How do you measure the return you get on equities?

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

1. Time-weighted return;
2. Money-weighted return;
3. Linked time-weighted return;
4. Modified Dietz method;
5. Geometric mean return; and
6. 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:

1. Divide the investment horizon into discrete sub-periods, such as days, months, or quarters, during which no external cash flows (contributions or withdrawals) occur.
2. Calculate the return for each sub-period using the following formula:
   1. Sub-period return = (ending value – beginning value + cash flows)/beginning value.
   2. Ending value: Portfolio value at the end of the sub-period.
   3. Beginning value: Portfolio value at the beginning of the sub-period.
   4. Cash flows: Any contributions or withdrawals made during the sub-period.
3. 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.
4. Multiply the decimal form of the sub-period returns to get the cumulative return over the entire investment horizon.
5. 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%)