XYZ's stock price and dividend history are as follows: Year Beginning-of-Year Price Dividend Paid at Year-End 2017 $ 170 $ 3 2018 200 3 2019 150 3 2020 170 3 An investor buys three shares of XYZ at the beginning of 2017, buys another two shares at the beginning of 2018, sells one share at the beginning of 2019, and sells all four remaining shares at the beginning of 2020. a. What are the arithmetic and geometric average time-weighted rates of return for the investor

The arithmetic average time-weighted rates of return for the investor is 4.19%

The geometric average time-weighted rates of return for the investor is 2.124%

Explanation:

The arithmetic average return is simple average returns of stocks, calculated as: Arithmetic average return = Sum of returns/ number of years

While geometric average return is calculated as: Geometric average return = number of years√ {(1+r1)*(1+r2)*(1+r3)…} -1

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

Yearly Return = {(capital gains + dividend)/price}*100

Return from 2017-2018= {(200 - 170) + 3} /170 *100 = 19.41%

Return from 2018-2019 = {(150 - 200) + 3} /200*100 = -23.5%

Return from 2019-2020 = {(170 - 150) + 5} /150 *100 = 16.67%

Hence, Arithmetic mean = (19.41% -23.5% +16.67%)/3 = 12.58%/3 = 4.19%

While Geometric mean = [(1+19.41%)*(1-23.5%) *(1+16.67%)] ^ (1/3) -1

= (1.1941 *0.7650 * 1.1667) ^1/3 – 1 = 0.02124 = 2.124%

The arithmetic average time-weighted rates of return for the investor is 4.19%

The geometric average time-weighted rates of return for the investor is 2.124%

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