M04_MCDO8122_01_ISM_C04

# M04_MCDO8122_01_ISM_C04 - Chapter 4 Introduction to Risk...

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Chapter 4 Introduction to Risk Management n Question 4.1 The following table summarizes the unhedged and hedged profit calculations: Copper price in one year Total cost Unhedged profit Profit on short forward Net income on hedged profit \$0.80 \$0.90 - \$0.10 \$0.20 \$0.10 \$0.90 \$0.90 0 \$0.10 \$0.10 \$1.00 \$0.90 \$0.10 0 \$0.10 \$1.10 \$0.90 \$0.20 - \$0.10 \$0.10 \$1.20 \$0.90 \$0.30 - \$0.20 \$0.10 We obtain the following profit diagram:

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42 McDonald • Fundamentals of Derivatives Markets n Question 4.2 If the forward price were \$0.80 instead of \$1, we would get the following table: Copper price in one year Total cost Unhedged profit Profit on short forward Net income on hedged profit \$0.80 \$0.90 - \$0.10 \$0 - \$0.10 \$0.90 \$0.90 0 - \$0.10 - \$0.10 \$1.00 \$0.90 \$0.10 - \$0.20 - \$0.10 \$1.10 \$0.90 \$0.20 - \$0.30 - \$0.10 \$1.20 \$0.90 \$0.30 - \$0.40 - \$0.10 With a forward price of \$0.45, we have: Copper price in one year Total cost Unhedged profit Profit on short forward Net income on hedged profit \$0.70 \$0.90 - \$0.20 - \$0.25 - \$0.45 \$0.80 \$0.90 - \$0.10 - \$0.35 - \$0.45 \$0.90 \$0.90 0 - \$0.45 - \$0.45 \$1.00 \$0.90 \$0.10 - \$0.55 - \$0.45 \$1.10 \$0.90 \$0.20 - \$0.65 - \$0.45 \$1.20 \$0.90 \$0.30 - \$0.75 - \$0.45 Although the copper forward price of \$0.45 is below our total costs of \$0.90, it is higher than the variable cost of \$0.40. It still makes sense to produce copper, because even at a price of \$0.45 in one year, we will be able to partially cover our fixed costs. Note that we are assuming the fixed costs are sunk costs (i.e., they have already been incurred or are obligations XYZ must pay). n Question 4.3 Please note that we have given the continuously compounded rate of interest as 6%. Therefore, the effective annual interest rate is exp (0.06) 1 0.0618. - = The future value of the three put option premiums are: .0178 1.0618 .0189 × = for the \$0.95-strike put, .0376 1.0618 .0399 × = for the \$1-strike put, and .0665 1.0618 .0706 × = for the \$1.05-strike put. The following table shows the profit calculations for the \$1.00-strike put. The calculations for the two other puts are similar. The figure on the next page compares the profit diagrams of all three possible hedging strategies. Copper price in one year Total cost Unhedged profit Payoff on long \$1.00- strike put option Put premium Net income on hedged profit \$0.80 \$0.90 - \$0.10 \$0.20 \$0.0399 \$0.0601 \$0.90 \$0.90 0 \$0.10 \$0.0399 \$0.0601 \$1.00 \$0.90 \$0.10 0 \$0.0399 \$0.0601 \$1.10 \$0.90 \$0.20 0 \$0.0399 \$0.1601 \$1.20 \$0.90 \$0.30 0 \$0.0399 \$0.2601
Chapter 4 Introduction to Risk Management 43 Profit diagram of the different put strategies: n Question 4.4 The future value of the three call option premiums are: .0649 1.0618 .0689 × = for the \$0.95-strike call, .0376 1.0618 .0399 × = for the \$1-strike call, and .0194 1.0618 .0206 × = for the \$1.05-strike call. The following table shows the profit calculations for the \$1.00-strike call. The calculations for the two

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M04_MCDO8122_01_ISM_C04 - Chapter 4 Introduction to Risk...

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