Chartered Financial Analyst (CFA) Fixed Income, Derivatives, and Alternatives Syllabus

State and briefly explain the local expectations and pure (unbiased) expectations theories of the term structure.

The unbiased (pure) expectations theory says forward rates are unbiased predictors of future spot rates, so long rates are the geometric average of expected short rates. The local expectations theory is a risk-neutral version asserting that, over a short horizon, all bonds have the same expected return equal to the risk-free rate.

Explain the liquidity preference theory and the segmented markets theory of the yield curve.

Liquidity preference theory says investors demand a liquidity (term) premium for holding longer maturities, so forward rates exceed expected future spot rates. Segmented markets theory says yields at each maturity are set independently by supply/demand of investors who only operate in that maturity segment.

What is the swap rate curve (swap curve), and why is it widely used as a benchmark?

The swap curve plots fixed rates of interest-rate swaps against their maturities. It is used as a benchmark because swaps are issued by private banks at many maturities, reflect interbank credit, are not affected by sovereign-specific supply/regulation, and offer a continuous, liquid set of reference rates.

Define Macaulay duration in words and give its interpretation.

Macaulay duration is the weighted average time (in periods/years) to receipt of a bond's cash flows, where weights are each cash flow's present value as a fraction of price. It equals the investment horizon at which reinvestment risk and price (market) risk offset, immunizing the realized return.

Give the formula relating modified duration to Macaulay duration, and state what modified duration measures.

$$\text{ModDur} = \frac{\text{MacDur}}{1 + r}$$ where $r$ is the yield per period. Modified duration estimates the approximate percentage change in a bond's price for a 1% (100 bp) change in its yield to maturity: $\%\Delta P \approx -\text{ModDur} \times \Delta y$.

Write the formula for approximate modified duration using price changes.

$$\text{ApproxModDur} = \frac{PV_{-} - PV_{+}}{2 \times \Delta\text{Yield} \times PV_{0}}$$ where $PV_{-}$ and $PV_{+}$ are the prices if the yield falls and rises by $\Delta\text{Yield}$, and $PV_{0}$ is the initial price.

What is effective duration, and when must it be used instead of modified duration?

$$\text{EffDur} = \frac{PV_{-} - PV_{+}}{2 \times \Delta\text{Curve} \times PV_{0}}$$ Effective duration measures sensitivity to a parallel shift in the benchmark yield curve. It must be used for bonds with embedded options (or other uncertain cash flows), since their cash flows change as rates change.

Define money duration and the price value of a basis point (PVBP).

Money duration (dollar duration) = annual modified duration $\times$ full price, giving the price change in currency units for a 1.00 (100%) change in yield; for a $\Delta y$ change, $\Delta P \approx -\text{MoneyDur} \times \Delta y$. PVBP is the absolute price change for a 1 bp yield change: $$\text{PVBP} = \frac{PV_{-} - PV_{+}}{2}$$

What is convexity, and how is the bond price change estimated using both duration and convexity?

Convexity measures the curvature of the price-yield relationship (the second-order effect). The improved price-change estimate is $$\%\Delta P \approx (-\text{ModDur} \times \Delta y) + \left(\tfrac{1}{2} \times \text{Convexity} \times (\Delta y)^{2}\right).$$ The convexity term is always positive for option-free bonds, benefiting holders.

Define duration gap and explain its relationship to reinvestment risk and market price risk.

Duration gap = Macaulay duration $-$ investment horizon. If the gap is positive (horizon < MacDur), market price risk dominates (investor hurt by rising rates). If negative (horizon > MacDur), reinvestment risk dominates (investor hurt by falling rates). A zero gap immunizes the realized yield.

How do a bond's coupon rate and maturity each affect its interest-rate risk (duration), holding other factors constant?

Longer maturity increases duration (more interest-rate risk). A lower coupon increases duration, because more of the bond's value is in later cash flows. A higher yield level decreases duration. Thus a long-maturity, low-coupon, low-yield bond has the greatest interest-rate sensitivity.

List the main components of credit risk: default risk, loss severity, and the expected loss formula.

Default (default probability) risk is the chance the issuer fails to pay. Loss severity (loss given default, LGD) is the portion of value lost if default occurs, where LGD = 1 $-$ recovery rate. Expected loss = probability of default $\times$ loss severity (LGD) $\times$ exposure.

Define spread risk, downgrade (credit migration) risk, and market liquidity risk.

Spread risk is the loss from a widening of the bond's credit spread. Downgrade/credit migration risk is the risk that a rating agency lowers the issuer's rating, widening spreads. Market liquidity risk is the risk of a larger bid-ask spread or price concession when selling, especially in stressed markets.

What are the 'Four Cs' of traditional credit analysis?

Capacity (ability to repay debt from operations), Collateral (quality and value of assets pledged or available), Covenants (terms protecting lenders), and Character (management's integrity, track record, and commitment to repayment).

Name common profitability/leverage/coverage ratios used in corporate credit analysis.

Leverage: $\frac{\text{Debt}}{\text{EBITDA}}$ and $\frac{\text{Debt}}{\text{Capital}}$. Coverage: $\frac{\text{EBITDA}}{\text{Interest expense}}$ and $\frac{\text{EBIT}}{\text{Interest expense}}$. Profitability is often measured by operating margin and return on capital. Lower leverage and higher coverage indicate stronger credit quality.

What is the difference between investment-grade and high-yield bonds by rating, and what is a 'fallen angel'?

Investment grade is rated Baa3/BBB$-$ and above; high yield (speculative/junk) is rated Ba1/BB+ and below. A fallen angel is a bond that was originally investment grade but has since been downgraded to high yield.

Define securitization and the role of a special purpose entity (SPE/SPV).

Securitization pools financial assets (e.g., loans, mortgages) and issues securities backed by their cash flows. The originator sells the assets to a bankruptcy-remote SPE/SPV, which issues the asset-backed securities; this isolates the assets from the originator's credit and enables risk tranching.

What are the three sources of mortgage-backed security (MBS) cash flow, and what is prepayment risk?

Cash flows come from scheduled principal, interest, and prepayments (unscheduled principal). Prepayment risk is the uncertainty in timing of principal: contraction risk (faster prepayments when rates fall) and extension risk (slower prepayments when rates rise).

In a CMO, what is the purpose of creating sequential-pay tranches and a planned amortization class (PAC)?

A collateralized mortgage obligation (CMO) redistributes prepayment risk by directing cash flows to tranches in sequence. A PAC tranche has a predictable schedule and is protected against prepayment variation by companion (support) tranches, which absorb the excess contraction and extension risk.

Distinguish the internal and external credit enhancements used in structured securities.

Internal: tranching/subordination (senior-subordinated structure), overcollateralization, and excess spread/reserve accounts. External: third-party guarantees such as surety bonds, letters of credit, or cash collateral accounts. Enhancements raise the credit quality of senior tranches above that of the underlying pool.

What is a derivative, and what is the key distinction between a forward commitment and a contingent claim?

A derivative is a financial instrument whose value derives from an underlying asset, rate, or index. A forward commitment (forward, future, swap) obligates both parties to transact at a set price on a future date. A contingent claim (option) gives one party the right, but not the obligation, to transact.

Compare forwards and futures across customization, counterparty risk, and settlement.

Forwards are customized OTC contracts with counterparty (credit) risk, typically settled at expiration. Futures are standardized exchange-traded contracts, with a clearinghouse guaranteeing performance, daily mark-to-market via a margin account, and high liquidity.

What is the value of a long forward position at expiration, and what does 'price' versus 'value' of a forward mean?

At expiration the long's payoff is $V_{T} = S_{T} - F_{0}$, where $S_{T}$ is the spot price and $F_{0}$ the contracted forward price. The forward price is the fixed rate set so that initial value is zero; the forward's value changes thereafter as the underlying price moves.

Give the no-arbitrage forward price of an asset with carry costs and benefits (continuous and discrete forms).

Discrete: $$F_{0} = (S_{0} - PV_{\text{income}} + PV_{\text{cost}})(1+r)^{T}.$$ Continuous: $$F_{0} = S_{0}\,e^{(r + c - i)T}$$ where $r$ is the risk-free rate, $c$ carrying cost, and $i$ the income/convenience yield. The forward price rises with the cost of carry and falls with benefits of holding.

State put-call parity for European options and define each term.

$$c_{0} + \frac{X}{(1+r)^{T}} = p_{0} + S_{0}$$ where $c_{0}$ is the call price, $p_{0}$ the put price, $X$ the exercise price, $S_{0}$ the underlying price, $r$ the risk-free rate, and $T$ time to expiry. A fiduciary call (call + risk-free bond paying X) equals a protective put (put + underlying).

What is the value of a plain-vanilla interest rate swap at initiation, and how is the fixed (swap) rate determined?

At initiation the swap value is zero. The fixed swap rate is set so the present value of the fixed-leg payments equals the present value of the expected floating-leg payments: $$r_{\text{swap}} = \frac{1 - DF_{N}}{\sum_{t=1}^{N} DF_{t}}$$ where $DF_{t}$ are discount factors. A swap can be viewed as a portfolio of forward (FRA) contracts or as exchanging a fixed-rate for a floating-rate bond.

Identify each Greek: how do delta, gamma, vega, theta, and rho describe an option's value sensitivity?

Delta: sensitivity to a small change in the underlying price. Gamma: rate of change of delta (curvature). Vega: sensitivity to a change in volatility. Theta: sensitivity to passage of time (time decay). Rho: sensitivity to a change in the risk-free interest rate.

List the defining features that distinguish alternative investments from traditional investments.

Alternatives typically feature illiquidity of underlying assets, narrow specialization of managers, lower regulation and transparency, less historical/clean return data, unique legal/tax structures (often limited partnerships), and higher fees (e.g., management plus performance/incentive fees).

Explain the '2 and 20' fee structure and the role of a hurdle rate and high-water mark.

'2 and 20' means a 2% annual management fee on assets plus a 20% incentive (performance) fee on profits. A hurdle rate is a minimum return that must be earned before the incentive fee applies. A high-water mark ensures the manager earns incentive fees only on new net profits above the highest prior value, preventing double-charging after losses.

In private equity, contrast a leveraged buyout (LBO) with venture capital, and define carried interest.

An LBO acquires an established company using significant debt, aiming to improve operations and exit at a profit. Venture capital funds early-stage, high-growth startups with equity. Carried interest is the share of fund profits (typically ~20%) paid to the general partner as the performance fee.

Define the J-curve effect in private capital and the difference between committed and invested capital.

The J-curve describes how a private fund's returns are negative early (due to fees and start-up costs/drawdowns) then turn positive as investments mature and are exited. Committed capital is the total a limited partner pledges; invested (called/drawn) capital is the portion actually deployed via capital calls.

Compare the equity and debt investment forms in real assets/real estate, and name a key real estate valuation approach.

Equity forms include direct ownership and REITs; debt forms include mortgages and mortgage-backed securities. Real estate is commonly valued via the income approach (e.g., direct capitalization, value = NOI $/$ cap rate, or discounted cash flow), the comparable-sales approach, and the cost approach.

Describe how hedge fund strategies are broadly categorized.

Common categories are: equity hedge (e.g., long/short, market neutral), event-driven (merger arbitrage, distressed), relative value (fixed-income/convertible arbitrage), macro (directional bets on rates, currencies, commodities), and multi-strategy/fund of funds. Many use leverage, short selling, and derivatives.

What distinguishes a coin, a token, and a stablecoin among digital assets, and what is proof of work versus proof of stake?

A coin is a cryptocurrency native to its own blockchain (e.g., used as money). A token is built on an existing blockchain and can represent assets or utility. A stablecoin is pegged to a reference (e.g., fiat) to reduce volatility. Proof of work validates transactions via computational mining; proof of stake validates via validators staking the native coin.

Why are standard risk measures like the Sharpe ratio limited for alternative investments, and what biases affect reported alternative returns?

Alternative returns are often non-normal (negative skew, excess kurtosis/fat tails) and illiquid/smoothed, so volatility-based measures like Sharpe understate risk; downside measures (e.g., Sortino, VaR, max drawdown) are preferred. Reported indices suffer survivorship bias, backfill (instant history) bias, and self-selection/appraisal smoothing, which overstate returns and understate risk.

What does an internal rate of return (IRR) measure for a private capital fund, and why is it preferred over a time-weighted return?

IRR is the discount rate that sets the net present value of all cash flows (capital calls as outflows, distributions and residual NAV as inflows) to zero. It is preferred because the general partner controls the timing of cash flows (drawdowns and distributions), so a money-weighted measure like IRR better reflects the GP's performance than a time-weighted return.