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Question: You have recently joined an investment management team and are tasked by the lead portfolio manager with implementing an investment strategy that follows the Treynor-Black optimization model. The portfolio has a large-cap style focus, investing in listed U.S. equities and benchmarked to the S&P500 total return index. Working with the research analysts in your team, you compile data on a set of companies that meet the screening criteria. The relevant details, based on monthly excess return series, are contained in the accompanying spreadsheet ‘Report 2 – Data.xlsx’. Unless otherwise stated, assume these data represent the appropriate inputs to incorporate into your portfolio optimization and no further adjustments are required. Further, assume that your portfolio has no investment constraints regarding leverage or short-selling. Your deliverable to your portfolio manager is a report that addresses the points listed below. Report structure Assuming the Single Index Model (SIM) appropriately describes security returns and using the given input data, present the following results in a table for the optimal risky portfolio(ORP): The optimal active portfolio weight, The optimal market portfolio weight, The optimal weight of each individual security, The ORP expected risk premium The ORP beta The ORP variance The ORP information ratio The ORP Sharpe ratio Compare the Sharpe ratio for the ORP found in part (1) with the Sharpe ratio for the market portfolio and the Sharpe ratio for the active portfolio. Specifically for the active portfolio, present the following results in a table: The alpha of the active portfolio The beta of the active portfolio The information ratio of the active portfolio Comment on the influence of each statistic in part (3) on the composition of the ORP. How would changes in each of these inputs affect the weight of the active portfolio in the ORP? Determine the covariance matrix and correlation matrix for the stocks in the Information Technology sector, and present the results for each matrix in a separate table. Discuss your results in part (5). What, if anything, does the analysis in part (5) tell us about the appropriateness of the SIM for portfolio construction? What further analysis, if any, should you undertake to assess the appropriateness of the SIM? (Note: discussion only, no calculations required) Conclude with a brief discussion of the benefits and limitations of using the Single Index Model compared to the Markowitz approach to optimal portfolio construction. Alongside your report, you must submit an Excel spreadsheet with your workings and follow all further requirements outlined below. Further requirements Use the Single Index Model approach to determine optimal risky portfolios where directed to find asset weights in the report. It is recommended you review the prescribed textbook chapter reading to assist you with following the Treynor-Black optimization procedure. Written reports must be submitted via the Turnitin link labelled ‘Report 2’.
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