Question

XYZ stock price and dividend history are as follows:

Beginning of - Year Dividend Paid at Year-
Year Price End
2015 $132 $ 4
2016 147 4
2017 12e 4
2018 125 4
An investor buys five shares of XYZ at the beginning of 2015, buys another three 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
What are the arithmetic and geometric average time-weighted rates of return for the investor? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Anthetic mean
Geometric mean

Answer 1

Arithmetic Average time-weighted Return 1.56%

Geometric Average time-weighted Return 0.918%

Step-by-step explanation:

Computation for the arithmetic and geometric average time-weighted rates of return for the investor for XYZ

Time-weighted average returns are tend to be based on year by year or Holding period rates of return.

Therefore the first step is to calculate for the holding period return for each year.

Using this formula

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

Let plug in the formula to calculate for each return

2015 = (147-132+4)/132

2015=19/132

2015=14.39%

2016 = (120 -147+4)/147

2016=23/147

2016=-15.65%

2017 = (125 -120+4)/120

2016=9/120

2016=7.5%

Calculation for Arithmetic Average time-weighted Return = (14.39% - 15.65% + 7.5%)/4

=6.24%/4

= 1.56%

Calculation for the Geometric Average time-weighted Return

= [(1+0.1439) x (1-0.1565) x (1+0.075)]^1/4 - 1

= 0.918%

Therefore the Arithmetic Average time-weighted Return will be 1.56% While Geometric Average time-weighted Return will be 0.918%