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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 maximumpossible loss? Explain.

2. The investment bank you work for is writing its annual investments newsletter and you are in charge ofthe international markets outlook for next year. To prepare your section, you collect data on yearly returnsof 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 0.739

Standard Error 0.094

Observations 75

Coefficients Standard Error T-Stat

Intercept 0.0172 0.0125 1.3787

X Variable 1 0.7710 0.0525 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 withrespect 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 years prediction for the US market (S&P500

portfolio) as 10%. For the investment newsletter, you need to provide what is your best estimate of theperformance next year for WORLD_STOCKS. Using your answer to 2.a., what is your estimate of theexpected return on WORLD_STOCKS for next year? Explain.

3. Stock As expected return and standard deviation are E[rA] = 10% and A= 18%, while stock Bs

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 following alternative values of correlation between A and B: AB=0.6 and AB= -0.4.

3.b. Assume now that AB=-1.0 and find the portfolio (p) of stocks A and B that has no risk (i.e. such that

p=0). Can you do the same when AB=1.0? If not, why? If so, find that portfolio. Expain.

3.c. Finally, assume that AB=0. Find the standard deviations of portfolios with the following expectedreturns: 8%, 9%, 10%, 11%, 12%, 13%, 14% and 15%. Plot the pairs of expected return and standarddeviation on a graph (with the standard deviations on the horizontal axis, and the expected returns on thevertical axis).

4.Every time a certain asset A experiences a 1 percent jump in its rate of return, the return on asset Bexperiences exactly a 0.5 percent decrease (with no error). What is the correlation coefficient between thereturns of these two assets? Explain.

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