Suppose you invest a total of $110,000 in your portfolio over a two-year period:

• Scenario 1: you invest $100,000 in the first year and $10,000 the following year.
• Scenario 2: you invest $10,000 in the first year and $100,000 the following year.

Let's say, hypothetically, that the asset price of the portfolio rises 50% in the first year, and there is no change in the second year. Which scenario brings a higher return for you?

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Generally, two methods are commonly used to measure a portfolio's returns: time-weighted return and money-weighted return. Let's dive deeper into how your return differs when applying the two methods.

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Money-weighted return

The money-weighted return (MWR) takes a portfolio's inflows and outflows into account. It provides investors with information on the return earned on their actual investment. The calculation of the money-weighted return is similar to the internal rate of return (IRR).

Just like IRR, the amounts invested are cash outflows. The amounts returned/withdrawn by the investor, or the money that remains at the end of an investment cycle, is a cash inflow for the investor. The money-weighted return is the discount rate that makes the net present value zero.

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Combined with the above example, assuming that the investor puts money into the portfolio at the beginning of every year and withdraws all cash out at the end of the second year, let's see the MWR in two cases without considering fees:

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Because more money was invested in the first year than the second in scenario 1, the MWR is higher than in scenario 2 because the calculation of MWR accounts for the value of cash flows in given periods. That is the sense that returns in this method of calculating performance are "money-weighted."

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Time-weighted return

The time-weighted return (TWR) measures the compound rate of growth of $1 initially invested in the portfolio over a stated measurement period. TWR is calculated as the geometric means of the performance of the portfolio. It requires breaking up an investment portfolio across various time intervals (or holding intervals) and evaluating performance during each interval (thus the name "time-weighted").

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Let's see the TWR in two scenarios:

We can see that the two scenarios have the same TWR, as it neutralizes the effect of cash withdrawals or additions to the portfolio. Unlike MWT, which gives different weights to different periods, TWR gives the same weights to different periods.

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Let's Recap

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