Question

Abi invested 24,500 on 1/1/94. On 5/1/95 his balance was 28,212 and he withdrew 10,000. On 12/1/95 his balance was 15,892 and he deposited 8,000. On 1/1/97 his balance was 30,309.

a. Find the annual time-weighted yield for the 3-yr period.

b. Find an approximate annual dollar-weighted yield received by Abi for the 3 yr. period.

Answer 1

a.) Time-Weighted Yield = For period 1

[(28212-24500) / 24500] = 0.1515 or 15.15%

For Period 2  

[(15892 - 18212) / 18212] = -0.1273 or -12.73%

For period 3

[(30309 - 23892) / 23892] = 0.2685 or 26.85%

TWR = (1+Period 1) * (1+Period 2) *(1+Period 3) -1

= (1+0.1515) * (1 - 0.1273) * (1+0.2685) -1

= 1.2747 -1

= 0.2747 or 27.47%

b.) Dollar Weighted Yield = [1+(End Value1- Initial Value1 + Cash Flow1) / (Initial Value1 + Cash Flow1)] * [1+(End Value2- Initial Value2 + Cash Flow2) / (Initial Value2 + Cash Flow2)] * ...n - 1

= [1+ (28212 - 24500 - 10000) / (24500 - 10000)] * [1+ (15892 - 28212 + 8000) / (28212+8000)] * [1+ (30309 - 15892) / (15892-0)] - 1

= [0.566] * [0.880] * [1.907] -1

= - 0.05 or -5% for 3 Years