Practice Quiz 5 Solutions — Options Strategies & Payoffs

Setup: 100 shares at $50. Buy put with strike $45 for $2. Sell call with strike $55 for $2. (Collar.)

(a) Net upfront cost of the options (per share)?

Cost of put: $2. Premium received from selling call: $2.

\[\text{Net cost} = \$2 - \$2 = \$0\]

This is a zero-cost collar — the put premium is exactly offset by the call premium.

(b) Total portfolio value per share at expiration:

(i) Stock at $40:

Stock value: $40
Put payoff: $45 − $40 = $5 (exercised)
Call payoff: $0 (expires worthless)
Total: $40 + $5 = $45

(ii) Stock at $50:

Stock value: $50
Put payoff: $0 (expires worthless)
Call payoff: $0 (expires worthless)
Total: $50

(iii) Stock at $60:

Stock value: $60
Put payoff: $0 (expires worthless)
Call payoff: −$5 (assigned; you sell at $55 instead of $60)
Total: $60 − $5 = $55

(c) What is the trade-off?

You are giving up upside above $55 (the call strike) in exchange for downside protection below $45 (the put strike) — the collar limits both your maximum gain and your maximum loss.