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Time-weighted rate of return (TWRR) or TWR is a method for calculating the compound growth rate of an investment portfolio. It segregates the return on a portfolio into separate sub-periods or intervals based on the investments and redemptions made.

The method thereby removes the distorting effects of growth rates created by cash inflows and outflows.

TWR is also known as geometric mean as it multiplies the returns of all the sub-periods to generate the rate for the entire period.

The time-weighted rate of return is different from the annual rate of return, which is the percentage of profit or loss made from an investment over a particular period.

One limitation of the rate of return is that it does not consider the differences caused by cash inflows and outflows.

## What is the Importance of TWR?

Calculating the rate of returns from an investment portfolio where there are multiple deposits and withdrawals can be challenging.

Multiple investments and redemptions distort the rate of return for the entire period. And, the balance at the beginning cannot be simply subtracted from that at the ending, since the latter accounts for the rate of return along with cash inflows and outflows.

The time-weighted return gives the rate of return for each period when there was an investment or withdrawal.

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By doing so, it breaks up the rates for each particular period wherein changes to a portfolio took place. Thus, the rates generated are more precise.

## Where is TWR Primarily Useful?

TWR is particularly beneficial for public investment managers or fund managers who deal with public securities.

They have no influence over the timing and amount of cash flows to an investment portfolio, which makes TWR an ideal parameter for measuring the returns.

## What are the Factors to Consider for TWR Calculations?

When calculating the time-weighted rate of return –

1. Sub-periods or intervals must be similar in order to compare different investment portfolios.
2. Investment valuation is required for marking the commencement of a new sub-period after a deposit or redemption has been made.
3. It must be assumed that all returns are reinvested in a portfolio.

## What is the Formula for Calculating TWR?

The basic TWRR formula for a particular period is –

TWR = (ending value – beginning value) / beginning value

Example –

Mr. A invested Rs.50,000 in a mutual fund on 1st January 2018. On 31st December 2018, his invested amount was valued at Rs.51,000.

So, by putting these numbers in the formula, we get,

TWR = (51,1000 – 50,000) / 50,000.

Therefore, TWR = 0.02%.

This formula is used for calculating each sub-period when new investments or redemptions are made.

Hence, the time-weighted rate of return formula when multiple sub-periods are involved is given as –

TWR = [(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.

Example –

Mr. A, after receiving Rs.51,000 on 31st December 2018, invested a further Rs.20,000 on 1st January 2019. On 31st December 2019, his portfolio’s valuation stood at Rs.75,000. However, he withdrew Rs.10,000 from his investment on 1st January 2020. The total valuation of his portfolio on 31st December 2020 will be Rs.67,000.

The TWR calculation for each of the 3 sub-periods are done below –

• 1st January 2018 to 31st December 2018 (already calculated) – 2%.
• 1st January 2019 to 31st December 2019

During the 2nd sub-period, Mr. A invested a further Rs.20,000 into his portfolio, which was valued at Rs.75,000 for the year ended.

Here,

TWR = [75,000 – (51,000 + 20,000)] / 51,000 + 20,000

Therefore, TWR = 5.7%

• 1st January 2020 to 31st December 2020.

During the beginning of 2020, Mr. A made a withdrawal of Rs.10,000 from his investment portfolio. Hence, its valuation went down to Rs.65,000 (Rs.75,000 – Rs.10,000). At the end of 2020, his investment is set to be worth Rs.67,000.

Here,

TWR = (67,000 – 65,000) / 65,000

Therefore, TWRR = 3%.

Now, by linking the returns of all these sub-periods, we get the TWRR of the whole period, which is –

TWR = (1 + 2%) x (1 + 5.7%) x (1+ 3%) – 1

Therefore, the time-weighted rate of return = 12.7%

It should be noted here that this is the rate of return for the whole period and not an annual rate. However, it can be annualized.

An alternative to TWR calculation can be a money-weighted rate of return.

Money Weighted Rate of Return vs. Time-Weighted Rate of Return

 Particulars MWRR TWRR Definition Internal rate of return on an investment that equates the initial value of a portfolio with cash inflows and outflows in the future. Compound rate of return from an investment that segregates sub-periods where investments and withdrawals were made. Use For private investment managers, as they usually have some form of control over the timing and amount of cash flows. For public investment managers who have no influence over the timing and amount of cash flows. Effect of timing on cash flows Affected None

Drawbacks of Time-Weighted Rate of Return

TWR can be challenging to calculate owing to regular cash inflows and outflows. It also requires keeping track of all investments and redemptions.

Using any software or online tools to do such calculations is, thus, more effective.

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