12.2 Trading Strategies

Trading Strategies

FMP–14 turns single-option properties into portfolios. The exam expects you to recognize the economic story (income, insurance, directional debit/credit, volatility long/short), sketch the expiration payoff, and compute profit after net premium. Work in terminal stock price ST and remember: long option payoff is max(·, 0); short option payoff is the negative of the long payoff.

Covered Call

Covered call = long stock + short call (usually OTM or ATM).

Maximum profit ≈ (K − S0) + premium received (if stock bought at S0). Downside remains large if the stock collapses—premium is only a cushion, not a floor. Covered calls suit mildly bullish or range-bound views when the investor already owns the stock and will accept capped upside for income.

Worked covered-call example

Buy stock at $50; sell a 55-strike call for $2. At expiration:

• If ST = 40: stock loss −10, call expires → net −10 + 2 = −8.
• If ST = 55: stock +5, call expires → net +5 + 2 = +7.
• If ST = 70: stock +20, short call −15 → net +5 + 2 = +7 (capped).

Max profit = 7; breakeven = 50 − 2 = 48.

Protective Put

Protective put = long stock + long put with strike K.

Payoff at expiration: ST + max(K − ST, 0) − put premium = max(ST, K) − put premium (relative to a zero initial stock basis you’d adjust by S0). Economically this is portfolio insurance: downside floored near K − S0 − premium, upside retained minus the insurance cost.

Compare with covered call: protective put pays premium for a floor; covered call receives premium and accepts a ceiling.

Worked protective-put example

Stock at $50; buy 45-put for $1.50.

• ST = 30: stock −20, put +15 → net −5 − 1.50 = −6.50 (floor).
• ST = 60: stock +10, put 0 → net +10 − 1.50 = +8.50.

Floor roughly at 45 − 50 − 1.50 = −6.50 versus purchase price.

Principal-Protected Notes (PPNs)

A principal-protected note packages a zero-coupon bond (or deposit) that grows to the protected principal with a long call (or call spread / exotic) on an index. Structure:

1. Invest PV of principal in a zero: for face 100 at T years, buy e^(-rT) × 100 of zeros.
2. Spend residual proceeds on calls (participation rate = residual / call price).

If the issuer’s credit is sound and the zero is held to maturity, the investor receives at least principal; upside equals participation × index gain (subject to caps if call spreads are used).

Worked PPN sketch

r = 4%, T = 5, protect $100. Zero costs 100 × e^(-0.04×5) ≈ 100 × 0.8187 = $81.87. Residual $18.13. If ATM-forward calls cost $18.13 per 100 notional of full upside, participation ≈ 100%. If calls cost $24, participation ≈ 18.13/24 ≈ 75.5%. Credit risk of the note issuer remains—principal protection is only as good as the issuer (and any collateralization).

Spread Strategies

Spreads buy one option and sell another of the same type.

Bull and bear vertical spreads

Bull call spread: long call K1, short call K2 > K1. Debit = c(K1) − c(K2). Expiration payoff = max(ST − K1, 0) − max(ST − K2, 0).

Max profit = (K2 − K1) − net debit; max loss = net debit. Bear put spread: long put K2, short put K1 < K2—profits if market falls toward K1.

Worked bull call spread

Long 50-call at 5, short 60-call at 2; net debit 3. Width = 10.

• ST = 45: payoff 0; P&L = −3.
• ST = 55: payoff 5; P&L = 2.
• ST = 70: payoff 10; P&L = 7 (max).

Breakeven = 50 + 3 = 53.

Butterfly spread

Long butterfly (calls): long K1, short 2× K2, long K3 with K2 midpoint. Profits if ST finishes near K2; loses limited amounts in the wings. Net debit is small; max payoff = K2 − K1 − net debit (on equal spacing).

Calendar (time) spread

Calendar spread: sell near-dated option, buy longer-dated same strike (typically calls). Bets that near-term implied vol/time decay outpaces the back month, or that the stock stays near the strike until the front expires. Payoff is not a simple European expiration diagram for both legs at one date—value depends on the remaining long option’s mark after the short expires.

Combination Strategies

Combinations mix calls and puts.

Hull-style FRM convention: a strip overweight puts (larger payoff on a decline); a strap overweight calls (larger payoff on a rally).

Worked straddle P&L

Buy 50-straddle: call 4 + put 3 = net debit 7.

• ST = 50: payoff 0; P&L = −7.
• ST = 60: call 10, put 0; P&L = 3.
• ST = 40: put 10, call 0; P&L = 3.
• Breakevens at 43 and 57.

Worked strangle

Long 45-put at 1.50 and 55-call at 1.50; debit 3.

• Payoff nonzero only outside [45, 55].
• ST = 40: put 5; P&L = 2.
• ST = 50: 0; P&L = −3.
• Breakevens 42 and 58.

Strip versus strap payoffs at expiration (same K, ignore premium)

For strip (1 call + 2 puts): payoff = max(ST − K, 0) + 2 max(K − ST, 0). For strap (2 calls + 1 put): payoff = 2 max(ST − K, 0) + max(K − ST, 0). After subtracting net premium, the side with two options earns twice the intrinsic move.

Choosing a Strategy (Exam Heuristic)

Always subtract net premium and state max gain/loss when the question asks for profit, not raw payoff.