Assume 25% in Gold and 75% in Auto Rate of Return, % Scenario Recession Normal Boom Expected return Variance Standard deviation Probability 1/3 1/3 1/3 Auto Stock 8 Gold Stock Portfolio Return, %* +20 +4.5 +8.5 4 15.2 3.9 20 +18 5 112.7 10.6 268.7 16.4 Sensitivity analysis Portfolio Rate of Retumm Portfolio Weights Expected Standard Return Deviation Gold Autos Recession Normal Boom 0.0 0.2 0.4 0.6 0.8 5.0 4.2 3.4 2.6 1.8 1.0 1.0 0.8 0.6 0.4 0.2 0.0 8.0 2.4 3.2 8.8 14.4 20.0 5.0 4.6 4.2 3.8 3.4 3.0 10.6 5.2 0.6 5.6 11.0 16.4 18.0 10.4 2.8 4.8 -12.4 20.0 Example: Suppose that all the information given in the previous example is the same except that this time, the probability of the recession or boom is 0.30; and the probability of a normal period is 0.40 What would be the expected return and variance of the same stock- gold portfolio