Calculate Returns on ABC Stock Price and Dividend History

How can we calculate the returns for ABC stock based on the given stock price and dividend history?

Let's assume the stock prices and dividends for ABC are as follows:

Year 1:

Stock Price at the beginning of the year (P0): $100

Dividend during the year (D1): $4

Stock Price at the end of the year (P1): $110

Year 2:

Stock Price at the beginning of the year (P0): $110

Dividend during the year (D2): $5

Stock Price at the end of the year (P2): $120

Calculating Returns on ABC Stock Price and Dividend History

To calculate the returns for ABC stock based on the given stock price and dividend history, we can use different measures:

Arithmetic Average Return:

The arithmetic average return is the average annualized return over the given time period. It can be calculated using the formula:

Arithmetic Average Return = [(P1 - P0 + D1) / P0] / n

Year 1: Arithmetic Average Return = [(110 - 100 + 4) / 100] / 1 = 14%

Year 2: Arithmetic Average Return = [(120 - 110 + 5) / 110] / 1 = 14.54%

Overall Arithmetic Average Return for ABC stock = (14% + 14.54%) / 2 ≈ 14.27%

Geometric Average Return:

The geometric average return represents the compounded annualized return over the given time period and can be calculated using the formula:

Geometric Average Return = [(P2 - P0 + D1 + D2) / P0] ^ (1 / n) - 1

Geometric Average Return for ABC stock ≈ 15.25%

Continuous Compound Return:

The continuous compound return is calculated using the natural logarithm of the ratio of ending price to beginning price and can be calculated using the formula:

Continuous Compound Return = ln(P1 / P0)

Year 1: Continuous Compound Return ≈ 10.54%

Year 2: Continuous Compound Return ≈ 8.29%