Options Strategies

Q1 — Bull Call Spread (10)

(a) Net debit = $6.20 −$2.30 = $3.90**. Maximum loss = net debit = **$3.90 (occurs if both calls expire worthless, i.e. price ≤ 100). (1 debit + 1 max loss)

(b) Breakeven = lower strike + net debit = $100 +$3.90 = $103.90. (1 formula + 1 value) — above this the long call's intrinsic value exceeds the paid debit.

(c) Max profit = strike difference − net debit = (110 − 100) − 3.90 = 10 − 3.90 = $6.10 (for price ≥ 110). (1 + 1)

(d) At $107.50: long 100 call worth$7.50; short 110 call worth $0. Payoff = 7.50 − 0 = 7.50; net P/L = 7.50 − 3.90 = **+$3.60 profit**. (1 payoff + 1 net)

(e) Any valid reason: lower net cost/reduced capital outlay; short call premium reduces breakeven; reduces effect of time decay/vega since it's a defined-risk debit spread. (2)

Q2 — Collar (12)

(a) Net premium = put paid − call received = 1.40 − 1.10 = $0.30 net debit (paid). (2)

(b) Upside is capped at the short call strike $58. Max share gain = 58 − 48 = 10, minus net collar cost 0.30 = **$9.70**. (1 cap logic + 1 arithmetic + 1 net cost inclusion)

(c) Downside protected at put strike $52. Max share loss floor = 52 − 48 = +$2 (still a gain from cost basis), minus net cost 0.30 = **+$1.70**. So the "maximum loss relative to$48" is actually a minimum profit of +$1.70 (the put strike is above his cost, so he cannot lose). (1 floor at 52 + 1 subtract cost + 1 correct sign/interpretation)

(d) Because the protected floor (+$1.70) is already positive, the total position **never breaks even into a loss** — it is profitable across all expiry prices. Formally, "breakeven vs$48 cost" would require a value of 48; since the minimum outcome is $49.70 equivalent, there is no losing breakeven. (2 — accept: "position is always ≥ +1.70, no breakeven below profit")

(e) The premium from the sold call (which caps upside) pays for the protective put (downside protection), so protection is financed at low/zero net cost in exchange for surrendering gains above the call strike. (2)

Q3 — Long Strangle (12)

(a) Cost = 3.50 + 3.00 = $6.50. (1)

(b) Upper breakeven = call strike + total cost = 210 + 6.50 = $216.50**. Lower breakeven = put strike − total cost = 190 − 6.50 = **$183.50. (1 formula + 1 upper + 1 lower)

(c) At $178: put (190 strike) intrinsic = 190 − 178 = 12; call worthless. Profit = 12 − 6.50 = **+$5.50**. (1 payoff + 1 net)

(d) Advantage of strangle: cheaper (6.50 vs 11.50), lower max loss / lower capital. Disadvantage: wider breakevens (needs a larger move to profit — 183.50/216.50 vs straddle's 188.50/211.50). (1 advantage + 1 disadvantage + 1 quantified/clear) (Straddle breakevens: 200 ± 11.50 = 188.50 and 211.50.)

(e) Directional: an expected large move (either direction) around the event favours a long-volatility, market-neutral structure. Vega: long options have positive vega, so buying when IV is low and expected to rise means the position gains from the IV increase even before the move, and entry premium is cheaper. (1 directional + 1 vega mechanism + 1 low-IV entry advantage)

Q4 — Iron Condor (10)

(a) Net credit = (28 − 12) + (30 − 10) = 16 + 20 = $36. (1 call spread credit + 1 put spread credit → 2)

(b) Max profit = net credit = $36, achieved when all options expire worthless, i.e. INDX between the two short strikes: 4900 ≤ INDX ≤ 5100. (1 profit + 1 zone)

(c) Wing width = 100 on each side. Max loss = wing width − net credit = 100 − 36 = $64 (occurs if INDX ≤ 4800 or ≥ 5200). (1 wing width + 1 subtract credit + 1 value)

(d) Upper breakeven = short call strike + net credit = 5100 + 36 = 5136. Lower breakeven = short put strike − net credit = 4900 − 36 = 4864. (1 formula + 1 upper + 1 lower)

Q5 — Strategy Selection by View & IV (6)

(a) Short iron condor (or short strangle) — neutral/range-bound view collects premium, and high IV expected to fall gives positive theta and short-vega gains; iron condor gives defined risk. (2)

(b) Bull call spread — bullish directional view with defined risk; low IV makes the net-debit long-call-heavy structure cheaper than a naked long call while still cheaper than buying a single call. (2) (Accept "long call" only if defined-risk + cost not emphasised; bull call spread is the better fit for "lower cost + defined risk.")

(c) Collar (buy protective put, sell covered call) — protects an existing long position cheaply by financing the put with a sold call, capping upside as accepted. (2)

[
  {"claim":"Q1 breakeven 103.90, max profit 6.10, P/L at 107.50 is 3.60","code":"debit=6.20-2.30; be=100+debit; maxp=(110-100)-debit; pl=(107.50-100)-debit; result=(be==103.90 and maxp==6.10 and abs(pl-3.60)<1e-9)"},
  {"claim":"Q3 strangle breakevens 216.50/183.50, profit at 178 is 5.50","code":"cost=3.50+3.00; ub=210+cost; lb=190-cost; prof=(190-178)-cost; result=(ub==216.50 and lb==183.50 and prof==5.50)"},
  {"claim":"Q4 iron condor credit 36, max loss 64, breakevens 5136/4864","code":"credit=(28-12)+(30-10); maxloss=100-credit; ube=5100+credit; lbe=4900-credit; result=(credit==36 and maxloss==64 and ube==5136 and lbe==4864)"},
  {"claim":"Q2 collar net cost 0.30 and min outcome 1.70 above cost","code":"netcost=1.40-1.10; floor=(52-48)-netcost; cap=(58-48)-netcost; result=(abs(netcost-0.30)<1e-9 and abs(floor-1.70)<1e-9 and abs(cap-9.70)<1e-9)"}
]