1. An Investment has probabilities 0.2, 0.3, 0.15, 0.25 and 0.1 of giving returns equal to...

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1. An Investment has probabilities 0.2, 0.3, 0.15, 0.25 and 0.1 of giving returns equal to 25%, 15%, -8%, 10% and -5%. What are the expected returns and the standard deviations of returns? 2.The expected return on the market portfolio is 10% and the risk-free rate is 5%. What is the expected return on an investment with a beta of (a) 0.7, (b) 1.2? 3. The volatility of an asset if 20% per annum. What is the standard deviation of the percentage price change in one trading day (assume there are 250 trading days in a year)? Assuming a normal distribution with zero mean, estimate 99% confidence limits for the percentage price change in one day. (1 point) 4. Pick up a company (check out "How to download equity data from Yahoo finance.docx" in Module 1) from Dow Jones Index (yahoo.finance.com). You can consult with the Professor if you are not sure how to pick. Acquire "monthly" prices for your company's stock for the last 101 months (about 8.3 years) and provide a timeseries graph. (1 point) 5. Then calculate the monthly returns in Excel, and provide a histogram of the monthly returns (use 1% intervals from -10% to +10% ). What is the worst possible outcome next month (if history is a proxy for the future)? What is the Value-at-Risk (VAR) at 95% Confidence Level if you invested $100,000 to this stock? How about 99% VAR? (1 point) 6. Write down the Portfolio Theory formulas for a 3 stock portfolio. Pick 2 more stocks and acquire monthly prices for the last 101 months. Following the Excel examples posted on Canvas/Modules/Week 1, calculate the expected return and volatility of the portfolio for the next "month" assuming equal investments into 3 stocks. How would your answer change if the question asked the estimates for next "year" instead? (Hint: You need to use the time aggregation" rule described in Sample Excel File.) (1.5 point) 7. Using monthly returns of last 3 years downloaded above, perform a linear regression to get the BETA for your firm (Y: Individual Stock Returns, X: Stock Market Returns). Is the Beta you computed same as reported at Yahoo Finance? If not, what do you think would be the reason? (1.5 point) 1. An Investment has probabilities 0.2, 0.3, 0.15, 0.25 and 0.1 of giving returns equal to 25%, 15%, -8%, 10% and -5%. What are the expected returns and the standard deviations of returns? 2.The expected return on the market portfolio is 10% and the risk-free rate is 5%. What is the expected return on an investment with a beta of (a) 0.7, (b) 1.2? 3. The volatility of an asset if 20% per annum. What is the standard deviation of the percentage price change in one trading day (assume there are 250 trading days in a year)? Assuming a normal distribution with zero mean, estimate 99% confidence limits for the percentage price change in one day. (1 point) 4. Pick up a company (check out "How to download equity data from Yahoo finance.docx" in Module 1) from Dow Jones Index (yahoo.finance.com). You can consult with the Professor if you are not sure how to pick. Acquire "monthly" prices for your company's stock for the last 101 months (about 8.3 years) and provide a timeseries graph. (1 point) 5. Then calculate the monthly returns in Excel, and provide a histogram of the monthly returns (use 1% intervals from -10% to +10% ). What is the worst possible outcome next month (if history is a proxy for the future)? What is the Value-at-Risk (VAR) at 95% Confidence Level if you invested $100,000 to this stock? How about 99% VAR? (1 point) 6. Write down the Portfolio Theory formulas for a 3 stock portfolio. Pick 2 more stocks and acquire monthly prices for the last 101 months. Following the Excel examples posted on Canvas/Modules/Week 1, calculate the expected return and volatility of the portfolio for the next "month" assuming equal investments into 3 stocks. How would your answer change if the question asked the estimates for next "year" instead? (Hint: You need to use the time aggregation" rule described in Sample Excel File.) (1.5 point) 7. Using monthly returns of last 3 years downloaded above, perform a linear regression to get the BETA for your firm (Y: Individual Stock Returns, X: Stock Market Returns). Is the Beta you computed same as reported at Yahoo Finance? If not, what do you think would be the reason? (1.5 point)