Portfolio Management Project
You have been given $1,000,000 to invest. The aim of this case study is to apply the portfolio management theory to real data.
Main steps in the case study:
- Data collection and basic statistics calculation
- Portfolio construction
- Portfolio evaluation
The portfolio settings:
- Portfolio will be created with the closing prices as on 31/12/2015.
- First portfolio performance evaluation will be 30/06/2016.
- Second and final portfolio evaluation will be 31/12/2016.
- Portfolio currency is USD (or EUR if you prefer) - you can invest in foreign stocks and other instruments yet at the portfolio construction date and the evaluation dates you must recalculate the value of the position back into USD (or EUR) (you will need to find the exchange rates)
- Good place to find data is finance.yahoo.com
- You must choose minimum of 8 stocks and maximum of 12 - for the sake of diversification each stock must be from different industry
- You can propose other asset classes like commodities (have in mind that you have to find daily data for these assets)
- Find the appropriate risk free asset (American T-Bills or EUR short term risk free instruments - take 3% (the historical average)
- Try to estimate your risk aversion coefficient
If you decide that you are rather risk averse investor assume A=5 (risk aversion coefficient of 5-8), moderate risk aversion A=3 (risk aversion coefficient of 2-5), very low risk aversion - take A = 1, risk neutral A=0 / risk loving investor assume A=-1.
The final document should present the results of the analysis of the following steps:
Step 1: Data preparation
- Analyze the companies you want to consider in your portfolio (please check the rules mentioned before)
- Prepare short summary about the companies you will invest in
- Find the daily data for each stock (at least two years of data before the portfolio construction date of 31/12/2015, max of five years of the daily observations) - if you take shares quoted on different stock markets you will have to control for holidays and days when different stock markets are closed. The final aim is to have equal time series for the daily quotations of your stock prices.
- For each stock calculate the daily return and based on these returns calculate the average daily return and the standard deviation of the stock return (this will be your input in the portfolio construction) - comment on the results
- Since we are working with the annual returns we need to annualize the results you have obtained in the previous step - you should multiply the daily average return you have obtained in the previous step by 250 (approx. number of trading days over a year) and the daily standard deviation by sqrt(250) as we discussed in the class.
- For foreign stocks you can calculate the returns in the local currency but check also the statistical properties of the exchange rate and comment on the results
- Calculate the matrix of correlations of the daily stock returns (this is why you need to have equal time series for all the stocks) - comment on the results.
- Finally, you have to get the "full" (not just below-diagonal matrix that offers Excel) variance-covariance matrix of returns - use the correlation matrix and annual standard deviation to get this full variance-covariance matrix
- Please check the file "Data master file" posted in the class Key Portfolio Concepts
Step 2: Portfolio construction
With the input data prepared - you should have the estimates of the expected return and covariance matrix, please derive the efficient frontier for the portfolio composed of the risky assets you have previously selected.
Find the optimal risky portfolio y depending on your risk aversion score define the final optimal portfolio that will consist of the risky portfolio and risk free asset. This portfolio will be one of the portfolios we will evaluate at the end of the year and at the end of May.
You have to set up the second portfolio with weights as you wish with the only constraints that one share cannot have a weight larger than 25% in your portfolio (so at least 4 shares in this portfolio)
For each of these portfolios describe:
1. the weights of each asset in the portfolio
2. the amount of the initial capital invested in this asset
3. number of shares of each stock you will buy and the amount of remaining money invested in the risk free asset (remember that you can only buy X shares (integer number)) and that the initial capital is limited to $1,000,000
4. if you invest in foreign assets remember that you need to recalculate the amount in dollars
At the end of this step you should have clearly defined two portfolios - how many shares of each stock you are going to buy and the amount invested in the risk free asset.
Step 3: Portfolio evaluation - June 2016
Evaluate your portfolio as on 30/06/2016 - you need to find prices for each stock and multiply the number of shares in your portfolio by these prices - this should give you the current value of your portfolio (evaluate both portfolio you have constructed).
Now you have the opportunity to change the composition of your portfolio - you can buy additional shares, sell stock or invest in new companies. Trading is not costless - assume the flat fee of $8.95 per trade - for any buy or sell order (recent trend in the industry). Subtract the sum of the commissions from the value of your risk free investment.
Step 4: Portfolio evaluation - December 2016
Evaluate your portfolio as on 31/12/2016 - you need to find prices for each stock and multiply the number of shares in your portfolio by these prices - this should give you the current value of your portfolio (evaluate both portfolio you have constructed).
This will be the final step in the portfolio management case study.
Step 5: Final report
Prepare the written report about your investment portfolios, investment decision and the performance (please give me a printed copy of this report).
Prepare the final presentation to your colleagues in the class - max 10 minutes 5 slides:
1. discuss the companies you are going to consider in your portfolio construction step (why have you chosen them), discuss the statistical properties of the rate of return - mean, standard deviation, correlation matrix)
2. Composition of two portfolios as on 31/12/2015 - the optimal portfolio you have obtained taking into account you risk aversion score and the second "as you wish" portfolio.
3. Discuss the portfolios' performance as on 30/06/2016 (and any changes in the composition of the portfolios) and on 31/12/2016. What is the final amount of money your initial $1,000,000 has changed into?
4. All the comments and remarks.
Calculations and report of about 200-300 words.