. Given the following probability distributions for Naples Oil Inc. (NOI) and Sa

Question

. Given the following probability distributions for Naples Oil Inc. (NOI) and Sarasota Industrial (WI), answer the following questions: using formulas

                        State of Economy       Probability      NOI returns    SI returns

                        Exceptional                 5%                               22%     12%

                        Slight boom                 20%                             14%     11%

                        Average                       60%                             7%       8%

                        Recession                    15%                             -4%     2%

           

a) What is the standard deviation for both NOI and SI?

b) If this were a continuous distribution, approximately 95.44% of the time, the return for NOI will fall between _____ and _____.

c) If you invested $6,000 in NOI and $9,000 in SI, what is the expected return on the portfolio?

Explanation / Answer

a) What is the standard deviation for both NOI and SI?

standard deviation of NOI = Variance^(1/2)

standard deviation of NOI = 0.0038950^(1/2)

standard deviation of NOI = 6.24%

standard deviation of SI = Variance^(1/2)

standard deviation of SI = 0.000799^(1/2)

standard deviation of SI = 2.83%

Working

b) If this were a continuous distribution, approximately 95.44% of the time, the return for NOI will fall between _____ and _____.

Z value = normsinv(95.44%)

Z Value = 1.689

Lower Value = Expected Return - Z Value * SD

Lower Value = 7.5% - 1.689*6.24%

Lower Value = - 3.04%

Hiigher Value = Expected Return + Z Value * SD

Hiigher Value =7.5% + 1.689*6.24%

Hiigher Value = 18.04%

Answer

The return for NOI will fall between _-3.04%_ and _18.04%

c) If you invested $6,000 in NOI and $9,000 in SI, what is the expected return on the portfolio?

Expected return on the portfolio = 6000/(6000+9000)*7.5% + 9000/(6000+9000)*7.9%

Expected return on the portfolio = 7.74%

State of Economy Probability NOI SI [a] [b (return]) [c = a*b] Variance = [(b-expected Return)^2 * a] [d (return)] [e = a*d] Variance = [(d-expected Return)^2 * a] Exceptional      5% 22% 1.100%                                      0.0010513 12% 0.600%                                      0.0000840 Slight boom      20% 14% 2.800%                                      0.0008450 11% 2.200%                                      0.0001922 Average          60% 7% 4.200%                                      0.0000150 8% 4.800%                                      0.0000006 Recession        15% -4% -0.600%                                      0.0019838 2% 0.300%                                      0.0005222 Expected Return = 7.500%                                      0.0038950 Expected Return = 7.900%                                      0.0007990

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