Quant Problem : How to solve Time Weighted Rate of Return Problems?

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ados1984

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Guys,

I am not able to understand concept of time weighted rate of return, here is the question, would really appreciate if someone can share some thoughts on how to approach this problems.

An investor buys one share of stock for $100. At the end of year one she buys three more shares at $89 per share. At the end of year two she sells all four shares for $98 each. The stock paid dividend of $1 per share at the end of year one and year two. What is the investor’s time weighted rate of return?

A. 6.35%
B. 11.24%
C. 0.06%

Any idea on how to solve this problem, what approach to take in general for this kind of time weighted problems?
 
I haven’t practiced quants in awhile, but i believe time-weighted = find IRR
CF0 = -$100 to buy the first share
CF1 = -$266 = -89x3 shares +1 for dividend
CF2 = +$396 = 98x4 + 4 for dividends
solve for IRR = 6.35
A.
 
just fallow the steps indicated in solving the problem(i have them pretty clear explained in schweser i don’t know what materials do you use) and solve a few examples until you get used to it:)
 
Here is the solution of this question, but am not sure how calculation is done, any guidance will be much appreciated.
For Money Weighted Returns, we calculate IRR and for Time Weighted Returns, we need to calculate Holding Period Return and this would be based on Geometric Mean.

The Correct answer is C.
The Holding period return in year one is ($89 - $100+ $1) / $100 = -10.00%
The holding period return in year two is ($98 - $89 +$1) / $89 = 11.24%
the time weighted return is [{1+ (-0.1000)}{1+.1124}]^1/2 = .06%
 
Yeah ados, you pretty much got it right there. money weighted=IRR of the cash flows and time weighted is the geometric mean.
So take your cash flows on a per-period basis, basically as if you’re selling your holdings after each period and then buying them again at the start of the next one (so include the dividend on the close, don’t for the open). Time weighted returns basically tell us how good the investment did overall, on a per-period basis hence the dividend treatment.
 
Thanks chibwack, i do not understand the calculation here, can you solve this problem with details calculations? I would really appreciate it.
Ados.
 
nikhiljohn wrote:
Your approach is wrong because the money-weighted return = IRR.
Click to expand...
Agreed but am looking for Time weighted return in the problem and not money weighted return.
 
This is how I approach time-weighted returns problem :
1. From t=0 to t=1, one stock fell from 100 to 89, and gave a dividend of $1. (In effect from 100 to 90)
So his portfolio HPR(Holding Periiod Return) for year 1 is : ((90/100)-1) = -0.1 (or -10%)
2. Then he added 3 more stocks. He has 4 stocks now.
3. From t=1 to t=2, 4 stocks grew from $89/Stock ($356 for 4 stocks) to $98/stock ($392 for 4 stocks). He also got $1 dividend for each stock (He got a total of $4 as dividends). Effectively, its grew from $356 to 396.
Therefore his HPR for year 2 is : ((396/356)-1) = 0.1124 (or 11.24%)
4. Time weighted return can be calulated as : (( (1+HPR for first year)*(1+HPR for second year) )^1/2 ) - 1 = 0.00006 (or 6%)
Hope it helped
 
@nikhiljohn : thanks for explanation, this really helps.
 
pdub wrote:
I haven’t practiced quants in awhile, but i believe time-weighted = find IRR
CF0 = -$100 to buy the first share
CF1 = -$266 = -89x3 shares +1 for dividend
CF2 = +$396 = 98x4 + 4 for dividends
solve for IRR = 6.35
A.
Click to expand...
Above calculation is wrong as IRR is used for Money Weighted Rate of Return and Holding Period Rate of return is used for time weighted rate of return.
 
u know whats funny is that i started to type it out just like nikhiljohn did, and then i said wait..i think timeweighted is the IRR..erased it all and did it the other way..then when i saw answer A i figured i was right…
ados, this is an early lesson of what to expect on the exam…don’t assume that if u try it and ur answer is there u must have done it right..the wrong answers are strategically selected
 
@pdub: could not agree more with you, need to find a way of remembering all those formula’s…and their application…thinking what would be best way of remembering it…
 
time-weighted = split the times up
calculate the time periods separately
the best way to remember it though….this post..which is why this forum is helpful..you’ll probably never forget the difference again
*edit - and neither will i lol
 
I completed the reading 6 two weeks back, and when I saw this post today, I realised that I forgot how to solve both time-weighted and money weighted rate of return. Then I went through the concepts quickly and I was able to solve the question.
I guess from now I wont forget the difference between these 2 rates of return. And I think the best way to remember, revise and master any concept is to look at various questions across the forum.
@ados1984, @pdub, @chibwack :
How much have you guys covered till now?
 
i have completed 75% of study session 2, how about you guys…
 
nikhiljohn wrote:
4. Time weighted return can be calulated as : (( (1+HPR for first year)*(1+HPR for second year) )^1/2 ) - 1 = 0.00006 (or 6%)
Hope it helped
Click to expand...
Everything was fine on the solution up until the very last part of the last step.
Please note that answer is 0.00056 = 0.056% –> closest answer is 0.06%.
 
i’m finishing SS 8 w/schweser..so about half way through FRA
 
8…
im finished with 8 but they give u 2 weeks to do it so im going back over it and trying to drill down..will start 9 on sunday…ive done all of quant (but as u can see its slipping away) all of econ and now half of FRA
 
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