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#### Dollar-weighted and Time-weighted Rates of Return

The**dollar-weighted rate of return** is essentially the internal rate of return (IRR) on a portfolio. This approach considers the *timing* and *amount* of cash flows. It is affected by the timing of cash flows. If funds are added to a portfolio when the portfolio is performing well (poorly), the dollar-weighted rate of return will be inflated (depressed).
**time-weighted rate of return** measures the compound growth rate of $1 initial investment over the measurement period. *Time-weighted* means that returns are averaged over time. This approach is not affected by the timing of cash flows; therefore, it is the preferred method of performance measurement.
*Example*
^{2} = 0. You can use the IRR function on a financial calculator to solve for r to get the dollar-weighted rate of return: r = 17%.

The

The

Jayson bought a share of IBM stock for $100 on December 31, 2000. On December 31, 2001, he bought another share for $150. On December 31, 2002, he sold both shares for $140 each. The stock paid a dividend of $10 per share at the end of each year.

To calculate the dollar-weighted rate of return, you need to determine the timing and amount of cash flows for each year, and then set the present value of net cash flows to be 0: - 100 - 140/(1 + r) + 300/(1 + r)

To calculate the time-weighted rate of return:

- Split the overall measurement period into equal sub-periods on the dates of cash flows. For the first year:
- beginning price: $100
- dividends: $10
- ending price: $150

- beginning price: $300 (150 x 2)
- dividends: $20 (10 x 2)
- ending price: $280 (140 x 2)

- Calculate the holding period return (HPR) on the portfolio for each sub-period: HPR = (Dividends + Ending Price)/Beginning Price - 1. For the first year, HPR
_{1}: (150 + 10)/100 - 1 = 0.60. For the second year, HPR_{2}: (280 + 20)/300 - 1 = 0. - Calculate the time-weighted rate of return:
- If the measurement period < 1 year, compound holding period returns to get an annualized rate of return for the year.
- If the measurement period > 1 year, take the geometric mean of the annual returns.

Learning Outcome Statements

d. calculate and compare the money-weighted and time-weighted rates of return of a portfolio and evaluate the performance of portfolios based on these measures;

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