On January 1 you deposit 100000 On March 1, the balance is 102000 and you withdraw 50000. On May 1 the balance is 52500 and you deposit 50000. At the end of the year the balance is 111000. Find the time weighted and dollar weighted yields

Dollar weighted yield 21.09%

Time weighted yield 11.52%

Explanation:

Dollar weigthed:

Date Capital Weight Subtotal

Jan 1st 100,000 1 100,000

March 1st - 50,000 0.83 - 41,666.66667

May 1st 50,000 0.67 33,333.33333

Dec 31th 91,666.66667

Average capital: 91,666.67

Return: 111,000

Rate: 111.000 / 91.667 - 1 = 0,21090

Time weighted:

102,000 / 100,000 - 1 = 0.02 from Jan 1st to March 1st

Then 52,500 / 52,000 - 1 = 0,0096 From March 1st to May 1st

Finally 111,000 / 102,500 - 1 = 0.082926 From May 1st to Dec 31th

weighted Return:

1.02 x 1.0096 x 1.082926 - 1 = 0,115189 = 0.1152 = 11.52%