Question

A firm is expecting to receive $80M in 6 months and wishes to invest it for another 6 months. But the firm is worried about a potential decline in interest rates. Because of their flexibility, the firm decides to use call options on the 6-month T-bill. A call option on the 6-month T-bill with 6-month maturity exists with strike $95.8 (per $100 face value) and $0.34 premium. The current price of the 6-month T-bill is $96.92 per 100 face value.

Assume the firm thinks the initial cost of call options is too high. The firm considers alternatives to reduce the hedging costs. Discuss how the firms could reduce hedging costs through a collar. Assume there is a put option on the 6-month T-bill with 6-month maturity and a strike price of $94.00 (per $100 face value) and $0.20 premium. Draw the payoff diagram for the collar.

Answer 1

A collar strategy involves buying the call option of a higher strike price and selling a put option with a lower strike price

Here the company will Buy the call option to purchase T bill at $95.8 at $0.32 and sell a put option with a strike price of $94 for $0.20

Payoff of long call = max( Pt - K, 0) - premium = max (Pt-95.8,0)- 0.34

where Pt is the price of T bill after 6 months and max is a function which returns the maximum value

Payoff of short put = premium - max (K-Pt, 0) = 0.20 - max(94-St, 0)

So, the payoff table and the payoff diagram for various value of T Bills after 6 months (from $90 an increasing in step of $1 upto $100)  looks like

Figures in $
T Bill price	Long Call	Short Put	Total Payoff
after 6 months	with Strike 95.8	with strike 94
90.00	-0.34	-3.80	-4.14
91.00	-0.34	-2.80	-3.14
92.00	-0.34	-1.80	-2.14
93.00	-0.34	-0.80	-1.14
94.00	-0.34	0.20	-0.14
95.00	-0.34	0.20	-0.14
95.80	-0.34	0.20	-0.14
96.00	-0.14	0.20	0.06
97.00	0.86	0.20	1.06
98.00	1.86	0.20	2.06
99.00	2.86	0.20	3.06
100.00	3.86	0.20	4.06

the payoff diagram looks like

It can be seen that since the company wants to purchase the T bill after 6 months, the collar is in a loss after 6 months and the minimum price at which the company is able to buy the collar is $94 (courtesy the short put option) and the maximum that a company has to spend to purchase the T bill is $95.8 (courtesy the long Call option)

Using a collar , a company , rather than buying only call option, also sells a put option to fix its lower purchasing price and thereby hedges the upside of the exposure also. In this process, the company reduces the hedging costs. For example, in this case, the hedging costs reduced from $0.34 to $0.14 ($034 -$0.20)