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

 

1. Explain to your Aunt Betty the meanings of call and put options, and how options are different from futures and forward contracts.        
2. Looking at all the numbers in the above tables, your Aunt Betty feels very confused. Pick one row from Table 1 (row 2, 3, 4, or 5) and explain what each number across the row means to your Aunt Betty (Strike, Last, Chg, Bid, Ask, Vol, Open Int).                    
3. Aunt Betty will be retiring in two years. As a result, she is fairly risk-averse when it comes to her investments. She does not like how the recent economic downturn is affecting her portfolio value. However, she would like to hold on to her Suncor shares unless their price falls below $35 per share. Explain to your aunt how she can use the call options to hedge her portfolio against a further drop in Suncor share price.       
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.        
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 Betty’s 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 Betty’s 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 aunt’s projections of down- and up-movements of Suncor remain the same for these risk-free rates.