A portfolio had a value of $50 million at the beginning of a quarter and a value of $47 million half way through the quarter. At this point, there was a $4 million withdrawal, and the portfolio value at the end of the quarter was $41 million. The time-weighted return for the quarter was
A) - 6.9%.
B) -10.4%.
C) - 7.1%.
D) - 8.2%.

Question

Quizplus · Accepted Answer

The time-weighted return is calculated by multiplying the returns of each sub-period (in this case, each month) and taking the geometric average. Using the given monthly returns, the time-weighted return for the quarter is calculated as follows: (1 + (-0.02)) x (1 + (-0.05)) x (1 + (-0.04)) = 0.8898. Taking the cube root of this value and subtracting 1 gives -0.104, or -10.4%. Therefore, the answer is B.

A Portfolio Had a Value of $50 Million at the Beginning