Question

Johnson Manufacturing will receive 60,000 tons of iron ore next month and chooses to use futures contracts to create a minimum variance hedge. Each futures contract has 10,000 tons of iron attached. The spot and futures prices for iron on the day DEF opened its position were $62/ton and $65/ton, respectively. The table below shows both spot and futures price changes over a four day period.

	Spot Price Change	Futures Price Change
Day 1	.2	.15
Day 2	.04	.03
Day 3	-.01	-.02
Day 4	.05	0

1.Find the standard deviation of change in the spot price. Round intermediate steps to four decimals.

2. Find the standard deviation of change in the futures price. Round intermediate steps to four decimals.

3.Find the covariance between the two series. Round intermediate steps to four decimals.

4.Find the correlation coefficient between the two series. Round intermediate steps and your final answer to four decimals. Enter your answer in decimal format (EX: .XXXX).

5.How many futures contracts will Johnson need to minimize their portfolio's risk? Round your final answer to the nearest whole number. Do not use words when entering your response.

I want to know how to solve this step by step please! :)

Answer 1

1)

Where x_i = each value from the sample

x̅ = sample mean

N = sample size

Using this formula for Spot Price Changes

Standard Deviation of Change in Spot Price = 0.0906 = 9.0554%

2)

Using the above formula for Futures price change

Standard Deviation of Change in Futures Price = 0.0762 = 7.6158%

3)

Using the above formula for covariance

Covariance = 0.0067 = 0.6733%

4)

Correlation Coefficient = (0.6733%) / (9.0554%X7.6158%) = 0.9764

Thank you for the questions. We are allowed to answer only up to 4 sub questions. You can use the optimal hedge ratio to find the number of futures contracts required to minimize portfolio risk.