Question

Afund has 10,000 at the start of the year. Six months later, the fund has a value of 15,000 at which time, Stuart removes 5,000 from the fund. At the end of the year, the fund has a value of 10,000. Calculate the exact dollar weighted rate of return less the time weighted rate of return.

Answer 1

Money Weighted Return is calculated by arriving at the present value of the returns generated by the investment over the period, such that it signifies the exact dollar value of the return generated. It compares the initial investment with the outflow to calculate the return.

PVo = PVi = CF0 ​+ CF1 / (1+IRR) ​​+ CF2​​ / (1+IRR)2+...CFn / (1+IRR)n​

PVo = PV Outflows

PVi  = PV Inflows

CF = Initial Investment

IRR = Internal rate of return

$10,000 = $5,000 / (1 + IRR/2) + $10,000 / (1+ IRR/2)2

IRR = 56.16%

Time weighted returns are the tools used to analyse the return capabilty of a stock or a project, such that it helps the manager to take aware investment decisions. A manager may withdraw funds at any point of time and hence there a need to calculate times based analysis for the same.

Time Weighted Return = [(1+HP1​)×(1+HP2)×⋯×(1+HPn)] − 1

HP = Return corresponding to the holding period

= (End Value - Initial Value) / Initial Value

HP1 = ($15,000 - $10,000) / $10,000 = 50%

HP2 = [$10,000 - ($15,000 - $5,000)] / ($15,000 - $5,000) = 0%

TWR = [(1+0.5) x (1+0)] -1

= 50%

(Dollar Weighted Rate of Return) - (Time Weighted Rate of Return) = 56.16% - 50%

= 6.16%