When Fund H started on 1/1/21, it had $318,225,000 in assets under management (AUM). The annual holding period return was 3.65% in 2021, -20.48% in 2022, and 31.48% in 2023. Some investors redeemed shares, resulting in a net cash outflow of $120,204,000 on 12/31/21. There were also new investors buying the fund shares, resulting in a net cash inflow of $27,885,000 on 12/31/22. The time-weighted average return of the fund is ________ % per year during the three-year period.
Question
When Fund H started on 1/1/21, it had 120,204,000 on 12/31/21. There were also new investors buying the fund shares, resulting in a net cash inflow of $27,885,000 on 12/31/22. The time-weighted average return of the fund is ________ % per year during the three-year period.
Solution 1
To calculate the time-weighted average return, we need to calculate the geometric mean of the sub-period returns. Here are the steps:
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Calculate the ending value of the fund for each year after considering the return and cash flows.
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For 2021: The ending value = Initial AUM * (1 + return) - cash outflow = 120,204,000 = $209,674,912.5
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For 2022: The ending value = Previous year's ending value * (1 + return) + cash inflow = 27,885,000 = $194,282,912.5
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For 2023: The ending value = Previous year's ending value * (1 + return) = 255,374,912.5
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Calculate the sub-period returns.
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For 2021: The return = (Ending value / Initial AUM) - 1 = (318,225,000) - 1 = -34.15%
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For 2022: The return = (Ending value / Previous year's ending value) - 1 = (209,674,912.5) - 1 = -7.33%
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For 2023: The return = (Ending value / Previous year's ending value) - 1 = (194,282,912.5) - 1 = 31.48%
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Calculate the geometric mean of the sub-period returns.
The geometric mean = [(1 + return1) * (1 + return2) * (1 + return3)]^(1/3) - 1 = [(1 - 34.15%) * (1 - 7.33%) * (1 + 31.48%)]^(1/3) - 1 = -4.01%
So, the time-weighted average return of the fund is -4.01% per year during the three-year period.
Solution 2
To calculate the time-weighted average return, we need to break down the calculation into several steps:
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Calculate the ending value of the fund for each year, taking into account the net cash inflow or outflow.
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For 2021: The ending value = Initial AUM * (1 + annual return) - net cash outflow = 120,204,000 = $209,674,912.5
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For 2022: The ending value = Previous year's ending value * (1 + annual return) + net cash inflow = 27,885,000 = $194,271,912.5
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For 2023: The ending value = Previous year's ending value * (1 + annual return) = 255,357,912.5
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Calculate the geometric mean of the growth factors for each year.
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The growth factor for each year is (1 + annual return), or the ending value divided by the beginning value if there is a cash inflow or outflow.
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For 2021: The growth factor = Ending value / (Initial AUM * (1 + annual return)) = 318,225,000 * (1 + 3.65%)) = 0.618
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For 2022: The growth factor = Ending value / (Previous year's ending value * (1 - 20.48%)) = 209,674,912.5 * (1 - 20.48%)) = 1.133
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For 2023: The growth factor = Ending value / (Previous year's ending value * (1 + 31.48%)) = 194,271,912.5 * (1 + 31.48%)) = 1.314
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The geometric mean of the growth factors = (0.618 * 1.133 * 1.314)^(1/3) - 1 = 0.016 or 1.6%
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So, the time-weighted average return of the fund is 1.6% per year during the three-year period.
Solution 3
To calculate the time-weighted average return of the fund, we need to follow these steps:
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Calculate the ending value of the fund for each year after applying the annual holding period return.
- For 2021: 329,881,837.5
- After the net cash outflow on 12/31/21: 120,204,000 = $209,677,837.5
- For 2022: 166,781,926.02
- After the net cash inflow on 12/31/22: 27,885,000 = $194,666,926.02
- For 2023: 255,875,926.02
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Calculate the geometric mean of the growth factors for each year.
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Growth factor for 2021: 318,225,000 = 1.0365
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Growth factor for 2022: 209,677,837.5 = 0.9284
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Growth factor for 2023: 194,666,926.02 = 1.3148
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Geometric mean = [(1.0365) * (0.9284) * (1.3148)]^(1/3) - 1 = 0.0857 or 8.57%
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So, the time-weighted average return of the fund is 8.57% per year during the three-year period.
Similar Questions
Whan Fund H started on 1/1/21, it had $318,225,000 in assets under management (AUM). The annual holding period return was 3.65% in 2021, -20.48% in 2022, and 31.48% in 2023. Some investors redeemed shares, resulting in a net cash out flow of $120,204,000 on 12/31/21. There were also new investors buying the fund shares, resulting in a net cash inflow of $27,885,000 on 12/31/22. The arithmetic average annual return of the fund is ________ % and the standard deviation is ________% during the three year period.
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An equity mutual fund will likely have
How are the funds going to be utilized?
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