HPR for Time-weighted return

CFA Level I Quant
#1

Have a problem with understanding concept in this example

Compute the investment performance of the fund during 2014:

  • On 1.01.2014 , the fund had market value of $100 million

  • During the period, 1.01 to 30.04 , the stocks in the fund showed a capital gain of $10 million

  • On 1.05 the stocks in the fund paid a total dividend of $2 million. All dividens were reinvested in additional shares

  • Because the fund’s performance had been exceptional, institutions invested an additional $20 million in the fund on 1.05 , raising assets under management to $132 million

  • On 31.12 , fund received total dividends of $2.64 million. The fund’s market value on 31.12 , not including $2.64 million in dividends, was $140 million.
    And this is how it’s calculated in the book :

-> 1.01 beginning portfolio value = 100 mln

-> 1.05 dividends received before additional investment = 2 mln ending portfolio value = 110 mln hpr1= [2+ (110-100)]/ 100 = 12 % new investment = 20 mln -> 31.12 beginning market value for last 2/3 of year = 132 million dividends received = 2.64 mln ending portfolio value = 140 mln hpr2= [2.64 + (140-132)] / 132 = 8,06 % And my questions: - shouldn’t we calculate the HPR for the period 1.01 to 30.04? - on 1.05 they use $100 mln as the beginning value instead of the $110 mln - why is that ? there was a capital gain of $10 mln during the period 1.01 to 30.04** - how to include the $20 mln investment made on the 1.05 ? it’s not included in calculating the HPR in this period earlier. They use it as the beginning value on the 31.12 - $132 mln**

#2

The dividends are paid on 5/1. But they were earned before that. The ex-dividend date (the date upon which anyone holding the stock is entitled to the next dividend) comes before the dividends are actually paid. The dividends paid need to be included in the return for the period when you held the stock and to which they apply.

That’s what HPR1 is. HPR1 = (110 - 100 + 2) / 100 = 12% Starting Value = 100 mil, Ending Value = 110, Dividends = 2

The question is worded poorly - that’s kind of how it goes with Schweser questions.

I’m not seeing this. It looks like they’re using $132 mil as the beginning value 100 + 10 capital gain + 2 in reinvested dividends + 20 new investment = 132 your starting value for HPR2. Remember: HPR = (P1 - P0 + D1) / P0 = (Ending Value - Starting Value + Dividends) / Starting Value

#3

Thanks