Question

Your company plans to sell 2000 ounces of silver next week decides to use silver futures contracts to create a minimum variance hedge. Each futures contract has 125 ounces of silver attached. The spot and futures prices for silver the day your company opened its position were $16/ounce and $20/ounce, respectively. The table below shows both spot and futures price changes over a three day period.

	Spot Price Change	Futures Price Change
Day 1	-.03	-.06
Day 2	.04	.08
Day 3	.05	.01

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

2.Find the covariance between changes in the spot price and changes in the futures price. Round intermediate steps and your final answer to four decimals. Enter your answer in decimal format (EX: .XXXX).

3.Find the correlation coefficient between the spot and futures price changes. Round intermediate steps to four decimals.

4. How many futures contracts will you need to minimize your 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

Standard deviation (SD) = variance^0.5 where

Variance = Sum of (price change per day - average price change)^2

Average price change = sum of price change per day/3

Covariance = Sum of [(spot price per day - average spot price change)*(futures price per day - average futures price change)]/3

Correlation coefficient = covariance/(SDspot price change*SDfutures price change)

Calculations:

1). Standard deviation of change in spot price = 0.0361

2). Covariance between spot and futures price changes = 0.0016

3). Correlation coefficient between spot and future price changes = 0.7725

4). Minimum variance hedge ratio (h*) = correlation coefficient*SDspot price change/SDfutures price change

= 0.7725*0.0361/0.0574 = 0.4849

Number of futures contract required for hedging = h*(Size of position being hedged/size of one futures contract)

= 0.4849*(2,000/125) = 7.7584 contracts or 8 contracts.

Note: All intermediate calculations and final answers have been rounded off to 4 decimal places, as instructed in the question. If intermediate calculations are not rounded off then final answers may differ slightly from the given answers.