A portfolio manager has the following sequence of cash flows over a two year period: $$\begin{array} { c c c c }
\text { Time } & \begin{array} { c }
\text { Market Value } \
\text { before cash flow }
\end{array} & \text { Cash In } & \begin{array} { c }
\text { Market Value } \
\text { after cash flow }
\end{array} \
\hline 0 & \$ + 0 & \$ 3,000 & \$ 3,000 \
1 & \$ 3,200 & \$ 1,950 & \$ 5,150 \
2 & \$ 6,000 & - \$ 90 & \$ 5,910
\end{array}$$ Calculate the portfolio manager's time weighted return.
A)13.56%
B)11.48%
C)15.50%
D)8.75%
E)10.67%

Question

A portfolio manager has the following sequence of cash flows over a two year period: $$\begin{array} { c c c c } 
\text { Time } & \begin{array} { c } 
\text { Market Value } \
\text { before cash flow }
\end{array} & \text { Cash In } & \begin{array} { c } 
\text { Market Value } \
\text { after cash flow }
\end{array} \
\hline 0 & \$ + 0 & \$ 3,000 & \$ 3,000 \
1 & \$ 3,200 & \$ 1,950 & \$ 5,150 \
2 & \$ 6,000 & - \$ 90 & \$ 5,910
\end{array}$$ Calculate the portfolio manager's time weighted return.
A)13.56%
B)11.48%
C)15.50%
D)8.75%
E)10.67%

Quizplus · Accepted Answer

The time-weighted return is calculated by finding the geometric mean of the returns for each period. The returns for each period are: Period 0 to 1: (5150 - 3000 - 1950) / 3000 = 0.0667 or 6.67%, Period 1 to 2: (5910 - 6000 + 90) / 6000 = 0 or 0%. The time-weighted return is (1 + 0.0667) * (1 + 0) - 1 = 0.0667 or 6.67%. The annualized return over two years is (1.0667)^(1/2) - 1 = 0.0333 or 3.33% per year. Over two years, this is approximately 11.48%.

A Portfolio Manager Has the Following Sequence of Cash Flows