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FRM (Financial Risk Manager) Financial Markets and Products (Part I) Syllabus
The Financial Markets and Products (Part I) syllabus for FRM (Financial Risk Manager) in full: 4 chapters, 16 topics and 31 sub-topics, every one listed below, plus 51 Financial Markets and Products (Part I) flashcards with answers.
Financial Markets and Products (Part I) syllabus: all 4 chapters
Expand any chapter to see its topics and sub-topics.
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Derivatives Markets and Futures
4 topics- Structure of Derivatives Markets
- Exchange-traded vs. OTC markets
- Central clearing and counterparties
- Forwards and Futures Mechanics
- Margin accounts and marking to market
- Convergence of futures to spot
- Hedging with Futures
- Minimum variance hedge ratio
- Basis risk and cross-hedging
- Pricing Forwards and Futures
- Cost-of-carry model
- Contango and backwardation
- Structure of Derivatives Markets
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Interest Rates and Fixed Income
4 topics- Interest Rate Conventions
- Compounding frequencies and continuous compounding
- Spot, forward, and par rates
- Bond Pricing and Yields
- Yield to maturity and discount factors
- Term structure of interest rates
- Bond Risk Measures
- Duration and modified duration
- Convexity and DV01
- Rate-Linked Products
- Forward rate agreements
- SOFR and reference rate transition
- Interest Rate Conventions
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Swaps and Options
4 topics- Interest Rate and Currency Swaps
- Swap valuation and cash flows
- Comparative advantage argument
- Option Fundamentals
- Calls, puts, moneyness, and payoffs
- Put-call parity
- Option Trading Strategies
- Spreads, straddles, and strangles
- Covered calls and protective puts
- Exotic Options
- Asian, barrier, and lookback options
- Interest Rate and Currency Swaps
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Commodities, Currencies and Corporate Bonds
4 topics- Commodity Forwards and Futures
- Convenience yield and storage costs
- Lease rates
- Foreign Exchange Risk
- Covered and uncovered interest rate parity
- Currency exposure and hedging
- Corporate Bonds and Credit
- Credit ratings and spreads
- Default and recovery rates
- Mortgages and Securitized Products
- Prepayment risk
- Pass-through securities
- Commodity Forwards and Futures
FRM (Financial Risk Manager) Financial Markets and Products (Part I) flashcards — 51 questions with answers
What are the two broad categories of derivatives market structure, and how do they differ in standardization?
Exchange-traded markets (standardized contracts, fixed sizes/maturities, traded on an exchange) and over-the-counter (OTC) markets (customized, bilaterally negotiated contracts traded directly between parties).
List three key advantages of exchange-traded markets over OTC markets.
Standardization (liquidity and easy offset), a central clearinghouse that guarantees performance (low counterparty/credit risk), and price transparency.
List two key advantages of OTC markets over exchange-traded markets.
Customization of contract terms (size, maturity, underlying) to exactly match hedging needs, and access to instruments not available on exchanges.
In central clearing, what role does a central counterparty (CCP) play?
The CCP becomes the buyer to every seller and the seller to every buyer (novation), guaranteeing performance and mutualizing counterparty credit risk; it collects margin from members.
How did post-2008 regulation (e.g., Dodd-Frank) change OTC derivatives clearing?
It mandated that standardized OTC derivatives be cleared through central counterparties (CCPs) to reduce systemic counterparty risk, replacing purely bilateral clearing.
Define a forward contract.
A private OTC agreement to buy or sell an asset at a specified future date for a price (the delivery/forward price) agreed today; no cash changes hands at initiation.
Define a futures contract and state how it differs from a forward.
A futures contract is a standardized, exchange-traded agreement to buy/sell an asset at a future date. Unlike a forward, it is marked to market daily, requires margin, is cleared through a clearinghouse, and is highly standardized.
What is the payoff at maturity of a long forward/futures position with delivery price $K$ and terminal spot price $S_T$?
$$\text{Payoff}_{\text{long}} = S_T - K$$ The short position payoff is $K - S_T$.
What is an initial margin in a futures account?
The amount a trader must deposit with the broker when opening a futures position, serving as collateral against potential losses.
What is the maintenance margin, and what happens when the balance falls below it?
A threshold (below initial margin) that the account balance must not drop below. If it does, a margin call is issued and the trader must deposit a variation margin to restore the balance to the initial margin level.
Explain marking to market in futures.
At the end of each trading day, gains and losses are credited or debited to each trader's margin account based on the daily settlement price change, so contracts are effectively settled daily.
For a long futures position, what is the daily change in the margin account balance?
$$\Delta \text{Balance} = (F_{t} - F_{t-1}) \times N \times Q$$ where $F$ is the futures price, $N$ the number of contracts, and $Q$ the contract size (negative of this for a short).
What is the convergence property of futures prices?
As the delivery date approaches, the futures price converges to the spot price of the underlying; at expiration $F_T = S_T$ (otherwise arbitrage exists).
Why must the futures price equal the spot price at expiration?
At delivery the futures contract is equivalent to buying the asset immediately; any gap between $F_T$ and $S_T$ would create a riskless arbitrage profit, so $F_T = S_T$.
Distinguish a long hedge from a short hedge.
A short hedge (sell futures) protects against a fall in the price of an asset you own or will sell. A long hedge (buy futures) protects against a rise in the price of an asset you plan to buy.
Define basis in the context of hedging.
$$\text{Basis} = S - F$$ the spot price of the asset being hedged minus the futures price; basis risk arises when this relationship is uncertain.
What causes basis risk?
Mismatch between the hedge and exposure: differences in the asset vs. the futures underlying (cross-hedge), differences in maturity/delivery dates, or uncertainty in the spot-futures relationship over time.
What is a cross hedge?
Hedging an exposure using a futures contract whose underlying asset differs from the asset being hedged (e.g., hedging jet fuel with crude oil futures), introducing additional basis risk.
State the formula for the minimum variance hedge ratio $h^{*}$.
$$h^{*} = \rho \, \frac{\sigma_{S}}{\sigma_{F}}$$ where $\rho$ is the correlation between spot and futures price changes, $\sigma_S$ the std. dev. of spot changes, and $\sigma_F$ that of futures changes.
How does the minimum variance hedge ratio relate to a regression of spot changes on futures changes?
$h^{*}$ equals the slope coefficient ($\beta$) of a regression of changes in the spot price ($\Delta S$) on changes in the futures price ($\Delta F$).
Show the other 31 Financial Markets and Products (Part I) flashcards
What is the hedge effectiveness in a minimum variance hedge?
It is the proportion of variance of the hedged position's value eliminated, equal to $\rho^{2}$ (the $R^{2}$ of the spot-on-futures regression).
What is the optimal number of futures contracts $N^{*}$ for a hedge?
$$N^{*} = h^{*} \, \frac{Q_{A}}{Q_{F}}$$ where $Q_A$ is the size of the position being hedged and $Q_F$ is the size of one futures contract.
State the cost-of-carry model for the forward price of an investment asset paying no income.
$$F_{0} = S_{0} \, e^{rT}$$ where $S_0$ is the spot price, $r$ the continuously compounded risk-free rate, and $T$ the time to maturity.
State the forward price formula for an asset providing a known continuous dividend/convenience yield $q$.
$$F_{0} = S_{0} \, e^{(r - q)T}$$
State the forward price formula for an asset providing known discrete income with present value $I$.
$$F_{0} = (S_{0} - I)\, e^{rT}$$ where $I$ is the present value of income (e.g., dividends or coupons) paid during the contract's life.
State the full cost-of-carry forward price formula including storage cost $u$ and convenience yield $y$ (as continuous rates).
$$F_{0} = S_{0} \, e^{(r + u - y)T}$$ where $u$ is the storage cost rate and $y$ the convenience yield.
Define contango.
A market condition where the futures price exceeds the spot price ($F_0 > S_0$), typically the upward-sloping forward curve seen when carry costs exceed any convenience yield.
Define backwardation.
A market condition where the futures price is below the spot price ($F_0 < S_0$), a downward-sloping forward curve, often driven by a high convenience yield.
In the cost-of-carry model, what sign of $(r + u - y)$ produces backwardation?
A negative net cost of carry, i.e. $r + u - y < 0$ (convenience yield dominates), gives $F_0 < S_0$ and backwardation; positive gives contango.
Why might forward and futures prices differ when interest rates are stochastic?
Daily marking to market correlates margin cash flows with rates. If futures prices are positively correlated with rates, futures > forwards (gains reinvested at higher rates); if negatively correlated, futures < forwards.
Write the formula for converting an annual rate $R_c$ compounded $m$ times per year into its value $A$ after $T$ years on principal $P$.
$$A = P\left(1 + \frac{R_c}{m}\right)^{mT}$$
Write the future value with continuous compounding at rate $R$.
$$A = P\, e^{RT}$$
How do you convert a rate $R_m$ compounded $m$ times per year to an equivalent continuously compounded rate $R_c$?
$$R_c = m \ln\!\left(1 + \frac{R_m}{m}\right)$$
How do you convert a continuously compounded rate $R_c$ to an equivalent rate $R_m$ compounded $m$ times per year?
$$R_m = m\left(e^{R_c/m} - 1\right)$$
For a given nominal rate, how does the effective annual yield change as compounding frequency increases?
The effective annual yield increases with compounding frequency, approaching the continuous-compounding limit; for rate $R$ the effective annual rate is $e^{R} - 1$ when compounded continuously.
Define the spot (zero) rate.
The yield on a zero-coupon bond, i.e. the single interest rate for an investment that pays off entirely at one future date with no intermediate cash flows.
Define the forward rate.
The interest rate, implied by current spot rates, for a future period of time—e.g., the rate agreed today for borrowing/lending between times $T_1$ and $T_2$.
Give the formula for the continuously compounded forward rate $R_f$ between times $T_1$ and $T_2$.
$$R_f = \frac{R_2 T_2 - R_1 T_1}{T_2 - T_1}$$ where $R_1, R_2$ are the spot rates to $T_1$ and $T_2$.
Define the par rate (par yield).
The coupon rate that makes a bond's price equal to its face (par) value given the current term structure; equivalently the coupon yielding a price of 100% of par.
Define the discount factor $DF(t)$ for time $t$.
The present value today of $1 received at time $t$. With continuous compounding $DF(t) = e^{-R_t t}$; with discrete compounding $DF(t) = \frac{1}{(1 + R_t)^{t}}$, where $R_t$ is the spot rate.
Write the price of a coupon bond using discount factors.
$$P = \sum_{i=1}^{n} c_i \, DF(t_i) + F \, DF(t_n)$$ where $c_i$ are coupons, $F$ is face value, and $DF(t_i)$ are the discount factors.
Define yield to maturity (YTM) of a bond.
The single discount rate that sets the present value of all the bond's future cash flows equal to its current market price; the internal rate of return if held to maturity.
Write the bond pricing equation in terms of yield to maturity $y$ (annual compounding).
$$P = \sum_{i=1}^{n} \frac{C}{(1+y)^{i}} + \frac{F}{(1+y)^{n}}$$ where $C$ is the periodic coupon and $F$ the face value.
State the inverse relationship between bond price and yield.
Bond prices and yields move in opposite directions: when yields rise, bond prices fall, and when yields fall, prices rise (the price-yield curve is downward sloping and convex).
How does a bond's price relate to par when its coupon rate is above, equal to, or below its YTM?
Coupon > YTM: bond trades at a premium (price > par). Coupon = YTM: at par. Coupon < YTM: at a discount (price < par).
Define the term structure of interest rates.
The relationship between interest rates (spot/zero rates) and their maturities, depicted by the yield curve for otherwise identical (default-free) instruments.
Name three theories explaining the shape of the term structure.
Expectations theory (forwards reflect expected future spot rates), liquidity preference theory (investors demand a premium for longer maturities), and market segmentation theory (rates set by supply/demand within maturity segments).
What does an upward-sloping (normal) yield curve typically imply under the expectations theory?
Markets expect future short-term interest rates to rise; long-term rates exceed short-term rates.
What is bootstrapping in the context of the term structure?
A sequential method of extracting zero/spot rates from the prices of coupon-bearing bonds, solving for each successive spot rate using previously derived discount factors.
What is the relationship between forward rates and spot rates when the spot curve is upward sloping?
When the spot (zero) curve is upward sloping, forward rates lie above the spot rates; when it is downward sloping, forward rates lie below the spot rates.
Why is YTM an imperfect single measure of a coupon bond's return?
It assumes all coupons are reinvested at the YTM and that the bond is held to maturity; it also applies one rate to all cash flows, ignoring the actual term structure of spot rates.
FRM (Financial Risk Manager) Financial Markets and Products (Part I) FAQ
What is in the FRM (Financial Risk Manager) Financial Markets and Products (Part I) syllabus?
FRM (Financial Risk Manager) Financial Markets and Products (Part I) is split into 4 chapters: Derivatives Markets and Futures, Interest Rates and Fixed Income, Swaps and Options and Commodities, Currencies and Corporate Bonds. Together they contain 16 topics and 31 sub-topics.
How many chapters are in FRM (Financial Risk Manager) Financial Markets and Products (Part I)?
4 chapters, containing 16 topics and 31 sub-topics. The largest chapter is Derivatives Markets and Futures, with 4 topics.
Are there flashcards for FRM (Financial Risk Manager) Financial Markets and Products (Part I)?
Yes — a 51-card Financial Markets and Products (Part I) deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.