Explanation:
The time-weighted rate of return is calculated by finding the holding period returns for each period and then geometrically linking them.
Year 1 Calculation:
$100$89, dividend of $1.00 per share$89.00 - $100.00 + $1.00) / $100.00 = -$10.00 / $100.00 = -0.10 or -10.00%Year 2 Calculation:
$89 each (1 original + 3 new)$98, dividend of $1.00 per share$98.00 - $89.00 + $1.00) / $89.00 = $10.00 / $89.00 = 0.11236 or 11.24%Time-weighted return:
Option B (11.24%) is incorrect because it represents only the second year's holding period return, not the time-weighted return over both years. Option C (6.35%) is incorrect as it doesn't properly account for the geometric linking of returns.
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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
0.06%.
B
11.24%.
C
6.35%.
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