Time-Weighted Return (TWR) is a method of calculating the compound rate of growth in a portfolio by adjusting for the impact of cash inflows and outflows. Unlike other performance metrics that might be affected by the timing and size of contributions or withdrawals, such as the Money-Weighted Return (MWR), TWR aims to provide an accurate measure of an investment’s performance that is purely reflective of the asset manager’s decisions. This makes it a preferred metric for evaluating the performance of investment funds, advisors, and portfolio managers.
How is Time-Weighted Return Calculated?
The TWR calculation involves breaking down a time period into sub-periods where each sub-period ends at a time when a cash flow occurs. The return for each sub-period is calculated independently, and then these sub-period returns are geometrically linked together to give a cumulative performance metric.
The basic steps to calculate TWR are:
- Divide the investment period into sub-periods at each point a cash flow (investment or withdrawal) occurs.
- Calculate the return for each sub-period using the formula:
$$ R_i = \frac{V_{i+1} - V_i - CF_i}{V_i} $$where \(V_i\) is the portfolio value at the beginning of the sub-period, \(V_{i+1}\) is the portfolio value at the end of the sub-period, and \(CF_i\) is the net cash flow during that sub-period.
- Geometrically link the sub-period returns to calculate the overall TWR:
$$ TWR = \left(\prod_{i=1}^{n} (1 + R_i)\right) - 1 $$where \(R_i\) are the returns of each sub-period and \(n\) is the total number of sub-periods.
Applications and Significance of Time-Weighted Return
Performance Measurement
TWR is crucial for assessing the performance of portfolio managers and investment funds as it provides a return metric that is not influenced by the timing and size of external cash flows, hence purely reflecting the manager’s investment skill.
Comparison Across Portfolios
Since it eliminates the effects of cash flows, TWR allows for a fair comparison of performance across different portfolios, regardless of their size or the timing of investments and withdrawals.
Historical Context and Development
The concept of TWR was developed to address the shortcomings of traditional performance metrics like the Arithmetic Mean Return and the Money-Weighted Return, which could be heavily influenced by investor behavior (cash flows) rather than the actual performance of the investments.
FAQs
Why is TWR preferred over MWR for evaluating fund managers?
Can TWR be negative?
Is TWR useful for individual investors?
Related Terms
- Money-Weighted Return (MWR): Considers the timing and amount of cash flows, providing a return metric that is unique to the individual investor’s experience.
- Internal Rate of Return (IRR): The discount rate that makes the net present value of all cash flows (both inflows and outflows) from a particular project equal to zero.
- Horizon Analysis: Looks at investment performance over a specific horizon, often used for performance projections.
Summary
Time-Weighted Return (TWR) is a robust metric for measuring investment performance, particularly useful for evaluating fund managers and comparing across different investment portfolios. By eliminating the effects of external cash flows, it provides a pure indication of the value added by the investment strategies employed.
References
- CFA Institute. (n.d.). “Time-Weighted Rate of Return (TWRR)”. Accessed online at CFA Institute.
- Bodie, Z., Kane, A., & Marcus, A. J. (2014). “Investments”. McGraw-Hill Education.
By mastering the calculation and interpretation of TWR, investors and analysts can gain deep insights into the true performance of their investment endeavors.
