Maybe stupid question about time-weighted rate of return

[Linh_Ph_m]

I have a question about this example: My answer differed from the answer in the book and I realized that I have a problem in HPR2. Similar to the example of the time-weighted rate of return, I understand HPR2 beginning as the total price of 2 stocks bought in t=0 and t=1. I guess the first stock bought in t=0 was $40 and increased to $50 in t=1 (because you bought another share of the same stock for $50, which means the stock had increased to $50). So in total, the beginning of t=2 is $100.
So can you help me understand why I am wrong?

An investor buys a share of stock for $40 at time t = 0, buys another share of the
same stock for $50 at t = 1, and sells both shares for $60 each at t = 2. The stock
paid a dividend of $1 per share at t = 1 and t = 2. The time-weighted rate of
return on the investment for the period is closest to:
A. 24.7%.
B. 25.7%.
C. 26.8%.

The book answer: B
This is my answer: A

[Okachiang]

I can’t see where you’re wrong. And I searched for the same type of the question, I guess you are right. Check the errata.
In the following case, you’ll get the correct answer.

[MikeyF]

i get the sae answer as you

[brocollullu]

im doing schweser also. need to ask google for this quiz and saw your question :)) yeb, my answer is also A

[M_Y]

My answer is the same as yours. I believe the book makes a mistake.

[Mochi_Smoothie]

Hi I was wondering the same thing, I got same answer as you do

[Hengheng]

I go the same as you, i think the book made mistake.

[Kegong_Liu]

Chatgpt and I conclude the same answer with you.

[SayantiCK]

Answer is coming 25.7

[A3F]

If the calculation is done using the price of the stocks, the result is 25.74%.
If is done with the total amount for the second year, we get 24.72%.
The question is, which one is correct for CFA institute?

[ele]

that part! what are we to do… i think its safer to stick with the example

[guest]

@A3F

If the calculation is done using the price of the stocks, the result is 25.74%.
If is done with the total amount for the second year, we get 24.72%.

A3F: can you show us how you get 25.7% (Answer B)? Show your working.
Everyone else is getting 24.7% (Answer A)

Linh_Ph_m’s handwritten notes (the 2nd post) show where 24.7% comes from
Time-weighted rate of return =\sqrt{\frac{51}{40}\times\frac{61}{50}}-1=1.2472-1=24.72\%
where \frac{51}{40}=\frac{50+1}{40}=\frac{\textrm{share price at t=1 }+\;\textrm{dividend received at t=1}}{\textrm{share price at t=0}}
and \frac{61}{50}=\frac{60+1}{50}=\frac{\textrm{share price at t=2 }+\;\textrm{dividend received at t=2}}{\textrm{share price at t=1}}

The only way I can get 25.7% is to (WRONGLY) say that the dividend at time t=2 is 2 rather than 1, while still saying we received a dividend of 1 at time t=1, so that we (WRONGLY) get
Time-weighted rate of return =\sqrt{\frac{51}{40}\times\frac{62}{50}}-1=1.2574-1=25.74\%

[A3F]

I understand that dividend in t2 is equal to $2, considering that the investor now owns 2 shares.
Please explain why this is wrong.

[guest]

$2 but only $1 per share
Look at Linh_Ph_m’s handwritten notes in the second post

[A3F]

Just for the sake of the community, I wanted to clarify how we get wrong and how we interpret the right way:

Here on hpy2 is considering a dividend of 2, assuming that the investor holds two stocks paying $1 per share. That is not correct because the time weighted measured either by the total amount invested/received, or the cash flow per share.

Here on hpy2 we use the total proceeds. That’s were I got a little confused. It is a correct form but I do believe it’s less intuitive. We are considering here a “total value of position” approach.

Here is also correct but I do believe it’s much simple to calculate. We simply consider the cash flow per share and update the amount invested in time 2 as the increase in share price for end of year 1.
My suggestion is to always follow this last approach in order to have an easier calculation (not that the other ones are difficult rs)