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Smriwpltr Whinllu SD r] 32 2 LAM: m- mm. um um 33 2 in: mm mm mum! um 31 2 um em W169 um um Instructions Problem SludEnl Ana-Er meat Calculations I + I Due date: Problem Set: Submission guidelines: Sunday, June 25 by 11:59 pm EST List of questions is outlined in tab titled "Problem" Submissions through Dropbox on CourseLink only Submit single Excel file using this file as a template Student Answer sheet must be filled with your final answe However, your calculations and rough work must be show Failing to show your work in "Calculations" tab will result Notes: Section H of Problem 1 will require MS Excel's Solver. Co Refer to Assignments --> Portfolio Report 2 - Section Good luck young portfolio managers! itled "Problem" ourseLink only le as a template d with your final answers and will be used for grading. gh work must be shown in tab "Calculations" (no specific formatting guidelines are required) lations" tab will result in zero marks even if the answer is correct under the "Student Answer shee MS Excel's Solver. Completing this section will provide you with necessary tools required for PR2 o Report 2 - Section 3 Constructing Portfolio and Efficient Frontiers (Youtube video tutor are required) tudent Answer sheet". ls required for PR2 outube video tutorial + Excel template) Below is actual price and dividend data for three companies for each of seven months. Time 1 2 3 4 5 6 7 Security A Security B Security C Price Dividend Price Dividend Price Dividend $ 25.25 $ 125.00 $ 106.75 $ 24.50 $ 126.00 $ 108.25 $ 23.75 $ 0.50 $ 129.00 $ 2.50 $ 114.75 $ 1.25 $ 24.75 $ 126.50 $ 113.00 $ 25.25 $ 124.25 $ 115.00 $ 25.75 $ 0.25 $ 122.75 $ 2.50 $ 117.25 $ 2.25 $ 26.00 $ 125.00 $ 114.25 A dividend entry on the same line as a price indicates that the return between that time period and Securities A, B and C can be referred to Securities 1, 2 and 3 respectively. A. (3pts) Compute the rate of return for each company for each month (use simple retu B. (3pts) Compute the average rate of return for each company. C. (6pts) Compute the standard deviation of the rate of return for each company ( D. (6pts) Compute the covariance and correlation coefficients between all possible pair E. (8pts) Compute the average return and standard deviation for the following portfolio i. A + B ii. A + C iii. B + C iv. 1/3 A + 1/3 B + 1/3 C F. (15pts) Assuming short selling is not allowed: i. (2) For securities 1 and 2 find the composition, standard deviation, and e ii. (2) On the same graph plot the expected return and standard deviation iii. (1) Assuming that investors prefer more to less and are risk avoiders, in iv. (10) Repeat steps i), ii) and iii) for all other possible pairwise combination G. (15pts) Assuming short selling is allowed: i. (2) For securities 1 and 2 find the composition, standard deviation, and e ii. (2) On the same graph plot the expected return and standard deviation iii. (1) Assuming that investors prefer more to less and are risk avoiders, in iv. (10) Repeat steps i), ii) and iii) for all other possible pairwise combination H. (14pts) Assuming short selling is not allowed, for portfolio with ALL THREE securities i. (4) Find the composition, standard deviation, and expected return of the ii. (7) Construct the minimum variance portfolio frontier. iii. (1) Assuming that investors prefer more to less and are risk avoiders, in iv. (2) Find the composition and standard deviation for the efficient por Note: In Part H, you must setup Solver parameters (I will check these): Objective Variable Cells Constraints that time period and the previous period consisted of a capital gain (or loss) and the receipt of the dividend onth (use simple return formula). each company (use population variance formula. i.e. divide by N, not (N-1) ). ween all possible pairs of securities (again, use population formula). the following portfolios: dard deviation, and expected return of that portfolio that has minimum risk. d standard deviation for all possible combinations of securities 1 and 2 are risk avoiders, indicate those sections of the diagram in part ii) that are efficient. pairwise combinations of securities in Problem 1. dard deviation, and expected return of that portfolio that has minimum risk. d standard deviation for all possible combinations of securities 1 and 2 are risk avoiders, indicate those sections of the diagram in part ii) that are efficient. pairwise combinations of securities in Problem 1. ALL THREE securities: xpected return of the portfolio that has minimum risk. are risk avoiders, indicate those sections of the diagram in part ii) that are efficient. n for the efficient portfolio that has 1% expected return. check these): eceipt of the dividend. Q# Your final answers must be provided in cells highlighted in blue and your graphical answers Marks 70 in total A. Month Security 2 3 4 5 1 A -2.9703% -1.0204% 4.2105% 2.0202% 1 B 0.8000% 4.3651% -1.9380% -1.7787% 1 C 1.4052% 7.1594% -1.5251% 1.7699% B. 1 1 1 Security A B C Average monthly return 0.8684% 0.6810% 1.6940% 2 2 2 Security A B C Standard deviation 2.4485% 2.1540% 3.2489% 2 2 2 Covariance Security A B C C. D. Correlation A 0.0600% -0.0329% -0.0192% E. C -0.0192% 0.0395% 0.1056% Avg.Ret SD 0.7747% 1.4743% 1.2812% 1.7824% 1.1875% 2.4032% 1.0811% 1.4404% 2 2 2 2 i. ii. iii. iv. 2 2 2 Security pair i. A&B i. A&C i. B&C 2 1 Security pair ii. A&B iii. A&B F. B -0.0329% 0.0464% 0.0395% Weights 46.0628% 53.9372% 61.1798% 38.8202% 90.5831% 9.4169% SD 0.0099% 0.0292% 0.0458% E[r] 0.7673% 1.1889% 0.7764% graph goes somewhere here Efficient set 1.0000% 0.7673% 0.8000% A&B 0.8684% 0.6810% 0.6000% 0.4000% 0.2000% 0.0000% 0.0000% 2 1 ii. A&C iii. A&C 0.5000% 1.0000% graph goes somewhere here 2.0000% 1.5000% 2.0000% 0.5000% 3.0000% A&C Efficient set 1.6940% 1.5000% 1.1889% 1.0000% 2.5000% 0.8684% A&C Efficient set 2.0000% 1.6940% 1.5000% 1.1889% 0.8684% 1.0000% 0.5000% 0.0000% 0.0000% 2 1 ii. B&C iii. B&C 0.5000% 1.0000% 1.5000% graph goes somewhere here 2.0000% 1.5000% 2.0000% 2.5000% 3.0000% 3.5000% B&C 1.6940% Efficient set 0.7764% 1.0000% 0.6810% 0.5000% 0.0000% 0.0000% G. 2 2 2 Security pair i. A&B i. A&C i. B&C 2 1 Security pair ii. A&B iii. A&B 0.5000% 1.0000% Weights 46.0628% 53.9372% 61.1798% 38.8202% 90.5831% 9.4169% 1.5000% SD 0.0099% 0.0292% 0.0458% graph goes somewhere here 2.0000% 2.5000% 3.0000% E[r] 0.7673% 1.1889% 0.7764% A&B Efficient set 0.8684% 1.0000% 0.7673% 0.8000% 0.6810% 0.6000% 0.4000% 0.2000% 0.0000% 0.0000% 2 1 ii. A&C iii. A&C 0.5000% 1.0000% graph goes somewhere here 2.0000% 1.5000% 2.0000% 2.5000% 3.0 A&C 1.6940 Efficient set 1.5000% 1.1889% 0.8684% 1.0000% 0.5000% 0.0000% 0.0000% 2 1 ii. B&C iii. B&C 0.5000% 1.0000% graph goes somewhere here 2.0000% 1.5000% 2.0000% 0.5000% 3.0000% B&C Efficient set 1.6940 1.5000% 0.7764% 1.0000% 2.5000% 0.6810% B&C 2.0000% Efficient set 1.6940 1.5000% 0.7764% 1.0000% 0.6810% 0.5000% 0.0000% 0.0000% H. 4 Portfolio i. A&B&C 7 1 ii. A&B&C iii. A&B&C 2 iv. 0.5000% 1.0000% Weights 1.5000% 2.0000% SD graph goes somewhere here Weights SD 2.5000% 3.0000% e and your graphical answers in the approximate space provided in shaded green area 6 2.9703% 0.8048% 3.9130% 7 0.0000% 1.8330% -2.5586% Correlation Security A A 100.0000% B -62.3849% C -24.1529% 0.8684% 0.6810% 2.0000% 2.5000% 3.0000% 1.6940% 0.8684% B C -62.3849% -0.241529 100.0000% 0.564925 56.4925% 1 0% 1.6940% 0.8684% 2.5000% 3.0000% 3.5000% 1.6940% 0.6810% .0000% 2.5000% 3.0000% 3.5000% 0.8684% 0.6810% % 2.0000% 2.5000% 3.0000% 1.6940% 0.8684% 2.0000% 2.5000% 3.0000% 3.5000% 1.6940% 0.6810% 1.6940% 0.6810% 2.0000% 2.5000% E[r] E[r] 3.0000% 3.5000% A Rate of return=[(P1-P0)+Dividend ]/ P0 price 1 $ 2 $ 3 $ 4 $ 5 $ 6 $ 7 $ Security A dividend 25.25 24.50 23.75 24.75 25.25 25.75 25.75 $ $ return $ $ $ $ 0.25 $ $ 0.50 rate of return -0.75 -0.25 1.00 0.50 0.75 - B.AVERAGE C. -2.9703% -1.0204% 4.2105% 2.0202% 2.9703% 0.0000% 0.8684% Security A Rate of return Average rate [R] of return[T] (R-T)^2 -2.9703% 0.8684% -1.0204% 0.8684% 4.2105% 0.8684% 2.0202% 0.8684% 2.9703% 0.8684% 0.0000% 0.8684% sum Standard deviation 0.1474% 0.0357% 0.1117% 0.0133% 0.0442% 0.0075% 0.0600% 2.4485% D. Security A (R-T) -3.8387% -1.8888% 3.3421% 1.1518% 2.1019% -0.8684% Security B (R-T) Security 0.1190% 3.6840% -2.6190% -2.4597% 0.1238% 1.1520% C (R-T) -0.2888% 5.4654% -3.2190% 0.0759% 2.2191% -4.2526% E. Rate of return A Rate 2 -2.9703% 3 -1.0204% 4 4.2105% 5 2.0202% 6 2.9703% 7 0.0000% of returnBRate of return C 0.8000% 1.4052% 4.3651% 7.1594% -1.9380% -1.5251% -1.7787% 1.7699% 0.8048% 3.9130% 1.8330% -2.5586% average A Variance B 0.0600% C 0.0464% 0.1056% standard deviation F. A Variance SD rate of return SD-Protfolio 1 SD-Protfolio 2 SD-Protfolio 3 SD-Protfolio 4 a) A&B: A&C B&C 1 A GMV B B 0.0600% 2.4485% 0.8684% 1.4743% 1.7824% 2.4032% 1.4404% 0.0464% 2.1540% 0.6810% GMV XA= XB= XA= XC= XB= XC= SD C 0.1056% 3.2489% 1.6940% 46.0628% E[R]= 53.9372% 61.1798% E[R]= 38.8202% 90.5831% E[R]= 9.4169% E[r] 2.4485% 0.0099% 2.1540% standard deviation 0.7673% 1.1889% 0.7764% A&B 1.0000% 0.8684% 0.7673% 0.6810% 0.8000% 0.6000% 0.4000% 0.2000% 0.0000% 0.0000% 0.5000% 1.0000% 1.5000% 0.8000% 0.6000% 0.4000% 1 A GMV C SD 1 B GMV C SD 0.2000% E[r] 2.4485% 0.0292% 3.2489% 0.0000% 0.0000% 0.8684% 1.1889% 1.6940% 1.0000% 2.0000% 1.5000% 0.6810% 0.7764% 1.6940% 1.0000% 0.5000% 0.0000% 0.0000% 0.5000% 1.0000% B&C 1.8000% 1.6000% 1.4000% 1.2000% 1.0000% 0.8000% 0.6000% 0.4000% 0.2000% 0.0000% 0.0000% 0.5000% 1.0000% 1.5000% A&C E[r] 2.1540% 0.0458% 3.2489% 0.5000% 1.5000% 2.0000% 2.5000% 3.0000% 3.5000% 1.5000% idend ]/ P0 Price $ $ $ $ $ $ $ Security B Dividend 125.00 126.00 129.00 126.50 124.25 122.75 125.00 return $ 2.50 $ 2.50 $ $ $ $ $ $ rate of return 1.00 5.50 -2.50 -2.25 1.00 2.25 price $ 0.8000% $ 4.3651% $ -1.9380% $ -1.7787% $ 0.8048% $ 1.8330% $ 0.6810% 106.75 108.25 114.75 113.00 115.00 117.25 114.25 Security B Average rate of Rate of return [R] return[T] (R-T)^2 0.8000% 0.6810% 4.3651% 0.6810% -1.9380% 0.6810% -1.7787% 0.6810% 0.8048% 0.6810% 1.8330% 0.6810% A*A SUM Correlation (A,A) Correlation (A,B) 0.0001% 0.1357% 0.0686% 0.0605% 0.0002% 0.0133% 0.0464% 2.1540% A*B A*C 0.1474% 0.0357% 0.1117% 0.0133% 0.0442% 0.0075% -0.0046% -0.0696% -0.0875% -0.0283% 0.0026% -0.0100% 0.0111% -0.1032% -0.1076% 0.0009% 0.0466% 0.0369% 0.3597% 0.0600% -0.1974% -0.0329% -0.1153% -0.0192% 1.0000 -0.6238 -0.6238487463 000% Correlation Correlation Correlation Correlation (A,C) (B,B) (B,C) (C,C) -0.2415 1.0000 0.5649 1.0000 -0.2415287288 0.5649252532 Portfolio 1 Portfolio 2 Portfolio 3 portfolio 4 A + B A + C B + C 1/3 A + 1/3 B + 1/3 C -1.0851% -0.7826% 1.1026% -0.255% 1.6723% 3.0695% 5.7622% 3.501% 1.1363% 1.3427% -1.7315% 0.249% 0.1208% 1.8951% -0.0044% 0.670% 1.8876% 3.4417% 2.3589% 2.563% 0.9165% -1.2793% -0.3628% -0.242% 0.7747% 1.2812% 1.1875% 1.0811% 0.0217% 1.4743% 0.0318% 1.7824% A&B A&C -0.0329% 0.0578% 2.4032% B&C -0.0192% SD= 0.0099% SD= 0.0292% SD= 0.0458% 0.0395% A&B 1.0000% 1.5000% 2.0000% 2.5000% 3.0000% 0.0207% 1.4404% 000% 1.0000% 1.5000% 2.0000% 2.5000% 3.0000% A&C 000% 1.0000% 00% 3.5000% 1.5000% 2.0000% 2.5000% 3.0000% 3.5000% Secruity C dividend return $ 1.25 $ $ $ 2.25 $ $ $ $ rate of return 1.50 7.75 -1.75 2.00 4.50 -3.00 1.4052% 7.1594% -1.5251% 1.7699% 3.9130% -2.5586% 1.6940% Secruity C Rate of return Average rate of [R] return[T] (R-T)^2 1.4052% 1.6940% 0.0008% 7.1594% 1.6940% 0.2987% -1.5251% 1.6940% 0.1036% 1.7699% 1.6940% 0.0001% 3.9130% 1.6940% 0.0492% -2.5586% 1.6940% 0.1808% 0.1056% 3.2489% B*B B*C C*C 0.0001% 0.1357% 0.0686% 0.0605% 0.0002% 0.0133% -0.0003% 0.2013% 0.0843% -0.0019% 0.0027% -0.0490% 0.0008% 0.2987% 0.1036% 0.0001% 0.0492% 0.1808% 0.2784% 0.0464% 0.2372% 0.0395% 0.6333% 0.1056% Due date: Problem Set: Submission guidelines: Sunday, June 25 by 11:59 pm EST List of questions is outlined in tab titled "Problem" Submissions through Dropbox on CourseLink only Submit single Excel file using this file as a template Student Answer sheet must be filled with your final answe However, your calculations and rough work must be show Failing to show your work in "Calculations" tab will result Notes: Section H of Problem 1 will require MS Excel's Solver. Co Refer to Assignments --> Portfolio Report 2 - Section Good luck young portfolio managers! itled "Problem" ourseLink only le as a template d with your final answers and will be used for grading. gh work must be shown in tab "Calculations" (no specific formatting guidelines are required) lations" tab will result in zero marks even if the answer is correct under the "Student Answer shee MS Excel's Solver. Completing this section will provide you with necessary tools required for PR2 o Report 2 - Section 3 Constructing Portfolio and Efficient Frontiers (Youtube video tutor are required) tudent Answer sheet". ls required for PR2 outube video tutorial + Excel template) Below is actual price and dividend data for three companies for each of seven months. Time 1 2 3 4 5 6 7 Security A Security B Security C Price Dividend Price Dividend Price Dividend $ 25.25 $ 125.00 $ 106.75 $ 24.50 $ 126.00 $ 108.25 $ 23.75 $ 0.50 $ 129.00 $ 2.50 $ 114.75 $ 1.25 $ 24.75 $ 126.50 $ 113.00 $ 25.25 $ 124.25 $ 115.00 $ 25.75 $ 0.25 $ 122.75 $ 2.50 $ 117.25 $ 2.25 $ 26.00 $ 125.00 $ 114.25 A dividend entry on the same line as a price indicates that the return between that time period and Securities A, B and C can be referred to Securities 1, 2 and 3 respectively. A. (3pts) Compute the rate of return for each company for each month (use simple retu B. (3pts) Compute the average rate of return for each company. C. (6pts) Compute the standard deviation of the rate of return for each company ( D. (6pts) Compute the covariance and correlation coefficients between all possible pair E. (8pts) Compute the average return and standard deviation for the following portfolio i. A + B ii. A + C iii. B + C iv. 1/3 A + 1/3 B + 1/3 C F. (15pts) Assuming short selling is not allowed: i. (2) For securities 1 and 2 find the composition, standard deviation, and e ii. (2) On the same graph plot the expected return and standard deviation iii. (1) Assuming that investors prefer more to less and are risk avoiders, in iv. (10) Repeat steps i), ii) and iii) for all other possible pairwise combination G. (15pts) Assuming short selling is allowed: i. (2) For securities 1 and 2 find the composition, standard deviation, and e ii. (2) On the same graph plot the expected return and standard deviation iii. (1) Assuming that investors prefer more to less and are risk avoiders, in iv. (10) Repeat steps i), ii) and iii) for all other possible pairwise combination H. (14pts) Assuming short selling is not allowed, for portfolio with ALL THREE securities i. (4) Find the composition, standard deviation, and expected return of the ii. (7) Construct the minimum variance portfolio frontier. iii. (1) Assuming that investors prefer more to less and are risk avoiders, in iv. (2) Find the composition and standard deviation for the efficient por Note: In Part H, you must setup Solver parameters (I will check these): Objective Variable Cells Constraints that time period and the previous period consisted of a capital gain (or loss) and the receipt of the dividend onth (use simple return formula). each company (use population variance formula. i.e. divide by N, not (N-1) ). ween all possible pairs of securities (again, use population formula). the following portfolios: dard deviation, and expected return of that portfolio that has minimum risk. d standard deviation for all possible combinations of securities 1 and 2 are risk avoiders, indicate those sections of the diagram in part ii) that are efficient. pairwise combinations of securities in Problem 1. dard deviation, and expected return of that portfolio that has minimum risk. d standard deviation for all possible combinations of securities 1 and 2 are risk avoiders, indicate those sections of the diagram in part ii) that are efficient. pairwise combinations of securities in Problem 1. ALL THREE securities: xpected return of the portfolio that has minimum risk. are risk avoiders, indicate those sections of the diagram in part ii) that are efficient. n for the efficient portfolio that has 1% expected return. check these): eceipt of the dividend. Q# Your final answers must be provided in cells highlighted in blue and your graphical answers Marks 70 in total A. Month Security 2 3 4 5 1 A -2.9703% -1.0204% 4.2105% 2.0202% 1 B 0.8000% 4.3651% -1.9380% -1.7787% 1 C 1.4052% 7.1594% -1.5251% 1.7699% B. 1 1 1 Security A B C Average monthly return 0.8684% 0.6810% 1.6940% 2 2 2 Security A B C Standard deviation 2.4485% 2.1540% 3.2489% 2 2 2 Covariance Security A B C C. D. Correlation A 0.0600% -0.0329% -0.0192% E. C -0.0192% 0.0395% 0.1056% Avg.Ret SD 0.7747% 1.4743% 1.2812% 1.7824% 1.1875% 2.4032% 1.0811% 1.4404% 2 2 2 2 i. ii. iii. iv. 2 2 2 Security pair i. A&B i. A&C i. B&C 2 1 Security pair ii. A&B iii. A&B F. B -0.0329% 0.0464% 0.0395% Weights 46.0628% 53.9372% 61.1798% 38.8202% 90.5831% 9.4169% SD 0.0099% 0.0292% 0.0458% E[r] 0.7673% 1.1889% 0.7764% graph goes somewhere here Efficient set 1.0000% 0.7673% 0.8000% A&B 0.8684% 0.6810% 0.6000% 0.4000% 0.2000% 0.0000% 0.0000% 2 1 ii. A&C iii. A&C 0.5000% 1.0000% graph goes somewhere here 2.0000% 1.5000% 2.0000% 0.5000% 3.0000% A&C Efficient set 1.6940% 1.5000% 1.1889% 1.0000% 2.5000% 0.8684% A&C Efficient set 2.0000% 1.6940% 1.5000% 1.1889% 0.8684% 1.0000% 0.5000% 0.0000% 0.0000% 2 1 ii. B&C iii. B&C 0.5000% 1.0000% 1.5000% graph goes somewhere here 2.0000% 1.5000% 2.0000% 2.5000% 3.0000% 3.5000% B&C 1.6940% Efficient set 0.7764% 1.0000% 0.6810% 0.5000% 0.0000% 0.0000% G. 2 2 2 Security pair i. A&B i. A&C i. B&C 2 1 Security pair ii. A&B iii. A&B 0.5000% 1.0000% Weights 46.0628% 53.9372% 61.1798% 38.8202% 90.5831% 9.4169% 1.5000% SD 0.0099% 0.0292% 0.0458% graph goes somewhere here 2.0000% 2.5000% 3.0000% E[r] 0.7673% 1.1889% 0.7764% A&B Efficient set 0.8684% 1.0000% 0.7673% 0.8000% 0.6810% 0.6000% 0.4000% 0.2000% 0.0000% 0.0000% 2 1 ii. A&C iii. A&C 0.5000% 1.0000% graph goes somewhere here 2.0000% 1.5000% 2.0000% 2.5000% 3.0 A&C 1.6940 Efficient set 1.5000% 1.1889% 0.8684% 1.0000% 0.5000% 0.0000% 0.0000% 2 1 ii. B&C iii. B&C 0.5000% 1.0000% graph goes somewhere here 2.0000% 1.5000% 2.0000% 0.5000% 3.0000% B&C Efficient set 1.6940 1.5000% 0.7764% 1.0000% 2.5000% 0.6810% B&C 2.0000% Efficient set 1.6940 1.5000% 0.7764% 1.0000% 0.6810% 0.5000% 0.0000% 0.0000% H. 4 Portfolio i. A&B&C 7 1 ii. A&B&C iii. A&B&C 2 iv. 0.5000% 1.0000% Weights 1.5000% 2.0000% SD graph goes somewhere here Weights SD 2.5000% 3.0000% e and your graphical answers in the approximate space provided in shaded green area 6 2.9703% 0.8048% 3.9130% 7 0.0000% 1.8330% -2.5586% Correlation Security A A 100.0000% B -62.3849% C -24.1529% 0.8684% 0.6810% 2.0000% 2.5000% 3.0000% 1.6940% 0.8684% B C -62.3849% -0.241529 100.0000% 0.564925 56.4925% 1 0% 1.6940% 0.8684% 2.5000% 3.0000% 3.5000% 1.6940% 0.6810% .0000% 2.5000% 3.0000% 3.5000% 0.8684% 0.6810% % 2.0000% 2.5000% 3.0000% 1.6940% 0.8684% 2.0000% 2.5000% 3.0000% 3.5000% 1.6940% 0.6810% 1.6940% 0.6810% 2.0000% 2.5000% E[r] E[r] 3.0000% 3.5000% A Rate of return=[(P1-P0)+Dividend ]/ P0 price 1 $ 2 $ 3 $ 4 $ 5 $ 6 $ 7 $ Security A dividend 25.25 24.50 23.75 24.75 25.25 25.75 25.75 $ $ return $ $ $ $ 0.25 $ $ 0.50 rate of return -0.75 -0.25 1.00 0.50 0.75 - B.AVERAGE C. -2.9703% -1.0204% 4.2105% 2.0202% 2.9703% 0.0000% 0.8684% Security A Rate of return Average rate [R] of return[T] (R-T)^2 -2.9703% 0.8684% -1.0204% 0.8684% 4.2105% 0.8684% 2.0202% 0.8684% 2.9703% 0.8684% 0.0000% 0.8684% sum Standard deviation 0.1474% 0.0357% 0.1117% 0.0133% 0.0442% 0.0075% 0.0600% 2.4485% D. Security A (R-T) -3.8387% -1.8888% 3.3421% 1.1518% 2.1019% -0.8684% Security B (R-T) Security 0.1190% 3.6840% -2.6190% -2.4597% 0.1238% 1.1520% C (R-T) -0.2888% 5.4654% -3.2190% 0.0759% 2.2191% -4.2526% E. Rate of return A Rate 2 -2.9703% 3 -1.0204% 4 4.2105% 5 2.0202% 6 2.9703% 7 0.0000% of returnBRate of return C 0.8000% 1.4052% 4.3651% 7.1594% -1.9380% -1.5251% -1.7787% 1.7699% 0.8048% 3.9130% 1.8330% -2.5586% average A Variance B 0.0600% C 0.0464% 0.1056% standard deviation F. A Variance SD rate of return SD-Protfolio 1 SD-Protfolio 2 SD-Protfolio 3 SD-Protfolio 4 a) A&B: A&C B&C 1 A GMV B B 0.0600% 2.4485% 0.8684% 1.4743% 1.7824% 2.4032% 1.4404% 0.0464% 2.1540% 0.6810% GMV XA= XB= XA= XC= XB= XC= SD C 0.1056% 3.2489% 1.6940% 46.0628% E[R]= 53.9372% 61.1798% E[R]= 38.8202% 90.5831% E[R]= 9.4169% E[r] 2.4485% 0.0099% 2.1540% standard deviation 0.7673% 1.1889% 0.7764% A&B 1.0000% 0.8684% 0.7673% 0.6810% 0.8000% 0.6000% 0.4000% 0.2000% 0.0000% 0.0000% 0.5000% 1.0000% 1.5000% 0.8000% 0.6000% 0.4000% 1 A GMV C SD 1 B GMV C SD 0.2000% E[r] 2.4485% 0.0292% 3.2489% 0.0000% 0.0000% 0.8684% 1.1889% 1.6940% 1.0000% 2.0000% 1.5000% 0.6810% 0.7764% 1.6940% 1.0000% 0.5000% 0.0000% 0.0000% 0.5000% 1.0000% B&C 1.8000% 1.6000% 1.4000% 1.2000% 1.0000% 0.8000% 0.6000% 0.4000% 0.2000% 0.0000% 0.0000% 0.5000% 1.0000% 1.5000% A&C E[r] 2.1540% 0.0458% 3.2489% 0.5000% 1.5000% 2.0000% 2.5000% 3.0000% 3.5000% 1.5000% idend ]/ P0 Price $ $ $ $ $ $ $ Security B Dividend 125.00 126.00 129.00 126.50 124.25 122.75 125.00 return $ 2.50 $ 2.50 $ $ $ $ $ $ rate of return 1.00 5.50 -2.50 -2.25 1.00 2.25 price $ 0.8000% $ 4.3651% $ -1.9380% $ -1.7787% $ 0.8048% $ 1.8330% $ 0.6810% 106.75 108.25 114.75 113.00 115.00 117.25 114.25 Security B Average rate of Rate of return [R] return[T] (R-T)^2 0.8000% 0.6810% 4.3651% 0.6810% -1.9380% 0.6810% -1.7787% 0.6810% 0.8048% 0.6810% 1.8330% 0.6810% A*A SUM Correlation (A,A) Correlation (A,B) 0.0001% 0.1357% 0.0686% 0.0605% 0.0002% 0.0133% 0.0464% 2.1540% A*B A*C 0.1474% 0.0357% 0.1117% 0.0133% 0.0442% 0.0075% -0.0046% -0.0696% -0.0875% -0.0283% 0.0026% -0.0100% 0.0111% -0.1032% -0.1076% 0.0009% 0.0466% 0.0369% 0.3597% 0.0600% -0.1974% -0.0329% -0.1153% -0.0192% 1.0000 -0.6238 -0.6238487463 000% Correlation Correlation Correlation Correlation (A,C) (B,B) (B,C) (C,C) -0.2415 1.0000 0.5649 1.0000 -0.2415287288 0.5649252532 Portfolio 1 Portfolio 2 Portfolio 3 portfolio 4 A + B A + C B + C 1/3 A + 1/3 B + 1/3 C -1.0851% -0.7826% 1.1026% -0.255% 1.6723% 3.0695% 5.7622% 3.501% 1.1363% 1.3427% -1.7315% 0.249% 0.1208% 1.8951% -0.0044% 0.670% 1.8876% 3.4417% 2.3589% 2.563% 0.9165% -1.2793% -0.3628% -0.242% 0.7747% 1.2812% 1.1875% 1.0811% 0.0217% 1.4743% 0.0318% 1.7824% A&B A&C -0.0329% 0.0578% 2.4032% B&C -0.0192% SD= 0.0099% SD= 0.0292% SD= 0.0458% 0.0395% A&B 1.0000% 1.5000% 2.0000% 2.5000% 3.0000% 0.0207% 1.4404% 000% 1.0000% 1.5000% 2.0000% 2.5000% 3.0000% A&C 000% 1.0000% 00% 3.5000% 1.5000% 2.0000% 2.5000% 3.0000% 3.5000% Secruity C dividend return $ 1.25 $ $ $ 2.25 $ $ $ $ rate of return 1.50 7.75 -1.75 2.00 4.50 -3.00 1.4052% 7.1594% -1.5251% 1.7699% 3.9130% -2.5586% 1.6940% Secruity C Rate of return Average rate of [R] return[T] (R-T)^2 1.4052% 1.6940% 0.0008% 7.1594% 1.6940% 0.2987% -1.5251% 1.6940% 0.1036% 1.7699% 1.6940% 0.0001% 3.9130% 1.6940% 0.0492% -2.5586% 1.6940% 0.1808% 0.1056% 3.2489% B*B B*C C*C 0.0001% 0.1357% 0.0686% 0.0605% 0.0002% 0.0133% -0.0003% 0.2013% 0.0843% -0.0019% 0.0027% -0.0490% 0.0008% 0.2987% 0.1036% 0.0001% 0.0492% 0.1808% 0.2784% 0.0464% 0.2372% 0.0395% 0.6333% 0.1056%