Hi everyone,
I have a problem with the below question from a topic test from the CFAI:
Beginning of Year 1 Purchase 10 shares €160
End of Year 1 Purchase 5 shares €168
Dividend paid per year end of year 1, 3.00
End of Year 2 (price per share=) €175
Dividend paid per year end of year 1, 4.00
End of Year 3 Sell 15 shares €165
Dividend paid per year end of year 3, 0.00
The answer is: The holding period return (HPR) for the three years is calculated as follows:
HPR = (Pt+1 – Pt + Dt+1 )/Pt .
HPRYear 1 = (€ 1,680 – € 1,600 + € 30)/€ 1,600 = 6.88%.
HPRYear 2 = (€ 2,625 – € 2,520 + € 60)/€ 2,520 = 6.55%.
HPRYear 3 = (€ 2,475 – € 2,625)/€ 2,625 = –5.71%.
The time-weighted return (TWR) is found by taking the geometric mean of the three holding period returns:
TWR = [(1 + HPRYear 1 ) Å~ (1 + HPRYear 2 ) Å~ (1 + HPRYear 3 )]1/3 – 1.
TWR = [(1 + 6.88%) Å~ (1 + 6.55%) Å~ (1 – 5.71%)]1/3 – 1 = 1.07381/3 – 1 = 2.40%.
I do understand the concept of time-weighted return, I just have a problem with the number of shs. In this problem, it’s the HPY of the first year that I don’t really understand. At the end of the first year, the client has 15 shs so why is the total dividend 10x3 EUR? and what about the inital price? It’s like he only paid for 10 shs although he bought 15 of them the first year.
Thanks for your help!