Prepare for the FIS syllabus by treating it as one interconnected problem: a bond's price implies its yield, its cash flow timing implies its duration, its credit quality implies its spread, and its duration implies portfolio strategy. Study each topic by re-deriving it from the same worked bond, and check that premium-bond orderings, duration estimates, and portfolio choices remain logically consistent across topics.
Dirty Price, Clean Price, and Where Accrued Interest Enters Pricing
Bond quotes are usually clean prices that exclude accrued interest, while the amount actually paid at settlement is the dirty price. Exam questions test whether you can move between the two using accrued coupon interest.
The dirty (full) price is the present value of all remaining cash flows. The clean (quoted) price equals the dirty price minus accrued interest, which is the coupon payment multiplied by the fraction of the coupon period elapsed. The fraction depends on the market's day-count convention, and conventions differ across markets and instrument types. Treat the convention as given information in any question: the skill being tested is applying the stated day count correctly, not recalling which market uses which convention.
A practical trap appears when comparing two bonds or computing a return over a holding period. If you use clean prices while a coupon is accruing, part of the return appears to vanish, because accrued interest is real value the buyer pays and later receives back as a coupon. Before comparing prices or returns, decide whether the question refers to the quote, the invoice amount, or total return, and keep the accrued interest visible in your working.
Quick drill: take a bond with an annual coupon of 80 on 1,000 face, 40 days after its last coupon date. Accrued interest is 80 x 40/360 = 8.89 under a simplified 30/360-style count. Write down which of your subsequent calculations need the dirty price and which need the clean price.
Coupon Rate, Current Yield, and Yield to Maturity Answer Different Questions
The coupon rate fixes the cash flow; the current yield measures annual income against today's price; yield to maturity is the single discount rate equating price with all discounted cash flows. Their ordering signals premium or discount pricing.
For a standard option-free bond held to a single terminal principal payment, a consistent ordering holds: when the price is above par (a premium bond), the coupon rate exceeds the current yield, which exceeds the yield to maturity. When the price is below par, the ordering reverses. At par, all three are equal. This ordering is a self-check: if your computed YTM does not sit on the correct side of your current yield for a premium or discount bond, a calculation error is present.
Worked scenario: a five-year bond, face 1,000, annual coupon 80, priced at 1,040. A plausible mistake is to report 8% as the investor's return because that is the coupon rate. The current yield is 80/1,040 = 7.69%, and because the buyer overpays 40 that is repaid only at par, the YTM must be below 7.69%. Using the approximation YTM is roughly (coupon + annualized price change)/price: (80 - 8)/1,040 = 6.92%. The better decision when comparing this bond against a par bond yielding 7% is to compare YTM to YTM, not coupon to coupon, because the premium bond returns part of your purchase price as a capital loss rather than as income.
Check yourself with the reverse case: the same bond priced at 960. Current yield rises to 8.33%, and YTM exceeds it because of the gain at maturity. If your orderings flip in the wrong direction, revisit the cash flow logic before touching formulas.
| Measure | Question it answers | Premium bond (price above par) |
|---|---|---|
| Coupon rate | What cash is contractually paid each period? | Fixed by the contract; highest of the three |
| Current yield | What income does today's price buy? | Coupon / price; below coupon rate, above YTM |
| Yield to maturity | What single rate discounts all cash flows to today's price? | Lowest of the three; includes the capital loss to par |
Macaulay Duration, Modified Duration, and Money Duration Are Three Different Objects
Macaulay duration is a weighted-average time in years; modified duration divides it by (1 + y/k) to measure percentage price sensitivity; money duration scales that by portfolio value. Substituting one for another distorts risk estimates.
Macaulay duration answers a timing question: how long, on average, until cash flows arrive, weighted by present value? Modified duration answers a sensitivity question: by what percentage does price change for a small change in yield? Convexity refines this, because the true price-yield relationship is curved: for a positively convex bond, a linear duration estimate overstates the loss when yields rise and understates the gain when yields fall. Naming which object you are using is the first step of every duration question.
Worked scenario: a portfolio worth 50 million has modified duration 5.2, and yields rise 40 basis points. A plausible mistake is treating the duration figure loosely and computing 5.2 x 0.4 = 2.08, treating basis points as whole percentage points, which gives an absurd result; or using Macaulay duration directly as a percentage sensitivity. The better decision: convert first. Change = -5.2 x 0.004 = -2.08%, i.e. about -1.04 million. Why it matters: if you are sizing a hedge or reporting risk, a scale error here moves the answer by orders of magnitude. Add the convexity note that the true loss will be slightly smaller than the linear estimate.
Link the three measures in one line every time: money duration = modified duration x portfolio value; money duration per basis point (often called DV01-style) = money duration x 0.0001. Writing this chain in the margin of practice questions prevents unit confusion from spreading into portfolio questions later.
Credit Risk: Join Ratings, Spreads, and Recovery Instead of Reading Them Apart
Credit risk combines probability of default with loss given default. Ratings summarize relative default risk, while the spread over the benchmark compensates for expected loss, uncertainty, and liquidity. Analyze them jointly.
A credit spread is not a pure default forecast. It bundles compensation for expected loss (default probability times severity), a premium for the uncertainty around that loss, and liquidity and tax effects. This is why two bonds with similar ratings can carry different spreads, and why a spread can widen after a downgrade even before any default occurs. When a question gives you a spread and a recovery assumption, separate the components in your working rather than treating the spread as a single number.
Apply this with a comparison: two corporates with the same maturity, one spread at 150 basis points and one at 250. The better decision is not automatically the lower spread. Ask what recovery rate each structure implies, whether the wider spread compensates per unit of duration risk taken, and whether ratings or recent spread behavior suggest migration risk. A bond that loses value through spread widening hurts you without any default event, so a 'no default happened' reading of credit risk is incomplete.
Practice move: take one rated corporate bond and write one sentence each for its default-risk component, its recovery expectation, and its non-credit spread components. If you cannot fill the third sentence, you are reading the spread too narrowly.
T-Bills, PIBs, Sukuk, and Corporate Debt: Matching Each Pakistani Instrument to Its Pricing Logic
Short-term government bills are discount instruments, coupon-bearing government bonds price like standard bonds, sukuk carry Shariah-compliant structures, and corporates add credit spreads. Match each instrument to the pricing method it requires.
Treasury bills are typically short-tenor, zero-coupon instruments sold at a discount, so their pricing logic is a single discounted cash flow and their quoted yield conventions matter more than coupon mechanics. Pakistan Investment Bonds are fixed-coupon, bullet-style government bonds, so the full machinery from earlier sections applies: accrued interest, current yield, YTM, and duration. Recognizing which pricing template a question invokes is most of the work.
Sukuk differ structurally from conventional bonds because returns are tied to underlying assets or leases rather than to a pure lending contract, even though many sukuk produce fixed or quasi-fixed cash flows that can be analyzed with standard bond tools. Corporate debt layers a credit spread onto the government curve, and floating-rate instruments reference short-term benchmarks such as KIBOR, which changes their duration profile compared with fixed-rate bonds of the same maturity. Current auction, listing, and settlement details change over time, so treat this article's coverage as conceptual and confirm market-specific mechanics from issuer materials.
Sorting drill: list each instrument in two columns, 'cash flow pattern' and 'main risk added beyond the government curve'. If sukuk and conventional bonds end up indistinguishable in your notes, your structural notes need revisiting.
Ladder, Barbell, Bullet, or Immunization: Matching Strategy to the Stated Objective
Ladder, barbell, and bullet describe how maturities are distributed; immunization matches portfolio duration to the liability horizon. Exam questions give an objective and cash flow need, and expect the strategy that fits both.
A ladder spreads maturities evenly, smoothing reinvestment risk because a portion matures regularly. A barbell concentrates in short and long maturities, mixing liquidity with long-duration exposure but leaving the middle empty. A bullet concentrates maturities near one target date, which suits a known single future obligation. None is universally better: the trade-off runs between reinvestment risk (worst for a concentrated bullet funded at one rate) and price risk (worst for long-ended barbells if rates rise).
Immunization is the distinct case: it sets portfolio modified duration approximately equal to the investment horizon, so that for small parallel shifts in the yield curve, the reinvestment gain or loss offsets the price gain or loss. Its assumptions matter in answers: immunization protects against parallel shifts only, drifts out of alignment as time passes, and needs rebalancing. A plausible mistake is presenting a barbell as 'immunized' because its average maturity matches the horizon; average maturity does not control price sensitivity, duration does.
The Anchor-Bond Exercise, Scoring Rubric, and a Four-Week Study Sequence
Build one anchor bond and push it through every topic weekly, scoring your outputs against expected values. Follow a rotating four-week sequence: pricing and yields, duration, credit and Pakistani instruments, then portfolio strategy.
Exercise. Define the anchor bond: face 1,000, annual coupon 8% (80), four years to maturity, market yield 7%. Compute, from a blank page: the dirty price; accrued interest and clean price 40 days after a coupon date (simplified, ignoring pull-to-par over those days); current yield; the yield ordering; Macaulay and modified duration; and the linear percentage price estimate for a 50 basis point yield rise. Expected observations: dirty price about 1,033.9; accrued interest about 8.9, clean price about 1,025; current yield about 7.74%; ordering coupon 8% above current yield above YTM 7% because this is a premium bond; Macaulay duration about 3.59 years; modified duration about 3.35, smaller because it divides by 1.07; price change estimate about -1.67%.
Score yourself against the rubric below and rerun the exercise weekly with one variable changed, for example yield 9% to create a discount bond and flip the ordering. A suggested four-week sequence, adaptable to your calendar: week one, pricing, accrued interest, and yield measures; week two, duration and convexity drills including money duration; week three, credit spreads plus the Pakistani instrument set; week four, portfolio strategies and mixed timed sets combining all topics. Treat self-check scores as learning milestones for your own tracking, not as predictions of any exam outcome. Administrative matters such as registration and scheduling are set by the issuer; confirm them directly at the IFMP website.
- Rubric: dirty price within about 2 of 1,033.9 at a 7% yield shows your discounting is intact.
- Rubric: accrued interest near 8.9 and clean price near 1,025 show the day-count step is not skipped.
- Rubric: current yield near 7.74% and the ordering 8% > 7.74% > 7% show premium-bond logic.
- Rubric: modified duration (3.35) below Macaulay (3.59) shows you know which divisor applies.
- Readiness check: after switching the yield to 9%, you can state the new ordering without recomputing everything.
- Readiness check: you can size a hedge in currency terms using money duration, not just percentages.
- Readiness check: for the ladder, barbell, bullet, and immunization cases, you can name the objective each fits and the risk each leaves open.
References and further reading
Use these references to explore the concepts and check the latest information from the relevant organizations.