Question 1. You buy a stock for $20. After a year the price rises to $25 but falls back to $20 at the end of the second year. What was the average percentage return and what was the true annualized return?
Question 2: Given the following information concerning four stocks,
Price Number of Shares
Stock A $10 100,000
Stock B 17 50,000
Stock C 13 150,000
Stock D 20 200,000
a) Construct a simple price-weighted average, a value-weighted average, and a geometric average.
b) What is the percentage increase in each average if the stocks' prices become: i. A: $10, B: $17, C: $13, D: $40 ii. A: $10, B: $34, C: $13, D: $20?
c) Why were the percentage changes different in (i) and (ii)?
Question 3: An investor buys a stock for $35 and sells it for $56.38 after five years.
a) What is the holding period return?
b) What is the true annual rate of return?
Question 4: A stock costs $80 and pays a $4 dividend each year for three years.
a) If an investor buys the stock for $80 and expects to sell it for $100 after three years, what is the anticipated annual rate of return?
b) What would be the rate of return if the purchase price were $60?
c) What would be the rate of return if the dividend were $1 annually and the purchase price were $80 and the sale price were $100?
Question 5: You purchase a stock for $100 that pays an annual dividend of $5.50. At the beginning of the second year, you purchase an additional share for $130. At the end of the second year, you sell both shares for $140. Determine the dollar-weighted return and the time-weighted compounded (i.e., geometric) return on this investment. Repeat the process but assume that the second share was purchased for $110 instead of $130. Why do the rates of return differ?