To find the missing year's return, we can set up the equation based on the arithmetic average formula. Given four of the five years' returns and the overall average, we can solve for the missing year's return.

Let $x$ represent the return of the missing year. According to the arithmetic average formula:

$\frac{15.87 + 23.28 - 10.39 + 9.52 + x}{5} = 12.98$

1. Combine the known returns: $15.87 + 23.28 - 10.39 + 9.52 = 38.28$

2. Substitute into the equation and solve for $x$: $\frac{38.28 + x}{5} = 12.98$

3. Multiply both sides by 5: $38.28 + x = 64.9$

4. Subtract 38.28 from both sides: $x = 26.62$

So, the missing year's return is 26.62%.

Would you like more details or have any questions?

Here are five related questions:

1. How does the arithmetic average differ from the geometric average in finance?
2. Why is it important to know the average return over multiple years for stock performance?
3. What is the impact of a negative return on the overall average return calculation?
4. How do you calculate the standard deviation of stock returns over a period?
5. How would compounding affect the returns if calculated as a geometric mean?

Tip: Arithmetic averages are best for predicting short-term returns, while geometric averages are better for long-term investments due to compounding effects.