Question

In a call option bull spread, why is the short option position considered covered?

Answer 1

In a call option bull spread:

• We buy a call option with lower strike K1 (Long position)
• We short a call option with higher strike K2 (Short position)
• K2 > K1
• Payoff from portfolio on expiration = Payoff from Long position + Payoff from short position = max (S - K1, 0) - max (S - K2, 0)

Consider the three scenarios: (S is the stock price on expiration); K2 > K1

Sl. No.	Scenario	Payoff from Long position = max (S - K1, 0)	Payoff from short position = - max (S - K2, 0)	Payoff from portfolio (Sum of the payoff of the two positions)
1.	S ≤ K1	0	0	0
2.	K1 < S ≤ K2	S - K1	0	S - K1
3.	S > K2	S - K1	- (S - K2) = K2 - S	K2 - K1 > 0

Please look at the payoff from short position:

• Only time it results into a loss is when S > K2
• That loss is lower than the profit from the long position
• The resultant is still a profit of K2 - K1

Thus effectively, this short position never results into a loss. And hence, the short option position considered covered.