Time weighted return

Hey guys, Could someone help me with the step by step calculation of time-weighted return on the following question? Money weighted return = 14,35% is fine for me, but I didn’t really get the time return = 20% ! Tks

Amit Roy buys a share of stock for $100 at t=0. At t=1, the investor buys an additional share for $125. At t=2 he buys a third share for $150. At t=3 Amit Roy sells all shares for $140. During all 3 years, the investor is paid a per share dividend of $10. Calculate the time-weighted and money-weighted returns.

>>a) 20% ; 14,35% b) 11,87% ; 14,35% c) 20% ; 6,19%

It is a little tricky, but think the time-weighted rate of return calculation as the conjuntion of variations. I mean, to calculate the variation in the portfolio value each period.

At t=0 your portfolio is worth 100

At t=1 you buy a stock for 125. This means that the first stock at 100 values now 125, you you win 25 there and in addition you got 10 of dividends (from the 1st stock) your portoflio added 35 on value. Calculate the variation as (125+10)/100 -1 = 35%. Note your portfolio now worths 250 (125+125)

At t=2 you buy another stock for 150. Remember you already had 2 stocks that values now 150 each making a value of 300 (150+150) and in addition you got 20 on dividends (from the 2 previous stocks). Calculate the variation as (300+20)/250 -1 = 28%. Note your portfolio now worths 450 (150+150+150)

At t=3 you sell all your three stocks for 140 each making an income of 420. In addition you win 30 on dividends, so your portoflio value before the sale is worth 450. The previous value was exactly 450. So you win 0% in this stage.

Now calculate Time-Weighted rate:

[(1+0.35)*(1+0.28)*(1+0)]^(1/3) -1 = 20.00 %

Any question pls ask!

Got it, tks for the explanation!!

well explained Harrogath