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.

To calculate the arithmetic average annual return and the standard deviation, we first need to calculate the annual returns for each year.

1. Calculate the annual return for each year:

   • For 2021: The fund started with $318,225,000 and had a return of 3.65$318,225,000 * (1 + 3.65/100) = $329,816,862.5. But there was a net cash outflow of$120,204,000. So, the actual ending AUM for 2021 is $329,816,862.5 -$120,204,000 = $209,612,862.5.

   • For 2022: The fund started with $209,612,862.5 and had a return of -20.48$209,612,862.5 * (1 - 20.48/100) = $166,780,926. But there was a net cash inflow of$27,885,000. So, the actual ending AUM for 2022 is $166,780,926 +$27,885,000 = $194,665,926.

   • For 2023: The fund started with $194,665,926 and had a return of 31.48$194,665,926 * (1 + 31.48/100) = $255,875,000 (approximately).

2. Calculate the arithmetic average annual return:

   • The arithmetic average annual return is simply the average of the three annual returns. So, it would be (3.65 - 20.48 + 31.48) / 3 = 4.88%.

3. Calculate the standard deviation:

   • First, calculate the variance, which is the average of the squared differences from the mean. The differences from the mean are (3.65 - 4.88), (-20.48 - 4.88), and (31.48 - 4.88). Square these differences, add them up, and divide by the number of years (3) to get the variance.

   • Then, take the square root of the variance to get the standard deviation.

Please note that these calculations assume that the cash flows occurred at the end of the year and that the returns are compounded annually. The actual calculations may be slightly different if these assumptions are not accurate.