Question

Bill has been adding funds to his investment account each year for the past 3 years. He started with an initial investment of $1,000. After earning a 10% return the first year, he added $3,000 to his portfolio. In this year his investments lost 5%. Undeterred, Bill added $2,000 the next year and earned a 2% return. Last year, discouraged by the recent results, he only added $500 to his portfolio, but in this final year his investments earned 8%. What was Bill's dollar-weighted average return for his investments?

Answer 1

(assuming that the returns are not reinvested)

BILL Step 1: computation of Returns in each year Particulars Investment Returns (1) Returns ($) year - 0 Initial investments $1000 - year-I end • Returns 101 $ 100 Too X101.) • Additional investment $3000 Year 2 end o Returns (50%) ($ 200) (4000 x 51.) o Additional investment Year 3 end. Returns 20 $ 120 (6000 X2:1) • Additional investment $500 Year 4 end. Returns - 8.10 $ 520 (6500 X8.1) 2000 TOTAL $540 $6500 simple average Return = 10-5 +2+8 = 3.75.). .

(A) (B) 15.39 Les OXICO] 100 Step 2: Assigning, weights CC) (D)-CC)X(B) Particulars Investment ($) weight (%) Returns ($) weighted Retwins Year I 1000 15.39 Year 2 3000 46.15 50x100 (200) (92.30) Year 3 2000 30.77 (dox! Oo] 120 36.92 Year 4 soo 7.69 (00X100 520 39.99 6500 100 540 0 & weighted average Return = weighted Returns = weights The reason for negative weighted average return is due to substantial amount (61.5401) inwested is negative yielding option.