Fixed-Income Bond Valuation

First Principles Thinking: classification rule

A is correct. The CFA Curriculum distinguishes day-count methods by how they count days within a period and how many days they assume per period. Statement I is correct because 30/360 assumes 30 days per month and 360 days per year. Statement II fails because actual/actual uses the actual number of days in the year. Statement III also fails because actual/actual includes actual calendar days, so leap years matter. Therefore, only one item satisfies the criterion.

Why option B is incorrect: there is not a second correct statement once the actual/actual convention is applied properly.

Why option C is incorrect: the curriculum explicitly contrasts 30/360 with actual/actual, so all three cannot be correct.

First Principles Thinking: accrued interest versus market yield

D is correct. In the CFA Curriculum, accrued interest equals the coupon payment multiplied by the fraction of the coupon period that has elapsed. That amount is determined by coupon size and day-count convention, not by the market yield. Yield changes affect the flat price component of the bond's value, not accrued interest.

The assertion is false because accrued interest is not recalculated from yield-to-maturity.

The reason is true because interest-rate changes alter the flat price, while accrued interest remains based on elapsed time in the coupon period.

First Principles Thinking: quotation convention

A is correct. The CFA Curriculum states that a bond traded between coupon dates has a full price equal to flat price plus accrued interest. Dealers quote the flat price because accrued interest rises mechanically with time even if yield-to-maturity is unchanged. Quoting the full price would therefore create a misleading upward pattern unrelated to a change in market discount rates.

The assertion is true because the quoted or clean price is the flat price.

The reason is true and directly explains why the flat price, rather than the full price, is quoted.

Accrued interest equals $(42/180) \times 2.3125 = 0.539583$, which rounds to 0.540. Choice A understates the accrual. Choice C is the coupon payment rather than the accrued fraction.

First Principles Thinking: classification rule

A is correct. The CFA Curriculum defines matrix pricing as estimating the value of a new or illiquid bond from comparable bonds with similar time-to-maturity, coupon rate, and credit quality, so Statement I is correct. Statement II fails because derivative quotes are not the basis of matrix pricing. Statement III fails because matrix pricing is especially useful when recent transaction data for the bond itself are scarce or absent. Therefore, only one item qualifies.

Why option B is incorrect: neither Statement II nor Statement III matches the curriculum's matrix pricing process.

Why option C is incorrect: all three cannot be correct because Statements II and III reverse the purpose and source inputs of matrix pricing.

First Principles Thinking: classification rule

A is correct. The governing criterion in the CFA Curriculum is the maturity effect: generally, longer-maturity bonds show larger percentage price changes for the same yield change. Statement I matches that rule. Statement II fails because the curriculum notes rare exceptions for low-coupon, long-term bonds trading at a discount. Statement III fails because the curriculum says the maturity effect always holds for zero-coupon bonds. Therefore, only one item qualifies.

Why option B is incorrect: the count is not two because Statements II and III both contradict the stated boundary conditions.

Why option C is incorrect: all three cannot satisfy the rule when the exception is described so narrowly in the curriculum.

Between coupon dates, full price is $PV \times (1+r)^{t/T}$. So USD 96.735 \times (1.02)^{90/180} = 97.698$. Choice A ignores the passage of time. Choice C overstates the growth.

Use $PV_{Full} = PV \times (1+r)^{t/T}$. So USD 114.838 \times (1.035)^{256/366} = 117.635$. Choice A is the flat price after subtracting accrued interest. Choice B ignores the growth from the start of the period.

When the periodic coupon equals the periodic market discount rate, the bond is priced at par. Discounting the 10 semiannual cash flows at 1.6% gives 100.000. Choice A uses a higher discount rate. Choice C uses a lower discount rate.

First Principles Thinking: YTM conditions

C is correct. The CFA Curriculum states that an investor earns the bond's yield-to-maturity only if the bond is held to maturity, the issuer makes full coupon and principal payments on schedule, and all coupons are reinvested at the same yield-to-maturity. If reinvestment occurs at a different rate, the realized return can differ from the quoted YTM.

The assertion is true because failure to reinvest coupons at the YTM breaks one of the required conditions.

The reason is false because coupon reinvestment at the same YTM is explicitly required for realized return to equal YTM.

Discounting the bond's cash flows at a lower market discount rate increases the present value. Using 1.2% per semiannual period gives a price of 103.748. Choice A comes from a higher discount rate. Choice B would apply only if coupon and discount rate were equal.

Accrued interest equals $(t/T) \times PMT$. So $(43/184) \times 2.3125 = 0.540421$, or about 0.540. Choice B is the full coupon, not accrued interest. Choice C uses the wrong fraction.

Bond price is the present value of coupon and principal cash flows. Discounting 10 semiannual cash flows of 1.6 and the final 100 at 2.0% per period gives 96.407. Choice B incorrectly assumes par pricing. Choice C uses too low a discount rate.

Use the between-coupon full price formula: USD 108.584 \times (1.0975)^{131/365} = 112.271$. Choice A is the flat price after subtracting accrued interest. Choice C ignores the growth from the last coupon date.

Flat price equals full price minus accrued interest. So USD 97.698 - 0.800 = 96.898$. Choice B ignores accrued interest. Choice C adds instead of subtracts accrued interest.

First Principles Thinking: classification rule

A is correct. The CFA Curriculum states first that bond price and yield-to-maturity have an inverse relationship, so Statement I is correct. Statement II fails because the coupon effect says the lower-coupon bond has the greater percentage price change, not the smaller one. Statement III fails because the price-yield relation is convex rather than linear. Therefore, only one statement qualifies.

Why option B is incorrect: a second correct item would require either reversing the coupon effect or ignoring convexity, both of which conflict with the curriculum.

Why option C is incorrect: Statements II and III are both inconsistent with the stated bond price sensitivities.

For a zero-coupon bond, solve USD 100.763 = 100/(1+r)^5$. This gives $r \approx -0.0015$, or about -0.15% per year. Choice B has the wrong sign. Choice C is much too large.

Accrued interest is $(256/366) \times 4.625 = 3.234973$, which rounds to 3.235. Choice B is the full coupon. Choice C confuses elapsed days with coupon amount.

First Principles Thinking: classification rule

A is correct. The CFA Curriculum classifies fixed-rate bonds by comparing coupon rate with the market discount rate. Statement I satisfies the rule because a par bond has price equal to face value when coupon rate equals the market discount rate. Statement II fails because a discount bond has a coupon rate below the market discount rate. Statement III fails because a premium bond has a price above face value, not below it. Therefore, only one statement qualifies.

Why option B is incorrect: only Statement I meets the curriculum rule, so the count is not two.

Why option C is incorrect: Statements II and III conflict with the curriculum definitions of discount and premium bonds.

With semiannual coupon payments, discount six cash flows of 2 and the final 100 using the semiannual rate implied by 3.9318% annual yield. The present value is about 100.191. Choice A and Choice C are prices of comparable bonds, not the estimated price of the illiquid bond.

First Principles Thinking: coupon effect

A is correct. The CFA Curriculum states that, for bonds with the same maturity, the lower the coupon, the greater the percentage price change for a given change in yield-to-maturity. This follows because a lower-coupon bond places a greater proportion of its total cash flow in the final payment at maturity, and that distant cash flow is more sensitive to the discount rate.

The assertion is true because lower-coupon bonds are more yield-sensitive than higher-coupon bonds, all else equal.

The reason is true and correctly explains the coupon effect described in the CFA Curriculum.

First Principles Thinking: classification rule

A is correct. The CFA Curriculum defines the full price as the sum of the flat price and accrued interest, so Statement I is correct. Statement II fails because accrued interest is determined from the coupon payment and the fraction of the coupon period that has passed, not from yield-to-maturity. Statement III fails because dealers usually quote the flat price, also called the clean price. Therefore, only one statement qualifies.

Why option B is incorrect: neither Statement II nor Statement III matches the curriculum treatment of accrued interest and quoted price.

Why option C is incorrect: all three cannot qualify because only Statement I is consistent with the full-price identity.

Linear interpolation gives USD 0.038035 + ((3-2)/(5-2)) \times (0.041885 - 0.038035) = 0.039318$, or about 3.932%. Choice B uses the five-year yield directly. Choice C uses the two-year yield directly.

First Principles Thinking: classification rule

A is correct. The CFA Curriculum states that realized return equals yield-to-maturity only if the bond is held to maturity, the issuer makes full scheduled payments, and coupons are reinvested at the same yield-to-maturity. Statement I violates that criterion because selling before maturity breaks a required condition. Statements II and III satisfy the required conditions rather than prevent them. Therefore, only one item qualifies.

Why option B is incorrect: the count would be two only if either scheduled payment or same-rate reinvestment worked against earning yield-to-maturity, but both are required conditions.

Why option C is incorrect: all three do not prevent earning yield-to-maturity because Statements II and III are part of the required set.

First Principles Thinking: classification rule

A is correct. The CFA Curriculum's matrix pricing process first identifies comparable bonds, then calculates their yields, then linearly interpolates to estimate the new bond's yield, and finally uses that estimated yield to price the bond. Statement I matches that process. Statement II fails because yield estimation comes before price estimation. Statement III fails because comparable bonds should have similar, not materially different, credit quality. Therefore, only one item satisfies the criterion.

Why option B is incorrect: once the process order is applied correctly, there is no second valid statement.

Why option C is incorrect: the curriculum requires similarity in credit quality and sequence, so all three cannot qualify.

First Principles Thinking: pull-to-par

B is correct. The CFA Curriculum explains that with a constant yield, bond prices change as time passes because the number of periods to maturity declines. As maturity approaches, both discount and premium bond prices are pulled toward par, provided the issuer does not default.

The assertion is true because the constant-yield price trajectory causes prices to converge to par at maturity.

The reason is also true, but it is not the reason for convergence over time. Inverse price-yield movement explains what happens when yield changes, not the pull-to-par effect when yield stays constant.

First Principles Thinking: classification rule

A is correct. The CFA Curriculum explains the constant-yield price trajectory through the pull-to-par effect. Statement I is correct because a discount bond's price increases toward par as maturity nears when yield is unchanged. Statement II fails because a premium bond falls toward par, not farther above it. Statement III fails because discount and premium bond prices converge toward par rather than diverge. Therefore, only one statement satisfies the rule.

Why option B is incorrect: there is no second qualifying statement once the pull-to-par logic is applied.

Why option C is incorrect: the premium and discount paths both move toward par, so all three cannot be correct.

Flat price equals full price minus accrued interest. Thus, USD 117.635 - 3.235 = 114.400$. Choice B is the full price. Choice C adds accrued interest instead of subtracting it.