Fixed Income - 3 - Free MCQ Practice Test with solutions, CFA Level 2

A fixed income analyst is evaluating spread measures for a callable investment-grade corporate bond. The bond's Z-spread is quoted at 185 basis points over the Treasury spot curve, while its nominal spread is 175 basis points. The analyst notes the bond has a five-year maturity and an embedded call option exercisable in two years.

The option-adjusted spread (OAS) for this callable bond is best described as:

Rajiv Sharma, CFA, is calibrating a binomial interest rate tree to value a putable corporate bond. He uses market prices of on-the-run Treasury securities as benchmarks. His colleague questions why the risk-neutral probabilities at each node are set to 0.50 rather than estimated from historical rate movements.

The most appropriate rationale for using 0.50 risk-neutral probabilities in a calibrated binomial interest rate tree is that:

An analyst at a credit research firm is assessing expected loss on a corporate bond position. The bond has a notional value of $10 million. The analyst estimates a one-year probability of default (PD) of 2% and a recovery rate of 40%.

The one-year expected credit loss on this position is closest to:

A fixed income analyst is bootstrapping the spot rate curve from par bond yields. The one-year par yield (and spot rate) is 3.00%. A two-year par bond with a 4.00% annual coupon is priced at par ($100).

Using the bootstrapping method, the two-year spot rate is closest to:

In a structural credit model, a portfolio manager is analyzing the default risk of a leveraged manufacturing company. The company has total assets valued at $500 million with an asset volatility of 25% annually. The firm has a single zero-coupon debt issue with a face value of $400 million maturing in three years.

According to the Merton structural model, the equity of this firm is best described as:

A credit analyst is comparing structural and reduced-form credit models. She notes that one model treats the time of default as a surprise event governed by an exogenous stochastic process, while the other ties default directly to observable firm fundamentals.

The hazard rate used in reduced-form credit models is best described as the:

Maria Johansson, CFA, purchases credit default swap (CDS) protection on $8 million notional of a high-yield issuer's bonds. The reference entity subsequently defaults, and the recovery rate is determined to be 35% of par through the auction settlement process.

The cash settlement payment Johansson receives from the protection seller is closest to:

A bond analyst is measuring the interest rate sensitivity of a putable corporate bond. Using a calibrated binomial interest rate tree and a 50 basis point parallel rate shift, the analyst records the following prices: P₀ = $100.00 (unchanged), P₊ = $98.50 (rates up 50 bps), P_- = $101.50 (rates down 50 bps).

The effective duration of this putable bond is closest to:

A mortgage analyst is computing the conditional prepayment rate (CPR) for a mortgage pool under 200% PSA prepayment assumption. The pool is currently in its 20th month since origination.

According to the PSA benchmark, the CPR for this pool in month 20 at 200% PSA is closest to:

A structured finance analyst is explaining the risk characteristics of different tranches in a collateralized mortgage obligation (CMO) to a client. The CMO includes both planned amortization class (PAC) tranches and support (companion) tranches.

Regarding prepayment risk, which of the following statements is most accurate?

A fixed income portfolio manager is reviewing the assumptions underlying two single-factor short-rate models used by her team: the Vasicek model and the Cox-Ingersoll-Ross (CIR) model. Both models incorporate mean reversion in short-term interest rates.

The feature that most distinguishes the CIR model from the Vasicek model is that the CIR model:

An analyst values a two-year, 6% annual coupon bond (face value $100) using a two-period binomial interest rate tree. The calibrated rates are: current node r₀ = 4.0%; up node at t=1: r_u = 5.5%; down node at t=1: r_d = 3.5%. Risk-neutral probabilities are 0.50 at each node. The bond pays its final coupon and principal at t=2.

The arbitrage-free value of this bond today is closest to:

A bond portfolio manager is concerned that the yield curve may undergo a steepening twist rather than a parallel shift over the next quarter. She wants to identify which duration measure best captures the portfolio's sensitivity to such non-parallel yield curve changes.

The duration measure most appropriate for assessing exposure to non-parallel yield curve shifts is:

A mortgage-backed securities analyst is comparing the Z-spread and OAS for a pass-through MBS. She notes that the Z-spread for the MBS is 145 basis points, while the OAS computed using an interest rate model with prepayment assumptions is 95 basis points.

The difference between the Z-spread and the OAS for this MBS is best described as the:

A credit research team is debating whether to use a structural or reduced-form credit model to value a newly issued high-yield bond from a private company with limited public financial disclosures. The team notes that market CDS spreads for comparable issuers are readily observable.

The reduced-form model is most preferable in this context because it:

A term structure analyst observes the following spot rates: one-year spot rate (s₁) = 3.00% and two-year spot rate (s₂) = 4.00%. He wants to compute the one-year forward rate one year from now, denoted f(1,1), to assess whether the current yield curve embeds a rate increase.

The implied one-year forward rate one year from now is closest to:

An investor buys CDS protection on $10 million notional of a sovereign bond. The reference entity defaults and the auction process sets the recovery rate at 40% of par value. Settlement occurs on a cash basis.

The payment the CDS protection buyer receives from the protection seller is closest to:

A portfolio manager asks her junior analyst to explain the fundamental difference between spot rates and forward rates in the context of fixed income valuation. The analyst must provide a technically precise definition consistent with CFA Institute curriculum definitions.

Which of the following best distinguishes a spot rate from a forward rate?

An analyst is reviewing interest rate models used by her firm. She notes that one model - the Heath-Jarrow-Morton (HJM) framework - models the evolution of the entire forward rate curve, while another class of models - equilibrium models - derives the term structure from a short-rate process.

A key advantage of the HJM framework relative to equilibrium models such as Vasicek or CIR is that HJM:

A fixed income analyst is comparing the convexity characteristics of callable and putable bonds relative to an otherwise identical option-free bond. As market interest rates decline significantly, the callable bond's price appreciation becomes constrained by the call option.

Regarding effective convexity, which of the following statements is most accurate?

A mortgage analyst is calculating prepayment statistics for a mortgage pool in its 15th month using the Public Securities Association (PSA) prepayment benchmark at 100% PSA. She needs to compute the single monthly mortality (SMM) rate to estimate prepayment cash flows this month.

The CPR for this mortgage pool in month 15 at 100% PSA is closest to:

A credit analyst uses a risk-neutral framework to estimate the implied probability of default for a corporate issuer. The issuer's one-year credit spread over Treasuries is 180 basis points. The analyst assumes a loss given default (LGD) of 60% and uses the approximation: credit spread ≈ PD × LGD.

The implied risk-neutral probability of default is closest to:

An analyst is using a two-period binomial interest rate tree to value a 5% annual coupon bond (face value $100) with one period remaining to maturity. The following data is provided from the tree at t=1:

Up node: r_u = 6.00%, bond value (ex-coupon) = $98.11
Down node: r_d = 4.00%, bond value (ex-coupon) = $101.54

The current one-period risk-free rate at t=0 is r₀ = 4.50%. Risk-neutral probabilities are 0.50 each.

The value of the bond today (at t=0) is closest to:

A structured credit analyst is comparing spread measures for an auto loan ABS security that has no embedded options and is backed by fixed-rate receivables. The security's Z-spread over the Treasury spot curve is 125 basis points. The analyst runs an option-adjusted spread (OAS) analysis using a standard interest rate model.

For an ABS with no embedded options, the OAS relative to the Z-spread is most likely:

A credit analyst applies the Merton structural model to evaluate the default risk of a technology company. The firm's current asset value is $600 million with an asset value volatility of 30%. Total debt consists of a single zero-coupon bond with face value $350 million maturing in two years. A competitor firm has identical debt structure but an asset value of $450 million and volatility of 30%.

Compared to the competitor, the technology company's probability of default under the Merton model is most likely:

A fixed income arbitrageur observes that the five-year CDS spread for a corporate issuer is 220 basis points, while the same issuer's five-year bond trades at a credit spread of 185 basis points over the Treasury curve. The arbitrageur notes this represents a positive CDS basis.

The CDS basis in this context is best described as:

A structured finance analyst is reviewing the behavior of a PAC (planned amortization class) CMO tranche when actual prepayment rates fall significantly below the lower bound of the PAC's original PSA collar. The CMO was originally structured with a PAC collar of 100% to 300% PSA.

When actual prepayment rates persistently fall below 100% PSA, the PAC tranche will most likely:

An analyst at a fixed income asset management firm is selecting an interest rate model for pricing a portfolio of interest rate derivatives, including caps, floors, and swaptions. The derivatives are written on observable benchmark rates, and the firm requires that the model exactly reproduce current market prices of liquid benchmark instruments.

The most appropriate class of model for this application is:

A bond analyst measures the effective duration of a callable corporate bond using a calibrated binomial interest rate tree. The following prices are observed: P₀ = $102.50 at current rates; P_- = $105.80 when rates fall by 50 basis points; P₊ = $99.40 when rates rise by 50 basis points.

The effective duration of this callable bond is closest to:

A risk manager is comparing the Vasicek and Cox-Ingersoll-Ross (CIR) interest rate models for use in a bank's internal stress testing framework. Both models are single-factor mean-reverting short-rate models used for term structure modeling.

Which of the following statements most accurately describes the key limitation of the Vasicek model that the CIR model was specifically designed to address?