Interleaved — Phase 5

Stock-Market interleaved practice

printable — key stays hidden on paper

Instructions: Solve all problems. Each mixes a different subtopic — read carefully and pick the right method (cost-of-carry vs payoff vs Greek vs settlement logic). Show working. Use $...$ notation for math. Total: 50 marks.

Q1. (5 marks) A stock trades at spot $S = 2{,}000$ . The risk-free cost of carry is $10\%$ per annum. The 3-month (0.25 year) futures should trade at what fair value? If the actual futures price is $2{,}030$ , is the market in contango or backwardation, and what is the basis?

Q2. (5 marks) You buy 1 lot (lot size = 50) of a call option, strike $K = 1{,}500$ , premium $= 40$ . At expiry the spot is $1{,}560$ . Compute (a) intrinsic value per share, (b) net profit/loss on the lot, (c) the breakeven spot price.

Q3. (4 marks) An option has premium $= 85$ when spot $= 1{,}020$ and strike $= 1{,}000$ (call). Split the premium into intrinsic value and time value. State whether the option is ITM, ATM, or OTM.

Q4. (6 marks) You are long 1 futures contract (lot size 25) bought at $800$ . Over three days the settlement prices are Day1 $= 815$ , Day2 $= 790$ , Day3 $= 805$ . Compute the daily mark-to-market cash flows and the cumulative total.

Q5. (5 marks) A portfolio holds 400 shares of a stock at $1{,}250$ . Stock futures (lot 200) trade at $1{,}260$ . You want to fully hedge the position. How many futures lots do you short, and what is the direction of the hedge? If the stock falls to $1{,}150$ and futures to $1{,}160$ , what is the net P&L?

Q6. (5 marks) A call option has Delta $= 0.55$ and Gamma $= 0.04$ . The underlying rises by $\$ 10$. Estimate (a) the change in option price from delta alone, (b) the new delta after the move.

Q7. (4 marks) An option chain shows Call OI $= 1{,}20{,}000$ and Put OI $= 1{,}56{,}000$ . Compute the Put-Call Ratio (PCR) and state whether it leans bullish or bearish under the contrarian interpretation.

Q8. (6 marks) You short 1 put option, strike $K = 900$ , premium $= 25$ , lot size $= 40$ . (a) State your maximum profit. (b) Compute your payoff at expiry if spot $= 850$ . (c) State the breakeven and whether you as the seller want the option to expire ITM or OTM.

Q9. (5 marks) A futures position is being rolled from the near month (price $1{,}010$ ) to the next month (price $1{,}022$ ). Spot is $1{,}000$ . Compute the rollover cost and explain whether this reflects a contango or backwardation structure.

Q10. (5 marks) An at-the-money option has Theta $= -3.5$ per day and Vega $= 6.0$ per 1% vol. Over the weekend (2 days pass) implied volatility also rises by $2\%$ . Estimate the net change in the option premium from these two Greeks combined.

Answer keyMark scheme & solutions

Q1. — Subtopic 5.1.6 (basis & cost of carry) + 5.1.5 (contango/backwardation) Fair futures $F = S(1 + r\cdot t) = 2000(1 + 0.10\times0.25) = 2000\times1.025 = 2050$ . Actual $= 2030 < 2050$ … but note $2030 > 2000$ (spot), so futures > spot ⟹ contango. Basis $= \text{Spot} - \text{Futures} = 2000 - 2030 = -30$ (negative basis, typical of contango). Why this method: You must apply the cost-of-carry formula, not a payoff formula — futures pricing is deterministic given carry.

Q2. — Subtopic 5.2.10 (breakeven) + 5.2.4 (intrinsic) + 5.2.5 (buyer payoff) (a) Intrinsic $= \max(S-K,0) = \max(1560-1500,0) = 60$ . (b) Net per share $= 60 - 40 = 20$ ; on lot $= 20\times50 = \boxed{1000}$ profit. (c) Breakeven $= K + \text{premium} = 1500 + 40 = 1540$ . Why: A call buyer's breakeven is strike + premium, distinct from the futures MTM logic in Q4.

Q3. — Subtopic 5.2.4 (intrinsic vs time) + 5.2.3 (ITM/ATM/OTM) Intrinsic $= \max(1020-1000,0) = 20$ . Time value $= 85 - 20 = 65$ . Since $S > K$ for a call, it is ITM. Why: Total premium always decomposes as intrinsic + time; don't confuse premium with payoff.

Q4. — Subtopic 5.1.4 (mark-to-market) MTM references the previous settlement, not entry price, after Day1.

Day1: $(815-800)\times25 = +375$
Day2: $(790-815)\times25 = -625$
Day3: $(805-790)\times25 = +375$ Cumulative $= 375 - 625 + 375 = +125$ . Check: total $= (805-800)\times25 = +125$ . ✓ Why: MTM chains day-to-day settlements — a classic trap if you compare each day to entry.

Q5. — Subtopic 5.1.8 (hedging with futures) Shares held $= 400$ ; lot $= 200$ ⟹ short $400/200 = \mathbf{2}$ lots (short to hedge a long stock position). Stock P&L: $(1150-1250)\times400 = -40{,}000$ . Futures P&L: short at 1260, buy back at 1160 ⟹ $(1260-1160)\times400 = +40{,}000$ . Net $= 0$ (near-perfect hedge; small residual only from basis change). Why: Hedge ratio = exposure/lot size; short futures offsets a long stock — the opposite of speculation direction.

Q6. — Subtopic 5.3.1 (Delta) + 5.3.2 (Gamma) (a) $\Delta P \approx \text{Delta}\times\Delta S = 0.55\times10 = +5.5$ . (b) New delta $= 0.55 + \text{Gamma}\times\Delta S = 0.55 + 0.04\times10 = 0.95$ . Why: Delta gives first-order price change; Gamma tells how delta itself moves — you need both, not just delta.

Q7. — Subtopic 5.2.7 (OI & PCR) $\text{PCR} = \dfrac{\text{Put OI}}{\text{Call OI}} = \dfrac{156000}{120000} = 1.3$ . PCR $> 1$ ⟹ under the contrarian view this leans bullish (excess put writing/oversold sentiment). Why: PCR is a ratio of OI, not price — tests reading the option chain sentiment tool.

Q8. — Subtopic 5.2.5 (seller payoff) + 5.2.10 (breakeven) + 5.2.8 (exercise) (a) Max profit for a put seller $=$ premium received $= 25\times40 = \boxed{1000}$ . (b) At $S=850$ : put is ITM, intrinsic $= 900-850 = 50$ . Seller pays that out: payoff per share $= 25 - 50 = -25$ ; on lot $= -25\times40 = -1000$ loss. (c) Breakeven $= K - \text{premium} = 900 - 25 = 875$ . As the seller you want it to expire OTM (spot above 900) so you keep the full premium. Why: Seller payoff is the mirror image of the buyer's — capped gain, large loss.

Q9. — Subtopic 5.1.7 (rollover cost) + 5.1.5 (contango) Rollover cost $= F_\text{next} - F_\text{near} = 1022 - 1010 = 12$ (per share) — cost of carrying forward. Since far-month $>$ near-month $>$ spot, the curve is upward-sloping ⟹ contango. Why: Rollover cost is the spread between two futures months, not a spot comparison.

Q10. — Subtopic 5.3.3 (Theta) + 5.3.4 (Vega) Theta effect: $-3.5 \times 2\text{ days} = -7.0$ . Vega effect: $+6.0 \times 2\% = +12.0$ . Net $\Delta$ premium $= -7.0 + 12.0 = +5.0$ . Why: Time decay (Theta) and volatility (Vega) push in opposite directions here — you must combine both signed effects.

[
  {"claim":"Q1 fair futures = 2050","code":"S=2000; r=0.10; t=0.25; F=S*(1+r*t); result=(F==2050)"},
  {"claim":"Q4 cumulative MTM = 125","code":"d1=(815-800)*25; d2=(790-815)*25; d3=(805-790)*25; result=(d1+d2+d3==125)"},
  {"claim":"Q10 net premium change = +5.0","code":"theta=-3.5*2; vega=6.0*2; result=(theta+vega==5.0)"}
]