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FIN3500: Financial Modeling, Final Project Page 1 of 3 FIN 3500: Financial Modeling – Spring 2020 – Final Project Instructions: - This is an open book, open notes project. You are allowed to use any approved class- related materials to answer the questions, and you can go online to search for things. YOU CANNOT consult with each other or receive help from another person. - Download the R script template for this project from Canvas. When you are done, save the project script under your own name (for example John_Smith.R). You will upload this file on Canvas, or if any issue arises, you can email it to me before the due date and time. I will not accept any late submissions! - For every question, there are multiple ways to get to the right answer. I do not care which path you take if you provide the correct answer. MAKE SURE YOU ALSO TYPE IN THE ANSWER FOR EACH QUESTION IN THE PLACE PROVIDED IN THE R SCRIPT TEMPLATE (IF APPLICABLE)!!!! - Neatness counts!!! Make your final product easy to read and more self-explicable, and you will probably get a better grade! Make your code as efficient as possible (do not include additional lines that are not needed). - You have 24 hours to finish this project. Honor Code: By agreeing to work on this, you implicitly confirm that you did not give or receive aid for this project. For violating this honor code, you understand that you will be assigned an F for the course and be placed on probation or suspended until the final resolution of the case. GOOD LUCK!!!! FIN3500: Financial Modeling, Final Project Page 2 of 3 PART 1: Portfolio Optimization You have decided to form a portfolio of five stocks: Duke Energy Corporation (DUK), Goldman Sachs Group Inc. (GS), Costco Corporation (COST), Texas Instruments (TXN), and Starbucks Corporation (SBUX). Use stock prices from May 31st, 2015 to May 31st, 2020 to answer the following questions. 1.1. What was the minimum of the daily adjusted prices for Costco in the whole period? 1.2. What was the average monthly return for Texas Instruments over the whole period? 1.3. If you are a risk averse investor and would like to have an efficient portfolio with the lowest risk possible by going long in stocks, what percentage of your money should you invest in Duke Energy Corporation? (use monthly returns). 1.4. How much return is the portfolio constructed above expected to earn per year? What is the portfolio’s annual risk? 1.5. If you would like to construct a portfolio with the highest Sharpe Ratio by going long in stocks, what percentage of your money should you invest in Costco, assuming that the monthly risk-free rate is 0.2%? 1.6. If you are ok with shorting stocks, and would like to construct an efficient portfolio with a target annual return of 18%, which stocks do you need to sell short? Assume the monthly risk-free rate continues to be 0.2%. 1.7. If you would like to invest at least 5% in each stock, and no more than 30% in each stock, and exactly 60% in the group consisting of Duke Energy, Texas Instruments, and Starbucks, and at least 30% in the group consisting of Goldman Sachs and Costco, how much of your money (percentage-wise) should you invest in Texas Instruments in order to have an efficient portfolio with the lowest risk? (reset your portfolio specifications to the default values for this problem). 1.8. What is the monthly risk and return for your optimum (highest Sharpe Ratio) investment strategy if you want to only hold long positions? What if you are willing to short sell? • Compute the risk and return for each. Put them all in the same matrix (dataset) and discuss pros and cons. 1.9. Assume you are now dealing with the following restrictions (1) you want to have no more than 40% and no less than 20% in the group formed by Costco and Starbucks and (2) you want to have no less than 5% in each stock (only long positions). What is the minimum annual risk you can achieve under these constraints? Assuming that you are not constrained to minimizing risk, what is the annual risk of the optimal portfolio you can achieve (highest Sharpe ratio)? • Compute weights for each strategy and provide side-by-side pie charts of these weights in each case. Make sure your charts have appropriate titles. Discuss. 1.10. Considering the same restrictions as described in part 1.9 above, provide a bar plot of the weights corresponding to the portfolios on the efficient frontier set. Make sure your plot has an appropriate title and legend. FIN3500: Financial Modeling, Final Project Page 3 of 3 PART 2: Modeling Uncertainty Assume that 10 years ago you invested Delta Airlines (DAL) (you are running this analysis as of May 31st). You have employed a buy-and-hold strategy for the past 10 years, but you are now worried given current events. You would like to analyze your exposure if you continue to hold your DAL position. 2.1. What was your annual return for each of the last 10 years? 2.2. Study the distribution of your daily returns over your holding period. Graph it – does it look like it is normally distributed? 2.3. Estimate the annual mean returns and annual standard deviation of returns for DAL over the given period. 2.4. Simulate a given daily market value path for your DAL position for the next quarter (i.e. approximately 64 days). Produce a graph of that path. 2.5. Conduct a Value at Risk analysis (VaR) to see what is the worst-case scenario (with 95% certainty) for the price per share for DAL 15 days from now? 20 days from now? 45 days from now? • Use 10,000 values for your simulation of your future price.