An investor buys three shares of XYZ at the beginning of 2002 for $100 apiece. After one year,
the share price has increased to $110 and he receives a dividend per share of $4. Right after
receiving the dividend, he buys two additional shares at $110. After another year, the share price
has dropped to $90, but the investor still receives a dividend per share of $4. Right after
receiving the dividend, he sells one share at $90. After another year, the share price has gone up
to $95, the investor receives a dividend per share of $4 and sells all shares at $95 immediately
after receiving dividends.
1 What are the arithmetic and geometric average time-weighted rates of return and what is the
dollar-weighted rate of return of the investor in the above example (for the dollar-weighted
return assume that (i) the cash flows from dividends received at the end of a given year are based
on the number of shares held at the beginning of that year, and (ii) cash flows from dividends
occur on the same day as the cash flows from buying and selling shares)?
2 Why is the dollar-weighted average rate of return in the above example lower than the
geometric average rate of return?