Question

XYZ stock price and dividend history are as follows: YearBeginning-of-Year PriceDividend Paid at Year-End2015 $130 $5 2016 144 5 2017 120 5 2018 125 5 An investor buys six 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 eight remaining shares at the beginning of 2018.a. What are the arithmetic and geometric average time-weighted rates of return for the investor

Answer 1

Answer:

Arithmetic mean = 3.67%

Geometric mean = 3.02%

Explanation:

The following sorted data are given in the question:

Year           Beginning-of-Year Price         Dividend Paid at Year-End

2015                            $130                                            $5

2016                              144                                               5

2017                              120                                               5

2018                              125                                               5

Therefore, we have:

Arithmetic average return = Sum of returns/ number of years ………....….. (1)

Geometric average return = n * ((1+r1)*(1+r2)*(1+r3)…(1+rn)^(1/n) - 1 .……….. (2)

Where;

n = years 1, 2, 3….

r1, r2, r3… are the returns for year 1, 2, 3….

Return for each year = ((Current year Beginning-of-Year Price – Previous year Beginning-of-Year Price) + dividend) / Previous year Beginning-of-Year Price .................... (3)

Using equation (3), we have:

2016 Return = ((144 - 130) + 5) /130 = 0.146153846153846

2017 Return = ((120 - 144) + 5) /159 = -0.119496855345912

2018 Return = ((125 - 120) + 5) /120 = 0.0833333333333333

Using equation (1), we have:

Arithmetic mean = (2016 Return + 2017 Return + 2018 Return) / 3 = (0.1461538461538460 - 0.1194968553459120 + 0.0833333333333333) / 3 = 0.0367, or 3.67%.

Using equation (2), we have:

Geometric mean = ((1 + 2016 Return) * (1 + 2017 Return) * (1 + 2018 Return))^(1/3) - 1 = ((1 + 0.146153846153846) * (1 - 0.119496855345912) * (1 + 0.0833333333333333))^(1/3) - 1 = 0.0302, or 3.02%