Time-Weighted Return Calculation:

1. January – March period:

   • Beginning value: $50,000
   • Ending value: $51,000
   • Return = (51,000 / 50,000) - 1 = 1.02 - 1 = 2.00%

2. April – June period:

   • Beginning value: $51,000 + $10,000 deposit = $61,000
   • Ending value: $60,000
   • Return = (60,000 / 61,000) - 1 = 0.9836 - 1 = -1.64%

3. July – December period:

   • Beginning value: $60,000 - $30,000 withdrawal = $30,000
   • Ending value: $33,000
   • Return = (33,000 / 30,000) - 1 = 1.10 - 1 = 10.00%

4. Time-weighted return:

   • TWR = [(1 + 0.02) × (1 - 0.0164) × (1 + 0.10)] - 1
   • TWR = [1.02 × 0.9836 × 1.10] - 1
   • TWR = 1.1036 - 1 = 0.1036 or 10.36%

Why this is correct:

• Time-weighted return eliminates the impact of cash flows by calculating returns for each sub-period separately and then linking them geometrically.
• The calculation correctly accounts for the $10,000 deposit at the beginning of April and the $30,000 withdrawal at the beginning of July.
• 10.36% is closest to 10.4% among the given options.

Key concept: Time-weighted return is the preferred method for evaluating investment managers because it is not affected by the timing of cash flows into or out of the portfolio.