Option Replication Using Put Call Parity

First Principles Thinking: residual equity payoff

C is correct. The CFA Curriculum states shareholder payoff is $\max(0, V_T - D)$. Here that is $\max(0, 140 - 100) = 40$. Shareholders therefore receive the USD 40 residual after debt is fully paid.

Why option A is incorrect. USD 100 is the debtholder payment in solvency, not the shareholder residual.

Why option B is incorrect. Zero applies only in insolvency when firm value falls below debt face value.

First Principles Thinking: residual-claim mechanism

A is correct. The assertion is true because equity payoff is $\max(0, V_T - D)$, the same shape as a call option. The reason is also true and explains why: shareholders get nothing below the debt threshold and keep only residual value above it. That threshold nature is exactly what creates the call-like payoff.

Why option B is incorrect. The reason is not just related; it is the direct mechanism that generates the call-option shape.

Why option C is incorrect. The reason is true, not false, because the residual claim exists only after debt is covered.

Why option D is incorrect. The assertion is true because the module explicitly compares equity to a call on firm value.

First Principles Thinking: no-arbitrage identity

D is correct. The assertion is false because the CFA Curriculum says identical state-contingent cash flows must have the same value at inception. The reason is true and states the governing no-arbitrage rule directly. Because the assertion violates that rule while the reason states it correctly, the correct classification is A false, R true.

Why option A is incorrect. The assertion is not true, so both statements cannot be true together.

Why option B is incorrect. Again, the assertion fails first; there is no case in which both statements are true.

Why option C is incorrect. The reason is true, not false, because it is the curriculum's core parity logic.

First Principles Thinking: covered-call decomposition

C is correct. The assertion is true because the CFA Curriculum shows that a covered call, $S_0 - c_0$, is equivalent to a long risk-free bond and a short put. The reason is false because the correct rearrangement is $S_0 - c_0 = X(1+r)^{-T} - p_0$, not plus $p_0$. Therefore, A is true but R is false.

Why option A is incorrect. The reason is not true because it reverses the sign on the put term.

Why option B is incorrect. Both statements are not true once the sign error in the reason is recognized.

Why option D is incorrect. The assertion is true, so it cannot be classified as false.

First Principles Thinking: forward-parity valuation

C is correct. The CFA Curriculum gives $p_0 - c_0 = [X - F_0(T)](1+r)^{-T}$. With the present-value factor equal to 1, $p_0 - 8 = 50 - 46 = 4$. So $p_0 = 12$. The no-arbitrage put value is therefore USD 12.

Why option A is incorrect. This ignores both the call premium and the positive strike-minus-forward spread.

Why option B is incorrect. This stops at the spread between strike and forward price and does not solve for the put price.

First Principles Thinking: sign discipline

D is correct. The reason is true because the curriculum gives that exact rearrangement. But the assertion is false: $[X - F_0(T)](1+r)^{-T}$ corresponds to receiving the strike via a long risk-free bond and paying the forward price via a short forward, not the other way around. The trap is reversing both positions.

Why option A is incorrect. The assertion is false because it flips the signs of the two non-option positions.

Why option B is incorrect. Both statements are not true, so this classification cannot hold.

Why option C is incorrect. The reason is true because it is the exact curriculum identity.

First Principles Thinking: classification rule

B is correct. The CFA Curriculum defines the covered call as $S_0 - c_0$, so Item I is correct. Rearranging put-call parity gives $S_0 - c_0 = X(1+r)^{-T} - p_0$, so Item II is correct. Item III is incorrect because the short call caps upside above the exercise price rather than leaving it unlimited. Therefore, only two statements are correct.

Why option A is incorrect. Counting only one ignores that both the covered-call definition and its bond-minus-put replication are explicit in the curriculum.

Why option C is incorrect. All three cannot be correct because the covered call does not preserve unlimited upside once the short call is in place.

First Principles Thinking: classification rule

B is correct. From the CFA Curriculum, $p_0 = c_0 + X(1+r)^{-T} - S_0$ and $X(1+r)^{-T} = -S_0 + c_0 - p_0$. So Item I is correct and Item II is correct. Item III is incorrect because the underlying equals $-p_0 + c_0 + X(1+r)^{-T}$, which requires a long, not short, risk-free bond. Therefore, only two statements are correct.

Why option A is incorrect. Counting only one ignores that both the put and the risk-free bond rearrangements are stated directly by the parity identities.

Why option C is incorrect. All three cannot qualify because Item III reverses the sign on the bond position.

First Principles Thinking: risky-debt payoff

C is correct. The CFA Curriculum states debtholder payoff is $\min(V_T, D)$. With firm value USD 72 and debt face value USD 90, debtholders receive the lesser amount, USD 72. That is the insolvency outcome because the firm cannot fully cover the debt.

Why option A is incorrect. Full repayment of USD 90 occurs only in solvency when firm value exceeds debt.

Why option B is incorrect. USD 18 is the shortfall from full repayment, not the payoff received by debtholders.

First Principles Thinking: call from parity

B is correct. Rearranging the CFA Curriculum relation gives $c_0 = S_0 + p_0 - X(1+r)^{-T}$. Substituting the values gives $70 + 9 - 64 = 15$. So the no-arbitrage call price is USD 15.

Why option A is incorrect. This ignores most of the asset value and does not satisfy the parity relation.

Why option C is incorrect. This is a partial arithmetic error and still does not balance the parity equation.

First Principles Thinking: decision rule

A is correct. The defining criterion in the CFA Curriculum is that two portfolios with identical future cash flows must trade at the same price at inception under no arbitrage. A protective put and a fiduciary call match state by state at expiration, so their time-0 prices must be equal. That is exactly put-call parity.

Why option B is incorrect. The call premium is only one component of the fiduciary call and does not create an arbitrary pricing wedge when the total future cash flows are identical.

Why option C is incorrect. Initial moneyness does not override the no-arbitrage requirement once the full payoff profiles are the same.

First Principles Thinking: decision rule

C is correct. The CFA Curriculum shows that when the protective put side is overpriced relative to the fiduciary call side, the arbitrage is to sell the expensive side and buy the cheap side. Here, $S_0 + p_0$ exceeds $c_0 + X(1+r)^{-T}$, so the investor sells the protective put package and buys the fiduciary call package. The future cash flows offset and the initial positive difference is locked in.

Why option A is incorrect. That would buy the overpriced side and sell the underpriced side, reversing the arbitrage profit.

Why option B is incorrect. The trade is driven by relative pricing under parity, not by a directional view on the underlying.

First Principles Thinking: decision rule

C is correct. The defining criterion from the CFA Curriculum is that debtholders receive $\min(V_T, D)$, which is equivalent to risk-free debt minus a put sold to shareholders. That position has limited upside because full repayment is capped at $D$. It is therefore least like a direct call option, which would preserve upside above the strike.

Why option A is incorrect. Limited upside is exactly how the curriculum characterizes debtholder payoff in solvency.

Why option B is incorrect. Risk-free debt minus a put on firm value is the curriculum's explicit decomposition of risky debt.

First Principles Thinking: decision rule

C is correct. The CFA Curriculum states that shareholder payoff at maturity is $\max(0, V_T - D)$, which is exactly the payoff shape of a call option on firm value with exercise price equal to debt face value. Shareholders have upside if firm value exceeds debt and limited downside if it does not. That makes equity call-like, not bond-like.

Why option A is incorrect. The sold put interpretation belongs to debtholders, who absorb downside insolvency risk.

Why option B is incorrect. Equity does not have fixed upside capped at debt face value; it retains residual upside above debt.

First Principles Thinking: classification rule

C is correct. In the CFA Curriculum, the synthetic protective put contains a purchased put, a forward purchase, and a risk-free bond. Item I is correct because the put payoff is $X - S_T$ when exercised. Item II is correct because the long forward payoff is $S_T - F_0(T)$. Item III is correct because the total payoff is $X$ when $S_T < X$ and $S_T$ when $S_T \ge X$. Therefore, all three statements are correct.

Why option A is incorrect. Counting one ignores both the correct forward payoff and the correct state-contingent total shown in the curriculum.

Why option B is incorrect. Counting two still misses one of the three valid pieces of the synthetic protective put payoff construction.

First Principles Thinking: decision rule

B is correct. Rearranging the CFA Curriculum relation $S_0 + p_0 = c_0 + X(1+r)^{-T}$ gives $S_0 = -p_0 + c_0 + X(1+r)^{-T}$. So the underlying is replicated by a short put, a long call, and a long risk-free bond. That is the exact underlying synthesis under put-call parity.

Why option A is incorrect. This combination has the wrong signs on both options and therefore does not isolate the underlying payoff.

Why option C is incorrect. The short bond reverses the cash component that parity requires to complete the underlying replication.

First Principles Thinking: classification rule

A is correct. The CFA Curriculum states that in solvency, debtholders are repaid in full and receive $D$, so Item I is correct. In insolvency, shareholders receive zero rather than $V_T - D$, so Item II is incorrect. Item III is also incorrect because insolvent debtholders receive the firm value $V_T$, not the full debt face value $D$. Therefore, only one statement is correct.

Why option B is incorrect. Counting two would wrongly treat either a negative shareholder residual or full debtholder repayment in insolvency as valid.

Why option C is incorrect. All three cannot qualify because Items II and III both contradict the curriculum's insolvency outcomes.

First Principles Thinking: parity valuation

A is correct. The CFA Curriculum uses $S_0 + p_0 = c_0 + X(1+r)^{-T}$. Solving for the put gives $p_0 = c_0 + X(1+r)^{-T} - S_0 = 14 + 95 - 90 = 19$. The no-arbitrage put value is therefore USD 19.

Why option B is incorrect. This subtracts the present value of the strike instead of adding it when isolating the put.

Why option C is incorrect. This reflects only part of the parity difference and ignores one cash component.

First Principles Thinking: mispricing gap

B is correct. With the traded put at USD 22, the protective-put side costs $S_0 + p_0 = 90 + 22 = 112$. The fiduciary-call side costs $c_0 + X(1+r)^{-T} = 14 + 95 = 109$. Selling the expensive side and buying the cheap side locks in USD 3 at inception, with offsetting expiration cash flows. That USD 3 is the arbitrage profit per unit.

Why option A is incorrect. This understates the actual pricing gap between the two parity portfolios.

Why option C is incorrect. This confuses the arbitrage profit with a larger partial spread that is not supported by the parity arithmetic.

First Principles Thinking: classification rule

C is correct. The CFA Curriculum defines the synthetic protective put exactly as in Item I and states the parity relation in Item II. Rearranging that parity gives $p_0 - c_0 = [X - F_0(T)](1+r)^{-T}$, which the curriculum interprets as a long put plus short call being equivalent to a long risk-free bond and a short forward. Item III states that same equivalence in position form. Therefore, all three statements are correct.

Why option A is incorrect. Counting only one ignores that both the equation and the synthetic-protective-put construction are explicitly given in the curriculum.

Why option B is incorrect. Counting only two misses that the long-put/short-call equivalence is the direct rearrangement of put-call forward parity.

First Principles Thinking: classification rule

A is correct. The CFA Curriculum defines put-call parity by equating the payoff of a protective put with the payoff of a fiduciary call. Item I is not one of those equivalent portfolios because adding a risk-free bond to a protective put changes the payoff. Item II is the fiduciary call. Item III states the actual equivalent pair. Therefore, only one statement describes portfolios guaranteed to be identical.

Why option B is incorrect. Counting two incorrectly treats the extra-bond portfolio in Item I as unchanged, even though the additional bond alters the payoff.

Why option C is incorrect. All three cannot qualify because Item I does not match the CFA Curriculum parity construction.

First Principles Thinking: decision rule

A is correct. The CFA Curriculum rearranges put-call forward parity to $p_0 - c_0 = [X - F_0(T)](1+r)^{-T}$. That right-hand side is the present value of receiving $X$ and paying $F_0(T)$ at maturity, which is a long risk-free bond and a short forward position. So a long put plus short call matches that package.

Why option B is incorrect. A short risk-free bond would reverse the receipt of $X$ at maturity and break the parity identity.

Why option C is incorrect. A long forward gives the wrong exposure because the parity rearrangement requires paying, not receiving, the forward price.

First Principles Thinking: classification rule

B is correct. The CFA Curriculum states that shareholders receive $\max(0, V_T - D)$ and debtholders receive $\min(V_T, D) = D - \max(0, D - V_T)$. So Item I is correct. Item II is incorrect because $\max(0, D - V_T)$ is the put payoff, not the full debtholder payoff. Item III is correct because risky debt equals risk-free debt less the sold put on firm value. Therefore, only two statements are correct.

Why option A is incorrect. Counting one overlooks that the sold-put interpretation of risky debt is an explicit result in the module.

Why option C is incorrect. All three cannot qualify because Item II confuses the put component with total debtholder payoff.

First Principles Thinking: credit-risk premium

B is correct. The assertion is true because the curriculum states that the put may be interpreted as the credit spread or premium above the risk-free rate required by debtholders. The reason is also true because higher insolvency risk raises the value of the put-like transfer from debtholders to shareholders. But the reason describes how the component behaves with risk rather than directly defining why the component is called the credit spread.

Why option A is incorrect. The reason supports the intuition but does not directly establish the naming identity in the way the assertion states it.

Why option C is incorrect. The reason is true because increasing insolvency risk makes the sold-put exposure more painful for debtholders.

Why option D is incorrect. The assertion is true because the curriculum explicitly interprets the put as the debt credit spread.

First Principles Thinking: state payoff aggregation

A is correct. When $S_T = 48$ and the exercise price is USD 60, the put pays $60 - 48 = 12$. The long forward pays $48 - 52 = -4$, and the bond pays 52. Adding them gives $12 - 4 + 52 = 60$. That matches the curriculum result that the synthetic protective put pays the strike when $S_T < X$.

Why option B is incorrect. This is the underlying price in the no-exercise state, not the total in the exercised-put state.

Why option C is incorrect. This overcounts the protective floor by adding the strike and forward mismatch incorrectly.

First Principles Thinking: algebraic replication

A is correct. The assertion matches the rearranged parity identity exactly. The reason correctly derives the replication by isolating $S_0$ from the curriculum equation. Because the algebra in the reason is the direct basis for the assertion, both are true and the reason explains the assertion.

Why option B is incorrect. The reason is not merely related; it is the exact derivation of the asserted replication.

Why option C is incorrect. The reason is true because the rearrangement is numerically and conceptually correct.

Why option D is incorrect. The assertion is true, not false, because it restates the rearranged parity equation.

First Principles Thinking: forward-parity extension

B is correct. The assertion is true because the module defines the synthetic protective put exactly that way. The reason is also true because that synthetic underlying is the bridge from basic put-call parity to put-call forward parity. But the reason explains why the substitution matters conceptually, not the full construction details of the assertion itself, so it is not the direct explanation of every component in the assertion.

Why option A is incorrect. The reason is related, but it does not fully explain the specific composition of the synthetic protective put.

Why option C is incorrect. The reason is true; the synthetic underlying is precisely what extends the parity relation to forwards.

Why option D is incorrect. The assertion is true because it matches the curriculum's stated portfolio construction.

First Principles Thinking: decision rule

B is correct. The CFA Curriculum replaces the cash underlying with its synthetic form: a long forward plus a risk-free bond whose maturity value equals the forward price. Adding a purchased put to that synthetic underlying creates the synthetic protective put. Its payoff then matches the protective put and the fiduciary call.

Why option A is incorrect. The short forward and short bond reverse the synthetic underlying and do not reproduce the protective-put payoff.

Why option C is incorrect. A long call and short bond is the opposite side of the basic parity relation and does not define the synthetic protective put.