Dollar-weighted rate of return vs. Time-weighted rate of return

Dollar-weighted (or money-weighted) rate of return (DWR)
Dollar-weighted rate of return is the internal rate of return (IRR) of all the cash flows into and out of a portfolio, or the discount rate that makes the present value of inflows equal to that of outflows.

For asset portfolio, the cash flows include the purchase and sale of stock as well as dividends received.

DWR = Sum[CF₁/(1+r)^t] = C₀

Notes:

• If new fund adds to an investment portfolio when it is performing poorly, dollar-weighted method will end to be depressed.
• If new fund distributes to portfolio in favorable time, dollar-weighted method will tend to elevate the performance.
  

Time-weighted rate of return of portfolio (TWR)
Measure the compound growth rate of $1 over a specified measurement period. It is also called the "geometric mean return," as the reinvestment is captured by using the geometric total and mean.

TWR = [(P₁-P₀)/P₀] [(P₂-P₁)/P₁]…. [(P_n-P_n-1)/P_n]

Steps to calculate time-weighted rate of return

1. Value the portfolio immediately prior to any significant addition or withdrawal of funds
2. Break the overall evaluation period into equal subperiods based on the dates of inflows & outflows
3. Calculate Holding period return (HPR) for each subperiods
4. Link HPRs by multiplying, to derive the geometric mean
   

Notes:

• TWR is a preferred measurement as it is not be affected by the timing of cash flows and can compare the returns of investment managers.