12. Your friend Marc asks your advice for an investment he wants to make on two stocks, PowerEnergy and PCWorld.com. In order to provide him with some reasonable suggestions you download price information for these two companies in the last 2 years and calculate the expected returns and the standard deviations for each of them, as below. You also calculate the correlation between these two stocks, which is equal to 10%. Stock PowerEnergy PCWorld.com Expected Return 12% 35% Standard Deviation 4% 18% a) Calculate the expected return and the volatility of a portfolio of PowerEnergy's and PCWorld.com's stocks that is equally weighted. (5 marks) b) Marc has 15,000 to invest in these two stocks. i. Calculate the expected return and the volatility of a portfolio that consists of a long position of 22,500 in PCWorld.com and a short position of 7,500 in PowerEnergy. (4 marks) ii. What is the meaning of "short position" here? Briefly comment on the resulting portfolio. (5 marks) iii. If the correlation between the two stocks changes, how does the frontier of all combinations of the two stocks change? (5 marks) c) Now you suggest to Marc that on top of his initial capital of 15,000, he may borrow another 8,000 at 3% interest rate and invest the entire amount of 23,000 in the portfolio of PowerEnergy's and PCWorld.com's stocks of point a) (the equally weighted one). Given the expected return and volatility you found in point a): i. What is the expected return and volatility of the new investment? Briefly comment on your result. (5 marks) ii. What is your realized return if your portfolio goes up 20% over the year? And if it goes down by 10% over the year? (5 marks) 12. Your friend Marc asks your advice for an investment he wants to make on two stocks, PowerEnergy and PCWorld.com. In order to provide him with some reasonable suggestions you download price information for these two companies in the last 2 years and calculate the expected returns and the standard deviations for each of them, as below. You also calculate the correlation between these two stocks, which is equal to 10%. Stock PowerEnergy PCWorld.com Expected Return 12% 35% Standard Deviation 4% 18% a) Calculate the expected return and the volatility of a portfolio of PowerEnergy's and PCWorld.com's stocks that is equally weighted. (5 marks) b) Marc has 15,000 to invest in these two stocks. i. Calculate the expected return and the volatility of a portfolio that consists of a long position of 22,500 in PCWorld.com and a short position of 7,500 in PowerEnergy. (4 marks) ii. What is the meaning of "short position" here? Briefly comment on the resulting portfolio. (5 marks) iii. If the correlation between the two stocks changes, how does the frontier of all combinations of the two stocks change? (5 marks) c) Now you suggest to Marc that on top of his initial capital of 15,000, he may borrow another 8,000 at 3% interest rate and invest the entire amount of 23,000 in the portfolio of PowerEnergy's and PCWorld.com's stocks of point a) (the equally weighted one). Given the expected return and volatility you found in point a): i. What is the expected return and volatility of the new investment? Briefly comment on your result. (5 marks) ii. What is your realized return if your portfolio goes up 20% over the year? And if it goes down by 10% over the year
