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IFMP Financial Derivative Traders Certification (FDTC), Pakistan study materials
IFMP Financial Derivative Traders Certification (FDTC), Pakistan study resources

IFMP Financial Derivative Traders Certification (FDTC), Pakistan practice questions

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Question 1Financial Derivatives

Under the Pakistan Mercantile Exchange (PMEX) framework, what does a futures contract obligate each party to do?

  1. Settle the full contract value on the trade date
  2. Pay a premium to the exchange to keep the position open
  3. Deliver the underlying only if the buyer exercises an option
  4. Exchange a fixed quantity of the underlying at a price fixed today on a future settlement date Correct answer.

Explanation

A futures contract is a standardised, exchange-traded agreement in which both parties commit to buy and sell a specified quantity of the underlying at a price agreed today, with settlement deferred to a defined future date. Unlike an option, both sides carry a binding obligation, and no premium is paid by the buyer.

Question 2Financial Derivatives

A trader buys one PMEX gold futures contract and the exchange raises the initial margin requirement. What is the immediate effect on the trader's account?

  1. The margin increase is deferred until the contract's expiry date
  2. The trader's existing position is automatically liquidated at the settlement price
  3. The trader must post additional funds or reduce the position to meet the new requirement Correct answer.
  4. The contract price is adjusted downward to reflect the higher margin

Explanation

Margin is collateral, not a price adjustment, so a rise in the initial margin requirement obliges the holder to top up the account or cut the position. Exchanges and brokers raise margins to cover potential default risk when volatility increases. The contract's economic terms and price remain unchanged.

Question 3Financial Derivatives

In a standard option contract traded on an organised exchange, which right does the buyer of a put option acquire?

  1. The right to buy the underlying at the strike price before expiry
  2. The obligation to buy the underlying at the strike price at expiry
  3. The right to sell the underlying at the strike price before expiry Correct answer.
  4. The obligation to sell the underlying at the market price at expiry

Explanation

A put option confers on its buyer the right, but not the obligation, to sell the underlying at the agreed strike price within the option's life. The buyer pays a premium for that right and may simply let it lapse if it is not worthwhile. The writer, by contrast, bears the corresponding obligation.

Question 4Financial Derivatives

A Pakistani importer expects to pay USD 500,000 in three months and wishes to lock in the exchange rate today. Which derivative instrument most directly achieves this?

  1. A currency futures contract to sell US dollars in three months
  2. A forward rate agreement on the Karachi Interbank Offered Rate
  3. A put option on the rupee against the dollar
  4. A currency futures contract to buy US dollars in three months Correct answer.

Explanation

The importer needs to acquire dollars in three months, so a long position in a dollar futures contract fixes the purchase rate and removes upside currency risk. Selling dollars would create the opposite exposure. A forward rate agreement references interest rates, not exchange rates.

Question 5Financial Derivatives

What distinguishes a forward contract from an exchange-traded futures contract?

  1. Forwards are always settled through a central clearing house
  2. Forwards are customised and carry counterparty credit risk, while futures are standardised and cleared Correct answer.
  3. Forwards require daily mark-to-market cash flows, while futures do not
  4. Forwards can only be written on financial assets, while futures cover commodities

Explanation

A forward is a privately negotiated, bespoke agreement between two parties, so each side bears the other's default risk. A futures contract is standardised by the exchange and interposed by a clearing house, which manages counterparty risk through margins. Forwards are generally not marked to market daily.

Question 6Financial Derivatives

An investor holds a long call option on a stock with a strike of PKR 100 and the stock trades at PKR 115 at expiry. Ignoring the premium paid, what is the option's intrinsic value per share?

  1. PKR 15 Correct answer.
  2. PKR 100
  3. PKR 0
  4. PKR 115

Explanation

The intrinsic value of a call at expiry equals the excess of the underlying price over the strike, floored at zero. Here that is PKR 115 minus PKR 100, giving PKR 15 per share. The premium originally paid affects profit but not intrinsic value.

Question 7Financial Derivatives

In derivative markets, what is the primary economic function of a hedger?

  1. To profit from short-term price movements by taking speculative positions
  2. To earn bid-ask spreads by quoting two-way prices continuously
  3. To arbitrage price differences between related instruments
  4. To reduce or offset an existing exposure to adverse price changes Correct answer.

Explanation

A hedger uses derivatives to offset a pre-existing risk in the underlying, such as a future purchase or sale, aiming to stabilise cash flows rather than to profit from price moves. Speculators accept risk for profit, market makers quote prices, and arbitrageurs exploit mispricing.

Question 8Financial Derivatives

A futures position is marked to market daily. A trader with a long position sees the settlement price fall below the previous day's price. What happens to the account?

  1. The account is debited by the price difference and may require a margin top-up Correct answer.
  2. The position is automatically rolled to the next contract month
  3. The contract's strike price is reset to the new settlement price
  4. The account is credited with the price difference

Explanation

Daily mark-to-market credits gains and debits losses on open futures positions; a long position loses when settlement prices fall. If the resulting balance drops below the maintenance margin, a margin call requires the trader to restore the account to the initial level. Futures have no strike price to reset.

Question 9Financial Derivatives

An options trader buys a call and simultaneously writes a put on the same underlying with the same strike and expiry. What exposure does this combined position create?

  1. A position that profits when the underlying rises and loses when it falls, similar to a long forward Correct answer.
  2. A position that profits when the underlying falls and loses when it rises
  3. A position whose maximum loss is limited to the net premium paid
  4. A riskless position because the two options offset each other

Explanation

A long call gains as the underlying rises, while a short put loses as the underlying falls; combined, the payoff resembles a long forward position with linear exposure to the underlying price. The premium received on the written put partly offsets the call premium. The position is not riskless because the short put carries substantial downside.

Question 10Financial Derivatives

Using put-call parity, if a stock trades at PKR 250, a three-month call and put share a strike of PKR 240, and the risk-free rate is positive, which relationship should hold ignoring dividends?

  1. Call price minus put price equals the stock price minus the present value of the strike Correct answer.
  2. Put price minus call price equals the stock price minus the strike
  3. Call price plus put price equals the stock price
  4. Call price equals put price whenever the strike equals the stock price

Explanation

Put-call parity states that C minus P equals S minus the present value of the strike discounted at the risk-free rate. It follows from the equivalence of a fiduciary call and a protective put. The relationship holds for European options on the same underlying, strike and expiry.

Question 11Financial Derivatives

A wheat miller expects to buy wheat in two months and fears a price rise. The miller buys a call option on wheat futures with a strike of PKR 4,000 per tonne and pays a premium of PKR 150. If wheat is at PKR 4,500 at expiry, what is the net gain per tonne from the option position?

  1. PKR 350 Correct answer.
  2. PKR 500
  3. PKR 650
  4. PKR 150

Explanation

The call's payoff at expiry is the market price minus the strike, PKR 4,500 minus PKR 4,000, equal to PKR 500. Subtracting the PKR 150 premium gives a net gain of PKR 350 per tonne. The premium must be deducted to obtain profit rather than gross payoff.

Question 12Financial Derivatives

A speculator believes volatility in a stock will rise sharply but has no view on direction. Which strategy best expresses this view using options?

  1. Buying a call and writing a call at a higher strike
  2. Buying a call and writing a put at the same strike
  3. Buying a call and buying a put at the same strike and expiry Correct answer.
  4. Writing a covered call against a long stock position

Explanation

A long straddle, comprising a call and a put with the same strike and expiry, gains when the underlying moves substantially in either direction, so it profits from rising volatility. Directional spreads such as bull call spreads retain a directional bias. The straddle's maximum loss is the combined premium paid if the stock finishes at the strike.

Question 13Financial Derivatives

What is the role of a central counterparty (clearing house) in an exchange-traded derivatives market?

  1. It interposes itself between buyer and seller, becoming counterparty to each and managing default risk through margins Correct answer.
  2. It sets the daily settlement prices for all contracts
  3. It guarantees profits to retail traders who post margin
  4. It matches orders on the trading screen and executes client trades

Explanation

Through novation the clearing house becomes the buyer to every seller and the seller to every buyer, so each participant faces the clearing house rather than an unknown counterparty. It manages its resulting exposure with initial and variation margins and a default fund. It does not promise profits or set prices.

Question 14Financial Derivatives

A trader holds a short futures position of 10 contracts, each covering 100 units, and the settlement price rises by PKR 5 per unit. What is the mark-to-market cash flow for the day?

  1. A debit of PKR 5,000 Correct answer.
  2. A credit of PKR 5,000
  3. A debit of PKR 500
  4. A credit of PKR 500

Explanation

The position covers 10 contracts times 100 units, equal to 1,000 units. A short position loses when prices rise, so the loss is 1,000 units times PKR 5, a debit of PKR 5,000. The sign is critical: a long position would instead be credited.

Question 15Financial Derivatives

An arbitrageur observes that a stock futures contract expiring in one month trades above its theoretical fair value relative to the cash market. Which action captures the arbitrage?

  1. Sell both the futures and the stock to avoid directional risk
  2. Buy the futures and sell the stock short, investing the proceeds at the risk-free rate
  3. Buy both the futures and the stock to profit from the upward drift
  4. Sell the futures and buy the stock, funding the purchase by borrowing Correct answer.

Explanation

When futures are rich, the arbitrage is to sell the futures and buy the underlying, carrying the stock until expiry and financing the purchase. At expiry the two legs converge and the locked-in spread is realised. This is cash-and-carry arbitrage, and the reverse trade applies when futures are cheap.

Question 16Financial Derivatives

A company will issue a floating-rate bond in three months and wants protection against rising rates. Which derivative is most suitable?

  1. A short stock index futures position
  2. A receiver interest rate swap starting in three months
  3. A long currency forward on the dollar
  4. A payer interest rate swap starting in three months Correct answer.

Explanation

A payer swap pays fixed and receives floating, so it gains when rates rise and offsets the higher coupons the issuer would pay on a floating-rate bond. A receiver swap benefits from falling rates instead. Currency and equity derivatives do not hedge interest-rate exposure.

Question 17Financial Derivatives

Which statement correctly describes the payoff of a long put option at expiry?

  1. Maximum of zero and the strike price minus the underlying price Correct answer.
  2. The underlying price regardless of the strike
  3. The strike price plus the underlying price
  4. Maximum of zero and the underlying price minus the strike price

Explanation

A put pays the strike minus the underlying price when that amount is positive, and zero otherwise, so the payoff is max(0, K minus S). The put gains value as the underlying falls below the strike. The premium paid is then deducted to obtain profit.

Question 18Financial Derivatives

A portfolio manager holds a diversified equity portfolio and buys index put options to protect against a market decline. What is the main trade-off of this strategy?

  1. The manager faces unlimited downside if the market falls sharply
  2. The manager pays premiums that reduce returns if the market does not fall Correct answer.
  3. The manager forgoes all dividend income while the puts are held
  4. The manager must sell the underlying portfolio when the puts are exercised

Explanation

Protective puts act as insurance: they cap downside losses but the premium paid is a cost that drags on returns if the market stays flat or rises. The portfolio itself is retained, and dividends continue to be received. Downside risk is limited to the premium plus any gap between the portfolio and the index.

Question 19Financial Derivatives

In an interest rate swap, what is exchanged between the two counterparties?

  1. Physical delivery of government securities
  2. Periodic interest payments calculated on a notional principal Correct answer.
  3. The principal amounts at the start and end of the swap
  4. The credit risk of the underlying borrowers

Explanation

An interest rate swap involves periodic exchanges of interest calculated on a notional principal, typically one fixed leg and one floating leg. The notional itself is generally not exchanged. Only the net difference is usually paid, which reduces settlement risk.

Question 20Financial Derivatives

A stock index futures contract trades at 30,000 with a multiplier of PKR 50, and the initial margin is PKR 150,000 per contract. What is the approximate leverage on one contract?

  1. 20 times
  2. 5 times
  3. 10 times Correct answer.
  4. 50 times

Explanation

Contract notional value is 30,000 times PKR 50, equal to PKR 1,500,000. Dividing by the initial margin of PKR 150,000 gives leverage of about 10 times. Leverage magnifies both gains and losses relative to the margin posted.

Question 21Financial Derivatives

Which factor most directly increases the premium of a European call option, all else equal?

  1. A lower expected volatility of the underlying
  2. A lower spot price of the underlying
  3. A higher risk-free interest rate Correct answer.
  4. A shorter time to expiry

Explanation

A higher risk-free rate lowers the present value of the strike that must be paid at expiry, which raises the value of a call. Volatility and time to expiry increase call value, while a lower spot price reduces it. These relationships follow from the standard option pricing model.

Question 22Financial Derivatives

A trader writes a naked call option on a stock with a strike of PKR 200 and receives a premium of PKR 12. The stock then rallies to PKR 260 at expiry. What is the trader's net loss per share?

  1. PKR 72
  2. PKR 12
  3. PKR 48 Correct answer.
  4. PKR 60

Explanation

The writer must deliver at the strike while the stock is worth PKR 260, creating a payoff loss of PKR 60 per share. The premium received of PKR 12 partially offsets this, leaving a net loss of PKR 48. The theoretical loss on a naked call is unlimited as the stock price rises.

Question 23Financial Derivatives

A futures contract is priced at PKR 1,050 for delivery in three months, the spot price is PKR 1,000, and the three-month risk-free rate is 2 percent with no storage or convenience costs. Which statement is correct?

  1. No arbitrage conclusion can be drawn without knowing expected future spot prices
  2. The futures price is exactly at theoretical fair value
  3. The futures contract is overpriced and a cash-and-carry arbitrage exists Correct answer.
  4. The futures contract is underpriced and a reverse cash-and-carry arbitrage exists

Explanation

The theoretical futures price is the spot compounded at the risk-free rate, PKR 1,000 times 1.02, equal to PKR 1,020. Since the market price of PKR 1,050 is higher, the futures is rich and a cash-and-carry arbitrage, selling futures and buying the spot, locks in the gap. Arbitrage pricing does not depend on forecasts of the future spot price.

Question 24Financial Derivatives

An investor buys a bull call spread, purchasing a call at a strike of PKR 100 for PKR 8 and writing a call at a strike of PKR 120 for PKR 3. What are the maximum profit and maximum loss per share at expiry?

  1. Maximum profit PKR 25 and maximum loss PKR 5
  2. Maximum profit PKR 15 and maximum loss PKR 5 Correct answer.
  3. Maximum profit PKR 20 and maximum loss PKR 8
  4. Maximum profit PKR 5 and maximum loss PKR 5

Explanation

The net premium paid is PKR 8 minus PKR 3, equal to PKR 5, which is the maximum loss. The maximum payoff occurs above PKR 120 and equals the strike difference of PKR 20, so maximum profit is PKR 20 minus PKR 5, equal to PKR 15. The spread caps both profit and loss.

Question 25Financial Derivatives

A company has borrowed at a floating rate of KIBOR plus 2 percent and enters a swap to pay fixed 9 percent and receive KIBOR. If KIBOR rises to 8 percent, what is the company's effective all-in borrowing cost?

  1. 7 percent
  2. 15 percent
  3. 9 percent
  4. 11 percent Correct answer.

Explanation

On the loan the company pays KIBOR plus 2 percent, which is 10 percent when KIBOR is 8 percent. On the swap it pays 9 percent fixed and receives KIBOR of 8 percent, a net swap cost of 1 percent. The all-in cost is therefore 10 percent plus 1 percent, equal to 11 percent, which is fixed regardless of KIBOR.

Question 26Financial Derivatives

Under the Pakistan Mercantile Exchange framework, which party guarantees performance of an exchange-traded futures contract to both the buyer and the seller?

  1. The State Bank of Pakistan as regulator
  2. The individual counterparty on the other side of the trade
  3. The National Clearing Company of Pakistan acting as central counterparty Correct answer.
  4. The brokerage firm of the buyer alone

Explanation

Exchange-traded derivatives are novated to a central counterparty, which becomes the legal buyer to every seller and seller to every buyer. In Pakistan this clearing and settlement function is performed by the National Clearing Company of Pakistan. This structure removes bilateral counterparty credit risk between the original trading parties.

Question 27Financial Derivatives

A trader sells (writes) a European put option and receives the premium. What is the maximum profit this position can earn?

  1. The strike price plus the premium
  2. Unlimited profit
  3. The strike price minus the premium
  4. The premium received Correct answer.

Explanation

A short put keeps the premium if the option expires worthless, which happens when the underlying finishes at or above the strike. The premium is the entire gain; the loss side is what carries risk. Hence maximum profit equals the premium collected.

Question 28Financial Derivatives

Which term describes the process by which a futures clearing house records daily gains and losses and requires cash settlement of the resulting variation margin?

  1. Marking to market Correct answer.
  2. Position limit
  3. Delivery notice
  4. Novation

Explanation

Marking to market revalues open futures positions against the daily settlement price and converts the gain or loss into variation margin. This daily cash flow prevents losses from accumulating unchecked. Novation and position limits address different concerns, namely counterparty substitution and risk concentration.

Question 29Financial Derivatives

In a forward rate agreement (FRA), what does the buyer of the FRA effectively do?

  1. Purchase the underlying bond at a discount
  2. Lock in a lending rate for a past interest period
  3. Lock in a borrowing rate for a future interest period Correct answer.
  4. Exchange principal amounts in two currencies

Explanation

An FRA buyer fixes the interest rate payable on a notional amount for a future period, gaining if reference rates rise above the agreed rate. It is a cash-settled rate hedge with no exchange of principal. This makes it a borrowing-rate lock for the buyer.

Question 30Financial Derivatives

Which of the following best describes a swaption?

  1. An option granting the right to enter an interest rate swap on agreed terms Correct answer.
  2. An agreement to exchange equity for debt
  3. A swap in which both legs are floating
  4. A futures contract on a bond index

Explanation

A swaption is an option on a swap: the holder pays a premium for the right, but not the obligation, to enter a specified swap at a future date. It is used to hedge or take a view on future swap rates. The other choices describe unrelated instruments.

Question 31Financial Derivatives

A trader holds a long position in one gold futures contract where each contract represents 100 grams and the price rises from PKR 20,000 to PKR 20,150 per gram. What is the gross gain before costs?

  1. PKR 15,000 Correct answer.
  2. PKR 1,500
  3. PKR 150
  4. PKR 20,150

Explanation

The gain per gram is PKR 150, and the contract covers 100 grams, so the gross profit is 150 multiplied by 100, which equals PKR 15,000. Contract size must be applied to the unit price change. Ignoring the multiplier understates the result by a factor of one hundred.

Question 32Financial Derivatives

Which of the following is a distinguishing feature of an exchange-traded derivative compared with an over-the-counter derivative?

  1. Terms individually negotiated between the two parties
  2. Standardised contract terms and daily clearing through a central counterparty Correct answer.
  3. No requirement for margin
  4. Complete absence of price transparency

Explanation

Exchange-traded derivatives use standardised specifications and are cleared centrally with daily margining, which supports liquidity and transparency. OTC contracts are privately negotiated and carry bilateral credit exposure. This distinction is fundamental to how each market is regulated and risk-managed.

Question 33Financial Derivatives

A trader expects the price of a stock to fall substantially and wants a defined, limited loss if wrong. Which position matches this view?

  1. Buy the underlying stock
  2. Sell a call option
  3. Buy a put option Correct answer.
  4. Buy a call option

Explanation

A long put gains as the underlying falls and the most the buyer can lose is the premium paid, giving a defined risk. Selling a call also profits from a fall but carries potentially unlimited loss. Buying a call or the stock profits from a rise rather than a decline.

Question 34Financial Derivatives

A one-year futures contract on a non-dividend-paying stock trades at PKR 530 while the spot price is PKR 500 and the one-year risk-free rate is 5 percent. Which arbitrage action is indicated?

  1. Do nothing because the futures price equals fair value
  2. Buy the futures, short the stock and lend at the risk-free rate
  3. Buy both the futures and the stock
  4. Sell the futures, buy the stock and borrow at the risk-free rate Correct answer.

Explanation

The fair futures price is 500 compounded at 5 percent for one year, which is PKR 525. The contract at PKR 530 is overpriced, so the arbitrageur sells the rich futures and buys the underlying financed by borrowing. At expiry the deliverable stock covers the short futures and the difference is captured as riskless profit.

Question 35Financial Derivatives

A trader buys a straddle by purchasing a call and a put with the same strike of PKR 100 and the same expiry, paying premiums of PKR 6 and PKR 5 respectively. What is the breakeven on the upside at expiry?

  1. PKR 89
  2. PKR 100
  3. PKR 111 Correct answer.
  4. PKR 106

Explanation

Total premium paid is PKR 11, so the position breaks even when the underlying exceeds the strike by that amount, at PKR 111. The lower breakeven is the strike minus the premium, PKR 89. A straddle therefore needs a move larger than the combined premium to profit.

Question 36Financial Derivatives

A portfolio has a beta of 1.2 against a stock index and is worth PKR 60 million. The manager wants to reduce beta to 0.6 using index futures priced at 30,000 with a multiplier of PKR 50. How many contracts should be sold, approximately?

  1. 24 contracts Correct answer.
  2. 12 contracts
  3. 60 contracts
  4. 48 contracts

Explanation

The hedge ratio equals the beta change multiplied by portfolio value divided by futures contract value. The beta reduction is 0.6, portfolio value is 60,000,000, and each contract is worth 30,000 times 50, or 1,500,000. Hence 0.6 times 60,000,000 divided by 1,500,000 gives 24 contracts.

Question 37Financial Derivatives

In a plain vanilla interest rate swap, a corporate pays fixed 8 percent and receives KIBOR on a notional of PKR 100 million. If KIBOR resets to 9 percent for the period, what is the net cash flow to the corporate for that period, ignoring day-count conventions?

  1. Receive PKR 1,000,000 Correct answer.
  2. Receive PKR 8,000,000
  3. Pay PKR 1,000,000
  4. Pay PKR 9,000,000

Explanation

The corporate receives KIBOR of 9 percent and pays fixed 8 percent on the notional, a net inflow of 1 percent. One percent of PKR 100 million is PKR 1,000,000. Only the net difference is exchanged, not the gross legs.

Question 38Financial Derivatives

An investor converts a floating-rate exposure to fixed by entering a pay-fixed interest rate swap. What risk does the swap primarily remove?

  1. The risk of rising reference interest rates on the floating liability Correct answer.
  2. The credit risk of the swap counterparty
  3. The foreign exchange translation risk
  4. The liquidity risk of the underlying bond

Explanation

Paying fixed and receiving floating offsets a floating-rate liability, so when rates rise the swap gain offsets the higher interest cost. This converts the effective cost of funding to a known fixed rate. Counterparty, liquidity and currency risks are separate exposures that the swap does not eliminate.

Question 39Financial Derivatives

A trader sells a futures contract at PKR 1,000 and the initial margin is PKR 50,000 with a maintenance margin of PKR 35,000. The settlement price rises to PKR 1,015 on a contract of 1,000 units. What happens to the trader's margin account?

  1. The account is closed immediately at a profit
  2. A variation margin call restores the balance to the initial margin level after a PKR 15,000 loss Correct answer.
  3. Only the initial margin is doubled with no cash payment
  4. No action is needed because the loss is below the maintenance level

Explanation

The short position loses PKR 15 per unit on 1,000 units, a loss of PKR 15,000, reducing the balance from PKR 50,000 to PKR 35,000. Because the balance has fallen to the maintenance level, a call is triggered to top it back up to the initial margin. The variation margin required is PKR 15,000.

Question 40Financial Derivatives

Which combination creates a synthetic long stock position using options on the same underlying with the same strike and expiry?

  1. Buy a call and sell a put Correct answer.
  2. Sell a call and buy a put
  3. Buy a call and buy a put
  4. Sell a call and sell a put

Explanation

By put-call parity, a long call plus a short put replicates a long forward on the stock, which behaves like a leveraged long stock position. The payoff rises one-for-one with the underlying above or below the strike. This synthetic exposure is used to replicate stock without holding it.

Question 41Financial Derivatives

A European call on a stock is priced at PKR 15, the stock trades at PKR 105, the strike is PKR 100 and the present value of the strike is PKR 98. Using put-call parity, what is the fair value of the corresponding put?

  1. PKR 22
  2. PKR 12
  3. PKR 3
  4. PKR 8 Correct answer.

Explanation

Put-call parity gives the put value as call value minus stock price plus the present value of the strike. That is 15 minus 105 plus 98, which equals PKR 8. Any deviation from this value creates an arbitrage opportunity between the call, put and stock.

Question 42Financial Derivatives

A trader expects the underlying to stay almost flat and wants to collect premium with a defined maximum loss. Which strategy fits, assuming the trader also holds the underlying stock?

  1. Buy a straddle on the stock
  2. Buy an out-of-the-money call
  3. Write a naked put with no cash reserve
  4. Write a covered call on the stock held Correct answer.

Explanation

A covered call writes a call against stock already owned, so the premium is retained in a flat market and the stock holding covers the delivery obligation. The maximum loss is bounded by the decline in the stock less the premium. This matches a neutral-to-mildly-bullish view with defined risk.

Question 43Financial Derivatives

A futures contract on a stock index has a settlement price of 31,000 and the previous day's settlement was 30,800. A trader holds two long contracts with a multiplier of PKR 50. What is the variation margin credited to the account?

  1. PKR 1,000
  2. PKR 20,000 Correct answer.
  3. PKR 40,000
  4. PKR 10,000

Explanation

The index rose 200 points, and each point is worth PKR 50, so each contract gains PKR 10,000. With two contracts the credit is PKR 20,000. Variation margin is based on the change in settlement price, not the absolute level.

Question 44Financial Derivatives

Which statement correctly describes how a futures price relates to the expected spot price at delivery under the cost-of-carry model?

  1. The futures price equals the spot price minus the cost of carry plus income
  2. The futures price equals the spot price plus the cost of carry less any income from the asset Correct answer.
  3. The futures price always exceeds the expected spot price by the risk premium
  4. The futures price equals the spot price regardless of carry

Explanation

The cost-of-carry relationship prices a futures contract as the spot price compounded at the financing rate, adjusted for storage and other carrying costs, minus any income such as dividends or convenience yield. This anchors the futures price to a replicable cash-and-carry trade. Deviations are arbitraged away.

Question 45Financial Derivatives

A trader holds a long butterfly spread using calls with strikes of PKR 90, PKR 100 and PKR 110. What is the maximum profit achieved at expiry?

  1. When the underlying settles midway between PKR 90 and PKR 100
  2. When the underlying settles exactly at the middle strike of PKR 100 Correct answer.
  3. When the underlying settles above PKR 110
  4. When the underlying settles below PKR 90

Explanation

A long butterfly combines a bull call spread and a bear call spread and reaches its maximum value when the underlying finishes at the body strike. At PKR 100 the inner long call is at its peak intrinsic value while the outer short calls expire worthless. Movement away from the middle strike erodes the profit.

Question 46Financial Derivatives

A firm has a floating-rate loan at KIBOR plus 3 percent and wants to cap its maximum cost at 11 percent. Which derivative achieves this most directly?

  1. Enter a receive-fixed interest rate swap
  2. Buy a currency forward
  3. Sell an interest rate floor with a strike of 8 percent
  4. Buy an interest rate cap with a strike of 8 percent Correct answer.

Explanation

A cap pays the holder when the reference rate exceeds the strike, offsetting higher loan interest above that level. With a spread of 3 percent over KIBOR, a cap struck at 8 percent caps the all-in cost at 11 percent. The cap costs a premium but leaves the borrower able to benefit from falling rates.

Question 47Financial Derivatives

A trader observes that a European call on a non-dividend stock with a strike of PKR 100 trades at PKR 4 while the stock is PKR 102. What does this imply about the option's lower bound?

  1. The call's lower bound is zero because it is out of the money
  2. The call is above its intrinsic value of PKR 2, but rate and maturity information is needed to assess its lower bound Correct answer.
  3. The call must be worth at least PKR 102
  4. The call is fairly priced because time value is always positive

Explanation

The intrinsic value is PKR 102 − PKR 100 = PKR 2, so the PKR 4 price exceeds it. The European call's no-arbitrage lower bound is max(0, S0 - PV(K)). Without the risk-free rate and time to maturity, the discounted strike cannot be determined, so a lower-bound violation cannot be established.

Question 48Financial Derivatives

A company has a floating-rate liability and simultaneously enters a swap to pay fixed and receive floating. Which statement best describes the resulting exposure?

  1. The company has created a synthetic floating-rate asset
  2. The company remains fully exposed to rising rates on its original loan
  3. The company has created a synthetic fixed-rate liability and remains exposed to swap counterparty credit risk Correct answer.
  4. The company has eliminated all interest rate and credit risk

Explanation

Paying fixed and receiving floating on the swap offsets the floating leg of the loan, leaving a net fixed cost of funding. The company still bears counterparty credit risk on the swap and basis risk if the swap reference differs from the loan index. It has hedged rate direction, not all risk.

Question 49Financial Derivatives

An investor holds a long call and a long put with different strikes on the same underlying and expiry, structured so that the payoff at expiry is always positive. What must be true of the premiums paid for this to be a genuine arbitrage?

  1. The combined premium must exceed the maximum payoff at expiry
  2. The combined premium must be less than the present value of the minimum payoff guaranteed at expiry Correct answer.
  3. The premiums must be equal for both options
  4. The strikes must be identical for both options

Explanation

A payoff that is positive in every state is an arbitrage only if the cost of establishing it is below the present value of the guaranteed minimum payoff. Otherwise the investor is paying fair value or overpaying for the certain cash flow. Discounting matters because the payoff arrives at expiry.

Question 50Financial Derivatives

A futures trader faces a market where the convenience yield on a physical commodity exceeds the risk-free rate minus storage cost. What does the cost-of-carry model predict about the futures curve?

  1. The futures price will exceed the spot price, producing contango
  2. The futures price will be below the spot price, producing backwardation Correct answer.
  3. The futures curve will be flat regardless of storage
  4. The futures price will equal the spot price exactly

Explanation

When the benefit of holding the physical commodity, the convenience yield, outweighs financing and storage costs, the futures price falls below spot. This is backwardation, common in tight physical markets. The reverse situation produces contango.