Part 1 –Optimisation
Randomly select 10 stocks out of the sample of US stocksin S&P500 List. Ensure you identify how you randomly selected the stocks.
•Note:include the ‘Symbol’ for each of the selected stocksin the Cover worksheet.
For the sample selected, form an equally-weighted portfolio(Portfolio A)and estimate daily returns for the period 3 Mar 2020 –28 Aug 2020
For the sample selected, usethe Excel add-in Solverto form a portfolio(Portfolio B)which maximises the Sharpe Ratio for the period 3 Mar 2020 –28 Aug 2020, under the constraint that the total portfolio weightisone. Report the portfolio weights and comment on the feasibility of investing according to the weights obtained.
Part 2–Descriptive Analysis
Report daily and annualised descriptive statisticswhichsummarisethe historical return distribution for both, Portfolio A and Portfolio B, as well as any metrics you consider useful to depictthe historical performance of both portfolios.Comment on your findings.
Hints:-You can report both, the pre and post-covid performance of the portfolios and comment on the impact the pandemichashad on your selected stocks and/orthe industries they are in.
Part 3–Hypothesis Testing
Plot histograms to contrast the return distribution of:
1) Portfolio A vs S&P500, and 2) Portfolio B vs S&P500. Comment on your findings.
At 5% significance level, is the mean daily return ofany of these two portfolioshigherthan the mean return of the S&P 500 index? Comment on your findings.
Hints:-Start by properly establishing both the Null and Alternative hypotheses.
-Report the type of test you would use to answer this question.
-Present and interpret your results in terms of p-values.
Part 4–Simple Linear Regression
Estimate historical excess returns for both, Portfolio A and Portfolio B, as well as the S&P500 index.
Createscatterplotsto depict the historical returns of:
1) Portfolio A vs S&P500, and
2) Portfolio B vs S&P500. Comment on the relationshipsobserved.
Using the S&P500 index as the market portfolio, what is the market beta of both, Portfolio A and Portfolio B.Which portfolio is more exposed to Systematic Risk?
Based on these betas, what would be the expected change in the average excess return of both, Portfolio A and Portfolio B, to a 1% increase in the average excess return of the market portfolio?
Part 5–Multivariate Linear Regression
Estimate twoseparate regressions, one for Portfolio A and one for Portfolio B, in which your dependent variable is the daily excess returnsfor each portfolio, and your independent variable is the daily 7-day movingaveragepercentage changein new Covid-19 casesin the US.
Interpret your findings establishing:
a) whether for each Portfoliothe regressor is statistically significant at a 5% significance level; andb) the effect a 1% change in the regressor has in the average excess returns of eachportfolio.
•Do you think there is an underlying economic relationship between the daily percentage change in new Covid-19 cases and the returns of Portfolio A and Portfolio B? If so, what can explain that relationship?
Hints: -Discuss the impact the pandemic has had on your selected stocks and/orthe industries they are in.
Re-estimate the two regressionsabove, and this time include the following independent variables (regressors):
1.The excess returnsfor the S&P500index, and
2.The daily 7-day movingaveragepercentage changein new Covid-19 cases§After including this additional regressor,what can you say about the relationship between the daily percentage change in new Covid-19 cases and the returns of Portfolio A and Portfolio B?