Level 2 — RecallFutures

Futures

⏱ 30 minutes40 marksprintable — key stays hidden on paper

Chapter: 5.1 Futures Level: 2 — Recall (definitions, standard problems, short derivations) Time Limit: 30 minutes Total Marks: 40

Instructions: Answer all questions. Show working where calculations are required. Use $₹$ for currency.

Q1. Define a futures contract and state any two ways in which it differs from a forward contract. (3 marks)

Q2. The lot size of a stock future is 250 shares. If the stock trades at $₹1,840$ per share in the futures market, calculate the contract value. (2 marks)

Q3. State the cost-of-carry relationship between the fair futures price $F$ and spot price $S$ . Define basis in terms of $S$ and $F$ . (4 marks)

Q4. A stock trades at spot $S = ₹500$ . The risk-free rate is $8\%$ p.a. and there are no dividends. Using continuous compounding, find the fair 3-month futures price. (Take $e^{0.02} = 1.0202$ .) (4 marks)

Q5. Distinguish between contango and backwardation with one line each. (4 marks)

Q6. A trader buys 1 lot (lot size 500) of a future at $₹120$ . At the end of Day 1 the settlement price is $₹126$ ; at the end of Day 2 it is $₹123$ . Calculate the mark-to-market (MTM) cash flow on each day and the net MTM. (5 marks)

Q7. Define SPAN margin and exposure margin. State which is designed to cover worst-case single-day loss. (4 marks)

Q8. Explain rollover of a futures position. Write the formula for rollover cost in terms of the near-month price $F_{near}$ and next-month price $F_{next}$ . (4 marks)

Q9. An investor holds a portfolio worth $₹20,00,000$ and wants to hedge using index futures. The index future is at $10,000$ with a lot size of $50$ . Assuming portfolio beta $= 1$ , how many lots must be sold to fully hedge? (5 marks)

Q10. State two differences between index futures and stock futures. (5 marks)

End of paper

Answer keyMark scheme & solutions

Q1. (3 marks)

A futures contract is a standardized, exchange-traded agreement to buy or sell an underlying asset at a predetermined price on a specified future date. (1)
Differences from a forward (any two, 1 each):
- Futures are exchange-traded and standardized; forwards are OTC and customized.
- Futures are marked-to-market daily with margin; forwards settle only at maturity.
- Futures have negligible counterparty risk (clearing house guarantee); forwards carry counterparty/default risk. (2)

Q2. (2 marks) Contract value $= \text{lot size} \times \text{price} = 250 \times 1840 = ₹4,60,000$ .

Correct formula (1), correct answer (1).

Q3. (4 marks)

Cost of carry: $F = S(1 + r - d)^{T}$ (discrete) or $F = S\,e^{(r-d)T}$ (continuous), where $r$ = interest cost, $d$ = dividend yield, $T$ = time to expiry. (2)
Basis $= S - F$ (spot minus futures); often quoted as $F - S$ . Basis converges to zero at expiry. (2)

Q4. (4 marks) $F = S\,e^{rT} = 500 \times e^{0.08 \times 0.25} = 500 \times e^{0.02}$ (2) $= 500 \times 1.0202 = ₹510.10$ (2)

Q5. (4 marks)

Contango: futures price is higher than spot (normal market, positive cost of carry); $F > S$ . (2)
Backwardation: futures price is lower than spot; $F < S$ (often due to high dividend yield or supply shortage). (2)

Q6. (5 marks) Long position, lot size 500.

Day 1 MTM $= (126 - 120) \times 500 = +6 \times 500 = +₹3,000$ (2)
Day 2 MTM $= (123 - 126) \times 500 = -3 \times 500 = -₹1,500$ (2)
Net MTM $= 3000 - 1500 = +₹1,500$ (equals $(123-120)\times500$ ). (1)

Q7. (4 marks)

SPAN margin: initial margin computed by the SPAN system to cover the worst-case single-day loss of a portfolio under various price/volatility scenarios. (2)
Exposure margin: an additional margin over and above SPAN to cover extreme market moves / broker-level buffer. (1)
SPAN is the one designed to cover worst-case single-day loss. (1)

Q8. (4 marks)

Rollover: closing the near-month (expiring) futures position and simultaneously opening the same position in the next-month contract to carry the position forward. (2)
Rollover cost $= F_{next} - F_{near}$ (for a long position); the spread paid/received to shift the position. (2)

Q9. (5 marks)

Value per futures lot $= 10{,}000 \times 50 = ₹5{,}00{,}000$ . (2)
Number of lots $= \dfrac{\beta \times \text{Portfolio value}}{\text{Lot value}} = \dfrac{1 \times 20{,}00{,}000}{5{,}00{,}000} = 4$ lots. (2)
Sell 4 lots to fully hedge. (1)

Q10. (5 marks) Any two, well explained (2.5 each):

Underlying: index futures track a basket/index (e.g. Nifty); stock futures track a single company's shares.
Diversification / risk: index futures carry only systematic (market) risk; stock futures carry both systematic and company-specific risk.
Settlement: index futures are cash-settled; stock futures may be physically settled (delivery of shares).
Use: index futures used to hedge broad market/portfolio beta; stock futures for stock-specific exposure.

[
  {"claim":"Q2 contract value = 460000","code":"result = (250*1840 == 460000)"},
  {"claim":"Q4 fair futures = 510.10","code":"F = 500*1.0202; result = abs(F-510.10) < 0.01"},
  {"claim":"Q6 net MTM = 1500","code":"d1=(126-120)*500; d2=(123-126)*500; result = (d1+d2 == 1500)"},
  {"claim":"Q9 hedge requires 4 lots","code":"result = (1*2000000/(10000*50) == 4)"}
]