One of the major risks in the economy is the oil price. Many financial assets ar

Question

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:

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

You are planning to invest 40% of your investment in the natural gas company and the remaining in the automobile company. What is the variance of your portfolio?

3.36

4.56

10.14

1.5

12.54

Explanation / Answer

Here, we first compute the expected payoffs in each of the 3 conditions as:

Therefore, we get the distribution here as:

P(R = 5.2) = 0.3 + 0.4 = 0.7
P( R = 1.2) = 0.3

The expected return is computed as:

E(R) = 0.7*5.2 + 0.3*1.2 = 4%

The second moment of return here is computed as:

E(R2) = 0.7*5.22 + 0.3*1.22 = 19.36%

The variance is therefore computed here as:

Var(R) = E(R2) - E2(R) = 19.36 - 42 = 3.36%2

Therefore a is the correct variance value required here.

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