the portfolio weight on Company 1,and what is the return on the portfolio from Day 1 to Day 2? (Weight %,Return %)
A) 14%, 5%
B) 14%, 6%
C) 15%, 6%
D) 15%, 7%
E) 16%, 5%

Question

Consider a value-weighted market index that includes the following two companies.On Day 1 you form a portfolio to mimic the index.(In other words,to earn the same return as the index.)

What is the portfolio weight on Company 1,and what is the return on the portfolio from Day 1 to Day 2? (Weight %,Return %)
A) 14%, 5% 
B) 14%, 6% 
C) 15%, 6% 
D) 15%, 7% 
E) 16%, 5%

Quizplus · Accepted Answer

Value of Company 1 on Day 1 = $6.62 × 200 = $1,324 Value of Company 2 on Day 1 = $10 × 750 = $7,500 Total Value on Day 1 = $2,648 + $15,000 = $8,824 w_i = 11ea7fdb_fc07_3f4a_a768_95f7477fee28_TB2902_11 The weight of Company 1 = 11ea7fdb_fc07_3f4b_a768_5f9b860e13d9_TB2902_11 = 0.15 or 15% Next, calculate the return on the portfolio: The weight of Company 2 = (1 - 0.15) = 0.85 The return on company 1 = 11ea7fdb_fc07_3f4c_a768_8fd8a7fceab2_TB2902_11 = 11ea7fdb_fc07_3f4d_a768_43fd80ceadb7_TB2902_11 = 0.0937 The return on company 2 = 11ea7fdb_fc07_665e_a768_65d2e4f32dfa_TB2902_11 = 0.054 The return on the portfolio from Day 1 to Day 2: E(k_p) = w₁E(k₁) + w₂E(k₂) + w_nE(k_n) E(k_p) = 0.15 × 0.0937 + 0.85 × 0.054 = 0.05995 or 6%

Consider a Value-Weighted Market Index That Includes the Following Two