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XYZ stock price and dividend history are as follows: Year Beginning-of-Year Price Dividend Paid at Year-End...

XYZ stock price and dividend history are as follows:

Year	Beginning-of-Year Price	Dividend Paid at Year-End
2010	$ 124	$ 4
2011	$ 135	$ 4
2012	$ 115	$ 4
2013	$ 120	$ 4

An investor buys six shares of XYZ at the beginning of 2010, buys another two shares at the beginning of 2011, sells one share at the beginning of 2012, and sells all seven remaining shares at the beginning of 2013.

What are the geometric average time-weighted rates of return for the investor?

Expert Solution

Return from 2010 - 2011 = (( 135 - 124) + 4 ) / 124

= 12.09 %

Return from 2011 - 2012 = ((115 - 135 ) + 4 ) / 135

= -11.85 %

Return from 2012 -2013 = ((120 - 115 ) +4 ) / 115

= 7.82%

Arithmetic mean = ( 12.09 - 11.85 + 7.82 ) / 3

= 8.06 / 3

= 2.68 %

Geometric mean = [ ( 1 +12.09%) * (1 - 11.85% ) * ( 1 + 7.82% )] ^1/3 - 1

= ( 1.1209 * 0.8815 *1.0782 )^1/3 - 1

= 1.06534^1/3 - 1

= 1.02132 - 1

= 2.13 %

jeff jeffy answered 2 years ago

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XYZ stock price and dividend history are as follows: Year Beginning-of-Year Price Dividend Paid at Year-End...

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