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R tutorial: The Portfolio Return

Want to learn more? Take the full course at https://learn.datacamp.com/courses/in... at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- Analyzing the portfolio weights reveals the investment bets. The larger the weight of an asset in the portfolio, the more influential it will be in determining the future value of the portfolio. When studying this impact, investors typically do not analyze the change in the investment value in absolute terms, but in relative terms. This leads them to compute simple returns, defined as the change in value over the period, relatively to the initial value. The simple return is thus the final value minus the initial value, divided by the initial value. As an example, suppose the initial value is 100 USD, the final value is 120 USD. Then the return on that investment equals 20%, obtained by taking the difference between 120 and 100 USD and dividing it by 100. In the slide I show you how we can apply this definition for computing portfolio returns. This involves three steps. First, for the initial date, we need to compute the total value invested as the sum of the values of the different investments. Second, for the final date, we have to sum the final values of the individual investments to obtain the final portfolio value. Then, we can compute the portfolio return as the percentage change of the final value compared to the initial value. As an example, let us consider a 2-asset portfolio that invests 200 USD in asset 1 and 300 USD in asset 2. The end value is 180 and 330 USD. If we sum the values, we find that the total initial value of the portfolio is 500 USD, while the total final value is 510 USD. It follows that the simple return on the portfolio is the 10 USD change in value, divided by the initial 500USD invested, which gives us a return of 2%. A disadvantage of this calculation method is that it does not show how the portfolio weights determine the portfolio return. Let us, therefore, consider a different formula, in which the portfolio return is computed as the weighted average of the returns of the underlying assets. Its calculation proceeds also in three steps. First, the initial weights of the positions are computed. Secondly, the return on each of the individual positions is determined. Then, in the third step, the portfolio return is computed as the sum over the products between the initial weights and the corresponding returns. In the slide you see how to apply this formula to compute the return for our example portfolio with two assets. We first compute the initial portfolio weights. Since the initial value of the first asset is 200 USD and the total value invested is 500USD, the initial weight of asset 1 is 40%. The remainder of 60% is the weight of asset 2. Then, in a second step, we need to compute the returns for each of the assets. For asset 1, we obtain that the individual return is -10%, while for asset 2, the return is +10%. Finally, we can combine those results and compute the portfolio return by summing over the weights multiplied by their respective returns. The first term is the weight of 40% times the returns of -10%, which gives us -4%. The second term is the weight of asset 2, 60% times its return of 10%, which gives us +6%. Adding -4% and +6% give us a portfolio return of 2%, which is exactly the same number as obtained before. The next interactive exercises put this theory into practice. #DataCamp #RTutorial #PortfolioAnalysisinR