Question

1. Given the following probability distributions for Austin Tech Inc. (ATI) and Stephen’s Industrial (SI) answer the following questions: (Please show all work with formulas)

State of Economy             Probability          ATI Returns        SI Returns

Exceptional                         20%                        22%                        37%

Average                               50%                        9%                          6%

Recession                            30%                        1%                          -18%

1. What is the standard deviation for both ATI and SI?
2. Assuming a continuous distribution, approximately 95.44% of the time, the return for ATI will fall between _____ and _____.
3. What is the covariance between the returns of ATI and SI?
4. What is the correlation coefficient between ATI and SI?

Answer 1

1 ATI: Probability Expecte return 2 Return (r 22.00% 9.00% 1.00% 0.20 0.50 0.30 4.40%) 4.50% 0.30%) 12.80% -0.20% -8.20% 1.64% 0.00% 0.67% 0.33% 0.00% 0.20% 4 7 Expected return (μ) 9.20% Variance (gA2 0.005296 Standard deviation (o) | 7.28% 10 Probability Expecte return 12 Return (r rxP(r)- 37.00% 6.00% 18.00% 0.20 0.50 0.30 7.40%) 3.00%) 5.40% 32.00% 1.00% -23.00% 10.24% 0.01% 5.29% 2.05% 0.01% 1.59% 16 17 Expected return (μ) 18 19 5.00% Variance (ơ"2 0.036400 Standard deviation (o) | 19.08% 21 Covariance 0.013840-SUMPRODUCT(B3:B5,D3:D5,D13:D15) 22 Correlation 0.9980-CORREL(A3:A5,A13:A15)