The standard deviation of quarterly changed in the price of a commodity is $0.65, the standard deviation of quarterly changes in the futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. The minimum variance hedge ratio for a 3-month contract is:

Which of the following is a problem for the production of public goods?

Which of the following best describes vertical integration? a. produce goods or services previously purchasedb. develop the ability to produce products that complement the original productc. develop the ability to produce the specified good more efficiently than befored. build long term partnerships with a few supplierse. sell products to a supplier or a distributor

You wish to retire in 13 years, at which time you want to have accumulated enough money to receive an annual annuity of $23,000 for 18 years after retirement. during the period before retirement you can earn 9 percent annually, while after retirement you can earn 11 percent on your money. what annual contributions to the retirement fund will allow you to receive the $23,000 annuity? use appendix c and appendix d for an approximate answer, but calculate your final answer using the formula and financial calculator methods.