Portfolio Management Assignment on Part I -

The administrators of one pension fund, based in Dallas, have shortlisted the asset management company you work for to manage the US equity portion of their portfolio. Following the recommendations of the consultancy firm AM International Ltd, it has been decided that this specific mandate should be consistent with the latest insights from modern portfolio theory, emphasizing the benefits of benchmark construction. The investment universe is made up of US stocks. The administrators of the pension fund would be inclined to use a strategic benchmark based on efficient indexing.

Your benchmark is the Dow Jones Industrial Average (DJI).

You decide to compare the following strategies:

- The DJI - Equal-weighted strategy

- The DJI - Cap-weighted strategy (weights as of 30/12/2016)

- The Global Minimum Variance (GMV) using a structured matrix of variance covariance (built with the coefficient of correlation method).

- The Diversity Index (with p =0.5) and one, among the two following methods:

- The Max Diversification

- The Equal risk contribution (Risk parity)

1. Compute the allocation weights into the 30 stocks for the 3 strategies (GMV+ Diversity + your choice) using data from January 2015 to December 2016. Find the corresponding stock allocation by minimizing the portfolio variance while making sure to include an effective number of at least 20 stocks in your optimized portfolio. You can also make use of other constraints into the optimizer. Please explain them should you do it or explain why you don't.

2. Compare the contribution to risk of each stock composing the portfolio for these three strategies as well as with the Value-Weighted and Equally-Weighted strategies. Compare also these strategies regarding the effective number of stocks. Provide qualitative insights on the differences across strategies.

3. Assuming that you implement the investment schemes found at step 1 in 2017 (without rebalancing), compare the strategies regarding their risk and performance measures (Period: January 2017 (excluding the data used in step 1) - December 2017).

Compute AND interpret/comment the risk (higher-moments, drawdown, VaR adjusted or not for higher moments - please justify your choice -) and performance statistics (information ratio with regard to Cap-Weighted Index, YTD return, sharpe ratio or any relevant measures of your choice). Hint: the out-of-sample data can be found in the excel file "PM 2018 Assignment Part I - Student - Out-of-sample".

Attachment:- Assignment Files.rar