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

Question

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

                        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 _____.

Explanation / Answer

Question a. Return Expected Return Probability x Variance^2 State of Economy Probability NOI SI NOI SI NOI SI Exceptional 5% 22% 12% 1.10% 0.60% 0.00105 0.00008 Slight boom 20% 14% 11% 2.80% 2.20% 0.00085 0.00019 Average 60% 7% 8% 4.20% 4.80% 0.00002 0.00000 Recession 15% -4% 2% -0.60% 0.30% 0.00198 0.00052 Total 100% 7.50% 7.90% 0.00390 0.00080 Expected return = sum(Return x probability). Standard Deviation=square root(Probability x sum(return-expected return)^2) Standard deviation of NOI = (0.00390)^(1/2) 6.24% Standard deviation of SII = (0.00080)^(1/2) 2.83% Question b. Upper Limit for NOI = 7.50% + 6.24%=13.74% Lower Limit of NOI = 7.50-6.24% = 1.26% Answer is 1.26% and 13.74% NOI SI Total Investment 6000 9000 15000 Expected return on investment 7.50% 7.90% Portfolio return on investment 450 711 1161 Portfolio return = $1,161.

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