How to use the time-weighted rate of return (TWR) formula

Finding the most effective way to gauge investment returns and portfolio performance may be difficult for investors. One of the most popular methods for achieving this is the time-weighted return.

The time-weighted return (TWR) is one of the most often used algorithms for monitoring the success of investments. To put it briefly, it takes into consideration the times when cash flows happen and establishes sub-periods to assist investors in monitoring growth rates.

Although TWR is not the most straightforward portfolio management strategy, it is useful to know how it works. If you’re interested in learning how the time-weighted rate of return formula works, then keep reading.

What is the time-weighted rate of return (TWR) formula?

A measure of a portfolio’s compound rate of growth is called the time-weighted rate of return, or TWR. Depending on whether money was contributed to or taken out of the fund, the time-weighted return divides the return on an investment portfolio into several periods. The rate of return for each period with changes in cash flow is then provided. 

The purpose of this technique is to assist investors in removing the distorted impacts of withdrawals and deposits. By doing this, TWR displays a fund’s or portfolio’s actual market return over time.

TWR is a helpful metric for evaluating a fund’s performance against that of other funds as it considers external cash flows. However, ordinary investors often don’t depend on this indicator because of the calculation’s intricacy.

How to use the time-weighted rate of return (TWR) formula

The time-weighted rate of return may seem complicated at first glance, but it is quite easy to understand. Let’s go through how it is calculated, starting with the formula: 

TWR = [(1+HP1) x (1+HP2) x (1+HPn)] – 1

Where:

• n = the number of sub-periods
• HP = (End Value – (Beginning Value + Cash Flow)) / (Beginning Value + Cash Flow)
• HPn = Return for sub-period n

To understand it better, think of it in this way:

• For each sub-period, subtract the balance you had at the beginning from the balance you have at the end of the period, then divide the value by the balance you had at the beginning of the period.
• Each time there is a change in cash flow, whether deposit or withdrawal, create a new rate of return based on the method above. 
• Add one to each rate of return, and then multiply all the rate of return you created for each sub-period. Then, subtract 1 from the result, which gives you the TWR for that period.

Example of TWR

Let’s explore an example of TWR to better understand how the method works.

Let’s say you invest N1,000,000 in mutual fund A in December 2024. Your investment’s worth increases to N1,100,000 by the beginning of January 2025, and then you decide to increase your investment by N200,000 making your total investments worth N1,300,000. By the end of January, the value drops to N1,200,000. Let’s calculate the TWR using the formula:

TWR = [(1+HP1) x (1+HP2) x (1+HPn)] – 1

HP1= N1,100,000 – N1,000,000 / N1,000,000= 0.1 or 10%

HP2= N1,200,000 – (N1,100,000 + N200,000) / N1,200,000 = -0.083 or -8.33%

TWR = (1+0.1) * (1+-0.083) – 1 = 0.0087 or 0.87%

Let’s explore the opposite scenario and say you withdraw N200,000 instead of investing, reducing your total investment to N900,000. By the end of January, the value of your investment will still drop by 7.69% to N830,769. Let’s calculate the RWR.

HP1= N1,100,000 – N1,000,000 / N1,000,000= 0.1 or 10%

(End Value – (Beginning Value + Cash Flow)) / (Beginning Value + Cash Flow)

HP2= N830,769 – (N1,100,000 – N200,000) / N830,769 = -0.083 or -8.33%

TWR = (1+0.1) * (1+-0.083) – 1 = 0.0087 or 0.87%

Regardless of whether you invest or withdraw, the TWR remains the same, making it a very accurate method of measuring the worth of a portfolio. 

Advantages of TWR

TWR is a very valuable method to examine the performance of a portfolio and has been used by many investors over the years. Let’s explore some of its benefits: 

• It is a reliable gauge of the success of investments
• It eliminates the influence of cash flow
• It gives a transparent picture of returns after each withdrawal or deposit
• It is appropriate for evaluating the performance of investment managers
• Connects recurring returns

Disadvantages of TWR

Although there are several advantages to using the TWR, it still has its disadvantages. Before using this method it is best to consider both the advantages and disadvantages:

• When the money enters and exits the portfolio more often, computation may become difficult.
• The final figure may be skewed by the frequent adjustments, yielding less precise findings.
• The TWR does not account for the time interval or date of investment. 
• TWR is often used to monitor performance monthly. It might be challenging to use the TWR if there is a monthly or daily rise in cash flow.
• There may be mistakes as it might be impossible to use certain calculations when the portfolio change is equal to zero. 

Conclusion

An investment portfolio can be calculated using time-weighted return, which does not take into account the distorting influence of cash flows. 

The TWR method helps professionals determine growth for each period by concentrating on the times when cash flows occurred.

Despite being a standard in portfolio management, time-weighted return still has several drawbacks. However, investors and fund managers may get around these problems and accurately evaluate growth the growth of a portfolio.