How to Calculate Time-Weighted Return (TWR)

Time-Weighted Return (TWR) provides a standardized measure of investment portfolio performance. Financial professionals widely use it to evaluate investment strategies, independent of an investor’s cash contributions or withdrawals. By removing the influence of external cash flows, TWR allows for a fair comparison of investment managers. This method focuses on the portfolio’s compound growth rate, reflecting performance attributable solely to investment decisions.

Understanding Essential Components

Calculating Time-Weighted Return requires specific data points and an understanding of how cash flows influence measurement periods. The process begins with gathering accurate information about the portfolio’s value over time and any cash movements. This foundational data is necessary for subsequent calculations.

Initial Portfolio Value refers to the market value of the investment portfolio at the beginning of the measurement period. Final Portfolio Value is the market value of the portfolio at the end of the period being analyzed. Both values are snapshots of the portfolio’s worth at specific moments.

Cash flows are movements of money into or out of the investment portfolio. Deposits are inflows, and withdrawals are outflows. For accurate TWR calculation, record the precise date and amount of each cash flow. This timing detail is crucial because TWR isolates performance from the impact of these flows.

The concept of sub-periods is central to Time-Weighted Return. The overall measurement period divides into smaller intervals, with each cash flow event marking the boundary between sub-periods. A new sub-period begins immediately after any deposit or withdrawal. This segmentation ensures that performance within each sub-period is measured without cash flow distortion, reflecting only the market’s impact on existing capital.

Performing the Calculation Steps

With data gathered and sub-periods identified, the next phase involves calculating the Time-Weighted Return. This systematic process ensures each performance segment is accurately measured and geometrically linked to provide an overall return. The calculation neutralizes the influence of external cash flows on reported performance.

The first step is to calculate the return for each individual sub-period. For Time-Weighted Return, sub-periods are defined such that any cash flows occur at the very beginning or end of these periods, serving as boundaries. Therefore, within any given sub-period, there are no cash flows to consider. The sub-period return calculation simplifies to: (Ending Value – Beginning Value) / Beginning Value. This formula applies because the cash flow has either just occurred or is about to occur, adjusting the portfolio’s value for the next period.

Once each sub-period return is determined, the second step involves geometrically linking these individual returns. This compounding process yields the overall Time-Weighted Return for the entire measurement period. Geometrical linking ensures compounding is accurately captured across all sub-periods, reflecting the portfolio’s growth. The formula for linking is: [(1 + Return\_Subperiod1) \ (1 + Return\_Subperiod2) \ … \ (1 + Return\_SubperiodN)] – 1. This method chains together each segment’s performance, irrespective of varying capital amounts due to deposits or withdrawals.

This linking process treats each sub-period as an independent investment, allowing a pure measure of the investment strategy’s effectiveness. By compounding returns, TWR reflects how an initial dollar would have grown if invested throughout the entire period, unaffected by investor-initiated capital changes. This approach ensures the final calculated return is a standardized metric, suitable for comparing investment performance across different portfolios or managers, regardless of their cash flow patterns.

Applying the Calculation with an Example

To illustrate the Time-Weighted Return calculation, consider a portfolio over a nine-month period. The initial portfolio value on January 1 is $100,000. On March 31, the portfolio value has grown to $105,000, and a deposit of $20,000 is made on that same day. By June 30, the portfolio reaches $130,000, and a withdrawal of $10,000 occurs. Finally, on September 30, the portfolio’s value is $128,000.

The first step is to identify the distinct sub-periods based on the cash flow events. The initial period runs from January 1 to March 31. The deposit on March 31 marks the end of the first sub-period and the beginning of the second. The second sub-period extends from March 31 to June 30, with the withdrawal on June 30 ending this period and starting the third. The third and final sub-period spans from June 30 to September 30.

Next, calculate the return for each sub-period. For the first sub-period (January 1 to March 31), the beginning value is $100,000 and the ending value is $105,000. Since no cash flow occurred within this specific sub-period, the return is ($105,000 – $100,000) / $100,000, which equals 0.05, or 5%.

For the second sub-period (March 31 to June 30), the starting value needs to reflect the deposit. The portfolio value after the March 31 deposit is $105,000 (value before deposit) + $20,000 (deposit) = $125,000. The ending value for this sub-period is $130,000. The return is ($130,000 – $125,000) / $125,000, resulting in 0.04, or 4%.

For the third sub-period (June 30 to September 30), the beginning value must account for the withdrawal. The portfolio value immediately after the withdrawal on June 30 is $130,000 (value before withdrawal) – $10,000 (withdrawal) = $120,000. The ending value for this sub-period is $128,000. The return is ($128,000 – $120,000) / $120,000, which calculates to approximately 0.066667, or 6.67%.

Finally, link these sub-period returns geometrically to determine the overall Time-Weighted Return. Using the formula [(1 + Return\_Subperiod1) \ (1 + Return\_Subperiod2) \ (1 + Return\_SubperiodN)] – 1, the calculation becomes [(1 + 0.05) \ (1 + 0.04) \ (1 + 0.066667)] – 1. This simplifies to [1.05 \ 1.04 \ 1.066667] – 1, which is [1.1592] – 1, resulting in an overall Time-Weighted Return of 0.1592, or 15.92%. This final percentage represents the portfolio’s compound growth over the nine months, isolated from the timing and magnitude of the investor’s cash movements.