NO.PZ2023122201000116
问题如下：
A hedge fund with $98 million of initial capital charges a management fee of 2% and an incentive fee of 20%. The management fee is based on assets under management at year end and the incentive fee is calculated independently from the management fee. The fee structure has a high-water mark provision. The fund value is $112 million at the end of Year 1, $100 million at the end of Year2, and $116 million at the end of Year 3. The net-of-fees return earned by the fund in Year 3 is closest to:选项：
A.14.15%. B.12.33% C.11.87%.解释：
A is correct. The net-of-fees return to the fund in Year 3 is closest to 14.15%, calculated as follows:
Year 1:
Portfolio gain = Year-end value – Beginning value = $112 million − $98 million = $14 million
Management fee = Year-end value × Management fee % = $112 million × 2% = $2.24 million
Incentive fee = Portfolio gain × Incentive fee % = $14 million × 20% = $2.8 million
Total fees = Management fee + Incentive fee = $2.24 million + $2.8 million = $5.04 million
Ending Capital Position = Year-end value – Total fees = $112 million − $5.04 million = $106.96 million
High water mark = Ending capital position = $106.96 million
Year 2
No incentive fee is earned as the fund declines in value; the high water mark established in Year 1 is not exceeded.
Management fee = Year-end value × Management fee % = $100 million × 2% = $2 million
Ending Capital Position = Year-end value – Management fee = $100 million − $2 million = $98 million
High water mark = Highest ending capital position = $106.96 million
Year 3: Net-of-fee returns are affected by the Year 1 high water mark and the Year 2 net capital position (i.e. Year 3 beginning capital position).
Management fee = Year-end value × Management fee % = $116 million × 2% = $2.32 million
Incentive fee = (Year-end value – High water mark) × Incentive fee % = ($116 million – $106.96 million) × 20% = $1.81 million.
Total fees = Management fee + Incentive fee = $2.32 million + $1.81 million = $4.13 million
Net-of-fees return = (Year-end value – Total fees – Beginning capital position)/Beginning capital position = ($116 million – $4.13 million – $98 million)/$98 million = 14.15%.
The net-of-fees return earned by the fund in Year 3，让算第三年的收益率，为什么除以第一年的值，应该除以第二年年底的值100.
