"**Subjects**:Quantitative Methods **Module**:Rates and Returns **Knowledge Points**:Holding Period Return (HPR) **Holding Period Return (HPR) Calculation** The Holding Period Return (HPR) measures the total return earned from holding an asset over a specified period, combining capital gains and income received (if any). The formula to calculate HPR is as follows: \[ \text{HPR} = \frac{(P_1 - P_0) + I}{P_0} \] **Where:** - **\(HPR\)**: Holding Period Return - **\(P_0\)**: Price of the asset at the beginning of the holding period (time \(t = 0\)) - **\(P_1\)**: Price of the asset at the end of the holding period (time \(t = 1\)) - **\(I\)**: Income received from the asset during the holding period (such as dividends or interest) ### Step-by-Step Example 1. **Define Initial and Final Prices**: - Assume you bought a stock for \(P_0 = 100\). - After one year, you sell it for \(P_1 = 120\). 2. **Calculate Income**: - Let's say you receive an income of \(I = 5\) (such as dividends). 3. **Apply the HPR Formula**: \[ \text{HPR} = \frac{(120 - 100) + 5}{100} \] \[ \text{HPR} = \frac{20 + 5}{100} \] \[ \text{HPR} = \frac{25}{100} = 0.25 \] 4. **Convert to Percentage**: To express HPR as a percentage, multiply by 100: \[ \text{HPR} = 0.25 \times 100 = 25\% \] ### Visualization A simple graph could represent the price movement over the holding period, showing the initial price, final price, and income received to illustrate how the HPR is derived. ### Practical Application Understanding HPR is crucial for investors as it helps evaluate the performance of their investments over a specific period, accounting for both price changes and any income generated. This method facilitates better investment decision-making by providing an aggregate view of returns. If you have any more specific scenarios or calculations you'd like to cover, feel free to ask!"

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Welcome to our lesson on Holding Period Return, or HPR. HPR is a fundamental concept in finance that measures the total return earned from holding an asset over a specific period. It combines both capital gains from price changes and any income received during the holding period, such as dividends or interest. The formula is HPR equals P1 minus P0 plus I, all divided by P0, where P0 is the initial price, P1 is the final price, and I is the income received. Now let's break down the HPR calculation into clear steps. First, identify the initial price P0, which is the purchase price of the asset. Second, identify the final price P1, which is the selling price. Third, identify any income received during the holding period, such as dividends. Fourth, calculate the capital gain by subtracting the initial price from the final price. Fifth, add the income to the capital gain. Sixth, divide this total by the initial price to get the HPR as a decimal. Finally, multiply by 100 to express it as a percentage. Let's work through a concrete example. Suppose you bought a stock for 100 dollars and sold it one year later for 120 dollars. During this period, you also received 5 dollars in dividends. Using the HPR formula, we substitute our values: HPR equals 120 minus 100 plus 5, all divided by 100. This gives us 20 plus 5 equals 25, divided by 100, which equals 0.25. Converting to percentage, we multiply by 100 to get 25 percent. This means your total return for the holding period was 25 percent. Let's break down the components of HPR to better understand what contributes to the total return. In our example, the total return of 25 dollars consists of two parts. The capital gain, which is the difference between the final price and initial price, contributes 20 dollars or 80 percent of the total return. The income component, such as dividends, contributes 5 dollars or 20 percent. This pie chart visualization shows how each component contributes to the overall HPR. Understanding these components helps investors analyze the sources of their returns and make informed investment decisions. HPR has many practical applications in finance and investment analysis. It's used for evaluating investment performance, analyzing portfolio returns, comparing different assets, and assessing risk-return relationships. The formula we've learned, HPR equals P1 minus P0 plus I, all divided by P0, is fundamental for making informed investment decisions. As shown in our comparison table, HPR allows investors to easily compare the performance of different assets. Stock A with 25 percent HPR outperforms Stock B at 14 percent and Bond C at 6 percent. Remember that HPR includes both capital gains and income, can be expressed as a decimal or percentage, and is essential for sound investment decision-making.