CUET UG Applied Mathematics Booster Test 3 - Bonds, Yield and Bond Valuation -

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CUET UG Applied Mathematics Booster Test 3 - Bonds, Yield and Bond Valuation

⏱️ 30 Minutes

❓ 20 Questions

📌 Answers are locked once submitted — results and explanations appear at the end.

CUET UG Applied Mathematics Booster Test 3 - Bonds, Yield and Bond Valuation

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QUESTION 1 OF 20

In a network graph representing financial entities, if a bond is modeled as a directed edge from Node A (Lender) to Node B (Borrower), the weight of this edge when reversed at maturity represents:

Answer Review

1 In a network graph representing financial entities, if a bond is modeled as a directed edge from Node A (Lender) to Node B (Borrower), the weight of this edge when reversed at maturity represents:

A The initial loan principal

B The equity share ownership

C The depreciation schedule

D The redemption price along with periodic interest payments

💡 Short Explanation

The bond initially transfers funds from lender to borrower. At maturity, payments flow back to the lender. These include coupon payments and redemption of principal.

✅ Correct Answer Explanation

A bond represents a debt relationship where the lender provides funds to the borrower. During the bond's life: The borrower pays periodic coupon (interest) payments. At maturity, the borrower repays the redemption amount (principal). In a directed graph, reversing the direction of the financial flow at maturity represents these payments returning to the lender. Therefore, the reversed edge represents the redemption price together with periodic interest payments. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: The initial loan principal.
Incorrect because this represents the original flow from lender to borrower, not the reverse flow.
Option B: The equity share ownership.
Incorrect because bonds do not represent ownership.
Option C: The depreciation schedule.
Incorrect because depreciation has no relation to bond cash flows.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Interpret the financial meaning of the reverse cash-flow direction in the network graph.

Final Logic:

Reverse cash flow represents repayment of principal and coupon interest; therefore Option D.

🧠 Memory Trick

"Reverse Edge = Money Returns."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Definition of Bond ═════════════════════════════════════════════════════

2 A bond specifies equal time intervals (in months) between interest payments. For four consecutive payouts, the intervals are 6, 6, 6, and 6 months. What is the 2-period moving average of these intervals?

A 3

B 12

C 6

D 0

💡 Short Explanation

A moving average uses consecutive observations. Every interval equals 6 months. Therefore, every moving average is also 6.

✅ Correct Answer Explanation

A 2-period moving average is calculated by averaging two consecutive observations. For the last two intervals, (6 + 6) / 2 = 6 Since every interval is identical, every 2-period moving average equals 6 months. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: 3
Incorrect because the average of 6 and 6 is not 3.
Option B: 12
Incorrect because 12 is the sum, not the average.
Option D: 0
Incorrect because all intervals are positive.

🎯 Strategy

used

Substitution

Application:

Substitute the last two observations into the moving-average formula.

Final Logic:

Since
(6 + 6) / 2 = 6
Option C is correct.

🧠 Memory Trick

"Equal Numbers → Same Average."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Bond Contract Features

3 A company issues 100 bonds. Out of these, 40 bonds have a face value of ₹1,000 and 60 bonds have a face value of ₹2,000. What is the probability of randomly selecting a bond with face value ₹1,000?

A (0.6)

B (0.4)

C (0.5)

D (1.0)

💡 Short Explanation

Favorable bonds = 40. Total bonds = 100. Divide favorable outcomes by total outcomes.

✅ Correct Answer Explanation

The probability is P = Number of favorable bonds / Total number of bonds Substituting, P = 40 / 100 = 0.4 Therefore, the probability of selecting a ₹1,000 face-value bond is 0.04 Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: (0.6)
Incorrect because it represents the probability of selecting a ₹2,000 bond.
Option C: (0.5)
Incorrect because the favorable outcomes are not half the total.
Option D: (1.0)
Incorrect because selection is not certain.

🎯 Strategy

used

Substitution

Application:

Apply the probability formula using the given frequencies.

Final Logic:

Since
40 / 100 = 0.4
Option B is correct.

🧠 Memory Trick

"Probability = Favorable ÷ Total."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Face Value

4 For a theoretical bond with infinite maturity, the present value of the redemption amount is given by
\(C(1+i)^{-n}.\)
As \(n\rightarrow \infty\), what does this expression approach?

A (0)

B \(\infty\)

C (C)

D (1)

💡 Short Explanation

The discount factor decreases as (n) increases. For positive interest rates, the discount factor approaches zero. Hence, the present value of redemption tends to zero.

✅ Correct Answer Explanation

The present value of the redemption amount is P = C(1 + i)^(-n) where: C = Redemption value i > 0 = Interest rate n = Number of periods As n → ∞, (1 + i)^(-n) = 1/(1 + i)^n → 0 Therefore, lim(n → ∞) [C(1 + i)^(-n)] = C × 0 = 0 This means that a payment received infinitely far in the future has negligible present value. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: (\infty)
Incorrect because discounting decreases the present value over time.
Option C: (C)
Incorrect because the redemption amount is heavily discounted as maturity approaches infinity.
Option D: (1)
Incorrect because the expression approaches zero, not one.

🎯 Strategy

used

Elimination

Application:

Apply the limit of the compound discount factor for very large values of (n).

Final Logic:

Since
Plain text:
(1 + i)^(-n) → 0
the present value also approaches zero; therefore Option A.

🧠 Memory Trick

"Infinite Delay ⇒ Zero Present Value."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Present Value of Redemption

5 In a graphical interpretation, if the total area representing the face value is (F) and the area In a graphical interpretation, if the total area representing the face value is \(F\) and the area representing the market price is \(P_{0}\), where \(P_{0}<F\), what represents the discount?

A \(F-P_{0}\)

B \(P_{0}-F\)

C \(\frac{F}{P_{0}}\)

D \(F+P_{0}\)

💡 Short Explanation

Discount is the excess of face value over market price. Face value exceeds market price for a discount bond. Subtract market price from face value.

✅ Correct Answer Explanation

A bond sells at a discount when P₀ < F The amount of discount equals Discount = F − P₀ This represents the difference between the face value and the lower market price. Therefore, Discount = F − P₀.Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: (P₀ − F)
Incorrect because it produces a negative value for a discount bond.
Option C: (F/P₀)
Incorrect because this is a ratio, not the discount amount.
Option D: (F + P₀)
Incorrect because adding the two values has no financial meaning here.

🎯 Strategy

used

Substitution

Application:

Use the definition of discount by subtracting the market price from the face value.

Final Logic:

Since
Plain text:
F > P₀,
the discount equals
F − P₀.
therefore Option A.

🧠 Memory Trick

"Discount = Face − Market."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Discount Bond

6 Let a scalar (k) relate market price and face value such that
\(\vec{P}_{market}=k\vec{F}_{face}.\)
For a bond selling at a premium, which condition must (k) satisfy?

A (k=0)

B (k<1)

C (k=1)

D (k>1)

💡 Short Explanation

Premium bonds sell above face value. Therefore, market price exceeds face value. The scaling factor must be greater than one.

✅ Correct Answer Explanation

Given P⃗market = kF⃗face The scalar k represents the ratio k = Market Price / Face Value For a premium bond, Market Price > Face Value Therefore, k > 1. Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: (k=0)
Incorrect because a bond cannot have zero market price under normal conditions.
Option B: (k<1)
Incorrect because this represents a discount bond.
Option C: (k=1)
Incorrect because this represents a bond selling at par.

🎯 Strategy

used

Elimination

Application:

Interpret the scalar (k) as the ratio of market price to face value and compare it with premium bond conditions.

Final Logic:

Since premium bonds satisfy
Plain text:
Market Price > Face Value,
the scalar must satisfy
k > 1.
therefore Option D.

🧠 Memory Trick

"Premium ⇒ Ratio Above 1."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Premium Bond

7 Assertion (A):
The coupon rate is calculated as the coupon payment (C) expressed as a percentage of the face value (F).
Reason (R):
The coupon rate represents the annual interest rate paid by the issuer to the bondholder.

A Both A and R are false

B A is true, R is false

C Both A and R are true, and R is the correct explanation of A

D A is false, R is true

💡 Short Explanation

Coupon rate measures annual interest relative to face value. It is fixed when the bond is issued. Both the assertion and reason correctly describe the coupon rate.

✅ Correct Answer Explanation

The coupon rate is calculated as Plain text: Coupon Rate = (Annual Coupon Payment / Face Value) × 100 Equivalently, i_d = R / F where: • R = Annual coupon payment • F = Face value Thus, the coupon payment can also be written as R = F × i_d The coupon rate represents the annual interest rate promised by the issuer, expressed as a percentage of the bond's face value. Therefore, both the Assertion and the Reason are true, and the Reason correctly explains the Assertion. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: Both A and R are false.
Incorrect because both statements are correct.
Option B: A is true, R is false.
Incorrect because the reason correctly defines the coupon rate.
Option D: A is false, R is true.
Incorrect because the assertion correctly states the coupon-rate formula.

🎯 Strategy

used

Elimination

Application:

Recall the definition and formula for the coupon rate before evaluating the assertion and reason.

Final Logic:

Since the coupon rate equals annual coupon payment divided by face value and represents the annual interest rate, Option C is correct.

🧠 Memory Trick

"Coupon Rate = Coupon ÷ Face Value."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Coupon Rate

8 Arrange the steps to compute the periodic dividend payment (R):
1. Multiply the face value \(C\) by the periodic rate \(i_{d}\)
2. Identify the nominal rate of interest
3. Compute the rate per period \(i_{d}\)
4. Determine the face value \(C\)

A 1, 2, 3, 4

B 4, 2, 3, 1

C 2, 4, 1, 3

D 3, 1, 4, 2

💡 Short Explanation

First identify the face value. Then determine the nominal interest rate. Compute the periodic rate before calculating the coupon payment.

✅ Correct Answer Explanation

To compute the periodic dividend (coupon payment), follow these steps: Step 1: Determine the face value (C). Step 2: Identify the nominal rate of interest. Step 3: Convert it into the periodic rate (i_d), if necessary. Step 4: Calculate the periodic payment using R = C × i_d Thus, the correct sequence is 4 → 2 → 3 → 1 Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: 1, 2, 3, 4
Incorrect because multiplication cannot be performed before identifying the required quantities.
Option C: 2, 4, 1, 3
Incorrect because the periodic rate must be computed before multiplication.
Option D: 3, 1, 4, 2
Incorrect because the face value and nominal rate must be identified first.

🎯 Strategy

used

Elimination

Application:

Arrange the computational steps in the logical order followed during coupon calculation.

Final Logic:

Face Value → Nominal Rate → Periodic Rate → Coupon Payment; therefore Option B.

🧠 Memory Trick

"Face → Rate → Period → Multiply."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Periodic Coupon Payment

9 Match the yield types with their corresponding formulas or descriptions.

List I	List II
1. Coupon yield	a. Internal rate of return
2. Current yield	b. ( \dfrac{C}{F} \times 100 )
3. Yield to Maturity	c. ( \dfrac{C}{P_0} \times 100 )
4. Face Value	d. Par value

A 1–a, 2–b, 3–c, 4–d

B 1–c, 2–a, 3–d, 4–b

C 1–b, 2–c, 3–a, 4–d

D 1–d, 2–c, 3–b, 4–a

💡 Short Explanation

Coupon yield is based on face value. Current yield uses market price. Yield to Maturity is the internal rate of return.

✅ Correct Answer Explanation

The correct matching is: • Coupon Yield = (C / F) × 100 → b • Current Yield = (C / P₀) × 100 → c • Yield to Maturity → Internal rate of return (a) • Face Value → Par value (d) Thus, the correct matching is: • (1 → b) • (2 → c) • (3 → a) • (4 → d) Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A
Incorrect because Coupon Yield is not the internal rate of return.
Option B
Incorrect because Current Yield is not the internal rate of return.
Option D
Incorrect because Face Value means par value, not internal rate of return.

🎯 Strategy

used

Option Grouping

Application:

Recall the standard formulas for each type of bond yield before matching them.

Final Logic:

Coupon → Face Value, Current → Market Price, YTM → Internal Rate of Return, Face Value → Par Value; therefore Option C.

🧠 Memory Trick

"Coupon–Face, Current–Market, YTM–IRR."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Yield Concepts

10 A bond has a face value of ₹2000 and carries an 8% annual coupon rate. It is redeemable at the end of 10 years at 105% of face value. Determine the redemption value (C).
\(C=1.05\times 2000\)

A ₹2000

B ₹1000

C ₹2100

D ₹1050

💡 Short Explanation

Redemption is at 105% of face value. Multiply the face value by 1.05. The redemption value is ₹2100.

✅ Correct Answer Explanation

The redemption value is calculated as C = 1.05 × 2000 Thus, C = 2100. Therefore, the bondholder receives ₹2100 at maturity. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: ₹2000
Incorrect because redemption is above par (105%), not at par.
Option B: ₹1000
Incorrect because it is only half the face value.
Option D: ₹1050
Incorrect because it represents 105% of ₹1000, not ₹2000.

🎯 Strategy

used

Substitution

Application:

Use the redemption formula directly by substituting the given face value.

Final Logic:

Since
1.05 × 2000 = 2100
Option C is correct.

🧠 Memory Trick

"105% = 1.05 × Face Value."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Redemption Value

11 Which of the following mathematical statements is INCORRECT for a bond selling at a discount?

A Market price is less than its par value.

B Yield to Maturity (YTM) is less than the current yield.

C Current yield is greater than the coupon yield.

D \(YTM>Current Yield>Coupon Yield\)

💡 Short Explanation

Discount bonds sell below par. Their YTM is the highest yield. Hence, YTM cannot be less than current yield.

✅ Correct Answer Explanation

For a bond selling at a discount, the standard relationship is 1.05 × 2000 = 2100 This occurs because: Market price is below face value. Current yield exceeds the coupon yield. Yield to Maturity is highest because it includes both coupon income and capital gain at redemption. Therefore, the statement "YTM is less than the current yield" is mathematically incorrect. Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: Market price is less than its par value.
Correct because this is the definition of a discount bond.
Option C: Current yield is greater than the coupon yield.
Correct because the lower market price increases the current yield.
Option D:
YTM > Current Yield > Coupon Yield
Correct because this is the standard inequality for discount bonds.

🎯 Strategy

used

Elimination

Application:

Recall the yield relationships for discount bonds and eliminate the correct statements.

Final Logic:

Discount bonds always satisfy
YTM > Current Yield
therefore Option B is incorrect.

🧠 Memory Trick

"Discount → YTM Highest."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Yield Relations

12 When a bond sells at a premium, which of the following relations hold true?
I. Market price (>) Face value
II. Coupon yield (>) Current yield
III. Current yield (>) Yield to Maturity (YTM)

A I and II only

B II and III only

C I and III only

D I, II, and III

💡 Short Explanation

Premium bonds sell above face value. Coupon yield exceeds current yield. Current yield exceeds YTM.

✅ Correct Answer Explanation

For a premium bond: Since the market price exceeds face value Market Price > Face Value. Thus, Statement I is correct. The standard yield relationship is Coupon Yield > Current Yield > YTM. Therefore, Statement II is correct. Statement III is also correct. Hence, all three statements are true. Therefore, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: I and II only.
Incorrect because Statement III is also true.
Option B: II and III only.
Incorrect because Statement I is also true.
Option C: I and III only.
Incorrect because Statement II is also true.

🎯 Strategy

used

Elimination

Application:

Recall the standard inequalities associated with premium bonds before checking each statement.

Final Logic:

All three relationships hold for a premium bond; therefore Option D.

🧠 Memory Trick

"Premium → Price High, YTM Low."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Premium Bond Yield Relations

📄 Passage

"The theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present. The periodic payment is calculated as (R=C\times i_d). The final present value equation adds the present value of the annuity of periodic dividends and the present value of the redemption price."

According to the passage, how is the theoretical fair value of a bond determined from its expected cash flows?

A By compounding them to their future value

B By converting them into equity shares

C By multiplying them with the coupon rate

D By discounting them to the present using an appropriate rate

💡 Short Explanation

Bond valuation is based on present value. Future cash flows are discounted. Their sum gives the theoretical fair value.

✅ Correct Answer Explanation

According to the passage, a bond generates a stream of future cash flows consisting of: Periodic coupon payments, and Redemption value at maturity. Each future cash flow is discounted to its present value using an appropriate discount rate. The sum of these discounted values gives the theoretical fair value of the bond. Thus, Bond Value = PV of Coupons + PV of Redemption Value Therefore, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: By compounding them to their future value.
Incorrect because bond valuation uses discounting rather than compounding.
Option B: By converting them into equity shares.
Incorrect because bonds are debt instruments, not equity.
Option C: By multiplying them with the coupon rate.
Incorrect because coupon rate determines coupon payments but does not determine the present value.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Identify the valuation principle emphasized in the passage.

Final Logic:

Future cash flows are discounted to obtain present value; therefore Option D.

🧠 Memory Trick

"Bond Value = Discount Future Cash Flows."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Present Value Approach

📄 Passage

If the periodic payment is (R), the continuous present value of the cash flow stream over (n) periods is given by
\(\int_{0}^{n}\,Re^{-it} dt.\)
Evaluate this integral.

A \(\frac{R(1-e^{-in})}{i}\)

B \(Re^{in}\)

C \(\frac{R}{i}\)

D \(R(e^{-in}-1)\)

💡 Short Explanation

Integrate the exponential function. Apply the limits from (0) to (n). Simplify the resulting expression.

✅ Correct Answer Explanation

Evaluate ∫₀ⁿ Re^(-it) dt Since R is constant, = R ∫₀ⁿ e^(-it) dt Now, ∫ e^(-it) dt = -e^(-it) / i Applying the limits, R[-e^(-it)/i]₀ⁿ = R[(1 - e^(-in))/i] Hence, ∫₀ⁿ Re^(-it) dt = R(1 - e^(-in))/i Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

Option B:
Re^(in)
Incorrect because it is not the result of integration.
Option C:
R/i
Incorrect because this would be obtained only as n → ∞.
Option D:
R(e^(-in) − 1)
Incorrect because it omits the division by i and has the incorrect sign.
Incorrect because it is missing division by (i) and has the wrong sign.

🎯 Strategy

used

Substitution

Application:

Use the standard integral of an exponential function and apply the given limits.

Final Logic:

Integrating Re^(-it) from 0 to n gives
R(1 − e^(-in))/i
therefore Option A.

🧠 Memory Trick

"Integrate (e^{-x}) → Negative Exponential."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Continuous Present Value

15 Let the payment vector be
\(\vec{u}=[R_{1},R_{2},…,R_{n}]\)
and the discount vector be
\(\vec{v}=[d_{1},d_{2},…,d_{n}].\)
The present value (P_1) of these payments is given by:

A \(\vec{u}\times \vec{v}\)

B \(\vec{u}⋅\vec{v}\)

C \(∣\vec{u}∣+∣\vec{v}∣\)

D \(\frac{\vec{u}}{\vec{v}}\)

💡 Short Explanation

Each payment is multiplied by its discount factor. The discounted payments are added together. This is exactly the dot product of two vectors.

✅ Correct Answer Explanation

The present value of multiple cash flows is P₁ = R₁d₁ + R₂d₂ + ... + Rₙdₙ This expression is precisely the dot product of the payment vector and the discount vector: P₁ = u⃗ · v⃗ Therefore, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: u⃗ × v⃗
Incorrect because the cross product is defined only for three-dimensional vectors and does not represent present value.
Option C: |u⃗| + |v⃗|
Incorrect because adding vector magnitudes does not discount cash flows.
Option D: u⃗ / v⃗
Incorrect because vector division is not defined in standard vector algebra and does not represent present value.
Incorrect because vector division is not defined in this context.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Recognize that present value is obtained by multiplying corresponding entries and summing them.

Final Logic:

Discounted cash flows are summed using the dot product; therefore Option B.

🧠 Memory Trick

"PV = Dot Product."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Present Value of Cash Flows

16 Consider the function
\(P_{2}=C(1+i)^{-n}.\)
When plotted against continuous time (n), what is the nature of this curve?

A Exponential decay approaching zero

B Linear growth

C A circular curve

D Exponential growth approaching infinity

💡 Short Explanation

The exponent is negative. As (n) increases, the present value decreases. The curve approaches zero asymptotically.

✅ Correct Answer Explanation

The present value of the redemption amount is P₂ = C(1 + i)^(-n) where i > 0. As n increases, (1 + i)^(-n) = 1/(1 + i)^n, which decreases exponentially toward zero. Hence, P₂ → 0 as n → ∞. Therefore, the graph is an exponential decay curve approaching the horizontal axis. Thus, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: Linear growth.
Incorrect because the function decreases exponentially rather than increasing linearly.
Option C: A circular curve.
Incorrect because exponential functions do not form circular graphs.
Option D: Exponential growth approaching infinity.
Incorrect because the negative exponent causes exponential decay.

🎯 Strategy

used

Contextual/Tonal Matching

Application:

Recognize that a negative exponent produces exponential decay.

Final Logic:

Since
(1 + i)^(-n)
decreases continuously toward zero, Option A is correct.

🧠 Memory Trick

"Negative Exponent → Exponential Decay."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Present Value of Redemption

17 In a perfectly efficient market, what is the probability that a bond remains continuously overvalued for an infinite period without correction?

A 1

B 0

C 0.5

D 0.99

💡 Short Explanation

Efficient markets rapidly correct mispricing. Persistent overvaluation cannot continue indefinitely. Therefore, the probability is zero.

✅ Correct Answer Explanation

According to the Efficient Market Hypothesis (EMH), security prices quickly incorporate all available information. If a bond becomes overvalued, investors recognize the mispricing, selling pressure increases, the market price adjusts toward its intrinsic value. Hence, a bond cannot remain continuously overvalued forever in a perfectly efficient market. Therefore, the probability is Thus, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: 1
Incorrect because perpetual overvaluation contradicts market efficiency.
Option C: 0.5
Incorrect because no random probability applies under a perfectly efficient market assumption.
Option D: 0.99
Incorrect because persistent mispricing is inconsistent with the Efficient Market Hypothesis.

🎯 Strategy

used

Elimination

Application:

Recall the assumptions of a perfectly efficient market before evaluating the options.

Final Logic:

Efficient markets eliminate persistent overvaluation; therefore Option B.

🧠 Memory Trick

"Efficient Market = No Permanent Mispricing."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Price Analysis

18 The undervaluation gap (fair value − market price) for a bond over three months is ₹12, ₹15, and ₹18. What is the 3-month moving average of this gap?

A ₹12

B ₹18

C ₹15

D ₹16

💡 Short Explanation

Add the three monthly gaps. Divide by the number of observations. The result is ₹15.

✅ Correct Answer Explanation

A 3-month moving average is calculated by averaging the three observations: (12 + 15 + 18) / 3 = 45 / 3 = 15 Therefore, the average undervaluation gap is ₹15. Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: ₹12
Incorrect because it represents only the first month's gap.
Option B: ₹18
Incorrect because it represents only the final month's gap.
Option D: ₹16
Incorrect because the arithmetic average equals ₹15.

🎯 Strategy

used

Substitution

Application:

Substitute the given observations into the moving-average formula.

Final Logic:

Since
(12 + 15 + 18) / 3 = 15
Option C is correct.

🧠 Memory Trick

"Moving Average = Sum ÷ Number of Values."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Undervaluation Analysis

19 Arrange the correct sequence of steps in the relative pricing approach:
1. Determine the yield to maturity based on the bond's credit rating relative to the benchmark.
2. Identify a benchmark (usually a government security).
3. Assess the spread between the required return and the benchmark YTM.
4. Price the bond relative to this benchmark.

A 1, 2, 3, 4

B 4, 3, 2, 1

C 2, 4, 1, 3

D 2, 1, 3, 4

💡 Short Explanation

First identify a benchmark security. Determine the bond's required yield. Assess the spread and then price the bond.

✅ Correct Answer Explanation

The relative pricing approach follows a logical sequence: Step 1: Identify a suitable benchmark security, usually a government bond with a similar maturity. Step 2: Determine the bond's Yield to Maturity (YTM) based on its credit rating relative to the benchmark. Step 3: Assess the spread between the required return and the benchmark YTM. Step 4: Use this required return to price the bond relative to the benchmark. Thus, the correct order is 2 → 1 → 3 → 4 Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: 1, 2, 3, 4
Incorrect because the benchmark must be identified before determining the required yield.
Option B: 4, 3, 2, 1
Incorrect because pricing is the final step, not the first.
Option C: 2, 4, 1, 3
Incorrect because pricing cannot be done before determining the required return and spread.

🎯 Strategy

used

Elimination

Application:

Arrange the steps according to the logical workflow used in bond valuation through relative pricing.

Final Logic:

Benchmark → Required Yield → Spread → Pricing; therefore Option D.

🧠 Memory Trick

"Benchmark → Yield → Spread → Price."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Relative Pricing

20 A government benchmark security has a Yield to Maturity (YTM) of 5.0%. A highly rated corporate bond carries a credit spread of 1.5% over this benchmark. What is the required return (YTM) for the corporate bond?
\(Required Return=5.0\%+1.5\%=6.5\%\)

A 6.5%

B 3.5%

C 5.0%

D 7.5%

💡 Short Explanation

Required return equals benchmark yield plus credit spread. Add 5.0% and 1.5%. The result is 6.5%.

✅ Correct Answer Explanation

The required return for a corporate bond is calculated as Required Return = Benchmark YTM + Credit Spread Substituting the given values, = 5.0% + 1.5% = 6.5% Therefore, the corporate bond should offer a Yield to Maturity of 6.5%. Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: 3.5%
Incorrect because it subtracts the credit spread instead of adding it.
Option C: 5.0%
Incorrect because it ignores the additional risk premium.
Option D: 7.5%
Incorrect because the total exceeds the required return obtained from the given data.

🎯 Strategy

used

Substitution

Application:

Apply the standard formula for required return by adding the benchmark yield and the credit spread.

Final Logic:

Since
5.0% + 1.5% = 6.5%
Option A is correct.

🧠 Memory Trick

"Benchmark + Spread = Required Return."

📚 Class XII – Applied Mathematics – Chapter: Bonds and Debentures – Topic: Credit Spread

CUET UG Applied Mathematics Booster Test 3 - Bonds, Yield and Bond Valuation

Test Complete!

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