Money weighted Vs Time Weighted Return

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maparam

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An investor started the year with a $10,000 portfolio. He made a $1,000
contribution at the end of the first quarter, a $2,000 withdrawal at the end of
the third quarter, and ended the year with a portfolio value of $10,553. The
quarterly holding period returns for the investor’s portfolio are as follows.
Q1 Q2 Q3 Q4
3% -5% 8% 10%
The money-weighted and time-weighted returns for the year are closest to:
Money-Weighted Time-Weighted
a. –4.66% 3.84%
b. 3.59% 3.84%
c. 14.34% 16.25%
d. 16.00% 16.25%
 
I’ll go with C.
Time weighted = (1.03*.95*1.08*1.1)-1= 16.25%
Money weighted = CF0=-10000, CF1=-1000 CF2=0 CF3=2000 CF4=10533 CPT->IRR-> 3.58%
3.58%*4=14.34%
 
I think the answer is B as Time weighted is exactly same as Geometric mean and my answer is 3.84%.
What is the answer?
 
the answer is C.
Remember that the time series is per quarter. so you do not raise to the power 1/4 to get 3.84%. It has to be the full year’s which is 16.25%
For the money weighted – you get a quarter’s worth which is 3.84 – so multiply by 4 to get 14.34%.
 
To double check your time-weighted return, assume no contributions or withdrawals were made. In that case, the portfolio starts with $10,000 and ends with $11,624, a return of 16.24%. The assets in the portfolio returned 16.24%, but the investor took out some money and lowred his/her return.
For the money-weighted return, it is an IRR problem with cash flows timed quarterly.
 
Not sure what I am doing wrong but my BAII Plus professional calculator keeps giving me 3.54% and hence 14.167% as the IRR. Can someone point out what I might be doing wrong. I got the answer as C but slightly skewed results.
 
I got B as well… The money weighted return (MWR) is just the IRR in which you (Long onCFA) calculated. The time weighted return is the geometric mean in which I got the following:
{(1.03)(.95)(1.08)(1.1) }^(1/4) -1 = 3.84. Hence the answer that I got is a B.
 
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