Question

The price of Stock A and Stock B at time 0 is $66 and $84 respectively. At time 1, the price of stock A goes to $58 and price of stock B goes to $90. The number of shares outstanding for stock A and stock B are 450 and 310 respectively. Calculate the rate of return on a market value weighted index of the two stocks. (Do NOT include the \% sign or any other text. Enter your answer as a percent and round your final answer to 2 decimal places, e.g. 110.10)

Answer 1

The rate of return on a market value weighted index of the two stocks is -3.12%.

Step-by-step explanation:

To calculate the rate of return on a market value weighted index of the two stocks Stock A and Stock B, we follow the steps below:

1. Calculate the initial market values of both stocks by multiplying the initial prices by the number of shares outstanding. For Stock A, this is $66 × 450, and for Stock B, it is $84 × 310.
2. Calculate the final market values in the same way using the final prices. For Stock A, this is $58 × 450, and for Stock B, it is $90 × 310.
3. Add the initial market values of both stocks to determine the total initial market value.
4. Add the final market values of both stocks to find the total final market value.
5. Calculate the market value weighted index return by taking the difference of the total final market value and total initial market value, divided by the total initial market value, and then multiply by 100 to express it as a percentage.

Using the given values:

• Initial market value of Stock A = 66 × 450 = $29,700
• Initial market value of Stock B = 84 × 310 = $26,040
• Final market value of Stock A = 58 × 450 = $26,100
• Final market value of Stock B = 90 × 310 = $27,900

Total initial market value = $29,700 + $26,040 = $55,740

Total final market value = $26,100 + $27,900 = $54,000

Calculate the rate of return:

Rate of return = [(54,000 - 55,740) / 55,740] × 100 = [-1,740 / 55,740] × 100 = -3.12%