Question

INVESTMENTS/Ivkovich Problem Set 1 Due: 1/23/2020 Instructions: Each group will turn in one solution to the problem set. Recall that late submission will not be allowed: problem sets must be submitted at the beginning of class on the due date. Make sure to document your work: do not merely give a solution without adequate explanations and intermediate steps necessary to obtain the results. You will be graded not only on the basis of the accuracy of your results, but also on the clarity and completeness of your written solution. The total number of points for this problem set is 60. Problem 1 (40 points): Consider the following description of a two-security economy: State (Scenario) Probability Security 1 returns (%) 1 (Extreme boom) 0.05 11% 2 (Boom) 0.19 7% 3 (Normal growth) 0.45 6% 4 (Recession) 0.16 5 (Extreme recession) 0.15 3% Security 2 returns (%) 7% 12% 9% 3% -9% 4% 1.1) Basic summary statistics (10 points): Use Excel to compute the expected returns and standard deviations for both securities (E(ri), 01, E(ra), and 02), Cov(ri,r2), and p(ri,r2). Report these summary statistics in a simple table. 1.2) Portfolio summary statistics and other properties: a) Portfolio expected returns and standard deviations (10 points). Use Excel to compute the expected return, E(rp), and the standard deviation, Op, for a series of portfolios with the following weights wi: {-0.5, -0.25, 0.0, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5}. Graph E(rp) against Op for this series of portfolios. Connect the points with a smooth line.

Answer 1

Calculate (Pi* Xi) Calculate Calculate (Pi*Yi) (Xi-E(r1)) (Pi) (Yi) 0.05 05 0.6% 1.3% 2.7% 0.6% 0.5% 5.7% 0.4% 2.3% 4.1% 0.5% -1.4% 5.8% 5.3300% 1.3300% 0.3300% -1.6700% -2.6700% Calculate Calculate Calculate (Xi-E(r1))^2 P*(Xi-E(r1))^2 (Yi-E(r2)) 0.00284089 0.000142045 1.1900% 0.00017689 3.36091E-05 6.1900% 0.00001089 4.9005E-06 3.1900% 0.00027889 4.46224E-05 -2.8100% 0.00071289 0.000106934 -14.8100% 0.00033211 Calculate Calculate Calculate Calculate (Xi-E(r1))* Pi* (Xi-E(r1))* (Yi-E(r2))^2 P*(Yi-E(r2))^2 (Yi-E(r2)) (Yi-E(r2)) 0.0001416 7.0805E-06 0.00063427 3.17135E-05 0.0038316 0.000728006 0.00082327 0.000156421 0.0010176 0.000457925 0.00010527 4.73715E-05 0.0007896 0.000126338 0.00046927 7.50832E-05 0.0219336 0.003290042 0.00395427 0.000593141 0.00460939 0.00090373 Security 1 Security 2 Probability State returns (%) returns (%) (Xi) Extreme Boom 11% 7% Boom 0.19 7% 12% Normal Growth 0.45 6% 9% Recession 0.16 4% 3% Extreme Recession 0.15 3% -9% Total Formula Used Expected Returns E(r1)= Pi*Xi of Security 1 Expected Returns E(r2)= £ Pi*Yi of Security 2 Variance of Variance 1=2 Pi*(Xi-E(r1))^2 security 1 Standard deviation 01 = variance1^0.5 of security 1 Variance of Variance2 = Pi*(Yi-E(r2))^2 security 2 Standard deviation 02 = variance2^0.5 of security 2 5.7% Covariance =£ Pi*(Xi-E(r1))*(Yi-E(r2)) 0.00090373 Cov (r1,r2) Correlation (r1,r2) 5.8% p = Cov(r1,r2)/0102 0.00033211 1.822% 0.00460939 6.789%