"**Subjects**:Quantitative Methods **Module**:Rates and Returns **Knowledge Points**:Money-weighted vs time-weighted return **Subjects**: Quantitative Methods **Module**: Rates and Returns **Knowledge Points**: Money-Weighted Return, Time-Weighted Return **Calculation Methods and Differences Between Money-Weighted Return and Time-Weighted Return** ### Money-Weighted Return (MWR) **Definition**: The Money-Weighted Return (MWR), often referred to as the Internal Rate of Return (IRR), considers the timing and size of cash flows in and out of the investment. It reflects the rate of return the investor actually earned based on the amount of money invested over time. **Calculation Method**: To compute MWR, you identify the cash flows and use the following equation to find the rate \( r \) that equates the present value of cash inflows to the present value of cash outflows, resulting in a net present value (NPV) of zero: \[ \sum \frac{C_t}{(1 + r)^t} = 0 \] **Where:** - \( C_t \): Cash flows at time \( t \) (positive for inflows, negative for outflows) - \( r \): Money-weighted return - \( t \): Time period You can use financial calculators or software to compute IRR easily. --- ### Time-Weighted Return (TWR) **Definition**: The Time-Weighted Return (TWR) measures the compound growth rate of an investment portfolio, removing the impact of cash flows. It is designed to evaluate the performance of the investment manager, independent of the timing and size of deposits or withdrawals by investors. **Calculation Method**: To calculate TWR, follow these steps: 1. **Break down the total period into sub-periods** based on cash flows. 2. **Calculate the return for each sub-period** using the formula: \[ R_i = \frac{(V_{i+1} - V_i + CF_i)}{V_i} \] Where: - \( R_i \): Return for period \( i \) - \( V_i \): Portfolio value at the beginning of period \( i \) - \( V_{i+1} \): Portfolio value at the end of period \( i \) - \( CF_i \): Cash flows during period \( i \) 3. **Chain the results** of the sub-period returns to find the overall TWR: \[ (1 + TWR) = (1 + R_1) \times (1 + R_2) \times ... \times (1 + R_n) \] Subtracting one gives the TWR. --- ### Key Differences | **Aspect** | **Money-Weighted Return (MWR)** | **Time-Weighted Return (TWR)** | |-------------------------------|-------------------------------------------------------|------------------------------------------------------| | **Cash Flow Sensitivity** | Sensitive, affected by timing/size of cash flows | Not sensitive, isolates investment performance | | **Purpose** | Evaluates the investor's actual earned return | Measures manager's skill in investment management | | **Calculation Complexity** | Requires solving for IRR, often more complex | Straightforward chaining of sub-period returns | | **Impact of Contributions** | Significant impact from contributions/withdrawals | Contributions/withdrawals have no impact on TWR | ### Practical Example - **MWR**: If an investor makes a significant contribution just before a strong market upswing, the MWR will reflect that higher return. - **TWR**: If the portfolio manager structured the investments well, achieving solid growth irrespective of cash flows, the TWR will highlight that performance without being biased by the timing of those flows. Understanding these two methods is essential for evaluating investment performance and making informed investment decisions. If you have any further questions, feel free to ask!"

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