Time-Adjusted Rate of Return
The Time-Adjusted Rate of Return, more commonly known as the Time-Weighted Rate of Return (TWROR) or geometric mean return, measures the rate of return of an investment portfolio that accounts for the effect of cash flows into or out of the investment. This method eliminates the impact of the timing and amount of contributions and withdrawals, allowing for an accurate measure of the portfolio’s performance, which is not skewed by external cash flows.
TWROR is particularly useful when comparing the performance of different investment managers or strategies, as it focuses purely on investment performance, irrespective of when an investor added or withdrew funds.
The calculation of TWROR involves breaking down the investment period into sub-periods, based on when each external cash flow occurs, and then compounding the returns over those sub-periods.
Formula:
TWROR = (1 + R1) × (1 + R2) × … × (1 + Rn) − 1
Where:
- R1,R2,…,RnR1,R2,…,Rn are the returns for each sub-period.
Example of the Time-Adjusted Rate of Return
Let’s consider a practical example to understand the Time-Weighted Rate of Return (TWROR) more clearly.
Scenario: John starts the year by investing $10,000 in a mutual fund. Six months into the year, seeing some potential, he decides to invest an additional $5,000. By the end of the year, the value of his total investment has grown to $17,500.
To calculate John’s TWROR:
- First sub-period (January to June)
Initial Investment: $10,000
Six months later, just before his additional investment, let’s assume the value has grown to $12,000.
Return for the first sub-period:
R1 = (Ending Value / Starting Value) − 1
R1 = (12,000 / 10,000) − 1 = 0.20 or 20
- Second sub-period (July to December)
Now, John adds $5,000 in July, making his total investment $17,000 ($12,000 from growth and $5,000 additional).
By the end of December, the value of his total investment has grown to $17,500.
Return for the second sub-period:
R2 = (Ending Value / Starting Value) − 1
R2 = (17,500 / 17,000) − 1 ≈ 0.0294 or 2.94
- Calculating TWROR
Using the formula:
TWROR = (1 + R1) × (1 + R2) − 1
TWROR = (1 + 0.20) × (1 + 0.0294) − 1
TWROR ≈ 1.20 × 1.0294 − 1
TWROR ≈ 0.236 or 23.6
So, John’s Time-Weighted Rate of Return for the year is approximately 23.6%. This gives a true reflection of the mutual fund’s performance over the year, neutralizing the effect of the timing and amount of John’s additional contribution.
