Question

XYZ stock price and dividend history are as follows: Beginning-of-Year Dividend Paid at Year- Year Price $120 End 2015 2016 $ 3 145 3 2017 115 3 2018 120 3 An investor buys six shares of XYZ at the beginning of 2015, buys another two shares at the beginning of 2016, sells one share at the beginning of 2017, and sells all seven remaining shares at the beginning of 2018 a. What are the arithmetic and geometric average time-weighted rates of return for the investor? (Do not round intermediate calculations. Round your enswers to 2 decimal places.) Arithmetic mean % Geometric mean % b-1. Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2015, to January 1, 2018 (Negative amounts should be indicated by a minus sign.) Date Cash Flow 01/01/2015 01/01/2016 01/01/2017 01/01/2018

Answer 1

Solution to a

Time-weighted average returns are based on year-by-year/ Holding period rates of return.So, we have to calculate holding period return for each year which will be calculated as:

Holding Period Return = (End Value – Beginning Value + Cash Flow)/ Beginning Value

So, accordingly for each year return is as follows –

2015 = (145-120+3)/120 = 23.33%

2016 = (115-145+3)/145 = -18.62%

2017 = (120-115+3)/115 = 6.96%

Arithmetic Average time-weighted Return = (23.33% - 18.62% + 6.96%)/3 = 3.89%

Geometric Average time-weighted Return = [(1+0.2333) x (1-0.1862) x (1+0.0696)]^1/3 - 1 = 2.39%

Solution to b

Net Cash flow at each of the date would be as follows -

Date	Net Cash Flow ($)	Explanation
1/1/2015	- 720	Purchase of 6 shares at $120 each
1/1/2016	- 272	Purchase of 2 shares at $145 each, plus dividend income on 6 shares held @ $3 each
1/1/2017	139	Sale of 1 share at $115 each, plus dividend income on 8 shares held @ $3 each
1/1/2018	861	Sale of 7 shares at $120 each, plus dividend income on 7 shares held @ $3 each