Portfolio Management Assignment
Part I - Student - Out-of-sample"
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".
Part II -
Exercise 1: As the CIO of the IU Foundation, you are responsible for managing and monitoring a $100m dynamic portfolio implementing a CPPI strategy with the following rules:
- Satellite portfolio invested in a fund of high yield bonds
- Core portfolio invested in U.S. Treasuries
Using the data in the sheet "Exercise 1", fill in the blanks in the output data ' CPPI', comparing
- a CPPI strategy whose floor is indexed to the performance of U.S. Treasuries (k = 90%, m = 4),
- a constant mix strategy (40% constantly invested in high yield bonds),
- a buy-and-hold strategy (40% initially invested in high yield bonds),
- U.S. Treasuries.
Draw up the annual report on these portfolio and explain the results obtained over that period (comparing performance and risk incurred).
Exercise 2: You have just won a mandate to actively manage a €100m portfolio on behalf of a family office. Your objective is to outperform the Barclays Capital Euro Aggregate Bond Total Return Index in the long run. From this perspective, your recommendation is to implement a dynamic core-satellite (DCS) strategy. The core portfolio therefore replicates the performance of your benchmark through an index fund while the satellite portfolio should act as a return enhancer with moderate risk. You chose the MSCI Europe Min Volatility Equity Fund as Satellite.
1) Present to your client the benefits of employing a DCS strategy in general
2) The DCS strategy has been implemented over the out-of-sample period ranging from January 2013 to July 2015 using the following parameters: k = 95%, m = 4 (i.e. initial cushion = €5 million, initial investment in the satellite portfolio = €20 million). The floor is indexed to the performance of the benchmark. The guarantee on the relative level of performance is set at: benchmark value - 5. The initial value of the benchmark is equal to 100 to simplify matters. Your portfolio has been rebalanced at the end of each month using the above-mentioned parameters. Plot the graph of the (re)allocation to the satellite portfolio (after rebalancing - graph displayed from row 50 to row 72) with its cumulative outperformance using the file "Exercise 2 DCS Case Study Min Vol. Funds and T-Bonds" furthermore, we assume that the performance of the bond exchanged traded fund in column H perfectly replicates the performance of the benchmark displayed in column J - fill in the yellow cells with formulae.
3) Compute the following risk-return statistics for the DCS portfolio, the benchmark, the satellite, and the static core-satellite portfolio (i.e. buy-and-hold strategy without rebalancing: initial investment in the fund replicating the MSCI Europe Min Volatility index = 20% of the assets under management at the beginning of the out-of-sample period, see columns T, U, V, W):
a. Cumulative return
b. Annualized return
c. Annualized standard deviation of returns
d. Skewness
e. Excess Kurtosis
f. 1-month modified Value-at-Risk (Cornish-Fisher extension with a 99% confidence interval)
4) Compute the conditional tracking errors of your DCS portfolio. Compare the "good" tracking error with the "bad" one. What are your findings?
5) Prepare a performance report/commentary for your client based on these out-of-sample results.
References: Revisiting Core-Satellite Investing, a dynamic model of relative risk management, Amenc, Malaise, and Martellini, The Journal of Portfolio Management, Fall 2004.
Attachment:- Assignment Files.rar