FIN 3710 Investment Analysis Zicklin School of Business Baruch College Spring 2006 FIN 3710 Second (Practice) Midterm Exam 04/11/06 NAME: (Please print your name here) PLEDGE: (Sign your name here) SESSION: T TH 2:30 3:45 PM T TH 4:10 5:25 PM 1. The exam is closed book and closed notes. You can bring in one page, single-sided, 8 11 formula sheet. 2. You can (and probably have to) use a calculator. 3. You have a total of 60 minutes for the exam. 4. The whole exam has a total of 20 points. It will count 20% for your final course grade. There are total of 20 multiple choices questions. 5. Do not separate the exam book. Turn in the entire exam at the end. 6. Budgeting your time efficiently. 7. Good luck. Page 1
Please use the following table for your answer to the multiple choice questions Question Your Answer Question Your Answer 1 11 2 12 3 13 4 14 5 15 6 16 7 17 8 18 9 19 10 20 Total Page 2
1. What is the shape of CAL if your borrowing rate and lending rates are not the same A) A straight line B) A curve C) A kinked line with the kink at the point with 100% in risky security D) A combination of two straight lines and one curve 2. The arithmetic average of 12%, 15% and 20% is. A) 15.7% B) 15% C) 17.2% D) 20% 3. The geometric average of 10%, 20% and 25% is. A) 15% B) 18.2% C) 18.3% D) 23% 4. The dollar weighted return is the same as the. A) difference between cash inflows and cash outflows B) arithmetic average return C) geometric average return D) internal rate of return 5. The capital allocation line is also the. A) investment opportunity set formed with a risky asset and a risk-free asset B) investment opportunity set formed with two risky assets C) line on which lie all portfolios that offer the same utility to a particular investor D) line on which lie all portfolios with the same expected rate of return and different standard deviations 6. If you require a real growth in the purchasing power of your investment of 8%, and you expect the rate of inflation over the next year to be 3%, what is the lowest nominal return that you would be satisfied with? A) 3.00% B) 8.00% C) 11.00% D) 11.24% 7. A Treasury bill pays a 6% rate of return. A risk averse investor invest in a risky portfolio that pays 12% with a probability of 40% or pays 2% with a probability of 60% because. A) might; she is rewarded a risk premium B) would not; because she is not rewarded any risk premium C) would not; because the risk premium is small D) cannot be determined Page 3
8. Consider the following two investment alternatives. First, a risky portfolio that pays 20% rate of return with a probability of 60% or 5% with a probability of 40%. Second, a treasury that pays 6%. If you invest $50,000 in the risky portfolio, your expected profit would be. A) $3,000 B) $7,000 C) $7,500 D) $10,000 9. You invest $100 in a portfolio. The portfolio is composed of a risky asset with an expected rate of return of 12% and a standard deviation of 15% and a treasury bill with a rate of return of 5%. of your money should be invested in the risky asset to form a portfolio with an expected rate of return of 9% A) 87% B) 77% C) 67% D) 57% 10. You have $500,000 available to invest. The risk-free rate as well as your borrowing rate is 8%. The return on the risky portfolio is 16%. If you wish to earn a 22% return, you should. A) invest $125,000 in the risk-free asset B) invest $375,000 in the risk-free asset C) borrow $125,000 D) borrow $375,000 11. The expected return of a risky asset is 15%. The risk-free rate as well as the investor's borrowing rate is 10%. The standard deviation of return on the risky portfolio is 20%. If the standard deviation on the complete portfolio is 25%, the expected return on the complete portfolio is. A) 6.00% B) 8.47% C) 10.00% D) 16.25% Use the following to answer questions 12-15: You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of treasury bills that pay 5% and a risky portfolio, P, constructed with 2 risky securities X and Y. The weight of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14% and Y has an expected rate of return of 10%. 12. To form a complete portfolio with an expected rate of return of 11%, you should invest of your complete portfolio in treasury bills. A) 19% B) 25% C) 50% D) 65% Page 4
13. To form a complete portfolio with an expected rate of return of 7.96%, you should invest, and of your complete portfolio in the treasury bill, X, and Y respectively. A) 0%, 60%, 40% B) 25%, 45%, 30% C) 60%, 24%, 16% D) 50%, 30%, 20% 14. The dollar values of your positions in X and Y respectively would be and if you decide to hold 30% of your complete portfolio in the risky portfolio and 70% in the treasury bills. A) $280, $420 B) $180, $120 C) $120, $180 D) $420, $280 15. The dollar values of your positions in X, Y, and treasury bills respectively would be, and if you decide to hold a complete portfolio that has an expected return of 8%. A) $162, $595, $243 B) $243, $162, $595 C) $595, $162, $243 D) $595, $243, $162 16. Risk that can be eliminated through diversification is called risk. A) idiosyncratic B) firm-specific C) diversifiable D) all of the above 17. An investor's degree of risk aversion will determine his. A) optimal risky portfolio B) risk-free rate C) mix of risk-free asset and optimal risky asset D) choice of risk free asset 18. Diversification is most effective when security returns are. A) high B) negatively correlated C) positively correlated D) uncorrelated 19. Consider two perfectly negatively correlated risky securities, A and B. Security A has an expected rate of return of 16% and a standard deviation of return of 20%. B has an expected rate of return 10% and a standard deviation of return of 30%. The weight of security B in the global minimum variance portfolio is. A) 10% B) 20% C) 40% D) 60% Page 5
20. The optimal risky portfolio can be identified by finding. A) the minimum variance point on the efficient frontier B) the maximum return point on the efficient frontier C) the tangency point of the capital allocation line and the efficient frontier D) None of the above answers is correct 21. A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 25% while stock B has a standard deviation of return of 5%. Stock A comprises 20% of the portfolio while stock B comprises 80% of the portfolio. If the variance of return on the portfolio is.0050, the correlation coefficient between the returns on A and B is. A) -.225 B) -.474 C).474 D).225 22. The standard deviation of return on investment A is.10 while the standard deviation of return on investment B is.04. If the correlation coefficient between the returns on A and B is -.50, the covariance of returns on A and B is. A) -.0447 B) -.0020 C).0020 D).0447 23. If your risk aversion is A = 1, which one of the following portfolios will you prefer: A). E(r p ) = 8%; σ p = 10% B). E(r p ) = 10%; σ p =20% C). E(r p ) = 15%; σ p =30% D). E(r p ) = 20%; σ p =40% 24. At the beginning of 2002, you allocate half of your investment in a bond fund and half of your investment in a stock fund. Over the year, bond fund had a return of 10%, while the stock fund had a return of 40%. What is the portfolio weight in stock fund at the end of the year? A) 40.0% B) 50.0% C) 56.0% D) 60.0% 25. You paid $100 dollars to participate in a bet. If you win you will get $200 back. If you lose, you will get nothing. If the odds are 50-50, what is the mean and standard deviation of this bet (investment)? A) 100% and 100% B) 0 % and 50% C) 100% and 50 % D) 0 % and 0 % For more practice questions, please study the examples in your lecture notes and the questions in HW3 and HW4. Suggested Solutions: CABDA DBBDD DACBB DCBCC DBDCA Page 6
Detailed solutions on numerical questions for numerical questions in MT2 practice exam: Q2. Arithmetic Avg = (12%+15%+20%)/3 = 15.7% Q3. Geometric Avg = [(1+10%)(1+20%)(1+25%)] 1/3-1 = 18.2% Q6. r = (R-i)/(1+i) => R = i + r(1+i) = 3% + 8%*(1+3%) = 11.24% Q7. E(rp) = 0.4 * 12% + 0.6 * 2% = 6%. A risk averse investor will not be interested since risk premium = E(rp) rf = 0 Q8. E(rp) = 0.6*20% + 0.4*5% = 14%. Expected Profit = 50,000 * 14% = 7,000 Q9. If W is the portfolio weight on risky asset, then E(rp) = 9% = (1-W) * 5% + W * 12% W = 57.14% Q10. If W is the portfolio weight on riskfree security, then E(rp) = 22% = W * 8% + (1-W) * 16% W = -75% A negative portfolio weight in riskfree security means you need to borrow for 500,000*W = - 375,000 Q11. If W is the portfolio weight on the risky portfolio, then Std Dev of complete portfolio = W*20% = 25% W = 125% E(rc) = (1-W) * 10% + W * 15% = 16.25% Q12. The risky portfolio using X and Y has expected return of E(rp) = 0.6 * 14% + 0.4 * 10% = 12.4%. For complete portfolio E(rc) = W * 5% + (1-W) * 12.4% = 11%. W=18.92% Q13. E(rc) = W * 5% + (1-W) * 12.4% = 7.96%. W=60% So 40% will be in risky portfolio. Weight of X in the complete portfolio: = 60% * 40% = 24% Weight of Y in the complete portfolio: = (1-60%) * 40% = 16% Q14. Dollar value in risky portfolio = 30% * $1,000 = 300 Dollar value in X = 300 * 60% = 180 Dollar value in Y = 300 * 40% = 120 Page 7
Q15. E(rc) = W * 5% + (1-W) * 12.4% = 8%. W=59.46% Dollar value in riskfree = 1000 * 59.46% = 595 Dollar value in risky portfolio = 1000 * (1-59.46%) = 405 Dollar value in X = 405 * 60% = 243 and dollar value in Y = 300 * 40% = 162 Q19. GMVP when correlation is -1 is 0. So set up the equation: W A * 20% - (1-W A ) 30% = 0 W A = 60% Q21. Var = 0.0050 = (0.2*25%) 2 + (0.8*5%) 2 + 2*0.2*0.8*Correlation*25%*5% Correlation = 0.225 Q22. covariance = correlation * std dev 1 * std dev 2 = (-0.5) * 0.1 * 0.04 = -0.002 Q23. U(A) = r ce = 8% - ½ * 1 * (0.1) 2 = 7.5% U(B) = r ce = 10% - ½ * 1 * (0.2) 2 = 8.0% U(C) = r ce = 15% - ½ * 1 * (0.3) 2 = 10.5% U(D) = r ce = 20% - ½ * 1 * (0.4) 2 = 12.0% Q24. Assume you have $200 at beginning of 2002 (the amount does not matter), $100 in stock and $100 in bond. By the end of the year, the bond fund becomes $100*(1+10%) = $110 and the stock fund becomes $100*(1+40%) = $140 So your total investment becomes $110 + $140 = $250 and the portfolio weight in stock changes from 50% to 140 / 250 = 56% Q25. If you win, the return is (200-100)/100 = 100% If you lose, the return is (0-100)/100 = -100% E(r) = 0.5 100% + 0.5(-100%) = 0 Var(r)= 0.5 * (100%-0) 2 + 0.5*(-100% - 0) 2 = 10,000 Std Dev = 100% Page 8