ROI ≠ ROI
What's the simplest way to calculate the return on an investment? At school, you learned that you had to divide the profit by the invested amount and multiply that by 100 to get a percentage. If you invested €10,000 two years ago and sold the investment for €11,000, your profit would be 10% (1,000/10,000 x 100).
That's simple enough. But it's unlikely that you invest in this way. In practice, investors invest at different times, take some profit (or loss) in the interim, temporarily park a bit of cash or inject extra cash, accumulate or unwind positions, and so on. This simple method works if you invest once. But in other cases it is not a good indicator of return.
The most common methods used to show the return on investments are the money-weighted return and the time-weighted return. Both methods are useful to evaluate the performance of a portfolio over time. But they are calculated differently and therefore give a different result. Do you compare returns on investments? If so, you should check whether they were calculated using the same method.
- Time-weighted return: does not take into account the impact of cash flows into and from the portfolio.
- Money-weighted return: does take into account the impact of cash flows into and from the portfolio.
1. Time-weighted return
Time-weighted return does not take into account incoming and outgoing cash flows when calculating the return. This makes it ideal for calculating the performance of investment funds. Timing is important here because fund managers have no control over the timing of cash flows into and from the fund – after all, it's the investors who determine the ingoing and outgoing cash flows. In most cases, cash flows into and out of the fund every trading day. It is therefore unreasonable to include this effect in the evaluation of the fund manager's performance.
How does this work? With time weighting, the performance of the portfolio over the measured period is broken down into smaller 'sub-periods'. Each sub-period begins and ends with an inflow and/or outflow of cash. The return of each sub-period is then calculated before they are linked to calculate the average return for the entire period.
This is what it looks like schematically:
2. Money-weighted return
Unlike time weighting (which eliminates the impact of cash inflows or outflows), money weighting does take into account the impact of cash flows into and from the portfolio. Money weighting takes into account both the size and the timing of the cash flows (including any dividends and interest). As a result, periods in which the portfolio is the biggest are also given the most weight. When and how much you invest therefore has a strong influence on the return. For example, the returns of your fund investments over a certain period may differ from the returns shown by the fund managers.
For most investors, money weighting is the most appropriate method to measure the performance of the portfolio since, as an investor, you manage cash flows into and from the portfolio yourself.
3. Time-weighted return versus money-weighted return: three examples
Do you find it confusing? To help explain the difference between the two, let's imagine an investor who invests in a certain share in three ways over a period of two years.
- On 1 March 2017, you buy shares from Beyond Heat for €5,000.
- On 1 March 2018, Beyond Heat shares are listed at a value that is 10% higher than a year ago.
- On 1 March 2019, you sell your shares after the share price has again risen by 10%.
In this scenario, your profit is €1,050 in two years. You did not buy or sell any positions in that period, so the money-weighted and time-weighted returns are identical:
- The money-weighted method gives you a return of 21%
- The time-weighted method gives you a return of 21%
- On 1 March 2017, you invest €5,000 in Azanom shares.
- On 1 March 2018, Azanom shares are listed at a value that is 35% higher than a year ago. You believe in the growth potential and decide to buy shares for an additional €5,000.
- On 1 March 2019, you sell your Azanom shares after the share price has again risen by 20%.
In this scenario, your profits are €4,100 in two years.
- The money-weighted method gives you a return of 56.8%
- The time-weighted method gives you a return of 62%
- On 1 March 2017, you invest €5,000 in SnapCat shares.
- On 1 March 2018, SnapCat shares are listed at a value that is 35% higher than a year ago. You believe in the growth potential and decide to buy shares for an additional €5,000.
- On 1 March 2019, you sell your SnapCat shares after the share price has dropped by 20%.
In this scenario, your loss is €400 in two years.
- The money-weighted method gives you a negative return of -7.9%
- The time-weighted method gives you a return of +8%
Despite losing money in this third example, the time-weighted return is positive. This is because the time-weighted method only measures the underlying performance of the shares in the portfolio, and not the actions of the investor who buys or sells the shares (inflows and outflows), or the impact of the size of those actions during the measured period.
What is meant by annualised return and actuarial return?
An annualised return is a return that is converted into a yearly rate over a certain period of time. For example, if Fund A achieves a return of 5% in six months, the annualised return is 10%. If Fund B achieves a return of 75% over 5 years, this means that the fund achieves an average annualised return of 11.8% per annum.
The actuarial return is the actual return of an investment, taking into account all factors that can influence the actual return, such as taxes, interim income (interest and dividends), transaction costs, and so on.