Final answer:
The student wishes to learn how to calculate the arithmetic and geometric returns for a stock. Arithmetic return uses the simple average of annual returns, while geometric return takes into account compounding by multiplying the annual growth rates and takes the nth root over the period.
Step-by-step explanation:
The student is asking about calculating the arithmetic and geometric returns for a stock based on given end-of-year prices and dividends over six years. To calculate the arithmetic return, we take the average of the annual returns, where each year's return is computed as the sum of the dividend received and the change in price, divided by the starting price for that year. The geometric return is calculated using the product of (1 + each year's return) and then taking the nth root of that product, where n is the number of years, and subtracting 1. This accounts for compounding over the time period.
Arithmetic return calculation: For each year: [(Priceend - Pricestart + Dividend) / Pricestart], add up these returns, then divide by the number of years.
Geometric return calculation: For each year: Calculate (1 + annual return), then multiply all these values together, take the nth root (here, 6th root because of 6 years), and subtract 1 to get the overall geometric return.
SUMUP: Overall, the arithmetic return is a simple average of yearly returns, while the geometric return takes into account the compounding effect of investment over multiple periods.