AEM4060 Risk Simulation and Optimization Dr. C.G. Turvey Spring 2013 Assignment 4, Due April 29th Question 1 Part A: Using the file Stock Prices, CAPM and ROE.April 15.2013.xlsx posted on Blackboard 1) Generate the variance covariance matrix and correlation matrix for all stocks (ignore the portfolio column) 2) Make sure that the variance covariance matrix is fully symmetric 3) Build a variance minimizing portfolio choice model with expected returns and summing up constraints. 4) Assuming non-negativity, generate the EV-Frontier using a strict equality on the income constraint for returns starting at 7%, 10%, 13% up to 40%. a. Record the portfolio standard deviation for each return b. Graph the EV frontier 5) Relax non-negativity and regenerate the model as in (4). 6) Compare and interpret the two graphs in the context of say a mutual fund versus a hedge fund. 7) Assuming that short selling is allowed, add a riskless asset to the mix with a risk free return of 4%. Generate solutions from 4% to 40% and record portfolio standard deviations for each. 8) Plot this curve along with the results in (5). (You can invert the x and y axis if you like). 9) Summarize the stock portfolio solutions for an expected return of 25% for each of the three models (4,5,7). Compare the solutions along with their respective standard deviations. 10) What does the comparison in (8) show? How does this relate to the Capital Asset Pricing Model? 11) Using the correlation matrix develop a model to simulate portfolio returns for solutions at 25% without risk free borrowing and without short-selling (i.e. questions 4). What is the probability that portfolio returns will fall below 20% or rise above 30%?. Question 2. Option Pricing You have been asked by a client to price out a number of possible options on a stock over a six-month period (125 days). The current stock price is $25, and its expected risk neutral drift rate is 5%/year. It is also known that the annual volatility is 35%. 12) The…