A benchmark market value index is comprised of three stocks. Yesterday the three stocks were priced at $7, $13, and $11. The number of outstanding shares for each is 296,114 shares, 56,839 shares, and 364,366 shares, respectively. If the stock prices changed to $10, $11, and $11 today respectively, what is the 1-day rate of return on the index?

The 1-day rate of return on a market value index is calculated by determining the percentage change in the total market value of the index from one day to the next. Let's walk through the calculation step by step.

### Step 1: Calculate the total market value of the index for yesterday
We multiply the price of each stock by its respective number of outstanding shares.

- Stock 1: $ 7 \times 296,114 = 2,072,798 $
- Stock 2: $ 13 \times 56,839 = 739,907 $
- Stock 3: $ 11 \times 364,366 = 4,007,026 $

**Total market value for yesterday:**
\[
2,072,798 + 739,907 + 4,007,026 = 6,819,731
\]

### Step 2: Calculate the total market value of the index for today
We repeat the process for today's prices.

- Stock 1: $ 10 \times 296,114 = 2,961,140 $
- Stock 2: $ 11 \times 56,839 = 625,229 $
- Stock 3: $ 11 \times 364,366 = 4,007,026 $

**Total market value for today:**
\[
2,961,140 + 625,229 + 4,007,026 = 7,593,395
\]

### Step 3: Calculate the rate of return
The 1-day rate of return is the percentage change in the total market value of the index:

\[
\text{Rate of return} = \frac{\text{Today’s market value} - \text{Yesterday’s market value}}{\text{Yesterday’s market value}} \times 100
\]

\[
\text{Rate of return} = \frac{7,593,395 - 6,819,731}{6,819,731} \times 100 = \frac{773,664}{6,819,731} \times 100 \approx 11.34\%
\]

### Conclusion:
The 1-day rate of return on the index is approximately **11.34%**.

Would you like further details on this process? Here are 5 related questions to explore:

1. How does the rate of return change if one stock performs significantly better than the others?
2. What are the advantages of using a market value index over other types of indices?
3. How does the number of outstanding shares affect the index value?
4. Can you calculate the weighted average price of the stocks in the index?
5. How would a dividend payment impact the 1-day rate of return?

**Tip:** Always ensure that you are working with the same currency units when calculating market values for indices.

Understand how to calculate the 1-day rate of return on a market value index composed of three stocks. The problem involves determining the percentage change in total market value, using data like stock prices and the number of outstanding shares. Suitable for Grades 11-12.

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