Lower and upper bounds of the 45-call option

Case Scenario:

Your Aunt Jemima has a $100,000 investment portfolio comprising some bonds and 200 EnCana shares. At the time the portfolio was formed (two months ago), the shares were worth $12,782 and the bonds were worth $87,218. Today, EnCana shares are worth $44.20 per share, while the bond yields have decreased so that the bonds are now worth $90,000. The effective yield on the 3-month Canada Treasury Bill is 1.77% per annum.

Your aunt is a bit concerned about the drop in value of her EnCana shares and consequently, her overall portfolio value. Knowing that you are taking a finance course, she consults you to see what she can do to protect her portfolio from a further drop in value. She has heard a lot about call and put options and would like to know more about these.

You immediately go online to look for information on options on EnCana shares. You find the following pricing information on the call options on EnCana with expiry in one month:

EnCana Corp. (ECA) 44.20
Strike Last Chg Bid Ask Vol Open Int
40 5.00 +0.20 5.22 5.77 10 543
45 1.40 +0.10 1.45 1.50 11 1,781
50 0.25 +0.07 0.20 0.30 66 2,456
55 0.10 0.00 N/A 0.05 5 2,831
60 0.05 0.00 N/A 0.01 3 2,875

Your Aunt Jemima is fairly risk-averse and she does not like how the recent economic downturn is affecting her portfolio value. However, she is fiercely loyal to EnCana (she always says that EnCana is a good Canadian company that deserves to be supported by Canadian investors) so she wishes to hang on to its shares. Explain to your aunt how she can use the call options to hedge her portfolio against a further drop in EnCana share price.

Your aunt has heard about payoff profiles from BNN (Business News Network) and would like to learn more about them. Draw the payoff profiles for both long and short positions in the 45-call, the payoff profile for the EnCana stock, and finally, the payoff profile for a hedged position from part c (above) with the EnCana stock and the short position in the 45-call. Ignore the call premium in your plots. Carefully explain to your aunt what these payoff profiles mean. Be clear and concise, as your aunt is rather impatient and does not like long and drawn-out explanations when they are not necessary.

What are the lower and upper bounds of the 45-call option? Does the actual call price fall between these bounds?

Calculate the intrinsic values of the five call options in the table.

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Finance Basics: Lower and upper bounds of the 45-call option
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