Case 2: Options Case

Your Aunt Betty has a $120,000 investment portfolio comprising some Government of Canada three-month Treasury Bills and 2,000 Suncor shares. When the portfolio was formed (one month ago), the shares were worth $85,700 and the bonds were worth $34,300. Today, Suncor shares are worth $41.94 per share, while the bond yields have decreased so that the bonds are now worth $38,000. The effective yield on the three-month Canada Treasury Bill is 0.94% per annum.

Aunt Betty is a bit concerned about the drop in value of her Suncor 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 Suncor shares. You find the following pricing information on the call options (Table 1) and the put options (Table 2) on Suncor, with expiry in one month:

Table 1: Call option prices

Strike	Last	Chg	Bid	Ask	Vol	Open Int
41.50	0.43	0.01	0.42	0.45	98	96
42.00	0.33	+0.13	0.36	0.39	101	38
42.50	0.12	+0.02	0.10	0.16	62	11
43.00	0.05	0.00	0.05	0.08	2	12

Table 2: Put option prices

Strike	Last	Chg	Bid	Ask	Vol	Open Int
40.50	0.10	0.00	0.09	0.10	5	5
41.00	0.06	0.18	0.04	0.06	10	12
41.50	0.13	0.18	0.10	0.13	48	57
42.00	0.39	0.48	0.30	0.39	91	1
42.50	1.22	0.00	1.00	1.25	64	64

4. Aunt Betty has heard about payoff profiles from the Business News Network (BNN) and would like to learn more about them. Draw the payoff profiles for the following four positions:
   • long position in the 42-call (i.e., the Suncor call option with strike price of $42)
   • short position in the 42-call
   • long (purchased) Suncor stock
   • a hedged position with one long (purchased) Suncor stock and one short position in the 42-call.

Ignore the call premium in your payoff profile plots. Carefully explain to your aunt what these payoff profiles mean. Be clear and concise, as your aunt gets impatient with long, drawn-out explanations when they are unnecessary.

5. What are the lower and upper bounds of the 42-call option? Does the actual call price fall between these bounds?
6. Calculate the intrinsic values of the four call options in Table 1. Explain to your Aunt Betty what intrinsic value means in the call option case, and how this value relates to the concepts of in-the-money and out-of-the-money in the case of call options.

Intrinsic value is the measure of what the asset is worth. Finding the value of the asset is done by a complex model

7. Explain to Aunt Betty the relationship between the price of a call and its exercise price. Is this relationship confirmed by your calculations in #6 (above)?
8. From her own intensive investigations into the operations and financial statement fundamentals of Suncor, Aunt Betty believes that in one month, the share price of Suncor will either decrease further to $40 or will increase to $45. Calculate the value of the 42-call option using the Two-period Binomial Model.
9. How does the value you have calculated in #8 (above) compare to the market-traded price of the 42-call option? What does this tell us about Aunt Bettys expectations versus the market, generally speaking?
10. Upon further research, you find that there are two other 42-call options which expire in two and three months, respectively. Suppose Aunt Bettys projections of down- and up-movements of Suncor remain the same for up to three months. What are the theoretical call prices of these two 42-call options based on the Binomial Model? Are these prices higher or lower than the price of the 42-call that expires in one month?
11. Explain to your Aunt Betty the relationship between call value and time-to-expiration of the option. Is this relationship confirmed by your calculations in #10?
12. Explain to your aunt the relationship between call value and the risk-free rate. Illustrate your explanations by calculating the call value of the 42-call with one-month expiry at effective risk-free rates of 0.5%, 1.5%, and 2.0%. Assume that your aunts projections of down- and up-movements of Suncor remain the same for these risk-free rates.