Explanation

For an equal-weighted index that is not rebalanced, we need to calculate the price-weighted average return of the stocks, not the market-cap weighted return.

Step 1: Calculate the price return for each stock

• Stock 1: (€36 - €30) / €30 = 6/30 = 0.20 or 20%
• Stock 2: (€45 - €50) / €50 = -5/50 = -0.10 or -10%
• Stock 3: (€50 - €40) / €40 = 10/40 = 0.25 or 25%

Step 2: Calculate the average return

Since it's an equal-weighted index with 3 stocks: Average return = (20% + (-10%) + 25%) / 3 = (35%) / 3 = 11.667%

Step 3: Calculate the ending index value

Beginning index value = 100 Ending index value = 100 × (1 + 0.11667) = 100 × 1.11667 = 111.667

Rounded to one decimal place, this is 111.7.

Why this approach?

• For an equal-weighted index that is NOT rebalanced, the weights drift over time as prices change.
• However, the question asks for the index value if it's "not re-balanced during the year," which means we calculate the return based on the initial equal weights.
• The average of the individual stock returns gives us the index return.

Verification: The equal-weighted index return is simply the arithmetic average of the constituent returns, which is 11.667%. Applying this to the starting index value of 100 gives 111.667 ≈ 111.7.