# Weighted rates of return

### Merke

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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.

The money-weighted rate of return is the internal rate of return on a portfolio when all cash flows have been taken into account. It is calculated as the interest rate that guarantees

PV(outflows) = PV(inflows).

### Beispiel

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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.