MFM 225 Fixed Income Securities Notes cover all four units of the GGSIPU MBA (Financial Management) Semester 3 elective. The English printed book is listed as 54 pages and includes 37 worked illustrations, 37 solved short answers and 61 exam-style practice questions. Topics include government securities, bond valuation, yield to maturity, accrued interest, duration, convexity, yield curves, forward rates, interest-rate derivatives and bond portfolio strategies. The notes follow the MBA (FM) scheme labelled 2021-22 onwards.
Written by Prateek Talwar, Founder, Unnati Educations · Reviewed by Prateek Talwar · Checked against the MBA (Financial Management) Scheme and Syllabus, 2021-22 onwards · Updated 14 October 2026 · Editorial policy
Scheme: MBA (FM) 2021-22 onwards | Applies to: batches admitted from 2021-22 onwards, subject to subsequent revisions | Source record last verified: 14 October 2026
MFM 225 Fixed Income Securities at a glance: GGSIPU MBA (FM) Sem 3 credits, units and exam pattern
MFM 225 is a three-credit Semester 3 elective covering the Indian debt market, fixed-income valuation, bond price sensitivity and the term structure of interest rates.
| Code and title | MFM 225 · Fixed Income Securities |
|---|---|
| Course and semester | MBA (Financial Management), Semester 3 |
| Category and credits | Elective theory paper; 3 credits; L-3, T-0, P-0 |
| Marks | 100: 25 internal + 75 end-term |
| Pass mark | Not specified in the supplied scheme details; consult GGSIPU Ordinance 11 and applicable examination notifications |
| Applies to | Batches covered by the MBA (FM) scheme labelled 2021-22 onwards |
| End-term pattern | 75 marks; detailed question-paper pattern not confirmed in the supplied scheme details |
| Units and hours | 4 units, 42 teaching hours: 10 + 8 + 10 + 14 |
| Paired lab | None |
The supplied scheme summary describes the internal assessment as a 15-mark class test plus 10 marks for assignments, presentations, viva, group discussion or class participation.
MFM 225 appears among the Semester 3 elective options. Students should confirm the electives offered by their institute under the applicable scheme.
MFM 225 Fixed Income Securities Notes unit-wise: 37 worked illustrations and 37 solved short answers across 4 units
The supplied notes plan allocates pages 4 to 53 to four units. Together, they contain 37 worked illustrations, 37 solved short answers and 61 additional practice questions. The worked examples use rupee-denominated bond, money-market and portfolio calculations.
MFM 225 Unit 1: Introduction to Fixed Income Securities
Unit 1 (pages 4 to 21) introduces fixed-income instruments, bond features and 14 bond variations. It examines interest-rate, reinvestment, credit, liquidity, inflation, exchange-rate and tax risks, along with market participants and the structure of the Indian debt market.
The unit covers government securities, Treasury Bills, State Development Loans, call money, commercial paper, repo transactions, credit ratings, asset-backed securities and securitisation. The source also includes a timeline of debt-market reforms from 1992 to 2025.
Unit content: 6 worked illustrations, 9 solved short answers and 18 practice questions.
Quick look: calculating a seven-day repo (from page 16)
- Face value: ₹10 crore of government securities quoted at ₹101 per ₹100 face value.
- Market value: ₹10,00,00,000 × 101/100 = ₹10,10,00,000.
- First-leg cash with 2% haircut: ₹10,10,00,000 × 0.98 = ₹9,89,80,000.
- Seven-day repo interest at 5.50%: ₹9,89,80,000 × 0.055 × 7/365 = ₹1,04,403.56.
- Second-leg cash: ₹9,89,80,000 + ₹1,04,403.56 = ₹9,90,84,403.56.
The calculation uses a 365-day interest basis as specified in the supplied example. Actual transaction conventions should be checked against the relevant contract and market rules.
MFM 225 Unit 2: Fixed Income Valuation
Unit 2 (pages 22 to 32) concentrates on bond valuation. Topics include pricing coupon bonds, pull to par, accrued interest under different day-count conventions, clean and dirty prices, current yield, yield to maturity, yield to call, money-market yield measures, portfolio yield and total return.
The source describes Unit 2 as the most calculation-intensive unit, with 12 worked illustrations, 9 solved short answers and 15 practice questions.
Quick look: current yield and YTM of a discount bond (from page 27)
- Consider a five-year bond with ₹1,000 face value, a 10% annual coupon and a market price of ₹960.
- Annual coupon: ₹1,000 × 10% = ₹100.
- Current yield: ₹100 ÷ ₹960 × 100 = 10.42%.
- Approximate YTM: [₹100 + (₹1,000 − ₹960)/5] ÷ [(₹1,000 + ₹960)/2] × 100 = 11.02%.
- YTM using annual cash flows:
RATE(5,100,-960,1000)gives approximately 11.08%.
The exact annual-compounding result is approximately 11.0846%, assuming the first coupon is received one year from the valuation date and the price is measured consistently with that cash-flow schedule.
MFM 225 Unit 3: Bond Price Volatility
Unit 3 (pages 33 to 41) explains how bond prices respond to changes in required yields. The source uses a recurring five-year, 9% coupon bond example to illustrate price value of a basis point (PVBP), yield value of a price change (YVPC), Macaulay duration, modified duration and convexity.
The unit also covers Malkiel's bond price theorems and portfolio duration. It contains 9 worked illustrations, 9 solved short answers and 13 practice questions.
Quick look: duration and convexity estimates (from page 39)
The supplied illustration starts with a bond price of approximately ₹103.9927 per ₹100 face value at an 8% yield, modified duration of 3.9406 and convexity of 20.66.
| Yield change | Actual price change in source | Duration only | Duration plus convexity |
|---|---|---|---|
| +1 percentage point | −3.84% | −3.94% | −3.84% |
| −1 percentage point | +4.05% | +3.94% | +4.04% |
| +2 percentage points | −7.48% | −7.88% | −7.47% |
| −2 percentage points | +8.31% | +7.88% | +8.29% |
Illustrative percentage bond price changes for parallel yield shifts
- Yield change
- +1 percentage point
- Actual price change in source
- −3.84%
- Duration only
- −3.94%
- Duration plus convexity
- −3.84%
- Yield change
- −1 percentage point
- Actual price change in source
- +4.05%
- Duration only
- +3.94%
- Duration plus convexity
- +4.04%
- Yield change
- +2 percentage points
- Actual price change in source
- −7.48%
- Duration only
- −7.88%
- Duration plus convexity
- −7.47%
- Yield change
- −2 percentage points
- Actual price change in source
- +8.31%
- Duration only
- +7.88%
- Duration plus convexity
- +8.29%
The approximation uses ΔP/P ≈ −Dmod × Δy + 0.5 × Convexity × (Δy)^2. The convexity term improves the duration-only estimate for this conventional option-free bond example, although the approximation remains subject to its assumptions.
MFM 225 Unit 4: Term Structure of Interest Rates
Unit 4 (pages 42 to 53) has the largest teaching-hour allocation, at 14 hours. It explains benchmark spreads, yield curves, spot rates, forward rates, bootstrapping, the Nelson-Siegel curve, theories of the term structure and interest-rate derivatives.
The portfolio-management portion covers passive, active and structured strategies, including duration matching and immunisation. The source lists 10 worked illustrations, 10 solved short answers and 15 practice questions.
Quick look: forward rates from a spot-rate curve (from page 45)
Using the rounded annual-compounding spot rates supplied in the notes:
- One-year spot rate: 6.000%.
- Two-year spot rate: 6.516%.
- Three-year spot rate: 7.048%.
- One-year forward starting after Year 1:
(1.06516)^2 / 1.06 − 1, approximately 7.035%. - One-year forward starting after Year 2:
(1.07048)^3 / (1.06516)^2 − 1, approximately 8.119%. - Two-year annualised forward starting after Year 1:
[(1.07048)^3 / 1.06]^(1/2) − 1, approximately 7.576%.
Results may differ slightly when calculations use unrounded spot rates instead of the three-decimal inputs shown here.
Winner's curse in government bond auctions: excerpt from page 12 of the MFM 225 notes
Excerpt from page 12, Unit 1: Introduction to Fixed Income Securities
Finding the cut-off in a yield-based auction
Suppose an auction offers ₹1,000 crore of a new ten-year government security. Competitive bids are received at yields of 6.40% for ₹300 crore, 6.42% for ₹400 crore, 6.45% for ₹500 crore and 6.50% for ₹200 crore.
For this example, the bids are arranged from the lowest to the highest yield. The first two groups account for ₹700 crore. A further ₹300 crore is needed, so the cut-off falls within the ₹500 crore bid group at 6.45%.
- Accepted at 6.40%: ₹300 crore.
- Accepted at 6.42%: ₹400 crore.
- Accepted at 6.45%: ₹300 crore out of ₹500 crore, or 60% of that bid group, assuming proportional allotment at the cut-off.
- Rejected at 6.50%: ₹200 crore.
- Illustrative cut-off yield: 6.45%.
The source uses this simplified example to explain how the cut-off is identified. Actual auction allotment, pricing and coupon determination depend on the notified auction structure and applicable RBI rules.
What the winner's curse means
In a common-value auction, bidders estimate the value of the same underlying security using incomplete information. An especially aggressive bid can win because the bidder has overestimated the security's value relative to other participants.
In a multiple-price auction, successful bidders may pay prices corresponding to their individual bids. An aggressive bidder can therefore pay more than another successful bidder. The possibility of overpaying encourages bid shading, meaning bidders may submit less aggressive bids than their estimated value would otherwise suggest.
| Basis | Multiple-price auction | Uniform-price auction |
|---|---|---|
| Price paid | Successful bidders pay according to their accepted bids | Successful bidders pay the common auction-clearing price |
| Winner's curse exposure | Can be more pronounced for aggressive bidders | Can be reduced, though not necessarily eliminated |
| Bidding behaviour | May encourage greater bid shading | May encourage bids closer to estimated value |
| Price variation among winners | Different successful bids can receive different prices | A common price applies to successful competitive allotments |
Multiple-price and uniform-price auction comparison
- Basis
- Price paid
- Multiple-price auction
- Successful bidders pay according to their accepted bids
- Uniform-price auction
- Successful bidders pay the common auction-clearing price
- Basis
- Winner's curse exposure
- Multiple-price auction
- Can be more pronounced for aggressive bidders
- Uniform-price auction
- Can be reduced, though not necessarily eliminated
- Basis
- Bidding behaviour
- Multiple-price auction
- May encourage greater bid shading
- Uniform-price auction
- May encourage bids closer to estimated value
- Basis
- Price variation among winners
- Multiple-price auction
- Different successful bids can receive different prices
- Uniform-price auction
- A common price applies to successful competitive allotments
Why auction design matters
Auction format can affect bidding incentives, price discovery, participation and government borrowing costs. The source discusses uniform-price auctions and the non-competitive bidding facility as mechanisms relevant to Indian government securities.
The non-competitive facility allows eligible participants to apply without specifying a competitive yield or price, subject to the applicable RBI framework. It does not remove investment risk or guarantee a particular return.
How to write MFM 225 answers: cash-flow tables, YTM workings and long theory answers
MFM 225 combines numerical problems with descriptive questions. The source recommends showing the formula, substitution, calculation and financial interpretation for numerical answers.
- Bond valuation: Identify face value, coupon, maturity, yield and coupon frequency before calculating the present value of cash flows.
- Yield questions: Distinguish current yield, approximate YTM and cash-flow-based YTM. State the relevant compounding assumption.
- Duration and convexity: Use a cash-flow table with time, cash flow, discount factor, present value and duration-weighted present value.
- Term-structure numericals: Write the discount-factor or spot-rate relationship before deriving a forward rate.
- Theory answers: Use a definition, classification or comparison table, labelled diagram, application and limitation.
Worked example: price of a five-year 9% coupon bond at an 8% yield (page 22)
A bond has a ₹1,000 face value, a 9% annual coupon, five years remaining and an 8% annual required yield.
- Annual coupon: ₹1,000 × 9% = ₹90.
- Coupon present value:
90 × [1 − (1.08)^−5] / 0.08. - Principal present value:
1,000 / (1.08)^5. - Total bond price: approximately ₹1,039.93.
- Interpretation: The bond trades at a premium because its 9% coupon rate exceeds the 8% required yield.
For full working, retain intermediate calculations at sufficient precision and round the final price to two decimal places.
The source also recommends preparing a bond-features comparison table for Unit 1 and a four-theory comparison with a yield-curve diagram for Unit 4.
MFM 225 exam corner: 37 solved short answers and 61 practice questions by unit
| Unit | Solved short answers | Long practice | Short practice |
|---|---|---|---|
| Unit 1 | 9 | 10 | 8 |
| Unit 2 | 9 | 8 | 7 |
| Unit 3 | 9 | 7 | 6 |
| Unit 4 | 10 | 8 | 7 |
| Total | 37 | 33 | 28 |
MFM 225 solved short answers and additional practice questions
- Unit
- Unit 1
- Solved short answers
- 9
- Long practice
- 10
- Short practice
- 8
- Unit
- Unit 2
- Solved short answers
- 9
- Long practice
- 8
- Short practice
- 7
- Unit
- Unit 3
- Solved short answers
- 9
- Long practice
- 7
- Short practice
- 6
- Unit
- Unit 4
- Solved short answers
- 10
- Long practice
- 8
- Short practice
- 7
- Unit
- Total
- Solved short answers
- 37
- Long practice
- 33
- Short practice
- 28
The source lists 37 solved short answers and 61 additional practice questions, comprising 33 long and 28 short practice questions. The book separately includes 37 worked illustrations. The practice labels of 10–12.5 marks for long answers and 2.5–5 marks for short answers are editorial categories, not a confirmed official question-paper pattern.
One question per unit, with answer pointers:
- Unit 1: Explain securitisation, its process, participants, benefits and risks. Pointer: Discuss the six-step process, eight participant roles and the illustrative 80/15/5 tranche structure on page 18.
- Unit 2: What is total return, and how is it computed for a bond? Pointer: Use the five-step illustration on page 30, including the accumulated value of ₹1,309.23 and the source's reported bond-equivalent yield of 9.19%. Verify the yield convention when reproducing the calculation.
- Unit 3: Distinguish Macaulay duration and modified duration, and discuss duration properties. Pointer: State
Modified Duration = Macaulay Duration / (1 + y/k), using consistent yield and coupon-frequency conventions, then explain the properties listed on pages 37–38. - Unit 4: What is immunisation? Explain contingent immunisation. Pointer: Discuss matching assets and liabilities, Redington's conditions and the source's page 51 illustration of a ₹100 crore liability due in five years.
For the immunisation illustration, the present value of ₹100 crore due in five years at a 7% annual discount rate is approximately ₹71.30 crore. Immunisation also requires attention to duration, convexity, cash-flow structure and changing yields.
The separate MFM 225 important-questions page is planned; its publication is not confirmed in the supplied source.
MFM 225 and the GGSIPU MBA (FM) Sem 3 papers it connects to
Paired lab: None. MFM 225 is an elective theory paper with no separately identified practical component.
- MFM 203 Financial Derivatives: Connects with interest-rate derivatives and hedging instruments discussed in Unit 4.
- MFM 205 Financial Markets and Institutions: Connects with government securities, debt-market participants and money-market instruments in Unit 1.
- MFM 110 Investment Analysis and Portfolio Management: Introduces bond yield and duration concepts in Semester 2, which MFM 225 develops through dedicated calculations.
- MFM 209 Strategic Financial Management: Connects with financing decisions and risk management.
| Group | Papers |
|---|---|
| Summer training | MFM 201 Summer Training Report |
| Core and related papers | MFM 203 Financial Derivatives; MFM 205 Financial Markets and Institutions; MFM 207 Entrepreneurship Development and Start-Up; MFM 209 Strategic Financial Management; MFM 211 Business Analytics |
| Open elective and lab | MFM 213 MOOCs / Open Elective; MFM 227 Business Analytics Lab |
| Other elective options | MFM 215 Mergers, Acquisitions and Corporate Restructuring; MFM 217 International Financial Management; MFM 219 Venture Capital and Investment Banking; MFM 221 Financial Econometrics; MFM 223 Data Visualization for Decision Making |
Related Semester 3 MBA (Financial Management) papers and electives in the supplied scheme summary
- Group
- Summer training
- Papers
- MFM 201 Summer Training Report
- Group
- Core and related papers
- Papers
- MFM 203 Financial Derivatives; MFM 205 Financial Markets and Institutions; MFM 207 Entrepreneurship Development and Start-Up; MFM 209 Strategic Financial Management; MFM 211 Business Analytics
- Group
- Open elective and lab
- Papers
- MFM 213 MOOCs / Open Elective; MFM 227 Business Analytics Lab
- Group
- Other elective options
- Papers
- MFM 215 Mergers, Acquisitions and Corporate Restructuring; MFM 217 International Financial Management; MFM 219 Venture Capital and Investment Banking; MFM 221 Financial Econometrics; MFM 223 Data Visualization for Decision Making
Who writes and checks the MFM 225 Fixed Income notes?
- Prateek Talwar, author: Founder, Unnati Educations; Associate Company Secretary (ACS), ICSI, membership no. 58704, since 15 May 2019; B.Com, University of Delhi (School of Open Learning), 2012. Author profile
Prateek Talwar is also identified as the subject reviewer. The supplied editorial record states that the four units were mapped against the MBA (FM) scheme labelled 2021-22 onwards.
The source describes additional references to the RBI CP and NCD Directions, 2024, securitisation regulation and 2024–2025 Indian bond-index developments. These should be treated as edition-specific contextual topics, with their current regulatory status checked against official publications before making compliance claims.
Last updated and last recorded verification: 14 October 2026. Read the editorial policy.
Do the MFM 225 notes cover the full GGSIPU syllabus?
The supplied editorial mapping identifies matching content for all four MFM 225 units. This records the source's coverage assessment; the finished printed book has not been independently inspected page by page.
| Official unit | Official topics | Where in the notes | Status |
|---|---|---|---|
| I: Introduction to Fixed Income Securities | Bond features and risks, market participants, government securities, auctions, winner's curse, Treasury Bills, state bonds, call money, commercial paper, repo, credit ratings, securitisation and reforms | Topic mapping pages 4–20; unit extends to page 21 | Mapped in source |
| II: Fixed Income Valuation | Bond pricing, flat and full prices, accrued interest, yield measures, portfolio yield and total return | Topic mapping pages 22–31; unit extends to page 32 | Mapped in source |
| III: Bond Price Volatility | Bond price behaviour, PVBP, YVPC, Macaulay duration, modified duration, portfolio duration and convexity | Topic mapping pages 33–40; unit extends to page 41 | Mapped in source |
| IV: Term Structure of Interest Rates | Benchmark spreads, yield curves, bootstrapping, spot and forward rates, Nelson-Siegel, term-structure theories, rate derivatives and portfolio strategies | Topic mapping pages 42–52; unit extends to page 53 | Mapped in source |
MFM 225 syllabus topics mapped to the supplied notes
- Official unit
- I: Introduction to Fixed Income Securities
- Official topics
- Bond features and risks, market participants, government securities, auctions, winner's curse, Treasury Bills, state bonds, call money, commercial paper, repo, credit ratings, securitisation and reforms
- Where in the notes
- Topic mapping pages 4–20; unit extends to page 21
- Status
- Mapped in source
- Official unit
- II: Fixed Income Valuation
- Official topics
- Bond pricing, flat and full prices, accrued interest, yield measures, portfolio yield and total return
- Where in the notes
- Topic mapping pages 22–31; unit extends to page 32
- Status
- Mapped in source
- Official unit
- III: Bond Price Volatility
- Official topics
- Bond price behaviour, PVBP, YVPC, Macaulay duration, modified duration, portfolio duration and convexity
- Where in the notes
- Topic mapping pages 33–40; unit extends to page 41
- Status
- Mapped in source
- Official unit
- IV: Term Structure of Interest Rates
- Official topics
- Benchmark spreads, yield curves, bootstrapping, spot and forward rates, Nelson-Siegel, term-structure theories, rate derivatives and portfolio strategies
- Where in the notes
- Topic mapping pages 42–52; unit extends to page 53
- Status
- Mapped in source
Official reference: MBA (Financial Management) Scheme and Syllabus, 2021-22 onwards. The supplied source identifies MFM 225 on page 67 of the PDF and the Semester 3 elective list on pages 7–8.
The source also identifies spreadsheet applications on page 31, including Excel functions PRICE, YIELD, ACCRINT, RATE and IRR.
MFM 225 Fixed Income notes FAQs
How do I get the full MFM 225 notes?
Order through the WhatsApp button below. The complete MFM 225 notes are listed as a 54-page English printed book, not a full downloadable PDF. Delivery takes up to 5 to 7 days, depending on location.
Is MFM 225 a core paper or an elective in GGSIPU MBA (FM)?
MFM 225 Fixed Income Securities is a Semester 3 elective under the MBA (Financial Management) scheme labelled 2021-22 onwards. It carries three credits with three lecture hours per week and no paired lab. Students should confirm their institute's available elective options.
What is the passing mark for MFM 225?
The paper carries 100 marks, divided into 25 internal and 75 end-term marks. The supplied scheme details do not state a specific passing percentage for MFM 225. Consult GGSIPU Ordinance 11 and applicable examination notifications.
Which MFM 225 unit has the most numericals?
Unit 2, Fixed Income Valuation, has the most worked illustrations: 12. Unit 4 has 10, Unit 3 has 9 and Unit 1 has 6. The four units therefore contain 37 worked illustrations altogether.
Do the MFM 225 notes follow the GGSIPU MBA (FM) syllabus?
The supplied editorial mapping follows the MBA (FM) scheme labelled 2021-22 onwards and identifies content for all four units. Students should check whether subsequent university revisions apply to their admission batch.
How is MFM 225 different from the bond topics in MFM 110?
MFM 110 Investment Analysis and Portfolio Management introduces bond concepts within a broader investment syllabus. MFM 225 is dedicated to fixed income and develops the debt market, bond valuation, price volatility, yield curves, interest-rate derivatives and portfolio strategies through 37 worked illustrations.
Get the full MFM 225 Fixed Income Securities Notes on WhatsApp
The English printed book is listed as 54 pages with 37 worked illustrations, 37 solved short answers, 61 practice questions, six exam tips and five numbered figures.
| Part | Pages | Worked illustrations | Solved short answers | Practice questions |
|---|---|---|---|---|
| Cover and index | 1–3 (3) | — | — | — |
| Unit 1: Introduction to Fixed Income Securities | 4–21 (18) | 6 | 9 | 18 |
| Unit 2: Fixed Income Valuation | 22–32 (11) | 12 | 9 | 15 |
| Unit 3: Bond Price Volatility | 33–41 (9) | 9 | 9 | 13 |
| Unit 4: Term Structure of Interest Rates | 42–53 (12) | 10 | 10 | 15 |
| Final page to confirm | 54 (1; content not identified) | — | — | — |
| Listed book total | 54 | 37 | 37 | 61 |
MFM 225 printed notes: page allocation and question counts
- Part
- Cover and index
- Pages
- 1–3 (3)
- Worked illustrations
- —
- Solved short answers
- —
- Practice questions
- —
- Pages
- 4–21 (18)
- Worked illustrations
- 6
- Solved short answers
- 9
- Practice questions
- 18
- Pages
- 22–32 (11)
- Worked illustrations
- 12
- Solved short answers
- 9
- Practice questions
- 15
- Pages
- 33–41 (9)
- Worked illustrations
- 9
- Solved short answers
- 9
- Practice questions
- 13
- Pages
- 42–53 (12)
- Worked illustrations
- 10
- Solved short answers
- 10
- Practice questions
- 15
- Part
- Final page to confirm
- Pages
- 54 (1; content not identified)
- Worked illustrations
- —
- Solved short answers
- —
- Practice questions
- —
- Part
- Listed book total
- Pages
- 54
- Worked illustrations
- 37
- Solved short answers
- 37
- Practice questions
- 61
The source identifies 50 unit-content pages, three introductory pages and one final page whose content is not specified. The full book is available in print, not as a complete PDF. Price and payment details are shared through WhatsApp.
Delivery: within 5 to 7 days at most; the exact time may vary with your location.
Order the MFM 225 Fixed Income Securities Notes book on WhatsApp (4 units, 54 pages)
Unnati Educations is an independent education provider based in Vikaspuri, Delhi. We are not affiliated with, authorised by, or endorsed by Guru Gobind Singh Indraprastha University (GGSIPU). 'GGSIPU' and 'IPU' are used only to describe the syllabus our notes follow. For official information, visit ipu.ac.in.
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