Time-weighted return (TWR) calculates the performance of an investment portfolio or fund, taking into account external cash flows. TWR eliminates the distorting effect of cash inflows and outflows that occur in investment funds.
While TWR may not be the simplest calculation, understanding how it works can be beneficial. We will explain how TWR functions and provide examples to illustrate its application.
Understanding Time-Weighted Return (TWR)
Time-weighted return calculates the compound return of a fund by dividing the total investment period into sub-periods, each time cash flows in or out of the fund. This method shows the true market return of a fund over time.
Compare TWR with metrics like the rate of return (RoR), which only considers an investment’s performance based on the initial contribution. While RoR is useful, it cannot account for cash flow movements, making it potentially less reliable over time.
Since TWR considers external cash flows, it serves as a valuable benchmark for comparing a fund’s performance with others. However, due to its complexity, individual investors typically do not rely heavily on this metric.
How TWR Works
Time-weighted return (TWR) calculates the compound growth rate of an investment portfolio, factoring in the impact of cash flows into and out of the portfolio.
To achieve this, the total investment period is divided into sub-periods, with each cash flow event marking the start of a new sub-period.
Calculating Time-Weighted Return
The formula for calculating the cumulative return of the portfolio is as follows:
TWR = [(1 + HP1) × (1 + HP2) ×⋯× (1 + HPn)] − 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
Each sub-period’s TWR must be calculated individually, and then the returns must be linked to determine the total return for the entire period. Unlike a simple savings rate, TWR reflects a portfolio’s performance with compounding.
Example of Time-Weighted Return
To understand how TWR functions, let’s consider an example. Suppose you invest $10,000 in a portfolio on Jan. 1. After three months, the portfolio’s value increases to $10,500.
The return for the first sub-period can be calculated as:
HP1 = ($10,500 - $10,000) / $10,000 = 5%
Suppose you then invest an additional $5,000, bringing the portfolio value to $15,500. Over the next two months, the market struggles, causing the portfolio to decrease 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%
After withdrawing $1,000 from the portfolio, its value becomes $13,500. Subsequently, the market performs well, and the portfolio grows to $16,000 over the next three months.
The return for this sub-period is:
HP3 = (($16,000 – ($14,500 – $1,000)) / ($14,500 – $1,000) = 18.52%
To calculate the total TWR, the returns must be linked as follows:
TWR = (1 + 0.05) x (1 + (-0.0645)) x (1 + 0.1852) – 1 = 16.42%
Therefore, the total TWR for the 8-month period is 16.42%. Despite continuous contributions to the portfolio, the cash flows did not distort the growth rate, providing a more accurate assessment of the portfolio’s performance.
Time-Weighted Return vs. Rate of Return
The key distinction between TWR and rate of return (RoR) lies in whether the impact of cash flow is taken into account. As demonstrated in this article, TWR calculates a portfolio’s return between cash flows and then links these returns. While valuable, this calculation may be too complex for the average investor.
In contrast, RoR is simpler as it calculates the return over a specific period based on the initial investment.
When calculating the Rate of Return (RoR), there is no need for sub-periods. You can simply divide the change in dollars in the portfolio’s balance by the beginning balance to get the RoR.
RoR’s simple calculation can be advantageous if you want to show the impact of the investor’s decision to contribute or withdraw from the portfolio. However, if you don’t want to see the impact of cash flow, RoR may not be the ideal choice.
Ways to utilize 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 doesn’t mean it isn’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.
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Summary
Time-weighted return calculates a portfolio or fund’s performance without the distorting impact of cash flows. This can be useful for comparing the performance of different investment managers or funds. However, individual investors may prefer a simple formula for their own purposes, such as rate of return. Some online brokers may provide TWR automatically to investors, removing the need for manual calculation.