Solution of Derivative

04 004 004 004 net income on hedged profit 046 036

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Unformatted text preview: .00 $1.10 $1.20 Total Cost $5.70 $5.80 $5.90 $6.00 $6.10 $6.20 unhedged Profit $0.50 $0.40 $0.30 $0.20 $0.10 0 Profit on long $1.00-strike call 0 0 0 0 $0.10 $0.20 Call premium $0.04 $0.04 $0.04 $0.04 $0.04 $0.04 Net income on hedged profit $0.46 $0.36 $0.26 $0.16 $0.16 $0.16 We obtain the following profit diagrams: Question 4.10. Telco will sell collars, which means that they buy the call leg and sell the put leg. We have to compute for each case the net option premium position, and find its future value. We have for: a) ($0.0376 − $0.0178) × 1.062 = $0.021 b) ($0.0274 − $0.0265) × 1.062 = $0.001 c) ($0.0649 − $0.0178) × 1.062 = $0.050 27 Part 1 Insurance, Hedging, and Simple Strategies a) Copper price in one year Total Cost unhedged Profit $0.70 $0.80 $0.90 $1.00 $1.10 $1.20 Profit diagram: $5.70 $5.80 $5.90 $6.00 $6.10 $6.20 $0.50 $0.40 $0.30 $0.20 $0.10 0 Profit on short .95 put -$0.25 -$0.15 -$0.05 $0 0 0 Profit on long $1.00 call net hedged profit premium 0 0 0 0 $0.10 $0.20 $0.021 $0.021 $0.021 $0.021 $0.021 $0.021 $0.2290 $0.2290 $0.2290 $0.1790 $0.1790 $0.1790 Profit on long $1.025 call 0 0 0 0 $0.0750 $0.1750 Net premium $0.001 $0.001 $0.001 $0.001 $0.001 $0.001 Hedged profit b) Copper price in one year $0.70 $0.80 $0.90 $1.00 $1.10 $1.20 Total Cost $5.70 $5.80 $5.90 $6.00 $6.10 $6.20 Unhedged Profit $0.50 $0.40 $0.30 $0.20 $0.10 0 Profit on short .975 put -$0.275 -$0.175 -$0.075 $0 0 0 Profit diagram: 28 $0.2240 $0.2240 $0.2240 $0.1990 $0.1740 $0.1740 Chapter 4 Introduction to Risk Management c) Copper price in one year $0.70 $0.80 $0.90 $1.00 $1.10 $1.20 Total Cost $5.70 $5.80 $5.90 $6.00 $6.10 $6.20 Unhedged Profit $0.50 $0.40 $0.30 $0.20 $0.10 0 Profit on short .95 put -$0.25 -$0.15 -$0.05 0 0 0 Profit on long $.95 call 0 0 0 $0.050 $0.150 $0.250 Net premium $0.05 $0.05 $0.05 $0.05 $0.05 $0.05 Hedged profit $0.2 $0.2 $0.2 $0.2 $0.2 $0.2 We see that we are completely and perfectly hedged. Buying a collar where the put and call leg have equal strike prices perfectly offsets the copper price risk. Profit diagram: 29 Part 1 Insurance, Hedging, and Simple Strategies Question 4.12. This is a very important exercise to really understand the benefits and pitfalls of hedging strategies. Wirco needs copper as an input, which means that its costs increase with the price of copper. We may therefore think that they need to hedge against increases in the copper price. However, we must not forget that the price of wire, the source of Wirco’s revenues, also depends positively on the price of copper: the price Wirco can obtain for one unit of wire is $50 plus the price of copper. We will see that those copper price risks cancel each other out. Mathematically, Wirco’s cost per unit of wire: Wirco’s revenue per unit of wire: $3 + $1.50 + ST $5 + ST and ST is the price of copper after one year. Therefore, we can determine Wirco’s profits as: Profit = Revenue – Cost = $5 + S T − ($3 + $1.50 + ST ) = $0.50 We see that the profits of Wirco do not depend on the price of copper. Cost and revenue copper price risk cancel each other out. If we buy in this situation a long forward contract, we do in fact introduce copper price risk! To understand this, add a long forward contract to the profit equation: Profit with forward: = $5 + S T − ($3 + $1.50 + ST ) + ST − $1 = S T − $0.50 30 Chapter 4 Introduction to Risk Management To summarize, Copper price in one year $0.70 $0.80 $0.90 $1.00 $1.10 $1.20 Total Cost Total Revenue $5.20 $5.30 $5.40 $5.50 $5.60 $5.70 $5.70 $5.80 $5.90 $6.00 $6.10 $6.20 Unhedged profit $0.50 $0.50 $0.50 $0.50 $0.50 $0.50 Profit on long forward -$0.30 -$0.20 -$0.10 0 $0.10 $0.20 Net income on ‘hedged’ profit $0.20 $0.30 $0.40 $0.50 $0.60 $0.70 Question 4.14. Hedging should never be thought of as a profit increasing action. A company that hedges merely shifts profits from good to bad states of the relevant price risk that the hedge seeks to diminish. The value of the reduced profits, should the gold price rise, subsidizes the payment to Golddiggers should the gold price fall. Therefore, a company may use a hedge for one of the reasons stated in the textbook; however, it is not correct to compare hedged and unhedged companies from an accounting perspective. Question 4.16. a) Expected pre-tax profit Firm A: Firm B: E[Profit] = E[Profit] = 0.5 × ($1,000) + 0.5 × (− $600) = $200 0.5 × ($300) + 0.5 × ($100) = $200 Both firms have the same pre-tax profit. b) Expected after tax profit. Firm A: (1) (2) (3) (3b) bad state − $600 $0 0 $240 -$360 Pre-Tax Operating Income Taxable Income Tax @ 40 % Tax credit After-Tax Income (including Tax credit) good state $1,000 $1,000 $400 0 $600 This gives an expected after-tax profit for firm A of: E[Profit] = 0.5 × (− $360) + 0.5 × ($600) = $120 31 Part 1 Insurance, Hedging, and Simple Strategies Firm B: (1) (2) (3) (3b) bad state $100 $100 $40 0 $60 Pre-Tax Operating Income Taxable Income Tax @ 40 % Tax credit After-Tax Income (including Tax credit) good state $300 $300 $120 0 $180 This gives an expected after-tax profit for firm B of: E[Profit] = 0.5 × ($60) + 0.5 × ($180) = $120 If losses rece...
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This document was uploaded on 03/11/2014 for the course FIN 402 at FPT University.

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