A manager buys three shares of stock today, and then sells one of those shares each year for the next 3 years. His actions and the price history of the stock are summarized below. The stock pays no dividends. Time Price Action
0 $190 Buy 3 shares
1 200 Sell 1 share
2 200 Sell 1 share
3 200 Sell 1 share
A. Calculate the time-weighted geometric average return on this "portfolio."
B. Calculate the time-weighted arithmetic average return on this portfolio.
C. Calculate the dollar-weighted average return on this portfolio.

a. The Geometric average return  is 1.72%

b. The Arithmetic average return is 1.75%

c. The Dollar weighted average return is 2.61%

Explanation:

a) In order to calculate the time-weighted geometric average return we would have to calculate first the Holding period return as follows:

Holding period return = (200 - 190) / 190 = 5.263%

Hence, Geometric average return = (1 + .05263)^(1/3) - 1 = 1.72%

b) To calculate time-weighted arithmetic average return we have to make the following calculation:

Arithmetic average return = 5.263% / 3 = 1.75%

c) To calculate time-weighted arithmetic average return we would have to make the following calculation:

Dollar weighted average return=-190*3 + 200/(1+r) + 200/(1+r)^2 + 200 / (1+r)^3 = 0

= 2.61%