Can you explain how a long call option combined with a short put option, both with the same strike price and expiry, creates a synthetic long forward position? Take a moment. If your answer jumps straight to "it's just put-call parity" without specifying the zero net cash flow at initiation, you've found a core trap in CFA Level I Derivatives: memorizing rules without grasping the mechanics. The exam doesn't just ask what something is; it tests if you know how to build it and what it costs.
The CFA Level I Derivatives topic covers the characteristics, valuation, and risk management applications of forwards, futures, options, and swaps. It comprises 5-8% of the exam and tests your ability to apply core pricing principles like no-arbitrage and put-call parity to practical scenarios involving these instruments.
Key facts
- Official Body
- CFA Institute
- Topic Area Weight (2026)
- 5-8% of the Level I exam
- Study Hour Average
- Successful candidates report averaging over 300 hours for the entire Level I exam.
- Passing Score
- The Minimum Passing Score (MPS) is determined post-exam by the CFA Institute Board of Governors and varies by administration.
- Exam Format
- Multiple-choice questions presented in vignettes or as standalone items.
- Pass Rate
- The CFA Institute reports the historical Level I pass rate hovers around 40-45% (CFA Institute).
What Are the Must-Know Formulas and Rules?
Success in Derivatives requires a firm grasp of a few core formulas. But don't just memorize them. Understand that each one is simply an expression of the no-arbitrage principle. These are your essential tools for pricing and valuation.
Core Formulas for CFA Derivatives
| Instrument | Formula (Discrete Compounding) | Key Variables |
|---|---|---|
| Forward Price | F₀(T) = (S₀ − PV₀(D)) × (1 + r_f)^T | S₀=Spot Price, PV₀(D)=PV of Dividends, r_f=Risk-Free Rate |
| Value of Forward | Vₜ(T) = Sₜ − (F₀(T) ÷ (1 + r_f)^(T−t)) | Sₜ=Spot at time t, F₀(T)=Original Forward Price |
| Put-Call Parity | C₀ + (X ÷ (1 + r_f)^T) = P₀ + S₀ | C₀=Call Price, P₀=Put Price, X=Strike Price |
| Call Option Payoff | Max(0, Sₜ − X) | Payoff at expiration for the buyer. |
| Put Option Payoff | Max(0, X − Sₜ) | Payoff at expiration for the buyer. |
e. The forward price formula becomes F₀(T) = S₀ × e^(r_f × T). The present value of the strike becomes X × e^(−r_f × T). Always check the question for the required compounding convention.Key Rules to Memorize
- Option Moneyness: An option has intrinsic value if it is "in-the-money."
- Call Option: In-the-money when Spot Price > Strike Price (
S > X). - Put Option: In-the-money when Spot Price < Strike Price (
S < X). - American vs. European Options: European options can only be exercised at expiration. American options can be exercised at any time up to and including expiration. This early exercise feature gives American options at least as much value as their European counterparts, and sometimes more.
- Arbitrage: A risk-free profit opportunity exists if the law of one price is violated. Your job is to spot when
Market Price ≠ Theoretical Priceand construct the trades to capture the difference.
Step 1: State the Put-Call Parity Relationship
The no-arbitrage relationship is:C₀ + PV(X) = P₀ + S₀. We need to see if the two sides of this equation are equal.
Step 2: Calculate the Present Value of the Strike Price
The rate is continuous, so we use thee^(-rT) formula. Time (T) is 3 months, or 0.25 years.
PV(X) = X × e^(−r_f × T) = $52 × e^(−0.04 × 0.25) = $52 × e^(−0.01) = $52 × 0.99005 = $51.48
Step 3: Compare the Two Sides of the Parity Equation
- Fiduciary Call side:
C₀ + PV(X) = $2.50 + $51.48 = $53.98 - Protective Put side:
P₀ + S₀ = $3.75 + $50.00 = $53.75
Step 4: Identify the Arbitrage
The Fiduciary Call ($53.98) is overpriced relative to the Protective Put ($53.75). The strategy is always to sell the expensive side and buy the cheap side.- Sell the Fiduciary Call: Sell the call (receive $2.50) and lend the PV of the strike (outflow of $51.48).
- Buy the Protective Put: Buy the put (pay $3.75) and buy the stock (pay $50.00).
You have an immediate, risk-free profit of $0.23 per share. At expiration, the positions will perfectly offset regardless of the stock price, leaving you with your initial arbitrage profit.
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What Are the Most Common CFA Derivatives Traps?
The Derivatives section is notorious for questions that seem simple but hide a subtle trap. Knowing where candidates consistently lose points is your best defense.
Trap 1: Confusing Price vs. Value of a Forward Contract
This is the single most misunderstood concept for Level I candidates.
F₀(T)) is the agreed-upon price for a future transaction, determined at initiation to make the contract's value zero. The value of a forward contract (Vₜ) is its market value at any point after initiation, which fluctuates as the underlying spot price changes.
- At initiation (t=0): Value is zero. Price is not.
- During its life (t>0): Value can be positive, negative, or zero.
An exam question might ask for the "value" of a newly initiated forward contract. The answer is always zero. The tempting wrong answer will be the calculated forward price.
Trap 2: Ignoring the Buyer/Seller Perspective
Every derivative transaction has two sides. The exam will often describe a scenario from one perspective but ask you to calculate the profit or loss for the other.
Before you calculate, ask: am I the buyer (long) or the seller (short)?
- Option Buyer: Pays premium, has the right, limited loss, unlimited potential profit (call) or large potential profit (put).
- Option Seller: Receives premium, has the obligation, limited profit, unlimited potential loss (call) or large potential loss (put).
Trap 3: Forgetting to Adjust for Dividends
For derivatives on dividend-paying stocks, the forward price must be adjusted downwards. The holder of the underlying stock receives the dividend, but the holder of the forward contract does not. The no-arbitrage price accounts for this.
The formula F₀(T) = (S₀ − PV₀(D)) × (1 + r_f)^T explicitly subtracts the present value of the dividends from the spot price before growing it at the risk-free rate. Forgetting this step is a common source of error.
A 7-Day Sprint to Master CFA Derivatives
Use this cheat sheet for a focused, one-week push. This isn't about cramming; it's about structured reinforcement.
Day 1: Forwards & Futures. Read the formula section. Your goal is to master the distinction between price and value. Work through 15-20 practice questions from VoraPrep's adaptive question bank focusing only on forward pricing and valuation. Day 2: Option Payoffs & Moneyness. Ignore pricing for today. Focus entirely on the mechanics. Sketch payoff diagrams for long/short calls and puts. Drill the moneyness rules (ITM, ATM, OTM) until they are automatic. Day 3: Put-Call Parity & Synthetics. This is the core conceptual day. Work through the arbitrage example above. Then, use the parity formulaC + PV(X) = P + S to solve for each of the four components. Understand how to create a synthetic stock, put, call, or T-bill. If you get stuck, ask Vory, your 24/7 personal tutor, to explain synthetic positions.
Day 4: Option Pricing Factors. Memorize the factors affecting option prices (stock price, strike, time, volatility, risk-free rate, dividends). Create a simple table showing the effect of an increase in each factor on call and put values. Use VoraPrep's free CFA Level I practice questions to test your knowledge.
Day 5: Swaps. Level I swaps are primarily conceptual. Understand the structure of a plain vanilla interest rate swap. Know who pays fixed and who pays floating, and why the value of the swap is zero to both parties at initiation.
Day 6: Trap Identification Drill. Review the "Common Traps" section. Go back through your incorrect practice questions from the week and identify which trap you fell into. This self-correction is crucial for building exam-day awareness.
Day 7: Timed Testlet. Take a 30-minute, derivatives-only quiz in a VoraPrep exam simulator. Mimic test conditions. Review every explanation, especially for questions you got wrong. This builds stamina and exposes any remaining weak spots.