# How to Use the Time-Weighted Rate of Return (TWR) Formula

> **Definition**
>
> The time-weighted rate of return calculates the compounded growth rate of a portfolio over time.

## What Is the Time-Weighted Rate of Return (TWR)?

The time-weighted rate of return (TWR) measures a portfolio's compound growth rate while excluding the impact of deposits and withdrawals. It breaks the investment period into smaller segments, evaluates performance for each, and then links them together to provide an accurate reflection of the portfolio manager's decisions.

This is a highly useful way to assess fund managers' performance, whether against other funds, benchmark indexes, or even different types of investments.

### Key Takeaways

*   TWR eliminates the impact of external cash flows—deposits and withdrawals—providing a more accurate measure of portfolio performance.
*   It is the preferred method for evaluating and comparing fund managers' investment strategies and market benchmarks, as it isolates investment returns from investor-driven cash flows.
*   The formula links sub-period returns geometrically, ensuring a precise reflection of compounding over time.
*   While widely used, TWR does not reflect an investor's actual dollar-weighted return and may not be ideal for personal portfolios with frequent cash flows.

![Time-Weighted Rate of Return](https://www.investopedia.com/thmb/xYJTwHMyWNtbkFHAjuq22-Z27kc=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/TermDefinitions_TimeWeightedReturn_4-3-11ac35d01485475ab7b1a502f7c975e2.jpg)

*TWR is the preferred method for evaluating the performance of investment managers. — Investopedia / Crea Taylor*

## How to Calculate TWR

There are several simple steps to calculate the TWR:

*   **Step 1: Identify the Sub-Periods**. A sub-period is the interval during which each deposit or withdrawal happens.
*   **Step 2: Calculate the Sub-Period Returns.** The return is the percentage change of the value of the portfolio before any new [cash flows](https://www.investopedia.com/terms/c/cashflow.asp). It is "HP" in the formula below.
*   **Step 3: Calculate the Geometric Mean of All Sub-Periods**. Link the returns across all sub-periods as shown in the first line of the TWR formula below.

### Formula for TWR

Use this formula to determine the compounded rate of growth of your portfolio holdings.

$\begin{aligned}&TWR = \left [(1 + HP_{1})\times(1 + HP_{2})\times\dots\times(1 + HP_{n}) \right ] - 1\\&\textbf{where:}\\&TWR = \text{ Time-weighted return}\\&n = \text{ Number of sub-periods}\\&HP =\ \dfrac{\text{End Value} - (\text{Initial Value} + \text{Cash Flow})}{(\text{Initial Value} + \text{Cash Flow})}\\&HP_{n} = \text{ Return for sub-period }n\end{aligned}$  

## Example of TWR

Assume there are two mutual funds: Fund A and Fund B. At the beginning of one year, let's say they both have $1 million in [assets under management](https://www.investopedia.com/terms/a/aum.asp). The table below then provides the change in the values of the funds as well as their cash flows. (To simplify, we'll say new investments and withdrawals are only allowed after the close of trade on the last day of each quarter.)

The end-Q4 value represents their assets under management at the end of the year. You can see that at the end of the fourth quarter, Fund A had $1.9 million in assets under management, while Fund B had $1.85 million. So on the surface, Fund A returned 90% and Fund A returned 85%.

But, of course, it's not that simple. Let's break it down:

### For Portfolio A:

**Initial value**: $1 million

**First quarter**: Rises to $1.2 million, a 20% return, before adding $400,000 in investments, bringing the total value to $1.6 million.

**Second quarter:** Starting value of $1.6 million rises to $1.65 million, a 3.1% return, followed by $200,000 in withdrawals, bringing the total value to $1.45 million.

**Third quarter:** Starting balance of $1.45 million rises to $1.5 million, an increase of 3.4%, followed by $200,000 in inflows, bringing the total value to $1.7 million.

**Fourth quarter:** Initial balance of $1.7 million rises to $1.9 million, up 12%, followed by $300,000 in inflows. This brings the year-end balance to $1.9 million.

Therefore, Portfolio A's TWR = \[(1.2)\*(1.31)\*(1.34)\]\*(1.12) - 1 = 43%.

### For Portfolio B:

**Initial value**: $1 million

**First quarter**: Rises to $1.15 million, a 15% increase. Receives $50,000 in incoming cash flows, bringing the total value to $1.2 million.

**Second quarter:** With a starting value of $1.2 million, the fund rises to $1.4 million, an increase of 17%. It takes in another $50,000 in investments, bringing its total value to $1.45 million.

**Third quarter:** It rises from $1.45 million to $1.6 million, a return of 10%, followed by $100,000 in withdrawals, leaving a value of $1.5 million.

**Fourth quarter:** With a starting value of $1.5 million, it rises to $1.8 million, a return of 20%. It takes in $50,000 in investments, bringing its year-end value to $1.85 million.

Thus Portfolio B's TWR = \[(1.15)\*(1.17)\*(1.1)\]\*(1.2) - 1 = 77%

So Portfolio B clearly outperformed Portfolio A, even though it ended up with a slightly lower year-end value. Both calculations eliminated the effect of cash flows, providing a more useful comparison of returns.

## How to Use TWR

TWR is especially useful for evaluating [fund manager](https://www.investopedia.com/terms/f/fundmanager.asp) performance because it focuses on investment decisions rather than investor-driven cash movements. Furthermore, it ensures that returns are measured consistently regardless of when contributions or withdrawals occur. Indeed, investors and analysts also use TWR for benchmarking portfolios against market indices, helping to figure out whether an investment strategy is outperforming or lagging behind broader market trends.

Also, its compound structure enables investors to estimate future long-term portfolio growth. Nonetheless, users need to be wary of TWR's limitations. The metric does not reflect the actual dollar return experienced via the portfolio. For that, the [Money-Weighted Return](https://www.investopedia.com/terms/m/money-weighted-return.asp) is a better solution.

## The Bottom Line

Overall, TWR evaluates investment performance, ensuring an accurate comparison of portfolio returns by removing the impact of external cash flows. Whether used to assess fund managers, investment strategies, or to benchmark against market indices, TWR gives a clear view of portfolio growth over time.

> **Article Sources**
>
> 1.  J.P. Morgan Wealth Management, "[What is Time-weighted Rate of Return?](https://www.chase.com/personal/investments/learning-and-insights/article/what-is-time-weighted-rate-of-return)"
>     
> 2.  Dynamic Funds, "[Time-weighted vs. Money-weighted Returns](https://dynamic.ca/content/dam/docs/marketing/brochures/investing-strategies/14DYN050_DF_TimeVSMoney_Inv_EN.pdf)."