-If Purple, Indigo, and Violet are the only three stocks in the index, what is the value-weighted index return?

Question

Quizplus · Accepted Answer

To calculate the value-weighted index return, we need to consider the market value (price times shares) of each stock and their respective returns. The formula for a value-weighted return is the sum of the product of each stock's return and its weight in the index, where weight is determined by market value.Given data:- Purple has 1,000 shares priced at $100 each, with a return of 5%.- Indigo has 2,000 shares priced at $50 each, with a return of 6%.- Violet has 1,000 shares priced at $200 each, with a return of 8%.First, calculate the total market value of the index:- Purple: 1,000 shares * $100/share = $100,000- Indigo: 2,000 shares * $50/share = $100,000- Violet: 1,000 shares * $200/share = $200,000- Total market value = $100,000 + $100,000 + $200,000 = $400,000Next, calculate the weight of each stock in the index:- Purple: $100,000 / $400,000 = 0.25- Indigo: $100,000 / $400,000 = 0.25- Violet: $200,000 / $400,000 = 0.5Finally, calculate the value-weighted return:- Value-weighted return = (0.25 * 5%) + (0.25 * 6%) + (0.5 * 8%) = 1.25% + 1.5% + 4% = 6.75%However, since 6.75% is not an option and considering the possibility of a calculation or transcription error in the question or choices provided, the closest answer to the calculated value is 6.49%, which is option E.

-If Purple, Indigo, and Violet Are the Only Three Stocks