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M03_MCDO8122_01_ISM_C03

M03_MCDO8122_01_ISM_C03 - Chapter 3 Insurance Collars and...

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Chapter 3 Insurance, Collars, and Other Strategies n Question 3.1 This question is a direct application of put-call parity (Equation 3.1) of the textbook. Mimicking Table 3.1, we have: S&R Index S&R Put Loan Payoff - (Cost + Interest) Profit 900.00 100.00 - 1000.00 0.00 - 95.68 - 95.68 950.00 50.00 - 1000.00 0.00 - 95.68 - 95.68 1000.00 0.00 - 1000.00 0.00 - 95.68 - 95.68 1050.00 0.00 - 1000.00 50.00 - 95.68 - 45.68 1100.00 0.00 - 1000.00 100.00 - 95.68 4.32 1150.00 0.00 - 1000.00 150.00 - 95.68 54.32 1200.00 0.00 - 1000.00 200.00 - 95.68 104.32 The payoff diagram looks as follows:
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23 McDonald • Fundamentals of Derivatives Markets We can see from the table and from the payoff diagram that we have replicated a call option payoff with the index, put, and borrowing positions. The profit diagram on the next page shows the profit diagram of our strategy is also the same as that of a call option. n Question 3.2 This question constructs a position that is the opposite of the position of Table 3.1. Therefore, we should get the exact opposite results from Table 3.1 and the associated figures. Mimicking Table 3.1, we have: S&R Index S&R Put Payoff - (Cost + Interest) Profit - 900.00 - 100.00 - 1000.00 1095.68 95.68 - 950.00 - 50.00 - 1000.00 1095.68 95.68 - 1000.00 0.00 - 1000.00 1095.68 95.68 - 1050.00 0.00 - 1050.00 1095.68 45.68 - 1100.00 0.00 - 1100.00 1095.68 - 4.32 - 1150.00 0.00 - 1150.00 1095.68 - 54.32 - 1200.00 0.00 - 1200.00 1095.68 - 104.32 On the next page, we see the corresponding payoff and profit diagrams. Please note that they match the combined payoff and profit diagrams of Figure 3.5. Only the axes have different scales.
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Chapter 3 Insurance, Collars, and Other Strategies 24 Payoff-diagram: Profit diagram:
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25 McDonald • Fundamentals of Derivatives Markets n Question 3.3 In order to be able to draw profit diagrams, we need to find the future value (FV) of the index cost, the put premium, the call premium, and the investment in zero-coupon bonds. We have: FV of index cost: 1000 (1 0.02) $1020 FV of the put premium: $51.777 (1 0.02) $52.813 FV of the call premium: $120.405 (1 0.02) $122.813 FV of the zero-coupon bond: $931.37 (1 0.02) $950.00 × + = × + = × + = × + = Our index plus put position has a FV cost of $1072.813. Our payoff diagram is: From this figure, we can already see that the combination of a long put and the long index looks exactly like a certain payoff of $950, plus the payoff of a call with a strike price of 950 (i.e., max(0, 950)). T S - This is the alternative investment given to us in the question. Its FV cost is 950 122.813 1072.813 + = which is exactly the same as our index plus put position. We have thus confirmed the equivalence of the two combined positions for the payoff diagrams. Since the costs are the same, the profit diagrams for the two are identical.
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Chapter 3 Insurance, Collars, and Other Strategies 26 Profit diagram for a long 950-strike put and a long index (which is the same as the profit diagram for a bond plus call strategy): n Question 3.4 This question is another application of put-call-parity. For our initial cost, we receive $1,000 from the short sale of the index and we have to pay the call premium which is $120.405. Using Question 3.3’s FV calculations, the future value of the funds we receive is 1020 122.813 897.187. - = It is often confusing to use the term “cost” in this context (when we receive money initially). It can be done, but you must be careful about “plusses and minuses”. Initial cash inflows can be looked at as negative costs and initial cash outflows as positive costs; it might be easiest to just think of cash flows. Positive cash flows are greater than zero and negative cash flows are less than zero. In this case, the future value of our
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