Question

A stock has had the following year-end prices and dividends: year price dividend 1 64.83 – 2 71.70 .70 3 77.50 .75 4 63.77 .81 5 74.11 .90 6 84.75 .97. What are the arithmetic and geometric returns for the stock?

Answer 1

The arithmetic return for a stock is calculated by averaging the individual yearly returns, which include dividends and price changes, while the geometric return is computed by compounding the yearly returns and then taking the n-th root and subtracting 1.

Step-by-step explanation:

To calculate the arithmetic and geometric returns for the stock, we must consider both the dividends paid and the yearly price change, which represents capital gains or losses. The arithmetic return is computed by finding the average of the individual yearly returns, while the geometric return is calculated by finding the product of (1 + yearly return) for each year and then taking the n-th root of that product, where n equals the number of periods, and subtracting 1 from the result.

Here's how you can compute them for the stock in question:

1. Calculate the total return for each year by adding the dividend to the change in stock price (ending price - beginning price).
2. Divide the total yearly return by the beginning price for the arithmetic average, or 'arithmetic return'.
3. Calculate the product of all (1 + yearly return) percentages, take the n-th root (in this case, the 6th root since there are 6 periods), and subtract 1 to find the 'geometric return'.

Note that for exact calculations, you would need the specific prices and dividends for each year. However, the principles remain consistent with the given information.