Question 1 of 57
Using the '30/360' day-count convention, calculate the accrued interest for a 6% annual coupon bond (par USD 100). The last coupon was paid on May 15. The settlement date is August 25.
id: 12
Explanation
<h3>First Principles Thinking</h3>
<p><strong>Inputs:</strong>
Coupon = $6 per year.
Day Count = 30/360 (Every month has 30 days).
Time Period: May 15 to August 25.</p>
<p><strong>Count Days:</strong>
- May: 30 - 15 = 15 days (Treat May as 30 days total)
- June: 30 days
- July: 30 days
- August: 25 days (Settlement date)
Total Days = $15 + 30 + 30 + 25 = 100$ days.</p>
<p><strong>Calculation:</strong>
Accrued Interest = $\frac{Days}{360} \times Coupon$
$AI = \frac{100}{360} \times 6$
$AI = \frac{10}{36} \times 6$
$AI = \frac{60}{36} = \frac{10}{6} = 1.666...$
Result $\approx 1.67$.
<strong>Wait, check if coupon is annual or semi.</strong> The prompt says "6% annual coupon bond". Usually implies annual pay unless specified. If it were semi, the coupon would be 3, but the denominator would be 180? No, standard formula uses annual amount and annual days ratio.
Or: $\frac{Days}{Days in Period} \times Coupon_{Period}$.
If annual pay: $100/360 \times 6 = 1.67$.
If semi-annual pay: $\frac{100}{180} \times 3 = 1.67$.
The math works out the same. 1.67 is robust.</p>
Question 2 of 57
Assertion (A): The "true yield" of a fixed-rate bond is generally lower than its "street convention yield."
Reason (R): Calculating the true yield is computationally more complex because it requires referencing a calendar to identify weekends and holidays.
id: 1
model: Kimi k2
topic: True Yield vs. Street Convention Yield
Explanation
Assertion A is true: The true yield accounts for the delay in payments due to weekends and holidays, which lowers the internal rate of return (yield) compared to the street convention, which assumes timely payment. Reason R is also true: True yield calculation is indeed more complex due to the need for a holiday calendar. However, R is not the explanation for A. The reason the yield is lower is the *time value of money* impact of the delayed cash flows, not the computational difficulty.
Question 3 of 57
An investor purchases a 4% semiannual coupon bond with 3 years to maturity at a price of 102.50. Immediately after purchase, market yields rise by 50 bps. Which of the following statements about the bond's yield measures is *most accurate*?
id: 2
Explanation
<h3>First Principles Thinking</h3>
<p>This question tests definitions of yield measures vs. market movements.</p>
<p><strong>Option A (Incorrect):</strong> Current Yield = Annual Coupon / Price. The question asks about the bond <em>immediately after purchase</em>. The investor <em>purchased</em> at 102.50. The current yield at the moment of purchase is fixed based on that purchase price ($4 / 102.50$). If the question implies the <em>market's</em> current yield for <em>new</em> buyers, then yes, price drops and current yield rises. However, usually, yield metrics for a held bond are calculated based on the purchase price or current market price. If we look at the <em>market</em> current yield, it rises. But let's look at B.</p>
<p><strong>Option B (Correct):</strong> Street Convention Yield is a yield-to-maturity calculation. YTM is the Internal Rate of Return (IRR) of the bond's cash flows equal to its price. "Street convention" just means we ignore weekends/holidays for payment dates. The key here is: <strong>Did the price change?</strong> The prompt says "market yields rise". If we re-price the bond, the price falls. However, the yield (IRR) of the bond <em>at the moment of purchase</em> (locked in at 102.50) is a historical fact. But wait, usually "yield" refers to the current market requirement.
<em>Self-Correction/Refinement:</em> If market yields rise, the price falls. The street convention yield (which is just the standard YTM) <em>rises</em> to match the new market rate.
<em>However</em>, consider the perspective of the purchased bond's locked-in metrics. Actually, let's re-read the options. "Street convention yield" is a method of calculation. If the market yield rises, the calculated yield <em>rises</em>.
<em>Wait, let's look at it differently.</em> Is the question asking about the <em>nature</em> of the measure? No.
Let's re-evaluate Option A. Price falls -> Current Yield (Coupon/Price) increases. This is definitely true for the market security.
Let's re-evaluate Option B. Yields rise. Street convention yield rises.
Let's re-evaluate Option C. True yield tracks Street yield but adjusts for holidays. It would also rise.
<em>Wait, did I misinterpret "price of 102.50"?</em> The investor buys it. Then yields rise. The investor now holds a bond with a market value lower than 102.50.
<em>Alternative interpretation:</em> Perhaps the question implies calculating the yield based on the <em>purchase price</em> (yield-at-cost). If so, none change.
Let's assume standard market reporting. Market yields rise -> Price falls.
A) Current Yield = 4 / New Price. Since New Price < 102.50, Current Yield increases. Correct.
B) Street Yield rises. Incorrect.
C) True Yield rises. Incorrect.
<em>Hold on, look at the difficulty.</em> Is there a trick? "Street convention yield will remain unchanged." If we are talking about the yield <em>at issuance</em> or the yield <em>at purchase</em> as a recorded metric for the portfolio, it doesn't change. But usually, these are dynamic.
<em>Let's try a different angle.</em> Maybe the "price" in the prompt is fixed? No, "yields rise".
<em>Actually, let's look at the relationship between Street and True yield.</em> True yield is always slightly <em>lower</em> than Street yield because it pushes payments back to business days (same cash, later time = lower IRR).
<em>Let's go back to basics.</em> If market yields rise 50bps, the bond's YTM (Street) rises 50bps. The price falls. Current Yield (Coupon/Price) rises. So A is correct.
<em>Why might A be wrong?</em> Is it possible the price didn't change? No, "yields rise".
<em>Let's reconsider the "Tricky" requirement.</em>
Could "Current Yield" refer to the investor's return? No, that's holding period return.
<em>Let's look at B again.</em> Is it possible "Street Convention" refers to the convention itself? No.
<em>Let's look for a reason A is the answer.</em> 4% / 102.5 = 3.90%. If yield rises 50bps, YTM ~ 3.6% (approx) -> 4.1%. Price drops to ~100. Current Yield = 4/100 = 4%. It increases. A is robust.
<em>Let's try to construct a valid 'B' or 'C' answer question.</em>
What if the question is: "Which measure is always lower than the street convention yield?" Answer: True Yield.
<em>Let's stick to the provided question but ensure the logic holds.</em> A seems the only physically correct statement if we assume standard market marking behavior (Mark-to-Market).
<em>Wait, let me make the question harder/more specific to Module 7.</em>
Let's pivot the question to <strong>Yield to Worst (YTW)</strong> vs <strong>Option Adjusted Yield</strong>. Or <strong>Periodicity</strong>.
<em>Revised Question Idea:</em> Comparing Semiannual vs Annual YTM.
<em>Let's try the numerical one for the "Head" calculation.</em>
"A bond price is 98. Coupon 4% semi-annual. What is current yield vs YTM?"
CY = 4/98 > 4%. YTM > 4%.
<em>Let's go with a new question 2 entirely to ensure quality.</em>
<strong>New Question 2:</strong> A 2-year zero-coupon bond is priced at 92.00. A 2-year, 4% annual coupon bond is priced at 99.50. An analyst calculates the Yield-to-Maturity (YTM) for both using an <strong>annual</strong> periodicity. Which of the following is the *most accurate* comparison of their annual YTMs?</p>
<p><strong>First Principles:</strong>
Zero: $92 = 100 / (1+r)^2 \implies (1+r)^2 = 1.087 \implies 1+r \approx 1.0425 \implies r \approx 4.25\%$
Coupon: $99.50$. Since price < par (100), YTM > Coupon (4%). The discount is 0.50. Spread over 2 years is roughly 0.25/year. So YTM $\approx 4.25\%$.
They are very close.
Let's try the "Numerical in head" mandate.
<strong>Revised Question 2 (Numerical):</strong> A zero-coupon bond matures in 4 years and is priced at 82.27 (per 100 par). Using a <strong>semiannual</strong> periodicity (bond basis), the annualized yield-to-maturity is <em>closest</em> to:</p>
<p><strong>Calculation:</strong>
$P = 100 / (1 + r/2)^{2N}$
$82.27 = 100 / (1 + r/2)^8$
$(1 + r/2)^8 = 100 / 82.27 = 1.2155$
We need the 8th root of 1.2155.
Rule of 72ish? $1.2155 \approx 1.21$.
Try options like 4%, 5%, 6%.
If $r=5\%$, semi = 2.5%. $1.025^8 \approx 1.025^2^2^2 \approx 1.05^4 \approx 1.10^2 \approx 1.21$.
So 5% is the answer.
$1.2155$ is slightly more than $1.21$, so maybe 5.1%?
Actually, $1.025^8 \approx 1.218$. So 5% is very close.
Let's formulate this as Question 2.</p>
Question 4 of 57
A 5-year, semiannual-pay 6% bond trades at 102. It's callable at 101 in 4 years (8 periods). What is the yield to second call?
id: 20
model: Claude Sonnet
topic: Yield to Second Call
Explanation
<h3>First Principles Thinking: Multiple Call Scenarios</h3><p><strong>C is correct.</strong> Yield to second call uses the second call date (4 years, or 8 semiannual periods) and second call price (101). Given: N=8, PMT=3 (6%/2 of par 100), FV=101, PV=-102. Calculator: CPT I/Y = 2.830% semiannual. Quoted yield to second call = 2 × 2.830% = 5.66%. The investor pays 102, receives eight coupons of 3, and gets back 101 at call. The capital loss is smaller than with the first call (same starting price, same call price, but longer time to amortize the loss), making this yield slightly higher than yield to first call but still below the coupon rate due to the premium paid.</p><p>A is incorrect: 2.83% is the semiannual periodic rate, not the annualized yield to second call. This forgets the market convention of doubling the periodic rate to get the bond basis quotation.</p><p>B is incorrect: 5.54% is the yield to maturity (assuming the bond is held for all 5 years to par 100), not yield to second call. This uses the wrong terminal date and redemption value.</p>
Question 5 of 57
A 5-year, annual-pay bond with a 7% coupon is trading at 102.078. What is the bond's yield to maturity?
id: 1
model: Claude Sonnet
topic: Yield to Maturity Calculation
Explanation
<h3>First Principles Thinking: YTM as IRR</h3><p><strong>B is correct.</strong> YTM is the discount rate that equates the present value of all future cash flows to the current bond price. For this annual-pay bond, we have 5 annual coupon payments of 7 plus a par value of 100 at maturity. Setting PV = -102.078, we solve: 102.078 = 7/(1+r) + 7/(1+r)² + 7/(1+r)³ + 7/(1+r)⁴ + 107/(1+r)⁵. Using a financial calculator: N=5, PMT=7, FV=100, PV=-102.078, CPT I/Y = 6.5%. The bond trades at a premium (price > 100), so YTM must be below the coupon rate of 7%, which confirms our answer.</p><p>A is incorrect: 5.50% would produce a bond price significantly higher than 102.078, as the discount rate would be too low. This misconception arises from underestimating the premium's impact on yield.</p><p>C is incorrect: 7.50% would result in a bond price below par (discount bond), not the premium price of 102.078. This error confuses the relationship between coupon rate, YTM, and price—when price exceeds par, YTM must be less than the coupon rate.</p>
Question 6 of 57
If a corporate bond's yield increases from 6.25% to 6.50% while its spread remains constant, what factor most likely caused the yield increase?
id: 13
model: Claude Sonnet
topic: Yield Spread Analysis
Explanation
<h3>First Principles Thinking: Spread Decomposition</h3><p><strong>A is correct.</strong> A bond's yield equals the benchmark rate plus a spread. If the spread remains constant but yield rises, the benchmark must have increased by the same amount (6.50% - 6.25% = 0.25%). Benchmark rates reflect macroeconomic factors like real risk-free rates and inflation expectations that affect all securities. Constant spread indicates no change in issuer-specific or bond-specific risk premiums. Therefore, broad market forces—such as central bank policy, inflation data, or economic growth expectations—drove the yield increase across the entire rate structure.</p><p>B is incorrect: Deteriorating credit quality would increase the spread over the benchmark, not keep it constant. This microeconomic, issuer-specific factor would show up as spread widening, reflecting heightened default risk.</p><p>C is incorrect: Decreased liquidity would also widen the spread as investors demand higher compensation for illiquidity. Like credit deterioration, liquidity changes are captured in the spread, not the benchmark rate.</p>
Question 7 of 57
A USD 1,000 par value bond pays a 3% semiannual coupon and has a current market price of USD 950. The simple yield is 3.50%. Which of the following is *most likely* the remaining time to maturity?
id: 9
Explanation
<h3>First Principles Thinking</h3>
<p>This is a reverse-engineering numerical problem you can estimate in your head.</p>
<p><strong>Formula:</strong> Simple Yield = $\frac{\text{Coupon} + \text{Straight Line Amortization}}{\text{Flat Price}}$
$Simple Yield = \frac{C + (Par - P)/N}{P}$</p>
<p><strong>Inputs:</strong>
$Simple Yield = 0.035$
$P = 950$
$C = 30$ (3% of 1000)
$Par = 1000$</p>
<p><strong>Calculation:</strong>
$0.035 = \frac{30 + (50/N)}{950}$
Multiply both sides by 950:
$33.25 = 30 + (50/N)$
$3.25 = 50/N$
$N = 50 / 3.25$
$N \approx 15.38$ years.
<em>Wait.</em> 3% coupon is usually 30 dollars a year. 3.5% of 950 is 33.25.
So the amortization must provide 3.25 dollars per year. Total discount is 50. $50/3.25 \approx 15$.
This is not an option.
Let me re-read the "Simple Yield" definition in CFA context. It is often used for Japanese bonds (JGBs).
Maybe I used current yield?
Current Yield = 30 / 950 = 3.15%.
So Simple Yield (3.50%) includes amortization.
Let's check the options again.
If N=3: Amort = 50/3 = 16.66. Num = 46.66. Yield = 46.66/950 = 4.9%. Too high.
If N=5: Amort = 50/5 = 10. Num = 40. Yield = 40/950 = 4.2%. Too high.
If N=10: Amort = 50/10 = 5. Num = 35. Yield = 35/950 = 3.68%.
My derived N was 15 years.
Let's adjust the question parameters to fit Option C (10 years).
Target Yield = 3.68%? Or make price 900?
Let's calculate for N=10, Price=950. Simple Yield = 3.68%.
What if Price = 900? Discount = 100. Amort = 10. Num = 40. Yield = 40/900 = 4.44%.
Let's try to find inputs that result in exactly 3.50% for 10 years.
$0.035 * P = 30 + (1000-P)/10$
$0.035P = 30 + 100 - 0.1P$
$0.135P = 130$
$P = 130 / 0.135 = 962.96$
<strong>Revised Question Inputs:</strong> Price = 963. Coupon = 3%. Simple Yield = 3.50%.
Check N=10: Amort = (1000-963)/10 = 3.7. Num = 33.7. Yield = 33.7/963 = 3.499%.
This works.
Let's calculate for N=5 with these inputs:
Amort = 37/5 = 7.4. Num = 37.4. Yield = 37.4/963 = 3.88%.
N=3: Amort = 12.3. Num = 42.3. Yield = 4.4%.
So N=10 is the clear answer.
<strong>Final Question Text:</strong> Price = USD 963. Coupon = 3%. Simple Yield = 3.50%.</p>
Question 8 of 57
A 5-year, semiannual-pay 7% coupon bond is priced at 102.078. If the semiannual discount rate is 3.253%, what is the bond's quoted annual YTM?
id: 2
model: Claude Sonnet
topic: Semiannual Bond YTM
Explanation
<h3>First Principles Thinking: Bond Yield Quoting Convention</h3><p><strong>B is correct.</strong> By market convention, YTM for semiannual bonds is stated as twice the periodic (semiannual) rate. This is a bond equivalent yield (BEY) convention that enables comparability across bonds with different payment frequencies. The calculation is straightforward: YTM = 2 × 3.253% = 6.506%. This quoted rate represents simple annualization without compounding, not the effective annual rate. The convention arose historically to standardize yield comparisons in bond markets.</p><p>A is incorrect: 3.253% is the semiannual periodic rate, not the quoted annual YTM. This error stems from failing to annualize the periodic rate using the market convention of multiplying by 2.</p><p>C is incorrect: 6.607% appears to apply compounding [(1.03253)² - 1 = 6.607%], which would give the effective annual yield, not the quoted YTM. The standard quoting convention uses simple multiplication, not compound conversion.</p>
Question 9 of 57
A 2-year option-free bond pays a 5.00% annual coupon. The spot rate curve is flat at 3.00% for the 1-year tenor and 4.00% for the 2-year tenor. The Zero-volatility spread (Z-spread) for this bond is 50 basis points. The price of the bond is closest to:
id: 6
model: Gemini
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
<h3>First Principles: Z-Spread Valuation</h3><p><strong>A is correct.</strong> The Z-spread is the constant spread added to each spot rate on the yield curve to equate the present value of the bond's cash flows to its price. To find the price, we discount cash flows using $(Spot Rate + Z)$.</p><p>1. **Define Cash Flows:**<br>Year 1: 5.00<br>Year 2: 105.00</p><p>2. **Adjust Spot Rates:**<br>Adjusted Rate 1 ($z_1$) = $3.00\% + 0.50\% = 3.50\%$<br>Adjusted Rate 2 ($z_2$) = $4.00\% + 0.50\% = 4.50\%$</p><p>3. **Calculate Present Value:**<br>$$ PV = \frac{5.00}{(1.035)^1} + \frac{105.00}{(1.045)^2} $$<br>$$ PV = 4.8309 + 96.1516 $$<br>$$ PV = 100.9825 $$</p><p>B is incorrect because it calculates the price without the Z-spread (using raw spot rates).</p><p>C is incorrect because it discounts using the 1-year spot rate for both periods or similar discounting errors.</p>
Question 10 of 57
Consider the following statements regarding the decomposition of yield-to-maturity:
(1) The benchmark rate captures macroeconomic factors such as the expected rate of inflation and general economic growth.
(2) The yield spread captures microeconomic factors such as the issuer’s credit risk and liquidity.
(3) On-the-run government bonds typically trade at higher yields-to-maturity than off-the-run bonds with similar maturities.
Which of the statements given above are correct?
id: 5
model: ChatGPT
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
Statement (1) is correct because the benchmark (risk-free) rate reflects broad economic conditions like inflation and growth. Statement (2) is correct because the spread reflects issuer-specific risks. Statement (3) is incorrect because on-the-run bonds are more liquid and in higher demand, typically trading at lower (not higher) yields than off-the-run bonds. Therefore, only statements (1) and (2) are correct.
Question 11 of 57
A corporate bond has a 6% annual coupon and trades at par. The yield curve is flat at 6%. If the bond's yield-to-maturity switches from an annual basis to a semiannual bond basis, the reported yield will be:
id: 3
Explanation
<h3>First Principles Thinking</h3>
<p>This tests the concept of <strong>Periodicity</strong>.</p>
<p><strong>Logic:</strong>
1. <strong>Annual Basis (Periodicity = 1):</strong> The bond pays 6% annually. Since it trades at par, the YTM is 6%. The effective annual rate (EAR) is 6%.
2. <strong>Semiannual Basis (Periodicity = 2):</strong> We need to find a nominal rate ($r_{semi}$) that, when compounded semiannually, produces the same effective yield of 6%.
3. <strong>Equation:</strong> $(1 + \frac{r_{semi}}{2})^2 = 1 + 0.06$
4. <strong>Solving:</strong> $(1 + \frac{r_{semi}}{2}) = \sqrt{1.06} \approx 1.02956$
5. $\frac{r_{semi}}{2} = 0.02956 \implies r_{semi} \approx 5.91\%$
<strong>Intuition:</strong> By compounding more frequently (twice a year vs once), you earn interest-on-interest sooner. Therefore, you need a <em>lower</em> nominal rate to achieve the same final effective return. Thus, the semiannual basis yield (5.91%) is lower than the annual basis yield (6%).</p>
Question 12 of 57
A bond's Z-spread is 150 bps and its Option-Adjusted Spread (OAS) is 120 bps. What is the implied Option Cost in basis points, and what does it suggest about the bond?
id: 13
Explanation
<h3>First Principles Thinking</h3>
<p><strong>Relationship:</strong>
$Z\text{-spread} = OAS + \text{Option Cost}$
$\text{Option Cost} = Z\text{-spread} - OAS$
$\text{Option Cost} = 150 - 120 = 30$ bps.</p>
<p><strong>Interpretation:</strong>
1. <strong>Z-spread</strong> measures the total spread over the treasury curve.
2. <strong>OAS</strong> measures the spread after removing the value of the embedded option.
3. Since $Z > OAS$, the spread <em>shrank</em> when we removed the option. This means the option was accounting for some of the yield.
4. Investors demand <em>extra</em> yield (higher Z-spread) to compensate for options that hurt them (like Call options, where the issuer can buy back the bond when rates fall).
5. Therefore, a positive Option Cost implies the investor is short an option (Callable bond).
6. If the bond were Putable (investor owns option), the Z-spread would be <em>lower</em> than the OAS (Option cost would be negative), because the investor accepts a lower yield in exchange for the benefit of the Put.</p>
Question 13 of 57
An analyst observes a 3-year, 5% annual coupon bond priced at USD 102.75. The current Yield-to-Maturity (YTM) is 4.02%. The 'True Yield' of this bond is *most likely*:
id: 4
Explanation
<h3>First Principles Thinking</h3>
<p>This tests the distinction between <strong>Street Convention Yield</strong> and <strong>True Yield</strong>.</p>
<p><strong>Street Convention Yield:</strong> Calculates YTM assuming cash flows occur exactly on the scheduled dates (weekends/holidays ignored).</p>
<p><strong>True Yield:</strong> Calculates YTM using the <em>actual</em> payment dates. Since coupons falling on weekends/holidays are paid on the next business day (delayed), the investor receives the same cash flows but slightly <em>later</em> than the street convention assumes.</p>
<p><strong>Conclusion:</strong> Receiving cash later reduces the present value (or IRR) of the investment. Therefore, the True Yield is always slightly <strong>lower</strong> than the Street Convention Yield. Since the quoted 4.02% is likely the Street yield (standard quote), the True Yield will be lower.</p>
Question 14 of 57
A 4-year, semiannual-pay 7.125% bond trades at 102.347 and is callable at 101 in 2 years. What is the yield to call?
id: 11
model: Claude Sonnet
topic: Yield to Call Calculation
Explanation
<h3>First Principles Thinking: Call Option IRR</h3><p><strong>B is correct.</strong> Yield to call assumes the bond is called at the earliest call date at the specified call price. We have 2 years (4 semiannual periods) to call, semiannual coupon of 3.5625 (7.125%/2 of par 100), call price 101, and current price 102.347. Calculator: N=4, PMT=3.5625, FV=101, PV=-102.347, CPT I/Y = 3.167%. Quoted yield to call = 2 × 3.167% = 6.33%. The investor pays 102.347, receives four coupons of 3.5625, and gets back 101 at call. The capital loss (102.347 to 101) and shorter time horizon reduce the yield below the coupon rate.</p><p>A is incorrect: 3.17% is the semiannual periodic rate, not the annualized yield to call. This error stops at the periodic calculation without doubling to get the bond basis quotation.</p><p>C is incorrect: 7.13% is approximately the coupon rate, which ignores the bond pricing dynamics. When a bond trades above the call price (102.347 > 101), yield to call must be below the coupon rate due to the capital loss at call.</p>
Question 15 of 57
Assertion (A): The Interpolated Spread (I-spread) is often preferred over the G-spread for analyzing Euro-denominated corporate bonds.
Reason (R): The I-spread measures the yield spread of a bond over the standard interest rate swap rate in the same currency and tenor.
id: 6
model: Kimi k2
topic: I-Spread vs. G-Spread
Explanation
Assertion A is true: The I-spread is the standard for Euro bonds (often due to the lack of a single risk-free sovereign benchmark in the Eurozone). Reason R is true: It correctly defines the I-spread. However, R does not explain *why* it is preferred over G-spread; the preference is driven by the specific market structure of the Eurozone (fragmented sovereign debt), not just the definition of the spread.
Question 16 of 57
A 4-year zero-coupon bond is priced at USD 82.27 per USD 100 par value. Assuming a semiannual bond basis (periodicity of 2), the annualized yield-to-maturity is *closest* to:
id: 2
Explanation
<h3>First Principles Thinking</h3>
<p>The pricing equation for a zero-coupon bond with semiannual periodicity is:
$$P = \frac{FV}{(1 + \frac{r}{2})^{2 \times N}}$$
Where:
$P = 82.27$
$FV = 100$
$N = 4$ years (so $2 \times 4 = 8$ periods)
Rearranging to solve for $r$ (the annualized yield):
$$(1 + \frac{r}{2})^8 = \frac{100}{82.27} \approx 1.2155$$
To solve this in your head, work backward from the options or use approximations:
Try Option B (5.00%):
Semiannual rate = $2.5\%$ or $0.025$.
$1.025^2 \approx 1.0506$ (Year 1)
$1.0506^2 \approx 1.1038$ (Year 2)
$1.1038^2 \approx 1.218$ (Year 4)
Since $1.218$ is very close to our target of $1.2155$, 5.00% is the correct answer. (Specifically, $1.2155$ implies a slightly lower rate than the approximation, but 5.00% is the intended integer round number here. Exact calc: $1.2155^{(1/8)} - 1 = 0.02476 \to \times 2 = 4.95\%$. Wait. $1.025^8 = 1.2184$. Target is $1.2155$. So $r$ is slightly less than 5%. 4.85% might be closer?
Let's re-calculate $1.024^8 \approx 1.209$. 4.9% is likely the exact number. 5.0% is the closest round option among standard CFA-style distractors if they are spaced widely, but let's check A. 4.85% -> 2.425%. $1.02425^8 \approx 1.211$. 5.00% -> 1.218. The midpoint is roughly 1.2145. 1.2155 is closer to 5.00% than 4.85%. So B remains valid.)</p>
Question 17 of 57
A corporate bond has a 'Street Convention' yield of 5.25%. The bond's maturity date falls on a Saturday, causing the final principal and interest payment to be made on the following Monday. The 'True Yield' of this bond is most likely:
id: 7
model: Gemini
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
<h3>First Principles: True Yield vs. Street Convention</h3><p><strong>A is correct.</strong> The Street Convention yield assumes that cash flows are paid exactly on the scheduled coupon dates, regardless of weekends or holidays. The True Yield accounts for the actual delay in payments (e.g., moving a Saturday payment to Monday).</p><p><strong>Mechanism:</strong> If a payment is delayed (received later than scheduled), the present value of that cash flow decreases for a given discount rate. Conversely, to equate the same purchase price to these delayed (later) cash flows, the Internal Rate of Return (Yield) must be lower. You are effectively lending money for a few extra days without extra interest, which drags down the annualized return.</p><p>Therefore, True Yield < Street Convention Yield.</p><p>B is incorrect because weekends affect the actual timing of cash flows.</p><p>C is incorrect because delays reduce, not increase, the effective return.</p>
Question 18 of 57
A 4-year corporate bond with a 5.00% annual coupon paid semiannually is currently trading at a price of 103.00. The bond is callable in exactly 2 years at a call price of 101.00. The Yield-to-Worst (YTW) is closest to:
id: 2
model: Gemini
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
<h3>First Principles: Yield-to-Worst Logic</h3><p><strong>A is correct.</strong> The Yield-to-Worst is the lowest of the Yield-to-Maturity (YTM) and all possible Yield-to-Call (YTC) measures. For a bond trading at a premium (Price > Par), the YTC is often lower than the YTM, especially if the call price is near par, because the loss of premium value occurs over a shorter timeframe.</p><p>1. **Calculate Yield-to-Maturity (YTM):**<br>Inputs: $N = 4 \times 2 = 8$, $PV = -103.00$, $PMT = 5/2 = 2.50$, $FV = 100$.<br>Using a financial calculator or solver:<br>$$ 103 = \sum_{t=1}^{8} \frac{2.50}{(1+r)^t} + \frac{100}{(1+r)^8} $$<br>Semiannual $r \approx 2.0889\%$. Annualized YTM $= 2.0889\% \times 2 = 4.18\%$.</p><p>2. **Calculate Yield-to-Call (YTC):**<br>Inputs: $N = 2 \times 2 = 4$, $PV = -103.00$, $PMT = 2.50$, $FV = 101$ (Call Price).<br>$$ 103 = \sum_{t=1}^{4} \frac{2.50}{(1+r)^t} + \frac{101}{(1+r)^4} $$<br>Semiannual $r \approx 1.9558\%$. Annualized YTC $= 1.9558\% \times 2 = 3.91\%$.</p><p>3. **Determine YTW:**<br>YTW = $\min(YTM, YTC) = \min(4.18\%, 3.91\%) = 3.91\%$.</p><p>B is incorrect; it is the YTM.</p><p>C is incorrect; it is the coupon rate.</p>
Question 19 of 57
Consider a 10-year callable bond. Which of the following relationships between its yield measures is *always* true?
id: 6
Explanation
<h3>First Principles Thinking</h3>
<p><strong>Yield-to-Worst (YTW):</strong> The minimum of YTM and all possible Yield-to-Calls. By definition, YTW $\le$ YTM. So A is false.</p>
<p><strong>Yield-to-Call vs YTM:</strong> This depends on whether the bond is trading at a premium or discount. If trading at a discount, YTM is usually YTW. If at a premium, YTC is often lower. It is not <em>always</em> true that YTC < YTM. So C is false.</p>
<p><strong>Option-Adjusted Yield (OAY) vs YTM:</strong>
1. The market price of a callable bond is <em>lower</em> than an equivalent option-free bond because the investor sold a call option to the issuer.
2. Because the price is lower, the standard YTM (calculated on that depressed price) is <em>higher</em> to compensate for the call risk.
3. The Option-Adjusted Yield calculates the yield by removing the value of the option (i.e., adding the option value back to the price, simulating the 'option-free' price). Using a higher 'option-free' price results in a lower yield.
4. Therefore, for a callable bond: Option-Adjusted Yield < Yield-to-Maturity.</p>
Question 20 of 57
A 5-year corporate bond pays a 6% annual coupon and is priced at $98.00 per $100 par value. The current 5-year government spot rate is 4.0%. The bond's G-spread is 220 bps. Which of the following is *most likely* the bond's Z-spread?
id: 1
Explanation
<h3>First Principles Thinking</h3>
<p>The G-spread is the spread over a single point on the government yield curve (usually the yield-to-maturity of a matched-maturity Treasury). The Z-spread (Zero-volatility spread) is the constant spread added to the entire government spot rate curve to price the bond. </p>
<p>When the yield curve is upward sloping (which is the typical case), the spot rates for intermediate cash flows are lower than the final yield-to-maturity. To match the same market price, the spread added to these lower early rates (Z-spread) must be higher than the spread added to the single, higher yield-to-maturity (G-spread). Conversely, if the curve is flat, they would be equal. The steeper the curve, the greater the difference.</p>
<p><strong>First Principles Calculation/Logic:</strong>
1. **G-Spread:** Uses one single discount rate (YTM of benchmark) for all cash flows. $P = \sum \frac{CF_t}{(1 + YTM_{gov} + G)^t}$.
2. **Z-Spread:** Uses the spot rate curve ($z_t$). $P = \sum \frac{CF_t}{(1 + z_t + Z)^t}$.
3. **Relationship:** If the yield curve slopes upward, early spot rates are low. To discount early coupons to the same present value contribution as the G-spread method (which effectively uses an 'average' rate), the Z-spread must act as a 'plug' that is generally higher to compensate for the lower early spot rates. Typically, for an upward-sloping yield curve, $Z\text{-spread} > G\text{-spread}$.</p>
<p>Therefore, with a G-spread of 220 bps, the Z-spread is most likely slightly higher, making 224 bps the logical choice.</p>
Question 21 of 57
A corporate bond is quoted with a yield-to-maturity of 4.50% based on a 30/360 day count convention. An analyst wishes to calculate the spread against a sovereign benchmark that trades on an Actual/Actual basis. The Government Equivalent Yield (GEY) for the corporate bond is closest to:
id: 5
model: Gemini
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
<h3>First Principles: Day Count Convention Adjustments</h3><p><strong>C is correct.</strong> To compare yields calculated on different day count bases, one must restate the yield of one to match the other. The Government Equivalent Yield converts a corporate bond yield (typically 30/360) to an Actual/Actual basis.</p><p>The conversion formula assumes the corporate bond effectively pays interest for 360 days in a 'corporate year', while the government bond pays for 365 days. To equate them:</p><p>$$ \text{GEY} = \text{Yield}_{30/360} \times \frac{365}{360} $$</p><p>$$ \text{GEY} = 4.50\% \times 1.01389 $$</p><p>$$ \text{GEY} \approx 4.5625\% $$</p><p><strong>Mechanism:</strong> Since a 365-day year is longer than a 360-day year, the equivalent yield on a 365-day basis must be higher to generate the same absolute interest dollars per day.</p><p>A is incorrect because it multiplies by 360/365.</p><p>B is incorrect because it ignores the day count difference.</p>
Question 22 of 57
A bond has a stated YTM of 10% with semiannual periodicity. What is its effective annual yield?
id: 3
model: Claude Sonnet
topic: Effective Annual Yield
Explanation
<h3>First Principles Thinking: Compounding Effects</h3><p><strong>B is correct.</strong> Effective annual yield (EAY) accounts for within-year compounding. A 10% YTM with semiannual periodicity means 5% per half-year. Starting with $1, after six months we have $1.05, which then earns 5% for the next six months: 1.05 × 1.05 = 1.1025. The gain is 10.25%. Formula: EAY = (1 + stated rate/n)ⁿ - 1 = (1 + 0.10/2)² - 1 = (1.05)² - 1 = 0.1025 or 10.25%. Higher periodicity increases EAY because earnings are reinvested more frequently.</p><p>A is incorrect: 10% is the stated YTM, which ignores compounding within the year. This misconception treats semiannual payments as if they produce no reinvestment benefit, equivalent to simple interest rather than compound interest.</p><p>C is incorrect: 10.38% would correspond to quarterly periodicity [EAY = (1.025)⁴ - 1 = 10.38%], not semiannual. This error applies the wrong compounding frequency, confusing the number of periods per year.</p>
Question 23 of 57
A government bond yield is 2.5%. A comparable corporate bond yield is 4.0%. The 'G-Spread' is 150 bps. If the government bond yield was derived by interpolating between the on-the-run 5-year and 7-year Treasuries, this 150 bps is most accurately described as an:
id: 10
Explanation
<h3>First Principles Thinking</h3>
<p><strong>G-Spread (Government Spread):</strong> The difference between the corporate bond yield and a government bond yield. </p>
<p>There are two ways to get the government yield:
1. <strong>Match Maturity:</strong> Using a specific on-the-run bond with the exact same maturity. This is the standard G-Spread.
2. <strong>Interpolation:</strong> If no government bond exists with the exact same maturity, we calculate a weighted average of two government bonds (one shorter, one longer). The spread over this calculated synthetic rate is the <strong>Interpolated G-Spread</strong>.</p>
<p>The I-Spread uses <strong>Swap</strong> rates (Inter-bank rates) as the benchmark, not government bonds. Therefore, A is incorrect. C is related to derivatives.</p>
Question 24 of 57
A 1-year annual pay bond has a Yield-to-Maturity of 5.0%. The spot rates for 6-months and 1-year are 4.0% and 5.0% respectively. This bond is most likely:
id: 14
Explanation
<h3>First Principles Thinking</h3>
<p><strong>Bond Structure:</strong>
Since it is a "1-year annual pay bond", it has only <strong>one</strong> cash flow at $t=1$ year (Coupon + Principal).</p>
<p><strong>Pricing:</strong>
1. <strong>YTM Method:</strong> Discount the single cash flow at the 1-year YTM (5.0%).
2. <strong>Spot Rate Method:</strong> Discount the single cash flow at the 1-year Spot Rate (5.0%).
Note: The 6-month spot rate is irrelevant because there is no interim cash flow.</p>
<p><strong>Conclusion:</strong>
Since the discount rate used is identical (5.0%) in both cases, the calculated price is identical. There is no discrepancy between the market YTM and the theoretical spot-rate price. The bond is priced consistently with the spot curve, i.e., Arbitrage-free.</p>
Question 25 of 57
Consider the following statements regarding the yield-to-worst measure:
(1) Yield-to-worst is the lowest of the sequence of yields-to-call and the yield-to-maturity.
(2) The intent of the yield-to-worst measure is to provide the investor with the most conservative assumption for the rate of return.
(3) Yield-to-worst is calculated by assuming the bond is called on the date that results in the highest possible yield to the investor.
Which of the statements given above are correct?
id: 6
model: ChatGPT
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
Statement (1) is correct as it matches the definition of yield-to-worst. Statement (2) is correct because using the lowest possible yield provides a conservative estimate of return for the investor. Statement (3) is incorrect because yield-to-worst assumes the call date that results in the lowest (not highest) yield; it assumes the issuer acts in their own best interest to minimize their cost of debt. Therefore, only statements (1) and (2) are correct.
Question 26 of 57
Consider the following statements regarding Option-Adjusted Spread (OAS) and yield:
(1) The option-adjusted yield is the required market discount rate whereby the price is adjusted for the value of the embedded option.
(2) For a callable bond, the Option-Adjusted Spread (OAS) is equal to the Z-spread plus the option value in basis points per year.
(3) The option-adjusted price of a callable bond is calculated by adding the value of the embedded call option to the flat price of the bond.
Which of the statements given above are correct?
id: 4
model: ChatGPT
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
Statement (1) is correct as it defines the option-adjusted yield based on the option-adjusted price. Statement (2) is incorrect because the OAS is calculated as the Z-spread minus (not plus) the option value in basis points per year; the investor receives a higher Z-spread to compensate for the call risk. Statement (3) is correct because the option-adjusted price represents the value of the bond if it were option-free, which is the flat price plus the value of the call option (which the investor 'paid' for by accepting a lower flat price). Therefore, only statements (1) and (3) are correct.
Question 27 of 57
A 3-year, 8% coupon, semiannual-pay bond is priced at 90.165. What is the bond's simple yield?
id: 5
model: Claude Sonnet
topic: Simple Yield Calculation
Explanation
<h3>First Principles Thinking: Straight-Line Amortization</h3><p><strong>C is correct.</strong> Simple yield enhances current yield by including straight-line amortization of discount/premium. Discount from par: 100 - 90.165 = 9.835. Annual straight-line amortization: 9.835 / 3 = 3.278. Annual coupon: 8. Simple yield = (annual coupon + annual amortization) / flat price = (8 + 3.278) / 90.165 = 11.278 / 90.165 = 0.1251 or 12.51%, which rounds to 12.52%. The logic: each year you receive the 8 coupon plus gain 3.278 toward par, relative to your 90.165 investment. This is more accurate than current yield for discount/premium bonds but less precise than YTM.</p><p>A is incorrect: 8% is merely the stated coupon rate, not the simple yield. This overlooks both the discount amortization and the fact that the bond is purchased below par, which increases the investor's return.</p><p>B is incorrect: 11.52% might result from errors in calculating the amortization amount or incorrectly including only partial discount recovery. The calculation must add the full annual straight-line amortization to the coupon before dividing by price.</p>
Question 28 of 57
Bond X and Bond Y are both 5-year fixed-rate bonds. Bond X pays coupons annually. Bond Y pays coupons semiannually. Both have a Yield-to-Maturity of 6.0% (reported on their respective periodicity basis). Which bond offers the higher Effective Annual Rate (EAR)?
id: 7
Explanation
<h3>First Principles Thinking</h3>
<p>This question requires comparing yields with different compounding frequencies.</p>
<p><strong>Bond X (Annual):</strong>
Reported YTM = 6% with periodicity 1.
$EAR_X = (1 + 0.06/1)^1 - 1 = 6.00\%$</p>
<p><strong>Bond Y (Semiannual):</strong>
Reported YTM = 6% with periodicity 2.
This means the periodic rate is $6\% / 2 = 3\%$.
$EAR_Y = (1 + 0.03)^2 - 1 = 1.0609 - 1 = 6.09\%$</p>
<p><strong>Conclusion:</strong> $6.09\% > 6.00\%$. Bond Y offers the higher effective yield because it compounds more frequently at the same nominal rate.</p>
Question 29 of 57
Consider the following statements regarding periodicity and annualized yields:
(1) Compounding more frequently at a lower annual rate corresponds to compounding less frequently at a higher annual rate.
(2) The periodicity of the annual market discount rate for a zero-coupon bond is strictly determined by its time-to-maturity.
(3) An annual rate having a periodicity of two is known as a semiannual bond basis yield.
Which of the statements given above are correct?
id: 2
model: ChatGPT
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
Statement (1) is correct because to achieve the same effective return, a rate compounded more frequently must be lower than a rate compounded less frequently. Statement (2) is incorrect because the periodicity of a zero-coupon bond is arbitrary since there are no intermediate coupon payments; it can be quoted with any periodicity. Statement (3) is correct because a semiannual bond basis yield is defined as an annual rate with a periodicity of two. Therefore, only statements (1) and (3) are correct. Option A is incorrect because statement (2) is false. Option C is incorrect because statement (2) is false.
Question 30 of 57
A 20-year, $1,000 par value, 6% semiannual-pay bond trades at $802.07. What is the current yield?
id: 4
model: Claude Sonnet
topic: Current Yield Calculation
Explanation
<h3>First Principles Thinking: Income-Only Return</h3><p><strong>B is correct.</strong> Current yield measures only the annual coupon income relative to price, ignoring capital gains and reinvestment. Annual coupon = par × coupon rate = $1,000 × 6% = $60. Current yield = annual coupon / price = $60 / $802.07 = 0.0748 or 7.48%. Because the bond trades at a discount (below par), current yield exceeds the coupon rate—you receive the same dollar coupon on a smaller investment. Current yield is the same for annual-pay and semiannual-pay bonds with identical coupon rates and prices, as it uses total annual coupon payments.</p><p>A is incorrect: 6% is the stated coupon rate, not the current yield. This error treats coupon rate and current yield as equivalent, ignoring that current yield must be calculated relative to the actual market price, not par value.</p><p>C is incorrect: 7.66% appears to miscalculate the coupon payment or price relationship. This may result from incorrectly using the semiannual coupon ($30) instead of the full annual amount, or a computational error in the division.</p>
Question 31 of 57
Assertion (A): The Z-spread is theoretically superior to the G-spread for analyzing bonds with principal amortization scheduled prior to maturity.
Reason (R): It is mathematically impossible to calculate a G-spread for a bond that amortizes principal, as there is no single maturity date to reference.
id: 5
model: Kimi k2
topic: Z-Spread vs. G-Spread Application
Explanation
Assertion A is true: Z-spread uses the spot curve to discount each specific cash flow, making it accurate for amortizing structures where cash flows vary over time. G-spread uses a single YTM point, which assumes a flat curve and is ill-suited for amortizing bonds. Reason R is false: It is not *impossible* to calculate a G-spread (one could use the Weighted Average Life or final maturity), but it is simply a flawed/inaccurate metric.
Question 32 of 57
Consider the following statements regarding yield spread measures:
(1) The G-spread is the yield spread in basis points over an actual or interpolated government bond yield.
(2) An I-spread larger than the G-spread indicates that Treasury yields are higher than swap rates.
(3) The Z-spread assumes that the yield curve is flat and interest rate volatility is zero.
Which of the statements given above are correct?
id: 3
model: ChatGPT
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
Statement (1) is correct because the G-spread is defined as the spread over an actual or interpolated government bond yield. Statement (2) is correct because the I-spread compares the bond to the swap rate, while the G-spread compares it to the government yield; if I-spread > G-spread, the benchmark swap rate must be lower than the benchmark government yield (since Total Yield is constant). Statement (3) is incorrect because while the Z-spread (zero-volatility spread) assumes zero volatility, it does not assume a flat yield curve; it measures the spread over the entire spot rate curve. Therefore, only statements (1) and (2) are correct.
Question 33 of 57
Assertion (A): On-the-run government bonds typically trade at lower yields-to-maturity than off-the-run bonds of similar maturity.
Reason (R): On-the-run bonds possess higher liquidity and often command a scarcity premium in the repo market, lowering their financing costs.
id: 7
model: Kimi k2
topic: On-the-Run vs. Off-the-Run Yields
Explanation
Assertion A is true: The most recently issued (on-the-run) bonds trade at a premium price (lower yield). Reason R is true and explains the phenomenon: High demand for liquidity and specialness in the repo market (lower financing rates) drives the price up and the yield down relative to seasoned (off-the-run) issues.
Question 34 of 57
How does a bond's true yield typically compare to its street convention yield?
id: 19
model: Claude Sonnet
topic: Street Convention vs True Yield
Explanation
<h3>First Principles Thinking: Payment Timing Effects</h3><p><strong>A is correct.</strong> Street convention calculates yield using stated coupon payment dates from the indenture. True yield uses actual payment dates, accounting for holidays and weekends when payments are deferred to the next business day. When payments are delayed, present value increases (cash flows come later), so the bond is worth slightly more than street convention suggests. To maintain price equality, true yield must be slightly lower—if PV is higher, the discount rate must decrease. The difference is typically only a few basis points. Street convention is standard for quotation; true yield provides technical precision.</p><p>B is incorrect: True yield is lower, not higher, and the difference stems from payment timing, not compounding accuracy. Both methods use proper compounding; they differ only in which dates they use for cash flows.</p><p>C is incorrect: True yield and street convention yield differ whenever coupon dates fall on non-business days, which occurs regularly. They're identical only if all coupon dates happen to fall on business days.</p>
Question 35 of 57
A 4-year corporate bond with a 6.00% annual coupon is trading at a flat price of 94.00. The Simple Yield for this bond is closest to:
id: 4
model: Gemini
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
<h3>First Principles: Simple Yield Definition</h3><p><strong>B is correct.</strong> The Simple Yield (sometimes called the Japanese Simple Yield) is a specific yield measure defined as the sum of the coupon payment and the straight-line amortization of the gain (or loss), divided by the flat price. It simplifies the compound interest mechanism into a linear one.</p><p>$$ \text{Simple Yield} = \frac{\text{Coupon} + \text{Straight-Line Amortization}}{\text{Flat Price}} $$</p><p>1. **Calculate Straight-Line Amortization:**<br>The bond is at a discount (94.00), so the investor gains $100 - 94 = 6.00$ over 4 years.<br>$$ \text{Annual Amortization} = \frac{100 - 94}{4} = 1.50 $$</p><p>2. **Calculate Numerator (Total Linear Return):**<br>$$ \text{Coupon} + \text{Amortization} = 6.00 + 1.50 = 7.50 $$</p><p>3. **Calculate Simple Yield:**<br>$$ \text{Simple Yield} = \frac{7.50}{94.00} \approx 0.07978 = 7.98\% $$</p><p>A is incorrect because it is the Current Yield ($6/94$).</p><p>C is incorrect because it likely approximates the YTM using the approximation formula with average price in the denominator ($7.5 / 97 = 7.73\%$) or similar errors.</p>
Question 36 of 57
A 3-year corporate bond has a YTM of 6.82%. The interpolated 3-year government bond yield is 4.33%. What is the G-spread in basis points?
id: 9
model: Claude Sonnet
topic: G-Spread Calculation
Explanation
<h3>First Principles Thinking: Yield Differential</h3><p><strong>B is correct.</strong> G-spread (government spread) is the simple difference between a bond's YTM and its government benchmark yield, expressed in basis points. Calculation: G-spread = corporate YTM - government yield = 6.82% - 4.33% = 2.49% = 249 basis points. One basis point = 0.01%, so 2.49% × 100 = 249 bp. This spread compensates investors for credit risk, liquidity risk, and other factors beyond the risk-free government rate. The G-spread uses a single discount rate (YTM) comparison, not the full term structure like Z-spread.</p><p>A is incorrect: 149 basis points results from calculation error, possibly computing 1.49% difference instead of 2.49%. This might stem from misaligning decimal places or subtracting in the wrong direction.</p><p>C is incorrect: 349 basis points suggests adding rather than subtracting the yields (6.82% + 4.33% = 11.15%), or miscalculating the percentage difference. The spread must be the corporate yield minus the government yield, not a sum.</p>
Question 37 of 57
Compared to the G-spread, the Z-spread accounts for:
id: 14
model: Claude Sonnet
topic: Z-Spread Characteristics
Explanation
<h3>First Principles Thinking: Term Structure Recognition</h3><p><strong>A is correct.</strong> The G-spread uses a single YTM benchmark point, implicitly assuming a flat yield curve. The Z-spread (zero-volatility spread) adds a constant spread to each spot rate along the benchmark curve, then values each cash flow at its specific maturity's adjusted spot rate. This respects the yield curve's shape—upward-sloping, flat, or inverted. By discounting each cash flow at the appropriate maturity-specific rate plus spread, Z-spread provides a more accurate measure when the yield curve is non-flat. The method finds the constant spread that, when added to all spot rates, produces the bond's market price.</p><p>B is incorrect: The Z-spread does not remove embedded options; that is the role of the option-adjusted spread (OAS). Z-spread includes the option impact, just like raw yield, but accounts for yield curve shape rather than option value.</p><p>C is incorrect: Both G-spread and Z-spread capture credit and liquidity risk premiums—they differ in how they handle the term structure, not in which risk factors they include. Neither explicitly isolates credit from liquidity risk.</p>
Question 38 of 57
Assertion (A): For a callable corporate bond, the Option-Adjusted Spread (OAS) will typically be higher than the bond's Z-spread.
Reason (R): The Z-spread includes compensation for both the issuer's credit risk and the risk that the issuer will exercise the call option against the investor.
id: 2
model: Kimi k2
topic: Option-Adjusted Spread (OAS) vs. Z-Spread
Explanation
Assertion A is false. The OAS removes the value of the embedded call option (which is a cost to the investor/benefit to the issuer) from the spread. Therefore, the OAS is *lower* than the Z-spread (OAS = Z-spread - Option Cost in bps). Reason R is true: The Z-spread indeed reflects the total spread required by the market, which includes compensation for the call risk.
Question 39 of 57
An analyst is comparing a corporate bond quoted with a yield-to-maturity of 4.80% on a semiannual bond basis to a mortgage-backed security quoted on a monthly basis. To ensure a direct comparison, the analyst converts the bond's yield to a monthly annualized yield. The result is closest to:
id: 1
model: Gemini
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
<h3>First Principles: Periodicity Conversion</h3><p><strong>A is correct.</strong> Yield measures for fixed-income instruments depend heavily on the assumed periodicity (frequency of compounding). To compare yields with different periodicities, one must equate their Effective Annual Rates (EAR).</p><p>The governing relationship is:</p><p>$$ \left(1 + \frac{APR_m}{m}\right)^m = \left(1 + \frac{APR_n}{n}\right)^n $$</p><p>Where $m$ and $n$ are the compounding periods per year.</p><p>1. **Calculate EAR of the Semiannual Bond:**<br>Given $APR_2 = 4.80\%$, the semiannual periodic rate is $2.40\%$.<br>$$ EAR = (1.024)^2 - 1 \approx 1.048576 - 1 = 4.8576\% $$</p><p>2. **Convert EAR to Monthly Annualized Yield ($APR_{12}$):**<br>We need to find $APR_{12}$ such that:<br>$$ \left(1 + \frac{APR_{12}}{12}\right)^{12} = 1.048576 $$<br>Taking the 12th root:<br>$$ 1 + \frac{APR_{12}}{12} = (1.048576)^{1/12} \approx 1.0039605 $$<br>$$ \frac{APR_{12}}{12} = 0.0039605 $$<br>$$ APR_{12} = 0.0039605 \times 12 \approx 4.7526\% $$</p><p><strong>Mechanism:</strong> As the frequency of compounding increases (from 2 to 12), the stated annual rate required to achieve the same effective return decreases because the interest-on-interest effect is stronger.</p><p>B is incorrect because it ignores the periodicity conversion.</p><p>C is incorrect because it incorrectly assumes higher frequency requires a higher nominal rate (it's the opposite).</p>
Question 40 of 57
A corporate bond is quoted at a spread of +235 basis points over an interpolated 12-year U.S. Treasury bond yield. This spread is a(n):
id: 21
model: Claude Sonnet
topic: G-Spread Definition
Explanation
<h3>First Principles Thinking: Spread Type Taxonomy</h3><p><strong>A is correct.</strong> A G-spread (government spread) measures the difference between a bond's YTM and a government benchmark yield of equivalent maturity. The problem specifies the spread is over a U.S. Treasury yield, which is the classic government benchmark. Whether using an actual Treasury or interpolating between available maturities does not change the classification—it is still a G-spread because the reference is a government security. The letter G denotes the government benchmark nature. This is the most common spread measure in markets using liquid government bond benchmarks.</p><p>B is incorrect: I-spread (interpolated spread) refers to spreads over swap rates, not government yields. I-spreads are common in euro-denominated markets where swap rates serve as benchmarks, but the problem uses Treasury yields, not swap rates.</p><p>C is incorrect: Z-spread (zero-volatility spread) is calculated differently—it is the constant spread added to each spot rate on the benchmark curve such that the bond's discounted cash flows equal its price. The problem describes a simple YTM differential, not a Z-spread calculation involving the entire spot curve.</p>
Question 41 of 57
For a callable bond, relative to its option-adjusted spread, its Z-spread is most likely:
id: 16
model: Claude Sonnet
topic: OAS vs Z-Spread for Callable Bonds
Explanation
<h3>First Principles Thinking: Option Value Decomposition</h3><p><strong>C is correct.</strong> A callable bond's yield (and thus Z-spread) includes compensation for bearing call risk—the issuer's right to redeem the bond early when rates fall. The option-adjusted spread (OAS) removes this option component, isolating the spread due to credit, liquidity, and taxation. Relationship: Z-spread = OAS + option value (in basis points). Since option value is positive (the call option has value to the issuer, disadvantaging the investor), Z-spread exceeds OAS. Example: if Z-spread is 180 bp and call option value is 60 bp, then OAS = 180 - 60 = 120 bp. The Z-spread rewards all risks; OAS rewards only non-option risks.</p><p>A is incorrect: Z-spread cannot be lower than OAS for a callable bond because it includes the option value component. This reverses the relationship, incorrectly suggesting that removing the option increases the spread.</p><p>B is incorrect: Z-spread equals OAS only if the option has zero value, which occurs only for bonds with no embedded options or worthless embedded options. For typical callable bonds with valuable call options, the two measures differ.</p>
Question 42 of 57
Holding the effective annual yield constant, if the periodicity of a bond increases, its stated YTM will:
id: 7
model: Claude Sonnet
topic: Periodicity and Stated YTM
Explanation
<h3>First Principles Thinking: Yield Quotation Mechanics</h3><p><strong>A is correct.</strong> Stated YTM equals the periodic rate multiplied by the number of periods per year (periodicity). For a fixed effective annual yield (EAY), as periodicity increases, the periodic rate must decrease because more frequent compounding achieves the same annual return with smaller per-period rates. Example: EAY of 5% requires stated YTM of 4.94% with semiannual periodicity [solve (1 + YTM/2)² = 1.05] but only 4.91% with quarterly periodicity [solve (1 + YTM/4)⁴ = 1.05]. Higher compounding frequency means smaller stated rates produce equivalent effective yields.</p><p>B is incorrect: Stated YTM cannot remain unchanged when periodicity changes if EAY is constant. This misconception ignores that compounding frequency affects how periodic rates translate to effective annual returns.</p><p>C is incorrect: Increasing periodicity increases EAY for a given stated YTM, so holding EAY constant requires stated YTM to decrease, not increase. This reverses the cause-and-effect relationship between periodicity and stated rates.</p>
Question 43 of 57
An analyst is using matrix pricing to estimate the yield on an illiquid 3-year corporate bond. The bond is rated A-rated. Data for comparable liquid benchmark bonds is as follows:
- 2-year Benchmark Yield: 2.15%
- 5-year Benchmark Yield: 3.45%
The analyst estimates a required credit spread of 120 basis points over the interpolated benchmark. The estimated yield for the 3-year bond is closest to:
id: 3
model: Gemini
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
<h3>First Principles: Matrix Pricing and Linear Interpolation</h3><p><strong>C is correct.</strong> Matrix pricing estimates the yield of an illiquid bond by adding a credit spread to an interpolated benchmark yield matching the bond's maturity.</p><p>1. **Interpolate the Benchmark Yield:**<br>The bond has a 3-year maturity. The benchmarks are 2-year and 5-year.<br>Total interval = $5 - 2 = 3$ years.<br>Distance from lower bound = $3 - 2 = 1$ year.<br>Interpolation weight = $1 / 3$.<br>$$ \text{Benchmark}_{3y} = 2.15\% + \frac{1}{3} \times (3.45\% - 2.15\%) $$<br>$$ \text{Benchmark}_{3y} = 2.15\% + \frac{1}{3} \times (1.30\%) $$<br>$$ \text{Benchmark}_{3y} = 2.15\% + 0.433\% = 2.583\% $$</p><p>2. **Add the Credit Spread:**<br>Estimated Yield = Interpolated Benchmark + Spread<br>Estimated Yield = $2.583\% + 1.20\% = 3.783\%$.</p><p>A is incorrect because it is the benchmark yield without the spread.</p><p>B is incorrect because it incorrectly interpolates or calculates the spread application.</p>
Question 44 of 57
An investor buys a bond with a 5% annual coupon at a discount. Which of the following scenarios would *most likely* result in the realized rate of return being equal to the initial Yield-to-Maturity?
id: 11
Explanation
<h3>First Principles Thinking</h3>
<p>The <strong>Yield-to-Maturity (YTM)</strong> is an internal rate of return (IRR) calculation. A key assumption of the IRR method is that intermediate cash flows (coupons) are reinvested at the IRR itself.</p>
<p><strong>Logic:</strong>
1. If coupons are reinvested at a rate <em>lower</em> than the YTM (e.g., the lower coupon rate of a discount bond), the future value of the reinvested cash will be lower than what the YTM formula assumes. Thus, realized return < YTM.
2. If coupons are reinvested at the YTM, the 'interest-on-interest' component grows exactly as needed to validate the initial YTM calculation.</p>
<p>Therefore, B is the correct condition. Option A is incorrect because for a discount bond, Coupon Rate < YTM. Reinvesting at the lower coupon rate drags down the return.</p>
Question 45 of 57
Assertion (A): For a callable bond trading at a significant premium to par value in USD, the Yield-to-Worst (YTW) is most likely the Yield-to-First-Call rather than the Yield-to-Maturity.
Reason (R): The amortization of the bond's premium is effectively accelerated if the bond is called early, which reduces the investor's annualized rate of return.
id: 3
model: Kimi k2
topic: Yield-to-Worst logic for Premium Bonds
Explanation
When a bond trades at a premium, the investor loses that premium over the life of the bond. If the bond is called early (at the call price, which is usually lower than the market price), this loss happens faster, dragging down the return. Thus, the yield-to-call is the lowest potential yield (YTW). The reason correctly identifies this accelerated amortization mechanism.
Question 46 of 57
A 15-year, zero-coupon, $1,000 par value bond trades at $331.40. Based on semiannual compounding, what is its YTM?
id: 10
model: Claude Sonnet
topic: Zero-Coupon Bond YTM
Explanation
<h3>First Principles Thinking: Single Cash Flow Discounting</h3><p><strong>C is correct.</strong> For a zero-coupon bond, only one cash flow exists—the par value at maturity. Price equals par discounted at the yield: 331.40 = 1000 / (1 + r/2)³⁰, where r is the stated annual YTM and we have 30 semiannual periods (15 years × 2). Calculator: N=30, FV=1000, PMT=0, PV=-331.40, CPT I/Y = 3.750% (semiannual). Quoted YTM = 2 × 3.750% = 7.50%. The large discount (price well below par) and long maturity combine to produce this yield. Boundary check: 331.40/1000 = 0.3314, and (1.0375)³⁰ ≈ 3.02, so 1/3.02 ≈ 0.331, confirming our solution.</p><p>A is incorrect: 3.75% is the semiannual periodic rate, not the quoted annual YTM. This error fails to apply the market convention of doubling the semiannual rate to get the stated annual yield.</p><p>B is incorrect: 5.15% appears to use incorrect compounding, possibly attempting to calculate an effective annual yield but making computational errors. The standard quotation for semiannual bonds requires simple multiplication of the periodic rate by 2.</p>
Question 47 of 57
A bond has a stated YTM of 10% with quarterly periodicity. What is its effective annual yield?
id: 15
model: Claude Sonnet
topic: Effective Annual Yield with Quarterly Periodicity
Explanation
<h3>First Principles Thinking: Quarterly Compounding</h3><p><strong>C is correct.</strong> With quarterly periodicity, a 10% stated YTM means 2.5% per quarter (10%/4). Effective annual yield compounds this quarterly rate over four quarters: EAY = (1 + 0.10/4)⁴ - 1 = (1.025)⁴ - 1. Calculating: 1.025 × 1.025 = 1.050625, then 1.050625 × 1.050625 ≈ 1.1038, so EAY ≈ 10.38%. The more frequent compounding (quarterly vs. semiannual) produces a higher effective yield for the same stated rate. Each quarter's earnings are reinvested to generate earnings in subsequent quarters, creating compounding beyond simple interest.</p><p>A is incorrect: 10% is merely the stated YTM, which ignores intra-year compounding. This treats quarterly payments as producing no reinvestment benefit, equivalent to simple rather than compound interest.</p><p>B is incorrect: 10.25% is the effective annual yield for semiannual periodicity [(1.05)² - 1], not quarterly. This error uses two compounding periods instead of four, confusing the payment frequency.</p>
Question 48 of 57
The 1-year Treasury yields 3% and the 4-year Treasury yields 5%. What is the interpolated 3-year Treasury yield?
id: 12
model: Claude Sonnet
topic: Yield Interpolation
Explanation
<h3>First Principles Thinking: Linear Interpolation</h3><p><strong>B is correct.</strong> When a benchmark with exact maturity is unavailable, we interpolate linearly between adjacent maturities. The 3-year point is 2 years beyond the 1-year and 1 year before the 4-year. Fraction traveled: (3-1)/(4-1) = 2/3. Yield increment: 5% - 3% = 2%. Interpolated yield = starting yield + fraction × increment = 3% + (2/3) × 2% = 3% + 1.33% = 4.33%. This assumes a linear yield curve segment between the 1-year and 4-year points. While real yield curves are rarely linear, linear interpolation provides a reasonable approximation for spread calculations.</p><p>A is incorrect: 4% is the simple average of 3% and 5%, which ignores the maturity structure. This treats 3 years as equidistant from 1 and 4 years, but 3 years is actually 2/3 of the way from 1 to 4 years.</p><p>C is incorrect: 4.67% results from miscalculating the fraction—possibly using 2 years from 1-year or confusing the direction. The correct progression must place 3-year yield between 3% and 5%, closer to 5% since 3 years is 2/3 toward the 4-year maturity.</p>
Question 49 of 57
Consider the following statements regarding yield conventions and measures:
(1) The true yield is never higher than the street convention yield because weekends and holidays delay the time to payment.
(2) The government equivalent yield restates a corporate bond’s yield-to-maturity based on a 30/360 day count to one based on an actual/actual day count.
(3) The simple yield is calculated as the sum of coupon payments plus the straight-line amortized share of the gain or loss, divided by the flat price.
Which of the statements given above are correct?
id: 1
model: ChatGPT
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
Statement (1) is correct because the true yield accounts for the delay in payments due to weekends and holidays, which reduces the yield compared to the street convention yield that assumes payments on scheduled dates. Statement (2) is correct because the government equivalent yield is explicitly defined as a measure that restates a yield based on a 30/360 day count (typical for corporates) to an actual/actual basis (typical for governments). Statement (3) is correct as it accurately defines the simple yield, which is used mostly for Japanese government bonds. Therefore, all three statements are correct.
Question 50 of 57
Calculate the price of a 2-year, 5% annual coupon bond if the spot rates (zero-coupon rates) for Year 1 and Year 2 are 4% and 6%, respectively. (Par value = USD 100).
id: 8
Explanation
<h3>First Principles Thinking</h3>
<p>We must discount each cash flow by its specific spot rate.</p>
<p><strong>Cash Flows:</strong>
Year 1: $5 (Coupon)
Year 2: $105 (Coupon + Principal)</p>
<p><strong>Discount Factors:</strong>
$PV_1 = 5 / (1 + 0.04)^1 = 5 / 1.04 \approx 4.8077$
$PV_2 = 105 / (1 + 0.06)^2 = 105 / 1.1236 \approx 93.4496$</p>
<p><strong>Total Price:</strong>
$Price = 4.8077 + 93.4496 = 98.2573$
<em>Wait, let me double check the calculation in head/approx.</em>
$5/1.04 \approx 4.81$
$105/1.1236$: $105/1.12 = 93.75$. Denominator is slightly bigger, so result is slightly smaller. $93.45$ looks right.
Sum $\approx 98.26$.
<em>Checking the options:</em> 98.17 vs 98.34. My calc is right in the middle. Let's do precise math.
$5/1.04 = 4.80769$
$105 / (1.06*1.06) = 105 / 1.1236 = 93.4496$
Sum = $98.257$.
<em>Why are the options slightly off?</em> Perhaps the question implies semiannual discounting? "Annual coupon bond... spot rates..." Usually implies annual spot rates. Maybe the spot rates are continuously compounded? No, standard CFA level 1 is discrete.
Let's re-read the options. Maybe A is using YTM=6%? $5/1.06 + 105/1.06^2 = 4.71 + 93.45 = 98.16$. This matches Option A very closely ($98.17$).
So if YTM was used at the 2-year spot rate, we get A.
But the correct method is spot rates.
Maybe Option B is using something else?
Let's check Option B calculation again. Is it possible the spot rates are semi-annual bond equivalent?
If 4% and 6% are BEY (Bond Equivalent Yields):
Year 1 CF is at year 1. Rate is 4% BEY -> 2% semi. $(1.02)^2 = 1.0404$.
$PV_1 = 5 / 1.0404 = 4.8058$
Year 2 CF is at year 2. Rate is 6% BEY -> 3% semi. $(1.03)^4 = 1.1255$.
$PV_2 = 105 / 1.1255 = 93.29$
Sum = $98.09$. No match.
Let's re-calculate $105 / 1.1236$. $100/1.1236 = 89$. $5/1.1236 = 4.45$. $89+4.45 = 93.45$. Correct.
So the correct answer is 98.26.
Option B is 98.34. Option A is 98.17.
Let's check if the Year 1 spot rate is 4% but Year 2 is 5%? No.
Let's adjust the question to match the math for a clear answer.
If I change Year 2 spot to 5.5%?
$105 / 1.113 = 94.34$. Total $99.1$.
Let's adjust the options to match 98.26 exactly. Or change the input numbers to make it simpler.
<strong>New Inputs:</strong> Year 1 Spot = 5%, Year 2 Spot = 6%.
$PV_1 = 5/1.05 = 4.76$
$PV_2 = 105/1.1236 = 93.45$
Sum = $98.21$.
Let's stick to the calculation: $5/1.04 + 105/1.1236 = 98.26$.
I will provide option C as $98.26$ and adjust the others.
<em>Wait, let's keep the question "Tricky".</em>
Maybe the coupon is semiannual? "Annual coupon bond". No.
Let's assume the question asks for 98.26 and I will define Option B as 98.26.
<em>Self-Correction:</em> I will generate a new set of options for the JSON.
A: 98.17 (Calculated using flat 6% YTM)
B: 98.26 (Correct Spot Rate pricing)
C: 99.08 (Calculated using flat 4% YTM - impossible but distractor)
Price at 4% flat: $5/1.04 + 105/1.0816 = 4.81 + 97.08 = 101.89$.
Price at 5% flat (avg): $5/1.05 + 105/1.1025 = 4.76 + 95.23 = 100$.
So 98.26 is the correct value.</p>
Question 51 of 57
A floating-rate note (FRN) has a quoted margin (QM) of +120 bps and a required margin (discount margin, DM) of +150 bps. The reference rate is constant. This FRN will most likely trade at:
id: 5
Explanation
<h3>First Principles Thinking</h3>
<p>Pricing an FRN involves comparing what the bond <em>pays</em> vs. what the market <em>requires</em>.</p>
<p>1. <strong>Numerator (Cash Flows):</strong> The bond pays Reference Rate + Quoted Margin (QM = +120 bps).
2. <strong>Denominator (Discount Rate):</strong> The market requires Reference Rate + Discount Margin (DM = +150 bps).
3. <strong>Comparison:</strong> The bond is paying 120 bps over the index, but investors demand 150 bps over the index. The bond is paying <em>less</em> than the required rate of return.
4. <strong>Result:</strong> When the coupon rate (QM) is lower than the required yield (DM), the price must adjust downward to boost the effective return. Therefore, the bond trades at a <strong>discount</strong>.</p>
Question 52 of 57
Yield to worst for a callable bond is defined as:
id: 17
model: Claude Sonnet
topic: Yield to Worst
Explanation
<h3>First Principles Thinking: Worst-Case Return Scenario</h3><p><strong>A is correct.</strong> Yield to worst identifies the minimum yield an investor could realize across all possible redemption scenarios—maturity or any call date at its respective call price. For each possibility, calculate the yield: YTM (if held to maturity), yield to first call, yield to second call, etc. The lowest of these is the yield to worst. This conservative measure protects investors by revealing the worst plausible outcome if the issuer exercises the call option in its own interest. It assumes the issuer acts optimally from its perspective, which typically means calling when yields are low (disadvantaging the bondholder).</p><p>B is incorrect: Yield to worst does not consider default scenarios; it examines different redemption paths assuming the issuer honors its obligations. Default analysis involves recovery rates and credit spreads, not yield to worst calculations.</p><p>C is incorrect: YTM minus call option value conceptually describes the option-adjusted yield, not yield to worst. Yield to worst is a scenario-based minimum yield calculation, not an option-value adjustment.</p>
Question 53 of 57
Current yield measures which component of bond return?
id: 8
model: Claude Sonnet
topic: Current Yield Definition
Explanation
<h3>First Principles Thinking: Return Components</h3><p><strong>A is correct.</strong> Current yield is defined as annual coupon payment divided by bond price, capturing only the income stream. It explicitly excludes two other return sources: capital gains/losses (from price changes as the bond moves toward maturity or market yields shift) and reinvestment income (from reinvesting coupons at prevailing rates). Formula: current yield = annual coupon / price. This simplicity makes current yield easy to calculate but incomplete for assessing total return. It's useful for quick income assessment but ignores the pull-to-par effect and time value considerations embedded in YTM.</p><p>B is incorrect: Current yield does not incorporate capital gains or losses. This misconception confuses current yield with measures like simple yield (which includes straight-line amortization) or YTM (which fully accounts for price convergence to par).</p><p>C is incorrect: Total return including reinvestment income is measured by holding period return or realized yield, not current yield. Current yield is a static snapshot of income relative to price, not a dynamic measure of compounded returns.</p>
Question 54 of 57
Consider the following statements regarding the Z-spread:
(1) The Z-spread is the constant yield spread added to each benchmark spot rate to make the present value of a bond’s cash flows equal its price.
(2) The Z-spread is also known as the static spread because it is constant and has zero volatility.
(3) For a bond with a principal repayment at maturity and an upward-sloping yield curve, the Z-spread will always be identical to the G-spread.
Which of the statements given above are correct?
id: 7
model: ChatGPT
topic: Yield and Yield Spread Measures for Fixed-Rate Bonds
Explanation
Statement (1) is correct as it defines the Z-spread calculation using the spot curve. Statement (2) is correct because the term 'static spread' refers to the zero-volatility assumption of the Z-spread. Statement (3) is incorrect because the G-spread uses a single point on the curve (YTM), whereas the Z-spread uses the entire spot curve; they will typically differ unless the yield curve is perfectly flat. Therefore, only statements (1) and (2) are correct.
Question 55 of 57
A bond has a YTM of 4% on a semiannual bond basis. What is the equivalent yield on a quarterly bond basis?
id: 18
model: Claude Sonnet
topic: Yield Periodicity Conversion
Explanation
<h3>First Principles Thinking: Equivalent Periodic Rates</h3><p><strong>B is correct.</strong> A 4% yield on semiannual basis means 2% per 6-month period. To convert to quarterly basis, first find the effective quarterly rate equivalent to 2% semiannually: (1 + quarterly rate)² = 1.02, so quarterly rate = 1.02^(1/2) - 1 = 0.00995 or 0.995%. The quarterly-basis quotation multiplies by 4: 4 × 0.995% = 3.98%. This maintains the same effective annual yield (1.02² = 1.0404 from semiannual; 1.00995⁴ ≈ 1.0404 from quarterly) while adjusting the stated rate for different periodicity. Higher periodicity requires lower stated rates to achieve equivalent effective yields.</p><p>A is incorrect: 2% is the semiannual periodic rate, not the quarterly-basis quotation. This error fails to convert the periodicity, simply stating the semiannual rate rather than its quarterly equivalent.</p><p>C is incorrect: 4.04% is the effective annual yield, not the quarterly-basis stated yield. This uses the annual compounding result rather than converting to a quarterly quotation convention (4 times the quarterly periodic rate).</p>
Question 56 of 57
A 5-year, semiannual-pay 6% bond trades at 102 and is callable at 102 in 3 years. What is the yield to first call?
id: 6
model: Claude Sonnet
topic: Yield to First Call
Explanation
<h3>First Principles Thinking: Call Date IRR</h3><p><strong>B is correct.</strong> Yield to call calculates the IRR if the bond is called at the first call date and price. We have 3 years (6 semiannual periods) until call, semiannual coupon of 3 (6%/2 of par 100), call price of 102, and current price of 102. Calculator: N=6, PMT=3, FV=102, PV=-102, CPT I/Y = 2.941%. Quoted annual yield = 2 × 2.941% = 5.88%. The investor receives coupons for 6 periods plus the call price of 102, all discounted to present value of 102. Because price equals call price and the bond pays coupons, the yield exceeds zero even though there's no capital gain.</p><p>A is incorrect: 5.54% is the YTM (yield to maturity in 5 years at par 100), not the yield to call. This error uses the wrong terminal date and redemption value—maturity instead of first call date.</p><p>C is incorrect: 6% is the coupon rate. This misconception assumes yield to call equals coupon rate, but even when purchase price equals call price, coupons still generate return, producing a yield below the coupon rate for a premium/par situation.</p>
Question 57 of 57
Assertion (A): To provide the same Effective Annual Rate (EAR) to an investor, a bond paying quarterly coupons must typically carry a higher stated annual yield than a comparable bond paying semiannual coupons.
Reason (R): Increasing the frequency of coupon compounding allows a lower nominal stated rate to produce the same effective yield due to the interest-on-interest effect.
id: 4
model: Kimi k2
topic: Periodicity and Effective Annual Rate
Explanation
Assertion A is false. Because quarterly compounding happens more frequently than semiannual compounding, the interest-on-interest effect is stronger. Therefore, the stated nominal rate can be *lower*, not higher, to achieve the same EAR. Reason R is true and correctly describes the principle of compounding frequency.