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

Question

Quizplus · Accepted Answer

To calculate the time-weighted return (TWR), we first find the holding period returns (HPR) for each period, then geometrically link them. The formula for HPR is $\frac{\text{End Value} - \text{Beginning Value} + \text{Cash Flow}}{\text{Beginning Value} + \text{Cash Flow}}$ if cash flow occurs at the beginning of the period, but since cash flows occur at the end of each period here, we adjust the formula to $\frac{\text{End Value}}{\text{Beginning Value} + \text{Cash Flow}}$ for periods with cash flows.1. From time 0 to 1: $\frac{5,150}{3,000} = 1.7167$2. From time 1 to 2: $\frac{5,910}{5,150} = 1.1476$The TWR is the geometric mean of these holding period returns minus 1, so we calculate $((1.7167) \times (1.1476))^{1/2} - 1$.This gives us $(1.9664)^{1/2} - 1 = 1.11.48 - 1 = 0.1148$ or 11.48%.

A Portfolio Manager Has the Following Sequence of Cash Flows