 # MoneyWeighted Return Question

Q: An investor buys one share of stock for \$100. At the end of year one she buys three more shares at \$89 per share. At the end of year two she sells all four shares for \$98 each. The stock paid a dividend of \$1.00 per share at the end of year one and year two. What is the investor’s time-weighted rate of return?

A:
The holding period return in year one is (\$89.00 – \$100.00 + \$1.00) / \$100.00 = -10.00%.
The holding period return in year two is (\$98.00 – \$89.00 + \$1.00) / \$89 = 11.24%.
The time-weighted return is [{1 + (-0.1000)}{1 + 0.1124}]1/2 – 1 = 0.06%.

My question: Why is the dividend at the end of year 2 only \$1? Shouldn’t it be \$4 because they own 4 shares?

The return calculations are per share. Reread all of the numbers.

Because the periodic return is calculated before and after a withdrawal/addition from the client, the TWRR calculation can be done on a per-share basis or on a total-basis.

On a total basis:

Year 1:
You bought one share for \$100 (1 x \$100).
At the end of the year, the four shares are worth \$89 (1 x \$89).
You receive dividends amounting to \$1 (1 x \$1).

Holding period return in Year 1 is:
(\$89 - \$100 + \$1)/\$100 = -10%

Year 2:
You start off by buying 3 more shares at \$89 each, so now you have 4 shares worth \$356 (4 x \$89).
At the end of the year, you sell all four shares at \$98 each, so that is 4 x \$98 = \$392.
You receive dividends amounting to 4 x \$1 = \$4.

Holding period return for Year 2:
= (\$392 - \$356 + \$4)/\$356
= (4 x \$98 - 4 x \$89 + 4 x \$1)/(4 x \$89)
= (\$98 - \$89 + \$1)/\$89 <— just to show you that you get the same result for per-share basis
= 11.24%

The rest you can solve.

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