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A textile manufacturer has made an agreement to deliver 100,000 t-shirts in 2 months
A textile manufacturer has made an agreement to deliver 100,000 t-shirts in 2 months. There is a concern that the price of cotton, which is the main material used in manufacturing, may fluctuate considerably during the following months. It is estimated that 0.10 kg of cotton will be needed to manufacture each t-shirt. Currently, the spot price of cotton is C0=20$/kg and standard deviation of the cotton price is $2. It is also known that the price of silk is correlated with the cotton. The current price of silk is S0=$50/kg and the standard deviation of the silk price is $4. The correlation coefficient between the cotton price and the silk price is given as 0.80. Assume that the monthly interest rate is 10% per year compounded continuously. The manufacturer wants to hedge his risk against unexpected increases in the price of cotton
What is the total amount of cotton needed : kg
Suppose that the manufacturer can make forward contract with a counterpart to buy cotton in 2 months, what should be the forward price of cotton in the contract assuming that there is no holding cost? $ (Two decimal digits)
If there is a futures market for cotton, what is the strategy of the manufacturer if he wants to minimize his risk? Bo? (write long/short). units of cotton contract (in terms of kg of cotton).
Suppose that there is no futures market for cotton, but there is a futures market for silk. What position should the manufacturer take in silk futures to minimize his risk? (write long/short) units of silk contract (in terms of kg of silk).
Expert Solution
Total amount of cotton needed, Q = Total number of shirts x Quantum of cotton per shirt = 100,000 x 0.1 =10,000 kg
r = interest rate = 10%; t = 2 months = 2/12 years
Forward price of the cotton = C0er x t = 20e10% x 2/12 = 20.34
Hedging strategy should be: Long 10,000 units of contton contract.
Total exposure = C0 x Q = 20 x 10,000 = 200,000
Hence, quantum of silk required to match the value, Q = Total exposure / S0 = 200,000 / 50 = 4,000 kg
Optimal hedge ratio = Correlation coefficient x Std dev of the cotton / Std dev of silk = 0.8 x 2/4 = 0.4
Hence, quantum of silk that needs to be hedged = Optimal hedge ratio x Q = 0.4 x 4,000 = 1,600
Hence, the position to be taken in silk futures is: Long 1,600 kg of silk.
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