Your task is to form optimal portfolios under various conditions, and then compare and contrast their relative

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Your task is to form optimal portfolios under various conditions, and then compare and contrast their relative performance. (Write code in R)

• Estimation Window: 2010-2019
• Evaluation Window / holding period: Q1 2020
• Return Frequency: monthly
• Objective Function: Maximum Sharpe Ratio
• Investable Universe: Your choice of 100 of the SP500 constituents
• Benchmark: SP500
• Constraints: Long only, fully invested

(a)Describe how you trimmed the investable universe down to 100 assets. Note: you do not need to show any code for this part of the analysis, but I do want a complete articulation of your logic.

(b)Statistically describe your data. Do so for the full sample, as well as the estimation and evaluation windows.

(c)Backward Looking: Form an optimal portfolio using historical averages for future returns and (co)variances. Describe your portfolio's composition (e.g. weights relative to the benchmark). Describe your portfolio's risk and return. Discuss your portfolio's exposure to the Fama French 5 factors.

(d)Forward Looking: Your task is to outperform the backward looking portfolio. You must use the same objective function and constraints as the Backward Looking portfolio. However, you should forecast the returns. You may use any realistic forecasting technique. If you like, you may further trim your investable universe. Compare and contrast the composition, risk, and return of the Backward Looking and Forward Looking portfolios.

(e)Best Ideas: Get creative and attempt to improve either the Backward Looking or the Forward Looking portfolios. You may deploy multiple types of improvements (e.g. rebalancing, constraints, other forecasting techniques, different objectives, etc..). However, focus on improving either the Backward Looking or the Forward Looking. Extra points will not be awarded if you attempt to improve both.