(a) Data collection: Collect two years of weekly historical prices for 5 ETFs. The data can be collected, for example, from Yahoo Finance. The choice of ETFs is yours; you can get inspiration by searching most popular etfs" or something similar online. Explain how you collected the data (b) Statistics: Calculate the mean weekly return for each ETF, as well as the covariances of the weekly returns between all pairs of ETFs. Present your results, either in an Excel table or in text. Again, please explain how you accomplished the task! (c) Optimisation: By solving a sequence of Markowitz problems, produce a graph that shows the efficient frontier. Present the optimal portfolio composition for three selected portfolios (low return/low risk, medium return/medium risk and high return/high risk). Also plot each of the 5 individual ETFs that you selected in the graph. Provide the Markowitz problem that you used for computing the portfolios! (It can be implemented in Excel, please explain your implementation, however!) Which portfolio would you choose? Justify your answer! (d) Additional constraints: How would you incorporate additional constraints to ensure that you invest at least 10% and at most 35% of your wealth into any single ETF? You do not have to resolve your problem from part (c) a description of the constraint is sufficient. (e) Backtesting: Prior to implementing a portfolio in practice, one would first verify the performance of the portfolio through a procedure called backtesting. Describe how you would implement a backtesting procedure for your portfolio problem! A verbal description is sufficient; you do not need to implement your backtesting procedure. (We assume that you are not familiar with the concept of backtesting; this requires some online research on your behalf (a) Data collection: Collect two years of weekly historical prices for 5 ETFs. The data can be collected, for example, from Yahoo Finance. The choice of ETFs is yours; you can get inspiration by searching most popular etfs" or something similar online. Explain how you collected the data (b) Statistics: Calculate the mean weekly return for each ETF, as well as the covariances of the weekly returns between all pairs of ETFs. Present your results, either in an Excel table or in text. Again, please explain how you accomplished the task! (c) Optimisation: By solving a sequence of Markowitz problems, produce a graph that shows the efficient frontier. Present the optimal portfolio composition for three selected portfolios (low return/low risk, medium return/medium risk and high return/high risk). Also plot each of the 5 individual ETFs that you selected in the graph. Provide the Markowitz problem that you used for computing the portfolios! (It can be implemented in Excel, please explain your implementation, however!) Which portfolio would you choose? Justify your answer! (d) Additional constraints: How would you incorporate additional constraints to ensure that you invest at least 10% and at most 35% of your wealth into any single ETF? You do not have to resolve your problem from part (c) a description of the constraint is sufficient. (e) Backtesting: Prior to implementing a portfolio in practice, one would first verify the performance of the portfolio through a procedure called backtesting. Describe how you would implement a backtesting procedure for your portfolio problem! A verbal description is sufficient; you do not need to implement your backtesting procedure. (We assume that you are not familiar with the concept of backtesting; this requires some online research on your behalf
