A portfolio manager has the following sequence of cash flows over a two year period: $$\begin{array} { l c c c }
\text { Time } & \mathbf { 0 } & \mathbf { 1 } & \mathbf { 2 } \
\hline \text { outflows } & - \$ 2,000 & - \$ 500 & \
\text { inflows } & & \$ 50 & \$ 3,090
\end{array}$$ Calculate the portfolio manager's dollar 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: $$\begin{array} { l c c c } 
\text { Time } & \mathbf { 0 } & \mathbf { 1 } & \mathbf { 2 } \
\hline \text { outflows } & - \$ 2,000 & - \$ 500 & \
\text { inflows } & & \$ 50 & \$ 3,090
\end{array}$$ Calculate the portfolio manager's dollar weighted return.
A)13.56%
B)11.48%
C)15.50%
D)8.75%
E)10.67%

Quizplus · Accepted Answer

The dollar-weighted return is calculated as the average return of the portfolio over the investment period, weighted by the amount of money invested at each point in time. In this case, the portfolio manager has two cash outflows and two cash inflows. The dollar-weighted return is calculated as follows:$$DWR = \frac{\sum_{t=0}^{n} CF_t * (1+r)^t}{\sum_{t=0}^{n} CF_t}$$where:* $CF_t$ is the cash flow at time t* $r$ is the discount rate* $n$ is the number of periodsIn this case, the cash flows are as follows:* $CF_0 = - \$ 2,000$* $CF_1 = - \$ 500$* $CF_2 = \$ 3,090$The discount rate is not given, so we will assume it is 0%. The number of periods is 2.Plugging these values into the formula, we get:$$DWR = \frac{(- \$ 2,000) * (1+0)^0 + (- \$ 500) * (1+0)^1 + \$ 3,090 * (1+0)^2}{(- \$ 2,000) + (- \$ 500) + \$ 3,090}$$$$DWR = \frac{\$ 3,090}{\$ 590}$$$$DWR = 5.24$$Therefore, the portfolio manager's dollar-weighted return is 5.24%.

A Portfolio Manager Has the Following Sequence of Cash Flows