Please explain the Money-weighted and time-weighted return in CFA Level 1 in plain and simple language, with concise and intuitive visuals. Center and enlarge the content, add some animation effects to fill the screen completely without leaving too much blank space. Highlight key points with bright colors, ensure no typographical overlaps in the content, and maintain a complete structure (from the definition of the knowledge point to the summary, with intermediate content progressing step by step).

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Welcome to understanding investment returns! When you invest money, you want to measure how well your investments are performing. This becomes especially important when you add or withdraw money at different times. In CFA Level 1, we focus on two main methods for measuring investment performance: Money-Weighted Return and Time-Weighted Return. Let's explore these concepts step by step. Money-Weighted Return, or MWR, is like your personal Internal Rate of Return on an investment. It's the discount rate that makes the present value of all cash inflows equal to all cash outflows. The key characteristic of MWR is that it considers both the performance of the investment and the timing and size of your cash flows. This means MWR is heavily influenced by when large sums of money are invested. If you invest a lot just before good performance, your MWR looks high. If you invest a lot before bad performance, your MWR looks low. Time-Weighted Return, or TWR, measures the compounded growth rate of one dollar invested in the portfolio over the entire period. It works by breaking the total investment period into sub-periods based on when cash flows occur. For each sub-period, it calculates the return, then links or compounds these sub-period returns together. The key advantage of TWR is that it removes the impact of cash flows. This shows you how the investment strategy performed, regardless of when money was added or withdrawn. This makes TWR the standard method for comparing investment managers. Now let's compare MWR and TWR with their key differences. MWR is heavily influenced by cash flows, while TWR removes their impact completely. MWR measures the investor's actual return like an IRR, while TWR measures the investment's pure performance. MWR is used when investors control cash flows, while TWR is the standard for comparing managers. Here's a simple scenario: You invest 100 dollars, it grows 50% to 150. You add 100 dollars for a total of 250. Then the investment drops 50% to 125. MWR will likely be negative because you invested a large sum right before bad performance. TWR calculates each period separately and links them, showing negative 25% as the pure investment performance. To summarize, MWR equals your personal return, affected by when you add or remove money, similar to an IRR calculation. TWR equals the investment's return, not affected by your cash flows, and is the standard method for comparing investment managers. Understanding these two concepts is crucial for CFA Level 1, as they represent different perspectives on investment performance measurement. MWR focuses on the investor's experience, while TWR focuses on the pure investment strategy performance. Remember, both have their place in investment analysis depending on what question you're trying to answer.