Ch4. CFA Study Guide — Derivatives and Alternative Investments

Derivatives Overview

Derivatives are financial contracts whose value is linked to the price of an underlying asset. Underlying assets include equities, bonds, currencies, commodities, interest rates, and stock indices.

Derivatives account for approximately 5–8% of CFA Level I weight; alternative investments account for 7–10%. The two topics complement each other and are efficiently studied together.

Primary functions of derivatives:

1. Hedging: Reducing risk in an existing position
2. Speculation: Profiting from directional price bets using leverage
3. Arbitrage: Exploiting price discrepancies across markets for risk-free profit

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Forwards vs. Futures

Forward Contract

A forward contract is a private (OTC) bilateral agreement to buy or sell an asset at a predetermined price on a specified future date.

Forward Contract Characteristics:
- OTC (over-the-counter): contract terms customized by parties
- Settlement: at contract expiry (typically one settlement date)
- Counterparty risk exists
- No margin requirement
- Examples: FX forwards, forward rate agreements (FRAs)

Futures Contract

A futures contract is a standardized forward contract traded on an exchange, with daily mark-to-market settlement in which gains and losses are exchanged in cash each day.

Futures Contract Characteristics:
- Exchange-listed: standardized terms
- Daily settlement (mark-to-market): daily cash exchange of price changes
- Initial Margin + Maintenance Margin system
- Minimal counterparty risk (exchange clearinghouse acts as counterparty)
- Most contracts closed via offsetting trades before expiry

Feature	Forward	Futures
Venue	OTC	Exchange
Standardization	Customized	Standardized
Counterparty risk	High	Low (clearinghouse)
Margin	None	Required
Liquidity	Low	High
Daily settlement	No (at expiry)	Yes (daily)

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Futures Pricing — Cost-of-Carry Model

The cost-of-carry model determines the theoretical futures price based on the no-arbitrage principle.

Basic Futures Price Formula (no carrying costs, financial asset):

F₀ = S₀ × (1 + r)ᵀ

Where:
F₀ = theoretical futures price
S₀ = current spot price
r  = risk-free rate (annualized)
T  = time to maturity (years)

For dividend-paying assets (stocks, indices):
F₀ = (S₀ - PV(D)) × (1 + r)ᵀ
or with continuous dividend yield δ:
F₀ = S₀ × e^(r - δ)T

For commodities (storage cost c, convenience yield y):
F₀ = S₀ × e^(r + c - y)T

Futures arbitrage: If F₀ > theoretical price → sell futures + buy spot (cash-and-carry). If F₀ < theoretical price → buy futures + sell spot (reverse cash-and-carry). Arbitrageurs force prices back to equilibrium.

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Options — Types and Basic Structure

An option grants the buyer the right (not obligation) to buy or sell an asset at a specified price (strike price). The seller (option writer) is obligated to fulfill the buyer’s right upon exercise.

Option Classifications

Call Option: right to buy the underlying at the strike price
Put Option:  right to sell the underlying at the strike price

American Option: exercisable at any time before expiry
European Option: exercisable only at expiry

Intrinsic Value and Exercise Decision

Call payoff at expiry = max(S_T - X, 0)
Put payoff at expiry  = max(X - S_T, 0)

Where:
S_T = underlying price at expiry
X   = strike price

In-the-Money (ITM): exercise is profitable
  - Call: S > X / Put: S < X
At-the-Money (ATM): S = X
Out-of-the-Money (OTM): exercise is not profitable
  - Call: S < X / Put: S > X

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Option Price Components

Option premium = Intrinsic Value + Time Value

Intrinsic Value:
- Call: max(S - X, 0)
- Put:  max(X - S, 0)
- OTM options have zero intrinsic value

Time Value:
- Longer time to expiry → more opportunity for favorable price moves
- Decreases as expiry approaches (time decay)
- Time value = 0 at expiry

Six factors affecting option price:

Factor	Effect on Call	Effect on Put
Underlying price (S) ↑	Increases	Decreases
Strike price (X) ↑	Decreases	Increases
Time to expiry (T) ↑	Increases	Increases
Volatility (σ) ↑	Increases	Increases
Risk-free rate (r) ↑	Increases	Decreases
Dividends (D) ↑	Decreases	Increases

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Put-Call Parity

Put-call parity is the no-arbitrage relationship between European calls and puts with the same underlying, strike price, and expiry.

Put-Call Parity (European options):

C + PV(X) = P + S₀

Alternatively:
C - P = S₀ - PV(X)

Where:
C     = call premium
P     = put premium
S₀    = current underlying price
PV(X) = present value of strike = X / (1 + r)^T

Synthetic Positions:
Synthetic call  = long put + long underlying − long bond
Synthetic put   = long call − long underlying + long bond
Synthetic stock = long call + long bond − long put

Put-call parity is used to identify arbitrage opportunities, construct synthetic positions, and verify option pricing.

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The Greeks

The Greeks measure how sensitive an option’s price is to changes in each underlying variable.

Delta (Δ):
- Change in option price per unit change in underlying price
- Call delta: 0 to +1 / Put delta: −1 to 0
- ATM option delta ≈ ±0.5
- Delta hedging: eliminates directional risk in option positions

Gamma (Γ):
- Rate of change in delta per unit change in underlying price
- High gamma → delta changes rapidly → frequent hedge rebalancing needed
- Gamma is highest for ATM options

Vega (ν):
- Change in option price per 1% change in underlying volatility
- Volatility increase → both calls and puts increase in value (vega always positive)
- Vega is highest for ATM options

Theta (Θ):
- Change in option price per day elapsed (time decay)
- Accelerates as expiry approaches
- Unfavorable for buyers; favorable for sellers

Rho (ρ):
- Change in option price per change in the risk-free rate

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Swaps

A swap is an OTC agreement between two parties to exchange future cash flows.

Interest Rate Swap (most common):
- Fixed-rate payer: pays fixed rate ↔ receives floating rate
- Floating-rate payer: pays floating rate ↔ receives fixed rate
- Notional principal is NOT exchanged (reference amount only)
- Application: floating-rate borrower uses swap to create synthetic fixed-rate exposure

Currency Swap:
- Exchange principal and interest in different currencies
- Both initial and final principal amounts are exchanged

Credit Default Swap (CDS):
- Insurance-like instrument transferring credit risk
- Protection buyer: pays periodic premium → receives compensation on default
- Protection seller: collects premium → bears loss on default

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Alternative Investments

Alternative investments are asset classes beyond traditional stocks and bonds. CFA Level I covers private equity, hedge funds, real estate, commodities, and infrastructure.

Private Equity

Types:
1. Venture Capital (VC): equity investment in early-stage startups
2. Buyout: acquisition of mature companies (often using leverage → LBO)
3. Growth Capital: expansion-stage investment in mid/late-stage companies

Key features:
- Long holding periods (5–10 years)
- Illiquidity premium sought
- J-Curve effect: negative returns early (fees, underperforming investments)
  → performance recovers as portfolio matures and exits occur
- Carried interest: 20% of profits above the hurdle rate

Hedge Funds

Key features:
- Use long/short, leverage, derivatives — wide range of strategies
- Target absolute returns: profitable regardless of market direction
- High minimum investment (institutional and high-net-worth clients)
- "2 and 20" fee structure: 2% management fee + 20% performance fee

Major strategies:
- Long/Short Equity
- Global Macro
- Event-Driven (M&A, distressed debt)
- Relative Value (arbitrage strategies)

Real Estate

Types:
- Direct ownership: buying and managing physical properties
- REITs: publicly traded real estate investment trusts (like stocks)
- CMBS: commercial mortgage-backed securities
- Private real estate funds

Key features:
- Inflation hedge
- Lower correlation with equities → diversification benefit
- Disadvantages: illiquidity, management costs

Commodities

Investment methods:
- Physical ownership (gold, silver)
- Futures contracts
- Commodity ETFs / commodity company stocks

Key features:
- Inflation hedge (energy, agriculture)
- Cyclical sensitivity (except gold, which has safe-haven characteristics)
- Roll costs in contango markets (near-month futures premium → losses on rolling)

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Key Concept Cards

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Practice Questions

Q1. How does daily mark-to-market in futures contracts reduce counterparty risk?

Daily mark-to-market requires the losing party to pay gains to the winning party each trading day. Losses cannot accumulate unchecked. If a party’s account falls below the maintenance margin, a margin call is triggered — requiring additional deposits or forced position liquidation. This mechanism prevents the large bilateral credit exposures that can accumulate in forward contracts over their lifespan.

Q2. Using put-call parity (C + PV(X) = P + S₀), construct a synthetic call option.

Rearrange to: C = P + S₀ − PV(X). A synthetic call = long put + long underlying + short bond (borrowing the PV of the strike). In practice: buy a put option, buy the underlying asset, and borrow an amount equal to the present value of the strike price. This replicates the payoff profile of a call option exactly.

Q3. How does a hedge fund’s “absolute return” strategy differ from a traditional equity fund?

A traditional equity fund targets outperformance relative to a benchmark (e.g., S&P 500). If markets fall, the fund typically falls too. Hedge funds target positive returns regardless of market direction. For example, a long/short equity strategy buys undervalued stocks while shorting overvalued ones, creating a market-neutral position. Note: absolute returns are not guaranteed — hedge funds carry risks from leverage, complex strategies, and high fees.

Q4. List three advantages of REITs compared to direct real estate investment.

① Liquidity: Exchange-listed REITs can be bought and sold like stocks, solving the illiquidity problem of physical property. ② Small-ticket diversification: Investors can gain exposure to diverse property portfolios with modest capital. ③ Professional management: REIT managers handle property acquisition, leasing, and maintenance — no direct involvement required. Additionally, many REITs are required to distribute at least 90% of taxable income as dividends (US standard), providing stable income.

Q5. In what market environment does a high-vega position perform best?

Vega measures the change in an option’s price per 1% change in implied volatility. A high-vega position (e.g., long ATM options, long straddle) benefits from rising volatility. Events such as major economic data releases, earnings announcements, or geopolitical shocks that cause volatility spikes increase option premiums, generating gains. Conversely, high-vega positions suffer when volatility contracts after uncertainty resolves.