What Is Time Weighted Rate of Return & How Is It Calculated?

When you’re tracking investment performance, cash deposits and withdrawals can skew your returns, making it hard to judge how well your portfolio is really doing. That’s where the Time-Weighted Rate of Return (TWRR) comes in. TWRR isolates your portfolio’s performance by removing the impact of cash inflows and outflows. This gives a better picture of how your investments or fund manager are truly performing.

In this article, we’ll break down how TWRR works and show you exactly how to calculate it with the help of real-world examples.

What Is the Time-Weighted Rate of Return?

Time-weighted rate of return is a calculation method used for measuring the compound growth rate of an investment portfolio over time. In other words, (TWR) provides the compound growth rate of each fund after eliminating the effects of deposits and withdrawals. It splits the portfolio’s return into sub-periods based on the investments and redemptions made throughout the investment.

Moreover, this financial metric removes the twisted effects of growth rates created by external cash flows, providing a more accurate measure of portfolio performance. The time-weighted rate of return is also known as the geometric mean, as it multiplies all the sub-periods to generate the rate for the whole period. 

Remember, there is a difference between time-weighted return and annual rate of return, which is the percentage of profit and loss generated from an investment over a certain period.

Importance of TWR

In any investment portfolio, frequent deposits and withdrawals can make it difficult to accurately calculate the overall rate of return. Due to these cash flows, simply comparing the starting and ending balances doesn’t provide a clear picture, as the ending balance reflects both investment performance and the effects of cash inflows and outflows.

This is where the time-weighted rate of return (TWRR) proves useful. TWRR calculates the return for each period between cash flow events, effectively isolating the portfolio’s actual performance. By breaking down the total return into individual time segments, TWRR provides a more accurate and consistent measure of investment performance.

Formula for Calculating TWR

Calculation of the time-weighted rate of return formula for a certain period is done as below-

Time-weighted return formula = (Ending value – beginning value) / beginning value

For example – 

Vivek invested ₹60,000 in a mutual fund on 1 January 2019. On 31 December 2019, his portfolio stood at ₹61,000.

Let’s put these numbers into the formula-

TWR = (61,000 – 60,000) / 60,000

Therefore, TWR = 0.0167 = 1.6%

The TWR formula is useful for calculating each sub-period when new investments or redemptions are made. 

Thus, the time-weighted rate of return formula is useful when multiple sub-periods are involved and is given below – 

Time-weighted return formula = [(1 + rate of return from the 1st period) x (1 + rate of return from the 2nd period) x…x (1 + rate of return from the nth period)] – 1

Let’s understand the above formula with the help of an example – 

Vivek, after receiving ₹61,000 on 31 December 2019, invested a further amount of ₹30,000 on 1 January 2020. On 31 December 2020, his portfolio was valued at ₹95,000. But he later withdrew ₹20,000 from his investment on 1 January 2021. Now, on 31 December 2021, his portfolio valuation will be ₹77,000. 

The time-weighted rate of return calculation for each of the three sub-periods is given below-

• 1 January 2019 to 31 December 2019 (already calculated) is 2%
• 1st January 2020 to 31st December 2020

During the second sub-period, Vivek invested an additional amount of ₹30,000 into his portfolio, which was valued at ₹90,000 at the end of the year.

So, 

TWR = [95,000 – (61,000 + 30,000)] / 91,000

Therefore, TWR = 0.044 = 4.4%

• 1st January 2021 to 31st December 2021.

On 1st January 2021, Vivek withdrew Rs 20,000 from his investment portfolio. As a result, the valuation dropped to Rs 75,000 (95,000 – 20,000). At the end of 2021, his investment was worth Rs 77,000.

So,

TWR = (77,000 – 75,000) / 75,000

Therefore, TWR = 0.027 = 2.7%

Now, by applying the formula, we will link all the sub-period returns. Therefore, we get the time-weighted rate of return, which is given below-

TWR = (1 + 1.6%) x (1 + 4.4%) x (1 + 2.7%) – 1 

Therefore, the TWR = 8.7%

This rate represents the whole period, not an annual rate, but it can be calculated annually as well.

Factors for Time Weighted Return Calculation and the Time Weighted Return Formula

To understand the mechanics of TWRR in depth, let’s look at the key factors included in its calculation and formula:

• One of the key factors is that sub-periods must be similar in order to help compare different investment portfolios.
• Valuation of investment is vital to mark the commencement of a new sub-period after a deposit or redemption has been made.
• It is necessary to assume that all the returns are reinvested in a portfolio.
• To calculate return in each sub-period, subtract the value at the start of the period from the value at the end of the period.
• To complete the calculation, link the rates of all sub-periods together multiplicatively:

            Time-Weighted Rate of Return = [(1+ R1) × (1+ R2) ×……….× (1+ Rn)] – 1

This compounded return gives a clear and accurate picture of your investment performance, devoid of any influence from investor-driven cash flows.

Conclusion

TWRR is calculated to evaluate the performance of the investment portfolio. It ensures an accurate comparison of returns in the portfolio by removing the effect of external cash flows. It is highly useful in assessing fund managers’ performances, whether against other funds or benchmark indices, or different types of investments. TWR provides an accurate and clear view of portfolio growth over time.