*How does one measure the return you’re getting on equities? I’ve invested some spare funds in EasyEquities. You can see the percentage of profit/loss since inception, but I was wondering if it is best to measure annually. And how do you do this? Also, the dividends received, do you bring these into the calculation?*

There are various ways to determine the return over a certain period for an investment portfolio, to name a few:

- Time-weighted return;
- Money-weighted return;
- Linked time-weighted return;
- Modified Dietz method;
- Geometric mean return; and
- Arithmetic mean return.

Of these the most popular and suitable for a client’s investment portfolio would be the time-weighted return.

Time-weighted return measures the compound rate of growth of a portfolio’s value over time, independent of cash flows. It is particularly useful for assessing the investment manager’s skill since it eliminates the impact of external cash flows. Time-weighted return accounts for the effects of contributions and withdrawals and gives a better sense of the portfolio’s investment performance.

A sample calculation is shown below. The dividends received will increase the portfolio value used at the end of your measurement period and thus already be incorporated:

The formula for time-weighted return:

Time-weighted return = [(1 + R1) * (1 + R2) * … * (1 + Rn)] – 1

Where:

R1, R2, …, Rn are the sub-period returns (expressed as decimals).

**Step-by-step calculation:**

- Divide the investment horizon into discrete sub-periods, such as days, months, or quarters, during which no external cash flows (contributions or withdrawals) occur.
- Calculate the return for each sub-period using the following formula:
- Sub-period return = (ending value – beginning value + cash flows)/beginning value.
- Ending value: Portfolio value at the end of the sub-period.
- Beginning value: Portfolio value at the beginning of the sub-period.
- Cash flows: Any contributions or withdrawals made during the sub-period.

- Convert the sub-period returns into decimal form by adding 1 to each return and then multiplying. This is because returns are typically expressed as percentages, so they need to be in decimal form for compounding.
- Multiply the decimal form of the sub-period returns to get the cumulative return over the entire investment horizon.
- Subtract 1 from the cumulative return to get the time-weighted return.

**Example:**

Let’s consider a simple example with two sub-periods:

Sub-period 1: 1 January to 31 March

- Beginning value: R100 000
- Ending value: R110 000
- No cash flows during this period

Sub-period 2: 1 April to 30 June

- Beginning value: R110 000
- Ending value: R120 000
- Cash flows: R5 000 added on 15 April

*Calculations:*

Sub-period 1 return = (110 000 – 100 000 + 0)/100 000 = 0.1 (or 10%)

Sub-period 2 return = (120 000 – 110 000 + 5 000)/110 000 = 0.1364 (or 13.64%)

*Cumulative return:*

Cumulative return = (1 + 0.1) * (1 + 0.1364) = 1.24704

Time-weighted return = 1.24704 – 1 = 0.24704 (or 24.704%)

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