Application

1. Real world example

In the fourth and final chapter of the course, you will apply what you have learned in the first 3 chapters to solve a problem that mimics a real world example.

2. Real world example

You will walk through each step of the problem where you specify a portfolio, run the optimization with periodic rebalancing, analyze the output of the optimization, and make refinements in an effort to improve the risk adjusted performance of the portfolio. You will assume the role of an analyst that is tasked with constructing a portfolio of hedge fund strategies with different style definitions. The exercises in this chapter will walk you through the portfolio construction and historical performance analysis. The dataset you will use in the exercise is monthly returns from January 1997 to March 2016 of the EDHEC-Risk Alternative Indexes. While you cannot directly invest in this index, it was chosen to represent investing in hedge funds with different styles. This problem is very similar to the types of projects that an analyst or portfolio manager at a fund of funds or large bank would be involved in.

3. Benchmark

Defining a benchmark is important for accurately measuring the relative performance of your portfolio. For example, if the universe of assets for the portfolio is US Equity Large Capitalization stocks, then a very reasonable choice of a benchmark is the S&P 500. It is also common for the benchmark to be set based on the fund mandate. However, there may be cases where no publicly available benchmark exists that is reasonable for your portfolio problem and it is valuable to have the ability to construct your own custom benchmark. The example in this slide creates an equal weight benchmark of the first 4 columns in the indexes dataset. The first four columns of the dataset represent the returns of US Bonds, US Equities, International Equities, and Commodities. A reasonable approach for the custom benchmark is equal weighting with annual rebalancing. The intuition for equal weighting is that you have no preference for any of the assets in the universe, so you assign each of them an equal weight. You can then calculate performance measures such as annualized return and annualized standard deviation of your custom benchmark.

4. Base portfolio definition

You will start with a very simple approach for defining the optimization problem with the base portfolio specification, then hypothesize ways to improve the risk adjusted performance of the portfolio by refining constraints, objectives, and moment estimates in later exercises. The base portfolio specification is to minimize portfolio standard deviation subject to full investment and long only constraints. In this slide, you can see that a portfolio specification is created using the returns data defined in the previous slide with full investment and long only constraints and an objective to minimize portfolio standard deviation. In the coming exercises, you will run an optimization with periodic rebalancing to get historical performance of the base portfolio. Setting rebalancing parameters depends on the specific problem and available data.

5. Let's practice!

Let's move on to the exercises and start on the application problem.

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