Investment portfolio analysis
NATIONAL UNIVERSITY OF SINGAPORE
NUS BUSINESS SCHOOL
FIN 3102 Investment Analysis and Portfolio Management
Luis Goncalves-Pinto / Sem 1, AY 14/15
Practice Problems #1
1. You sell short 100 shares of Loser Co. at a market price of $45 per share. What is your maximum possible loss? Explain.
2. The investment bank you work for is writing its annual investments newsletter and you are in charge of the international markets outlook for next year. To prepare your section, you collect data on yearly returns of World Stocks (WORLD_STOCKS) and those of the US S&P500 portfolio over the last 75 years. Then, you run the following regression: r WORLD_STOCKS = a + r SP500 + error
The regression produces the following output:
SUMMARY OUTPUT
Regression Statistics
R Square
Standard Error
Observations
Intercept
X Variable 1
0.739
0.094
75
Coefficients
0.0172
0.7710
Standard Error
0.0125
0.0525
T-Stat
1.3787
14.6943
2.a. What is the regression estimate for the beta of WORLD_STOCKS with respect to the S&P500?
2.b. What is the 95% confidence interval around this estimate for the beta of WORLD_STOCKS with respect to the SP500? Give both the lower and the upper bounds of the interval. Explain.
2.c. Is the beta of WORLD_STOCKS with respect to the SP500 statistically different from one? Explain.
2.d. The research department in your bank has put out next year’s prediction for the US market (S&P500 portfolio) as 10%. For the investment newsletter, you need to provide what is your best estimate of the performance next year for WORLD_STOCKS. Using your answer to 2.a., what is your estimate of the expected return on WORLD_STOCKS for next year? Explain.
3. Stock A’s expected return and standard deviation are E[r A] = 10% and A= 18%, while stock B’s expected return and standard deviation are E[rB] = 12% and B= 21%.
3.a. Determine the expected return and standard deviation of the return on a portfolio with weights A=0.3 and B=0.7 for the
NUS BUSINESS SCHOOL
FIN 3102 Investment Analysis and Portfolio Management
Luis Goncalves-Pinto / Sem 1, AY 14/15
Practice Problems #1
1. You sell short 100 shares of Loser Co. at a market price of $45 per share. What is your maximum possible loss? Explain.
2. The investment bank you work for is writing its annual investments newsletter and you are in charge of the international markets outlook for next year. To prepare your section, you collect data on yearly returns of World Stocks (WORLD_STOCKS) and those of the US S&P500 portfolio over the last 75 years. Then, you run the following regression: r WORLD_STOCKS = a + r SP500 + error
The regression produces the following output:
SUMMARY OUTPUT
Regression Statistics
R Square
Standard Error
Observations
Intercept
X Variable 1
0.739
0.094
75
Coefficients
0.0172
0.7710
Standard Error
0.0125
0.0525
T-Stat
1.3787
14.6943
2.a. What is the regression estimate for the beta of WORLD_STOCKS with respect to the S&P500?
2.b. What is the 95% confidence interval around this estimate for the beta of WORLD_STOCKS with respect to the SP500? Give both the lower and the upper bounds of the interval. Explain.
2.c. Is the beta of WORLD_STOCKS with respect to the SP500 statistically different from one? Explain.
2.d. The research department in your bank has put out next year’s prediction for the US market (S&P500 portfolio) as 10%. For the investment newsletter, you need to provide what is your best estimate of the performance next year for WORLD_STOCKS. Using your answer to 2.a., what is your estimate of the expected return on WORLD_STOCKS for next year? Explain.
3. Stock A’s expected return and standard deviation are E[r A] = 10% and A= 18%, while stock B’s expected return and standard deviation are E[rB] = 12% and B= 21%.
3.a. Determine the expected return and standard deviation of the return on a portfolio with weights A=0.3 and B=0.7 for the