Calculate, interpret and distinguish between the money-weighted and time-weighted rates of return of a given portfolio. Appraise the performance of portfolios based on these measures.
To calculate portfolio returns in a multi-period setting, when the portfolio is subject to additions and withdrawals, we can use two different methods:
Money-weighted weighted rates of return.
Can be appropriate if the investor has control over additions and withdrawals to the portfolio.
Time-weighted rate of return.
Standard in the investment management industry.
PV(outflows) = PV(inflows).
If you invest €300 in a portfolio today that will earn €100 next year and €350 in two years, calculate the money-weighted rate of return.
We calculate for the interest rate r that satisfies the equation
300 = 100/(1 + r) + 350/(1 + r)2.
Using a financial calculator, we get r = 25.9573 percent. To show that this is correct, we can insert that value and get 100/(1 + 0.259573) + 350/(1 + 0.259573)2 = 79.3920 + 220.608 = 300, as indicated.
The time-weighted rate of return, on the other hand, stresses the compound rate of growth of one dollar invested over a certain measurement period. It removes the effect of timing and the effect of withdrawals and additions to the portfolio.