Minimum variance hedge Suppose a farmer is expecting that he

Minimum variance hedge

Suppose a farmer is expecting that her crop of grapefruit will be ready for

harvest and sale as 150,000150,000 pounds of grapefruit juice in 33

months time. She would like to use futures to hedge her risk but unfortunately there

are no futures contracts on grapefruit juice. Instead she will use orange juice futures.

Suppose each orange juice futures contract is for 15,00015,000

pounds of orange juice and the current futures price is F_0 = 118.65F0?=118.65 cents-per-pound.

The volatility, i.e. the standard deviation, of the prices of

orange juice and grape fruit juice is 20\\%20% and 25\\%25%, respectively,

and the correlation coefficient is 0.70.7. What is the approximate number

of contracts she should purchase to minimize the variance of her payoff?

Please submit your answer rounded to the nearest integer. So for example, if your calculations result in 10.78 contracts you should submit an answer of 11.

Incorrect

0 / 1 points

5. Question 5

Call Options

Consider a 11-period binomial model with R=1.02R=1.02, S_0 = 100S0?=100,

u=1/d= 1.05u=1/d=1.05. Compute the value of a European call option on the stock

with strike K=102K=102. The stock does not pay dividends.

Please submit your answer rounded to two decimal places. So for example, if your answer is 3.45673.4567 then you should submit an answer of 3.463.46.

Incorrect

0 / 1 points

6. Question 6

Call Options II

When you construct the replicating portfolio for the option in the previous question how many dollars do you need to invest in the cash account?

Please submit your answer rounded to three decimal places. So for example, if your answer is -43.4567?43.4567 then you should submit an answer of -43.457?43.457.

Solution

Each Orange Juice contract is = 15,000 pounds

Quantity of Grapefruit Juice to be hedged = 150,000 pounds

Current Futures Price of Orange Juice = 118.65 Cents per pound = 118.65*15,000 Cents per contract

Standard Deviation of Orange Juice (?_Orangejuice)        = 20%

Standard Deviation of Grapefruit Juice (?_Grapejuice)    = 25%

Correlation coefficient (?) = 0.70

Hedge Ratio = ? * ?_Orangejuice / ?_Grapejuice

= 0.70*(0.25/0.20)

=0.875

Number of contracts = HedgeRatio * PortfolioValue / ValueFuturesContract

= 0.875 * 150,000 pounds/15,000 pounds

=8.75

i.e., 9 Contracts.