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##### All answers should be prepared in an excel spreadsheet.

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All answers should be prepared in an excel spreadsheet.;1. Suppose you are trying to pick one stock out of the three alternatives listed below based on the Value-at-Risk (VaR) measure of the return distributions. The return of each stock is normally distributed with the following means and standard deviations;Stock Mean return Standard deviation;A 20% 25%;B 15% 30%;C 10% 7%;Further assume that you have $1M to invest. Compute the following for each stock;a. What is the distribution of the end-of-year portfolio value?;b. What is the probability of a loss of more than $200K by year-end?;c. With 1% probability, what is the maximum loss at the end of the year?;d. Which stock would you pick based on the VaR measure?;2. Kevin is 30 years old. He has a new job and intends to save $5,000 today and in each of the next 29 years. He has decided on an investment policy in which he invests 30% of his assets in a risk-free security (Treasury bills) with 2% continuously compounded annual return and the remainder in the market portfolio that has lognormal returns of 10% and standard deviation of 30%.;a. Prepare a spreadsheet showing Kevin?s accumulation by the time he is 60.;b. What if he puts everything in the market portfolio?;c. What if he finds another risky asset with the same annual return but half the riskiness of the market portfolio and decides to put all in this asset?;3. Kevin decides that he needs at least $2M by the time he hits 60.;a. Run 250 simulations to determine the approximate probability of achieving this goal.;b. Compute the average and standard deviation of the terminal wealth.;c. Create a Data Table to determine the relation between the proportion invested in the market portfolio and the probability of achieving the minimum at 60. Set the proportions in the market portfolio to 0%, 10%, 20%, ?, 100%. Discuss the optimal allocation to the market portfolio, i.e., which proportion of the market portfolio has the highest probability of success?;d. Click F-9 to re-run the simulation (wait about 10 seconds until the run is complete, you will see numbers changing, wait until it is done), did the optimal allocation change? Notice that after you click F-9 the probabilities have changed compared to Part c. Record the new probabilities in a different tab. Now hit F-9 as many times as you like (minimum of ten) and record the probabilities after each time. Can you make any conclusive statements regarding the relationship between the proportion invested in the market portfolio and the probabilities of success?;4. Pick any five stocks from the Dow 30 portfolio provided in the following link: http://money.cnn.com/data/dow30/. Download daily prices between January 1, 1990 and December 31, 2013 (a total of 24 years) using Yahoo Finance into separate spreadsheets (check out the attached jpg files, the Download to spreadsheet is at the bottom of the data webpage). Then copy ONLY adjusted closing prices of each into one file, label appropriately.;a. Compute the overall daily return statistics: average and standard deviation.;b. Annualize these statistics, assuming that there are 250 days per year.;c. Compute the annualized return statistics by year.;d. Compute the correlation matrix during the following four 6-year periods as well as the whole time period between 1990 and 2013, and elaborate on the results. Compare the results using daily versus monthly returns.;Period 1: January 1, 1990 ? December 31, 1995;Period 2: January 1, 1996 ? December 31, 2001;Period 3: January 1, 2002 ? December 31, 2007;Period 4: January 1, 2008 ? December 31, 2013

Paper#21836 | Written in 18-Jul-2015

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