ZZBU8701 Project 2 Markowitz and SIM-Based Portfolio Optimization

PART B: 10 STOCK MARKOWITZ AND SIM-BASED

OPTIMISATION

B1 Allocated Stocks – 10 Stock Portfolio
Now, please add the following 5 stocks to your portfolio: (vi) HD-US, (vii) IBM-US, (viii) JPM-US, (ix) WMT-US (x) CVX-US. You should now have 10 stocks in your portfolio with no duplicates.

B2 Data Download and Basic Portfolio Statistics
▪ For the period from January 2014 through December 2018, download from FactSet the monthly returns (inclusive of dividends) for each of the 5 new stocks that you have been assigned above (60 observations). Combine this new data with the data you have downloaded for your previously allocated 5 stocks so that you have a spreadsheet covering 10 stocks.
▪ For the period from January 2014 through December 2018, download from FactSet the monthly returns for the S&P 500 Index (FactSet identifier: SP50) (60 observations).
▪ All returns should be total returns inclusive of dividends - in the FactSet dropdown box "Total Return" select "% Return.". For the S&P500 "Total Return", select "% Return (Gross, Unhedged)"
▪ Compute the annualised average return, standard deviation and variance for each stock.
▪ Compute the annualised average return, standard deviation and variance for the S&P 500.

B3 Markowitz Portfolio Optimisation 10 Stocks
B3.1 Global Minimum Variance Portfolio Under Markowitz
▪ Derive the 10-stock sample variance-covariance matrix using any method demonstrated in Part A.
▪ For the portfolio without any position-size constraints (long/short portfolio), identify the Global Minimum Variance Portfolio (GMVP). What is its ...
QB1. ... annualised expected return?
QB2. ... annualised standard deviation?
▪ For the portfolio with the constraint that no stock can be shorted (long only portfolio), identify the Global Minimum Variance Portfolio (GMVP). What is its ...

QB3. ... annualised expected return?
QB4. ... annualised standard deviation?
▪ For the portfolio without any position-size constraints only, derive the Minimum Variance Frontier for all target annualised expected returns between 0% and 30% in increments of 10%. Discard any portfolio that is inefficient (returns below the GMVP).
QB5. Plot the Efficient Frontier, clearly label it, and include it in your submission for Question 21. B3.2 Optimal Risky Portfolio P* Under Markowitz
▪ For the portfolio without any position-size constraints (long/short portfolio), identify the
Optimal Risky Portfolio (P*). What is its ...
QB6. ... annualised expected return?
QB7. ... annualised standard deviation?
▪ For the portfolio with the constraint that no stock can be shorted (long only portfolio), identify
the Optimal Risky Portfolio (P*). What is its ...
QB8. ... annualised expected return?
QB9. ... annualised standard deviation?
QB10. For the portfolio without any position-size constraints only, plot the Capital Allocation
Line (CAL) showing where it intersects the y-axis and the efficient frontier, and include it
in your submission for Question 21.

B4 Single Index Model (SIM) Portfolio Optimisation 10 Stocks
B4.1 Derive Excess Returns
▪ For each stock in your portfolio, calculate monthly excess return: Rit = rit − rf where rit is the

return on stock i for month t, and rf is the risk-free rate. (Make sure you use the fixed monthly risk- free rate). Compute the annualised average excess return for each stock in your portfolio over the

sample period.
▪ For the S&P 500 index, calculate monthly excess return: RMt = rMt − rf where, rMt is the return on the S&P 500 for month t. Compute the annualised average excess return for the S&P 500 over the sample period.

B4.2 Single Index Model (SIM) Regression
▪ Estimate the SIM beta βi

, for each stock in your portfolio using the regression equation:
Rit = αi + βiRMt + εit
QB11. What was the highest beta out of your 10 stocks?
QB12. What was the lowest beta out of your 10 stocks (including negative values)?
B4.3 SIM Variance-Covariance Matrix
▪ Calculate the variance-covariance matrix for your 10-stock portfolio using these SIM estimates.
▪ For the matrix diagonal, simply use the individual variances for each stock σi
2 derived in B2.
▪ For the off-diagonal covariances, assume no residual covariance between stocks (the standard assumption of the SIM), and apply the following equation:
Cov(ri , rj) = βi βj σM
2
for all i, j,....n = 10 stocks
B4.4 Global Minimum Variance Portfolio and Optimal Risky Portfolio Under SIM
▪ Use the (already annualised) sample variance-covariance matrix derived in B4.3 for all SIM optimisations.
▪ For the portfolio without any position-size constraints (long/short portfolio), identify the Global Minimum Variance Portfolio (GMVP) under the SIM. What is its ...
QB13. ... annualised expected return?
QB14. ... annualised standard deviation?
▪ For the portfolio with the constraint that no stock can be shorted (long only portfolio), identify the Global Minimum Variance Portfolio (GMVP) under the SIM. What is its ...
QB15. ... annualised expected return?
QB16. ... annualised standard deviation?

▪ For the portfolio without any position-size constraints (long/short portfolio), identify the Optimal Risky Portfolio (P*) under the SIM. What is its ...
QB17. ... annualised expected return?
QB18. ... annualised standard deviation?
▪ For the portfolio with the constraint that no stock can be shorted (long only portfolio), identify the Optimal Risky Portfolio (P*) under the SIM. What is its ...
QB19. ... annualised expected return?
QB20. ... annualised standard deviation?
QB21. Submit your Excel spreadsheet through the Moodle Assignment link (marked on Moodle as “Project 2 Excel Submission”) with your graphs for B5 and B10 well labelled.