Please explain the Average return（Arithmetic,Geometric,Harmonic mean 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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Understanding different ways to calculate average return is crucial in finance, especially in CFA Level 1. The three main types are Arithmetic, Geometric, and Harmonic means, each used for specific situations to represent investment performance accurately. Let's break down how we measure average investment returns. It's not always a simple average! Imagine your investment goes up 50% one year, then down 50% the next. Simple average gives zero percent, but did you actually end up with the same money? No! This shows why the type of average matters. The Arithmetic Mean Return is the most basic average. You simply sum up all the returns and divide by the number of periods. For example, if you have returns of 10%, negative 5%, 15%, and 8% over four periods, you add them up to get 28%, then divide by 4 to get 7%. This method is useful for estimating the average return you might expect in a single future period. However, it tends to overstate the actual growth of an investment over multiple periods because it doesn't account for compounding effects. The Geometric Mean Return accounts for compounding effects. It tells you the average compounded rate of return per period. Using the same example with returns of 10%, negative 5%, 15%, and 8%, we multiply one plus each return: 1.10 times 0.95 times 1.15 times 1.08, which equals 1.2789. Then we take the fourth root and subtract 1, giving us 6.33%. Notice this is lower than the arithmetic mean of 7%. The geometric mean represents the actual average annual return achieved, considering how returns build on each other through compounding. The Harmonic Mean Return is a specialized average often used for rates or ratios when the amount invested changes over time. It's most commonly seen in Dollar-Cost Averaging scenarios. For example, if you invest $100 monthly and stock prices are $10, $5, $20, and $8, you buy different numbers of shares each month. The harmonic mean of these prices gives you $8.42, which better reflects your actual average cost per share compared to the arithmetic mean of $10.75. This is because the harmonic mean gives more weight to lower prices when you're buying more shares. Let's summarize the three types of average returns. The Arithmetic Mean gives you the average return per period and is good for forecasting single future periods, but it overstates long-term growth. The Geometric Mean represents the actual compounded return over multiple periods and shows true historical growth. The Harmonic Mean is specialized for rates and ratios, particularly in dollar-cost averaging. There's a general relationship: Arithmetic Mean is greater than or equal to Geometric Mean, which is greater than or equal to Harmonic Mean. Choosing the right average depends entirely on what question you're trying to answer about investment performance. Remember, the choice significantly impacts your analysis and decision-making!