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:A.−5.0%.B.−1.3%.C.0.0%.
Question
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:A.−5.0%.B.−1.3%.C.0.0%.
Solution
To calculate the time-weighted rate of return, we need to consider each period's return and its impact on the total portfolio. Here are the steps:
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Convert each quarter's return to a decimal. For example, 20% becomes 0.20, -20% becomes -0.20, etc.
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Calculate the portfolio value factor for each quarter by adding 1 to each return. For example, for Q1, the value factor is 1 + 0.20 = 1.20. For Q2, it's 1 - 0.20 = 0.80, and so on.
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Multiply all the value factors together. So, 1.20 * 0.80 * 1.10 * 0.90 = 0.9504.
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Subtract 1 from the result and multiply by 100 to get the percentage return. So, (0.9504 - 1) * 100 = -4.96%.
So, the time-weighted rate of return is closest to -5.0% (Option A).
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