Time-weighted return (TWR) calculates an investment portfolio or fund’s performance while accounting for external cash flows. Investment funds usually have money flowing in or out at various times. TWR calculates performance without the distorting effect of these cash inflows and outflows.

TWR is not the simplest calculation, but understanding how it works is helpful. Weâ€™ll break it down and provide examples to show what TWR may look like in action.

## What is time-weighted return (TWR)?

Time-weighted return calculates a fundâ€™s compound return using sub-periods, which are created each time cash moves into or out of the fund or portfolio. In doing so, TWR shows the real market return of a fund or portfolio over time.

Contrast TWR with a metric like rate of return (RoR), which calculates an investmentâ€™s performance based solely on an initial contribution. While this calculation is helpful, it cannot account for cash flow movements, making it potentially less useful over time.

Because TWR accounts for external cash flows, it is also a useful benchmark for comparing a fundâ€™s performance to other funds. However, due to the complexity of the calculation, individual investors usually donâ€™t rely on this metric.

## How time-weighted return works

Time-weighted return (TWR) measures the compound growth rate of an investment portfolio, accounting for the impact of cash flows into or out of the portfolio.

To achieve this, divide the total investment period into sub-periods. Each time there is cash flow, such as a deposit or withdrawal, a new sub-period starts.

### How to calculate time-weighted return

The following formula calculates the cumulative return of the portfolio:

`TWR = [(1 + HP1) Ã— (1 + HP2) Ã—â‹¯Ã— (1 + HPn)] âˆ’ 1`

Where:

• TWR = Time-weighted return
• n = Number of sub-periods
• HP = (End Value – (Beginning Value + Cash Flow)) / (Beginning Value + Cash Flow)
• HPn = Return for sub-period n

As mentioned, you must calculate the TWR for each sub-period. Then, you must link the returns, which tells us the total return for the entire period. Unlike the simple savings rate, TWR shows us a portfolioâ€™s performance with compounding.

### Example of time-weighted return

To understand how TWR works, an example is helpful. Suppose you invest \$10,000 in a portfolio on Jan. 1. Three months later, the portfolio has grown to \$10,500.

Using these figures, your return for the first sub-period is:

`HP1 = (\$10,500 - \$10,000) / \$10,000 = 5%`

You decide to invest \$5,000 more, bringing the value to \$15,500. Over the next two months, the market struggles, and your portfolio decreases by \$1,000 to \$14,500.

The return for this sub-period is:

`HP2 = ((\$14,500 - (\$10,500 + \$5,000)) / (\$10,500 + \$5,000) = -6.45%`

Seeing your portfolio decrease, you decide to withdraw \$1,000, leaving its portfolio value at \$13,500. However, the market does very well over the next three months, and your portfolio grows to \$16,000.

Here is the return for the sub-period:

HP3 = ((\$16,000 – (\$14,500 – \$1,000)) / (\$14,500 – \$1,000) = 18.52%

To calculate the total TWR, link the returns:

TWR = (1 + 0.05) x (1 + (-0.0645)) x (1 + 0.1852) – 1 = 16.42%

The total TWR for the 8-month period is 16.42%. Even though you kept contributing to the portfolio, the cash flows didnâ€™t skew the growth rate, giving you a more accurate reading of the portfolioâ€™s performance.

## Time-weighted return vs. rate of return

The main difference between TWR and rate of return (RoR) is whether the impact of cash flow is considered. As weâ€™ve seen in this article, TWR works by calculating a portfolioâ€™s return between cash flows and then linking the returns. While useful, this calculation is a bit complex and cumbersome for the average investor.

RoR is much simpler because it calculates the return over a certain period, based on the initial investment. This means there is no need for sub-periods â€” you simply divide the change in dollars in the portfolioâ€™s balance by the beginning balance to get the RoR.

In addition to RoRâ€™s simple calculation, it can also be advantageous if you want to show the impact of the investorâ€™s decision to contribute or withdraw from the portfolio. However, if you donâ€™t want to see the impact of cash flow, RoR may not be the ideal choice.

## Ways to use time-weighted rate of return

Individual and beginning investors may prefer a simpler calculation for their purposes, but there are still many potential uses for TWR. Consider the following possibilities:

• Evaluating portfolio manager performance: You can use TWR to compare the performance of different portfolio managers or investment funds. Because the formula removes the impact of cash flow, it can help you gauge how each fund or portfolio manager has performed.
• Mutual and hedge fund reporting: These funds may use TWR to report their performance, often to comply with regulations.
• Institutional investment analysis: Large institutional investors like pension funds might use TWR to gauge the performance of their investment strategies and fund managers.
• Online brokers: Online brokers might provide analysis that automatically calculates TWR for investment funds and individual portfolios. This can help investors make better and more informed decisions.

While calculating TWR manually can be too much for individual investors, that doesnâ€™t mean it isnâ€™t a useful metric. It can be the ideal benchmark for larger investors, and you can also use it to compare the performance of various fund managers.