Introduction
The time-weighted rate of return (TWR) is a measure of the compound rate of growth in a portfolio. The TWR measure is often used to compare the returns of investment managers because it eliminates the distorting effects on growth rates created by inflows and outflows of money. The time-weighted return breaks up the return on an investment portfolio into separate intervals based on whether money was added or withdrawn from the fund.
The time-weighted return measure is also called the geometric mean return, which is a complicated way of stating that the returns for each sub-period are multiplied by each other.
The Power of the TWR Formula
Use this formula to determine the compounded rate of growth of your portfolio holdings.
TWR = [(1 + HP1) × (1 + HP2) × ⋯ × (1 + HPn)] − 1
\begin{aligned}
&\text{where:}\\
&TWR = \text{Time-weighted return}\\
&n = \text{Number of sub-periods}\\
&HP = \frac{\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}
Your Step-by-Step Guide to Calculating TWR
- Calculate the rate of return for each sub-period by subtracting the beginning balance of the period from the ending balance and dividing the result by the beginning balance.
- Create a new sub-period for each period where there is a change in cash flow, whether it’s a withdrawal or deposit, resulting in multiple periods, each with its rate of return. Add 1 to each rate of return, which simply makes negative returns easier to calculate.
- Multiply the rate of return for each sub-period by each other and subtract 1 from the result to achieve the TWR.
Unlocking Insights: What TWR Reveals
Determining the earnings of a portfolio with multiple deposits and withdrawals can be challenging. Rather than simply subtracting the starting balance from the ending balance, which reflects both returns and cash flows, TWR breaks down the return in a portfolio into separate intervals based on cash flow events, providing a clearer picture of the portfolio’s true performance. Thus, TWR isolates the returns from cash-flow changes, offering a more accurate measure of investment performance.
Key Takeaways
- The time-weighted return (TWR) multiplies the returns for each sub-period or holding period, helping to illustrate how returns are compounded over time.
- TWR helps eliminate distortions caused by money inflows and outflows.
A Practical Application: TWR in Action
Scenario 1
Investor 1 invests $1 million into Mutual Fund A on December 31. By August 15 of the next year, their portfolio is valued at $1,162,484. On August 15, they add $100,000 to Mutual Fund A, bringing the total value to $1,262,484. By the end of the year, the portfolio’s value drops to $1,192,328.
The holding-period return for the first period (December 31 to August 15) is:
Return = ($1,162,484 - $1,000,000) / $1,000,000 = 16.25%
The holding-period return for the second period (August 15 to December 31) is:
Return = ($1,192,328 - ($1,162,484 + $100,000)) / ($1,162,484 + $100,000) = -5.56%
The time-weighted return for the two periods is:
Time-weighted return = (1 + 16.25%) × (1 + (-5.56%)) - 1 = 9.79%
Scenario 2
Investor 2 also invests $1 million into Mutual Fund A on December 31. By August 15 of the next year, their portfolio is valued at $1,162,484. On August 15, they withdraw $100,000, bringing the value down to $1,062,484. By year-end, the portfolio’s value decreases to $1,003,440.
The holding-period return for the first period (December 31 to August 15) is:
Return = ($1,162,484 - $1,000,000) / $1,000,000 = 16.25%
The holding-period return for the second period (August 15 to December 31) is:
Return = ($1,003,440 - ($1,162,484 - $100,000)) / ($1,162,484 - $100,000) = -5.56%
The time-weighted return over the two periods is:
Time-weighted return = (1 + 16.25%) × (1 + (-5.56%)) - 1 = 9.79%
Both investors received an identical 9.79% time-weighted return, regardless of adding or withdrawing money. The TWR successfully eliminates the distorting effects of cash flow.
Comparing TWR and Rate of Return (ROR)
A rate of return (ROR) measures the net gain or loss on an investment over a period, expressed as a percentage of the initial cost. While ROR doesn’t account for cash flow differences, TWR does, making it a more insightful measure in scenarios with varying cash flows.
Recognizing the Limitations of TWR
Due to daily cash flow changes, TWR can be cumbersome to manually calculate. Using an online calculator or software is advisable. Another often-used calculation is the money-weighted rate of return.
Conclusion Understanding the time-weighted rate of return is paramount for investors seeking to gauge true portfolio performance and compare investment managers accurately. Thoroughly grasp its calculation and benefits to leverage TWR for your investment decisions.
Related Terms: Rate of Return, Geometric Mean, Internal Rate of Return, Cash Flow, Valuation.
References
- U.S. Securities and Exchange Commission. “Rate of Return”.
