You plan to invest $3 million in the construction of an oil well that has potential revenue of $10 million. The oil wells will be located in the Gulf of Mexico. As we all know, this region is constantly hit by hurricanes. Assuming that if there is a hurricane of category 1 or 2, this will disrupt your production and the well will produce half its capacity, and if there is a category 3, or 4, your well will produce one-fifth of its capacity, if there is a category 5 your wells will be closed. In order to reduce the risk on your investment, you plan to buy an insurance policy. One unit of this policy cost $1 and will pay $2 if the region is hit with a storm of category 1 or 2, $4 if the region is hit with a storm of category 3, or 4, and $6 if the region is hit by a storm of category 5. We know from the weather prediction that there is a 40% chance that the region will be hit with a category 1 or 2 storms, 20% for a category 3, or 4, and 10% for a category 5, 30% chance that the region will not be hit.

What is the variance of the rate of return on your investment if you buy u units of this policy?

(1.164 10¹³ + 1.256 10⁷u + 3.56u²)/(3 10⁶ - u)²

(1.164 10¹³ 1.256 10⁷u + 3.56u²)/(3 10⁶ + u)²

(1.164 10¹³ 1.256 10⁷u + 3.56u²)/(3 10⁶ - u)²

(1.164 10¹³ + 1.256 10⁷u + 3.56u²)/(3 10⁶ + u)²

(1.164 10¹³ + 1.256 10⁷u + 3.56u²)/(3 10⁶ - u)²