The quarterly returns on a portfolio are as follows:Quarter 1 2 3 4Return 20% -20% 10% -10%The time-weighted rate of return of the portfolio is closest to:
Question
The quarterly returns on a portfolio are as follows:
| Quarter | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Return | 20% | -20% | 10% | -10% |
The time-weighted rate of return of the portfolio is closest to:
Solution
To calculate the time-weighted rate of return, we need to consider each period's return and compound them. Here are the steps:
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Convert each quarter's return to a decimal. For example, 20% becomes 1.20, -20% becomes 0.80, 10% becomes 1.10, and -10% becomes 0.90.
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Multiply all these numbers together. So, 1.20 * 0.80 * 1.10 * 0.90 = 0.9504.
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Since the time-weighted rate of return is an annual rate, we need to raise this number to the power of 1/4 (since there are 4 quarters in a year) and then subtract 1 to convert it back to a percentage. So, (0.9504 ^ (1/4)) - 1 = -0.0127 or -1.27%.
So, the time-weighted rate of return of the portfolio is closest to -1.27%.
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