Derivatives

Based on put-call parity, a trader who combines a long asset, a long put, and a short call will create a synthetic: A. long bond. B. fiduciary call. C. protective put.

A is correct. A long bond can be synthetically created by combining a long asset, a long put, and a short call. A fiduciary call is created by combining a long call with a risk free bond. A protective put is created by combining a long asset with a long put.

A swap is: more like a forward than a futures contract. subject to simultaneous default by both parties. based on an exchange of two series of fixed cash flows.

A is correct. A swap is a bit more like a forward contract than a futures contract in that it is an OTC contract, so it is privately negotiated and subject to default.

If the net cost of carry of an asset is positive, then the price of a forward contract on that asset is most likely: lower than if the net cost of carry was zero. the same as if the net cost of carry was zero. higher than if the net cost of carry was zero.

A is correct. An asset's forward price is increased by the future value of any costs and decreased by the future value of any benefits: F0(T) = S0(1 + r)T - (γ - θ)(1 + r)T. If the net cost of carry (benefits less costs) is positive, the forward price is lower than if the net cost of carry was zero.

If the risk-free rate increases, the value of an in-the-money European put option will most likely: decrease. remain the same. increase.

A is correct. An in-the-money European put option decreases in value with an increase in the risk-free rate. A higher risk-free rate reduces the present value of any proceeds received on exercise.

A characteristic of forward commitments is that they: provide linear payoffs. do not depend on the outcome or payoff of an underlying asset. provide one party the right to engage in future transactions on terms agreed on in advance.

A is correct. Because forward commitments provide linear payoffs.

A swap that involves the exchange of a fixed payment for a floating payment is most likely equivalent to a series of: off-market forward contracts. forward contracts that all have an initial positive value. forward contracts that all have an initial value equal to the fixed payment.

A is correct. Because the cost of carrying an asset over different time periods will vary, the values of the implicit forward contracts embedded in the swap will not be equal: some may be positive, and some may be negative. Off-market forward contracts satisfy this condition because they can be set at any value.

Consider a call option selling for $4 in which the exercise price is $50. Determine the value at expiration and the profit for a buyer if the price of the underlying at expiration is $48. -$4 $0 $2

A is correct. CT = Max(0,ST - X) = Max(0,48 - 50) = 0

Compared with the underlying spot market, derivative markets are more likely to have: greater liquidity. higher transaction costs. higher capital requirements.

A is correct. Derivative markets typically have greater liquidity than the underlying spot market as a result of the lower capital required to trade derivatives compared with the underlying. Derivatives also have lower transaction costs and lower capital requirements than the underlying.

Knowledge about the degree of risk aversion of investors is most likely needed for: the pricing of assets, but not for the pricing of derivatives. both the pricing of assets and of derivatives. the pricing of derivatives, but not for the pricing of assets.

A is correct. Derivatives pricing makes use of the fact that arbitrage opportunities guarantee that a risk-free portfolio that combines the underlying with a derivative must earn the risk-free rate. As such, no knowledge about the degree of risk aversion of investors is needed. In contrast, the pricing of assets requires knowledge of the degree of risk aversion to adequately assess risk premia.

To the holder of a long position, it is more desirable to own a forward contract than a futures contract when interest rates and futures prices are: negatively correlated. uncorrelated. positively correlated.

A is correct. If futures prices and interest rates are negatively correlated, forwards are more desirable to holders of long positions than are futures. This is because rising prices lead to futures profits that are reinvested in periods of falling interest rates. It is better to receive all of the cash at expiration under such conditions. If futures prices and interest rates are uncorrelated, forward and futures prices will be the same. If futures prices are positively correlated with interest rates, futures contracts are more desirable to holders of long positions than are forwards.

Which of the following statements explains a characteristic of futures price limits? Price limits: help the clearinghouse manage its credit exposure. can typically be expanded intra-day by willing traders. establish a band around the final trade of the previous day.

A is correct. Price limits are important in helping the clearinghouse manage its credit exposure. Sharply moving prices make it more difficult for the clearinghouse to collect from parties losing money.

Under put-call-forward parity, which of the following transactions is risk free? Short call, long put, long forward contract, long risk-free bond Long call, short put, long forward contract, short risk-free bond Long call, long put, short forward contract, short risk-free bond

A is correct. Purchasing a long forward contract and a risk-free bond creates a synthetic asset. Combining a long synthetic asset, a long put, and a short call is risk free because its payoffs produce a known cash flow of the value of the exercise price.

For a holder of a European option, put-call-forward parity is based on the assumption that: no arbitrage is possible within the spot, forward, and option markets. the value of a European put at expiration is the greater of zero or the underlying value minus the exercise price. the value of a European call at expiration is the greater of zero or the exercise price minus the value of the underlying.

A is correct. Put-call-forward parity is based on the assumption that no arbitrage is possible within the spot, forward, and option markets.

Combining a protective put with a forward contract generates equivalent outcomes at expiration to those of a: fiduciary call. long call combined with a short asset. forward contract combined with a risk-free bond

A is correct. Put−call forward parity demonstrates that the outcome of a protective put with a forward contract (long put, long risk-free bond, long forward contract) equals the outcome of a fiduciary call (long call, long risk-free bond). The outcome of a protective put with a forward contract is also equal to the outcome of a protective put with asset (long put, long asset).

The clearing and settlement process of an exchange-traded derivatives market: provides a credit guarantee. provides transparency and flexibility. takes longer than that of most securities exchanges.

A is correct. The clearing and settlement process of derivative transactions provides a credit guarantee.

The notional principal of a swap is: not exchanged in the case of an interest rate swap. a fixed amount whenever it is matched with a loan. equal to the amount owed by one swap party to the other.

A is correct. The notional principal of a swap is not exchanged in the case of an interest rate swap.

The price of a pay-fixed receive-floating interest rate swap is most likely: the fixed rate that results in a market value of zero for the swap at initiation. the present value of the floating-rate payments minus the present value of the fixed-rate payments. the sum of the fixed-rate payments minus the sum of the floating-rate payments.

A is correct. The price of the swap is the fixed rate on the swap at the start of the transaction such that the present value of fixed payments is equal to the present value of the floating payments and the market value of the swap is zero.

Which of the following statements regarding commodity derivatives is correct? The primary commodity derivatives are futures. Commodities are subject to a set of well-defined risk factors. Commodity traders and financial traders today are distinct groups within the financial world.

A is correct. The primary commodity derivatives are futures, but forwards, swaps, and options are also used.

It is least likely true that a swap may be viewed as a series of forward contracts where the prices of the implicit forward contracts embedded in the swap: are equal. sum to zero. are not equal.

A is correct. The statement is incorrect. Although a swap may be viewed as a series of forward contracts expiring at various times where one party agrees to make a fixed payment and receive a variable payment, with swaps, the fixed payments are the same and are established at initiation. However, the prices of the implicit forward contracts embedded in a swap will not be equal.

Holding other factors constant, the value of a European put option will most likely decrease as the: risk-free interest rate increases. volatility of the underlying increases. value of the underlying decreases.

A is correct. The value of a European put option will decrease as the risk-free interest rate increases.

In the binomial model, the difference between the up and down factors best represents the: volatility of the underlying. moneyness of an option. pseudo probability.

A is correct. The volatility of the underlying is captured in the binomial model by the difference between the up and down factors.

According to put-call parity, for European options, a long call on an asset is equal to: long put + long asset + long risk-free bond. long put + long asset + short risk-free bond. short put + short asset + long risk-free bond.

B is correct That is, Long asset + Long put = Long call + Long risk-free bond. Rearranging terms gives Long call = Long put + Long asset + Short risk-free bond

Which of the following combinations replicates a long derivative position? A short derivative and a long asset A long asset and a short risk-free bond A short derivative and a short risk-free bond

B is correct. A long asset and a short risk-free asset (meaning to borrow at the risk-free rate) can be combined to produce a long derivative position.

Which of the following transactions is the equivalent of a synthetic long call position? Long asset, long put, short call Long asset, long put, short bond Short asset, long call, long bond

B is correct. According to put−call parity, a synthetic call can be constructed by combining a long asset, long put, and short bond positions.

At the initiation of a forward contract on an asset that neither receives benefits nor incurs carrying costs during the term of the contract, the forward price is equal to the: spot price. future value of the spot price. present value of the spot price.

B is correct. At initiation, the forward price is the future value of the spot price (spot price compounded at the risk-free rate over the life of the contract). If the forward price were set to the spot price or the present value of the spot price, it would be possible for one side to earn an arbitrage profit by selling the asset and investing the proceeds until contract expiration.

If a forward contract requires no cash outlay at initiation, it is most likely true that at initiation: value exceeds price. price exceeds value. price is equal to value.

B is correct. At initiation, value is equal to zero. Price is a positive number that states the amount that must be paid when the purchase takes place.

Convenience yield is best described as a nonmonetary benefit of holding a(n): option contract. asset. forward contract.

B is correct. Convenience yield represents the nonmonetary advantage of holding the asset.

Relative to spot markets, one key feature of derivatives markets is: high transaction costs. low capital requirements. restrictions on short selling.

B is correct. Derivatives markets provide the benefit of low capital requirements to hedgers and speculators.

Forward rate agreements are most likely used to hedge an exposure in the: foreign exchange market. money market. equity market.

B is correct. Forward rate agreements are used to hedge interest rate exposure present in the money market.

Which of the following statements best describes changes in the value of a long forward position during its life? As the time to maturity goes down, the value of the position goes up. As the price of the underlying goes up, the value of the position goes up. As interest rates go down, the value of the position goes up.

B is correct. Given the formula for the value of a forward contract: Vt (T) = St - F 0(T)(1 + r)-( T - t ) it follows that the value of the contract goes up as the price of the underlying goes up.

Which of the following statements is least accurate concerning differences in the pricing of forwards and futures? Differences in the pattern of cash flows of forwards and futures can explain pricing differences. Pricing differences can arise if futures prices and interest rates are uncorrelated. Interest rate volatility can explain pricing differences.

B is correct. If futures prices and interest rates are uncorrelated, the prices of forwards and futures will be identical.

For an investor with a long position, the price of a futures contract will most likely be higher than the price on a forward contract on the same asset with the same expiration date if there is a: zero correlation between the futures price and interest rates. positive correlation between the futures price and interest rates. negative correlation between the futures price and interest rates.

B is correct. If there is a positive correlation between futures prices and interest rates, an investor with a long position will favor futures over forwards because rising prices lead to futures profits that are reinvested at higher interest rates. With forwards, all the gains are received at expiration and thus there is no gain from reinvestment.

In contrast to contingent claims, forward contracts: have their prices chosen by the participants. could end in default by either party. can be exercised by physical or cash delivery.

B is correct. In a forward contract, either party could default, whereas in a contingent claim, default is possible only from the short to the long.

Which of the following statements most likely contributes to the view that derivatives have some role in causing financial crashes? Derivatives are the primary means by which leverage and related excessive risk is brought into financial markets. Growth in the number of investors willing to speculate in derivatives markets leads to excessive speculative trading. Restrictions on derivatives, such as enhanced collateral requirements and credit mitigation measures, in the years leading up to crashes introduce market rigidity.

B is correct. Opponents of derivatives claim that excessive speculative trading brings instability to the markets. Defaults by speculators can lead to defaults by their creditors, their creditors' creditors, and so on.

Prior to expiration, the lowest value of a European put option is the greater of zero or the: exercise price minus the value of the underlying. present value of the exercise price minus the value of the underlying. value of the underlying minus the present value of the exercise price.

B is correct. Prior to expiration, the lowest value of a European put is the greater of zero or the present value of the exercise price minus the value of the underlying.

Based on the binomial model, an increase in the actual probability of an upward move in the underlying will result in the option price: decreasing. remaining the same. increasing.

B is correct. The binomial model does not consider the actual probabilities of upward and downward movements in determining the option value. Thus, a change in this probability has no effect on the calculated option price.

There are two forward contracts, contract 1 and contract 2, on the same underlying. The underlying makes no cash payments, does not yield any nonfinancial benefits, and does not incur any storage costs. Contract 1 expires in one year, and contract 2 expires in two years. It is most likely that the price of contract 1: is equal to the price of contract 2. is less than the price of contract 2. exceeds the price of contract 2.

B is correct. The forward price is the spot price compounded at the risk-free rate over the life of the contract. Because contract 2 has the longer life, compounding will lead to a larger value.

The value of a swap is equal to the present value of the: fixed payments from the swap. net cash flow payments from the swap. underlying at the end of the contract.

B is correct. The principal of replication articulates that the valuation of a swap is the present value of all the net cash flow payments from the swap, not simply the present value of the fixed payments of the swap or the present value of the underlying at the end of the contract.

The underlying in a forward rate agreement is most likely a(n): growth rate of an equity index. interest rate. exchange rate.

B is correct. The underlying in a forward rate agreement is an interest rate.

The value of a European put option can be either directly or inversely related to the: exercise price. time to expiration. volatility of the underlying.

B is correct. The value of a European put option can be either directly or indirectly related to time to expiration. The direct effect is more common, but the inverse effect can prevail the longer the time to expiration, the higher the risk-free rate, and the deeper in-the-money is the put. The value of a European put option is directly related to the exercise price and the volatility of the underlying.

The value of a long position in a forward contract at expiration is best defined as: forward price agreed in the contract minus spot price of the underlying. spot price of the underlying minus forward price agreed in the contract. value of the forward at initiation minus spot price of the underlying.

B is correct. The value of a long position in a forward contract at expiration is defined as spot price of the underlying minus forward price agreed in the contract.

What is the most likely reason why arbitrage will not completely eliminate all pricing discrepancies for derivatives? Differences in risk aversion Transaction costs Inaccurate forecasts

B is correct. Transaction costs may render an arbitrage strategy unprofitable and can therefore prevent precise convergence of prices.

The value of a swap typically: is non-zero at initiation. is obtained through replication. does not fluctuate over the life of the contract.

B is correct. Valuation of the swap during its life appeals to replication and the principle of arbitrage. Valuation consists of reproducing the remaining payments on the swap with other transactions. The value of that replication strategy is the value of the swap. The swap price is typically set such that the swap contract has a value of zero at initiation. The value of a swap contract will change during the life of the contract as the value of the underlying changes in value.

Most derivatives are priced by: assuming that the market offers arbitrage opportunities. discounting the expected payoff of the derivative at the risk-free rate. applying a risk premium to the expected payoff of the derivative and its risk.

B is correct. Virtually all derivative pricing models discount the expected payoff of the derivative at the risk-free rate.

When interest rates are constant, futures prices are most likely: less than forward prices. equal to forward prices. greater than forward prices.

B is correct. When interest rates are constant, forwards and futures will likely have the same prices. The price differential will vary with the volatility of interest rates. In addition, if futures prices and interest rates are uncorrelated, forward and futures prices will be the same. If futures prices are positively correlated with interest rates, futures contracts are more desirable to holders of long positions than are forwards. This is because rising prices lead to future profits that are reinvested in periods of rising interest rates, and falling prices lead to losses that occur in periods of falling interest rates. If futures prices are negatively correlated with interest rates, futures contracts are less desirable to holders of long positions than are forwards. The more desirable contract will tend to have the higher price.

Assume a call option's strike price is initially equal to the price of its underlying asset. Based on the binomial model, if the volatility of the underlying decreases, the lower of the two potential payoff values of the hedge portfolio: decreases. remains the same. increases.

B is correct. When the volatility of the underlying decreases, the value of the option also decreases, meaning that the upper payoff value of the hedge portfolio combining them declines. However, the lower payoff value remains at zero.

If no cash is initially exchanged, a swap is comparable to a series of forward contracts when: the swap payments are variable. the combined value of all the forward contracts is zero. all the forward contracts have the same agreed-on price.

B is correct. When two parties engage in a series of forward contracts and initially agree on a price of FS0(T), some of the forward contracts have positive values and some have negative values, but their combined value equals zero.

Which of the following statements best portrays the full implementation of post-financial-crisis regulations in the OTC derivatives market? Transactions are no longer private. Most transactions need to be reported to regulators. All transactions must be cleared through central clearing agencies.

B is correct. With full implementation of these regulations in the OTC derivatives market, most OTC transactions need to be reported to regulators.

Consider a call option selling for $4 in which the exercise price is $50. Determine the value at expiration and the profit for a seller if the price of the underling at expiration is $52. -$2 $5 $2

C is correct. -CT = -Max(0,ST - X) = -Max(0,52 - 50) = -2

Which of the following derivatives is classified as a contingent claim? Futures contracts Interest rate swaps Credit default swaps

C is correct. A credit default swap (CDS) is a derivative in which the credit protection seller provides protection to the credit protection buyer against the credit risk of a separate party. CDS are classified as a contingent claim.

Using put-call parity, a long call can best be replicated by going: long the put, short the asset, and long the bond. short the put, long the asset, and short the bond. long the put, long the asset, and short the bond.

C is correct. According to put-call parity, a long call is equal to long put, long asset, short bond.

For a risk-averse investor, the price of a risky asset, assuming no additional costs and benefits of holding the asset, is: unrelated to the risk-free rate. directly related to its level of risk. inversely related to its level of risk.

C is correct. An asset's current price, S0, is determined by discounting the expected future price of the asset by r (the risk free rate) plus λ (the risk premium) over the period from 0 to T, as illustrated in the following equation:

An arbitrage transaction generates a net inflow of funds: throughout the holding period. at the end of the holding period. at the start of the holding period.

C is correct. Arbitrage is a type of transaction undertaken when two assets or portfolios produce identical results but sell for different prices. A trader buys the asset or portfolio with the lower price and sells the asset or portfolio with the higher price, generating a net inflow of funds at the start of the holding period. Because the two assets or portfolios produce identical results, a long position in one and short position in the other means that at the end of the holding period, the payoffs offset. Therefore, there is no money gained or lost at the end of the holding period, so there is no risk.

Which of the following factors is shared by forwards and futures contracts? Timing of profits Flexible settlement arrangements Nearly equivalent profits by expiration

C is correct. Comparing the derivatives, forward and futures contracts have nearly equivalent profits by the time of expiration of the forward.

A high convenience yield is most likely associated with holding: bonds. equities. commodities.

C is correct. Convenience yield is primarily associated with commodities and generally exists as a result of difficulty in shorting the commodity or unusually tight supplies.

A swap that involves the exchange of a fixed payment for a floating payment can be interpreted as a series of forward contracts with different expiration dates. These implied forward contracts will most likely have: different prices due to differences in the price of the underlying at expiration. identical prices. different prices due to differences in the cost of carry.

C is correct. Due to differences in the cost of carry, implied forward contracts will have different prices. The differences in the cost of carry stem from the timing differences of the payments.

If a call option is priced higher than the binomial model predicts, investors can earn a return in excess of the risk-free rate by: investing at the risk-free rate, selling a call, and selling the underlying. borrowing at the risk-free rate, buying a call, and buying the underlying. borrowing at the risk-free rate, selling a call, and buying the underlying

C is correct. If an option is trading above the value predicted by the binomial model, investors can engage in arbitrage by selling a call, buying shares of the underlying, and funding the transaction by borrowing at the risk-free rate. This will earn a return in excess of the risk-free rate.

In an efficient market, it is more likely that fundamental value will be reflected in the: underlying spot market before the derivative market. derivatives market and the underlying spot market at the same time. derivatives market before the underlying spot market.

C is correct. In an efficient market, the derivatives market is more likely to reflect fundamental value, even if only for a short period, before the underlying spot market because derivatives contracts require less capital, have lower transaction costs, and are easier to sell short.

A European put option on a dividend-paying stock is most likely to increase if there is an increase in: carrying costs. the risk-free rate. dividend payments.

C is correct. Payments, such as dividends, reduce the value of the underlying which increases the value of a European put option. Carrying costs reduce the value of a European put option. An increase in the risk-free interest rate may decrease the value of a European put option.

To determine the price of an option today, the binomial model requires: selling one put and buying one offsetting call. buying one unit of the underlying and selling one matching call. using the risk-free rate to determine the required number of units of the underlying.

C is correct. Pricing an option relies on the facts that a perfectly hedged investment earns the risk-free rate and that, based on the binomial option pricing model, the size of the two possible changes in the option price (meaning the potential step up or step down in the option value) after one period are equivalent.

The price of a swap typically: is zero at initiation. fluctuates over the life of the contract. is obtained through a process of replication.

C is correct. Replication is the key to pricing a swap. The swap price is determined at initiation by replication. The value (not the price) of the swap is typically zero at initiation and the fixed swap price is typically determined such that the value of the swap will be zero at initiation.

Replication is most likely used to: reduce portfolio risk. increase leverage. exploit pricing differentials.

C is correct. Replication is the process of creating an asset or portfolio from another asset, portfolio, and/or derivative. It is used to exploit pricing differentials.

Which of the following is least likely to be required by the binomial option pricing model? Spot price Two possible prices one period later Actual probabilities of the up and down moves

C is correct. The actual probabilities of the up and down moves in the underlying do not appear in the binomial option pricing model, only the pseudo or "risk-neutral" probabilities. Both the spot price of the underlying and two possible prices one period later are required by the binomial option pricing model.

Which of the following factors most likely explains why the spot price of a commodity in short supply can be greater than its forward price? Opportunity cost Lack of dividends Convenience yield

C is correct. The convenience yield is a benefit of holding the asset and generally exists when a commodity is in short supply. The future value of the convenience yield is subtracted from the compounded spot price and reduces the commodity's forward price relative to it spot price. The opportunity cost is the risk-free rate. In the absence of carry costs, the forward price is the spot price compounded at the risk-free rate and will exceed the spot price. Dividends are benefits that reduce the forward price but the lack of dividends has no effect on the spot price relative to the forward price of a commodity in short supply.

Which of the following statements best represents information discovery in the futures market? The futures price is predictive. Information flows more slowly into the futures market than into the spot market. The futures market reveals the price that the holder of the asset can take to avoid uncertainty.

C is correct. The futures market reveals the price that the holder of an asset could take and avoid the risk of uncertainty.

The law of one price is best described as: the true fundamental value of an asset. earning a risk-free profit without committing any capital. two assets that will produce the same cash flows in the future must sell for equivalent prices

C is correct. The law of one price occurs when market participants engage in arbitrage activities so that identical assets sell for the same price in different markets.

Assume an asset pays no dividends or interest, and also assume that the asset does not yield any non-financial benefits or incur any carrying cost. At initiation, the price of a forward contract on that asset is: lower than the value of the contract. equal to the value of the contract. greater than the value of the contract.

C is correct. The price of a forward contract is a contractually fixed price, established at initiation, at which the underlying will be purchased (or sold) at expiration. The value of a forward contract at initiation is zero; therefore, the forward price is greater than the value of the forward contract at initiation.

During its life, the value of a forward contract is most likely equal to the price of the underlying minus the price of the: forward. forward, discounted over the original term of the contract. forward, discounted over the remaining term of the contract.

C is correct. The value of a forward contract is the spot price of the underlying minus the present value of the forward contract. Calculating the present value requires adjusting the time period to account for the remaining term of the contract.

If the present value of storage costs exceeds the present value of its convenience yield, then the commodity's forward price is most likely: less than the spot price compounded at the risk-free rate. the same as the spot price compounded at the risk-free rate. higher than the spot price compounded at the risk-free rate.

C is correct. When a commodity's storage costs exceed its convenience yield benefits, the net cost of carry (benefits less costs) is negative. Subtracting this negative amount from the spot price compounded at the risk-free rate results in an addition to the compounded spot price. The result is a commodity forward price which is higher than the spot price compounded. The commodity's forward price is less than the spot price compounded when the convenience yield benefits exceed the storage costs and the commodity's forward price is the same as the spot price compounded when the costs equal the benefits.

The derivative markets tend to: transfer liquidity from the broader financial markets. not reflect fundamental value after it is restored in the underlying market. offer a less costly way to exploit mispricing in comparison to other free and competitive financial markets.

C is correct. When prices deviate from fundamental values, derivative markets offer a less costly way to exploit mispricing in comparison to other free and competitive financial markets.