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m48-ch04 shrunk v02

m48-ch04 shrunk v02 - Chapter 4 Introduction to Risk...

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Chapter 4 Introduction to Risk Management Question 4.1. The following table summarizes the unhedged and hedged proFt calculations: Copper price in Total cost Unhedged proFt ProFt on short Net income on one year forward hedged proFt \$0.70 \$0.90 \$0.20 \$0.30 \$0.10 \$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 proFt diagram: Question 4.2. If the forward price were \$0.80 instead of \$1, we would get the following table: 43

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Part 1 Insurance, Hedging, and Simple Strategies Copper price in Total cost Unhedged proft Proft on short Net income on one year Forward hedged proft \$0.70 \$0.90 \$0.20 \$0.10 \$0.10 \$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 Total cost Unhedged proft Proft on short Net income on one year Forward hedged proft \$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 fxed costs. 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 . 062. In this exercise, we need to fnd the Future value oF the put premia. ±or the \$1-strike put, it is: \$0 . 0376 × 1 . 062 = \$0 . 04. The Following table shows the proft calculations For the \$1.00-strike put. The calculations For the two other puts are exactly similar. The fgure on the next page compares the proft diagrams oF all three possible hedging strategies. Copper price in Total cost Unhedged Proft on long Put Net income on one year proft \$1.00-strike put premium hedged proft option \$0.70 \$0.90 \$0.20 \$0.30 \$0.04 \$0.06 \$0.80 \$0.90 \$0.10 \$0.20 \$0.04 \$0.06 \$0.90 \$0.90 0 \$0.10 \$0.04 \$0.06 \$1.00 \$0.90 \$0.10 0 \$0.04 \$0.06 \$1.10 \$0.90 \$0.20 0 \$0.04 \$0.16 \$1.20 \$0.90 \$0.30 0 \$0.04 \$0.26 44
Chapter 4 Introduction to Risk Management Proft diagram oF the diFFerent put strategies: Question 4.4. We will explicitly calculate the proft For the \$1.00-strike and show fgures For all three strikes. The Future value oF the \$1.00-strike call premium amounts to: \$0 . 0376 × 1 . 062 = \$0 . 04. Copper price in Total cost Unhedged Proft on short Call Net income on one year proft \$1.00-strike call premium hedged proft option received \$0.70 \$0.90 \$0.20 0 \$0.04 \$0.16 \$0.80 \$0.90 \$0.10 0 \$0.04 \$0.06 \$0.90 \$0.90 0 0 \$0.04 \$0.04 \$1.00 \$0.90 \$0.10 0 \$0.04 \$0.14 \$1.10 \$0.90 \$0.20 \$0.10 \$0.04 \$0.14 \$1.20 \$0.90 \$0.30 \$0.20 \$0.04 \$0.14 45

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Part 1 Insurance, Hedging, and Simple Strategies We obtain the following payoff graphs: Question 4.5. XYZ will buy collars, which means that they buy the put leg and sell the call leg. We have to compute for each case the net option premium position, and Fnd its future value. We have for a) ( \$0 . 0178 \$0 . 0376 ) × 1 . 062 =− \$0 . 021 b) ( \$0 . 0265 \$0 . 0274 ) × 1 . 062 \$0 . 001 c) ( \$0 . 0665 \$0 . 0194 ) × 1 . 062 = \$0 . 050 46
Chapter 4 Introduction to Risk Management a) Copper price in Total cost Proft on .95 Proft on short Net Hedged proft one year put \$1.00 call premium \$0.70 \$0.90 \$0.25 0 \$0.021 \$0.0710 \$0.80 \$0.90 \$0.15 0 \$0.021 \$0.0710 \$0.90 \$0.90 \$0.05 0 \$0.021 \$0.0710 \$1.00 \$0.90 \$0 0 \$0.021 \$0.1210 \$1.10 \$0.90 0 \$0.10 \$0.021 \$0.1210 \$1.20 \$0.90 0 \$0.20 \$0.021 \$0.1210 Proft diagram: b) Copper price in Total cost Proft on .975

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m48-ch04 shrunk v02 - Chapter 4 Introduction to Risk...

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