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One of the major risks in the economy is the oil price. Many financial assets are severely affected by the oil price. Consider a natural

One of the major risks in the economy is the oil price. Many financial assets are severely affected by the oil price. Consider a natural gas company and an automobile company. The natural gas company will be hit by a low oil price because the demand for natural gas will decrease as oil becomes cheaper. But the automobile company will benefit from a low oil price as more people can afford the cost of driving a car. The probability of the oil price next year is given by the following table:

Oil price Probability
drops 25%
does not change 50%
arises 25%

Contingent on the change in the oil price next year, the annual returns to the companies are expected as follows:

If oil price Natural gas Automobile
drops -8% 18%
does not change 6% 4%
arises 12% -10%

You are planning to invest 70% of your investment in the natural gas company and the remaining in the automobile company. What is the variance of your portfolio?

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