NISM CFA Level 1, Fixed Income. Updated Jun 2026, 15-minute read.
CFA Level 1 Fixed Income — Bond Valuation, Duration, and Credit Analysis
Fixed Income is 11–14% of CFA Level 1 (~20 questions). The emphasis at Level 1 is bond mechanics — pricing, yield measures, duration, convexity, and an introduction to credit analysis. Fixed income deepens significantly at Level 2 (interest rate models, spread analysis, structured products) and Level 3 (portfolio construction).
Key takeaways
- Bond price = PV of coupon payments + PV of face value — discounted at YTM (Yield to Maturity)
- YTM: the single discount rate that makes PV of bond cash flows equal to price — it's a promised yield, not guaranteed return
- Price-yield relationship is inverse: as yields rise, prices fall (and vice versa)
- Macaulay Duration = weighted average time to receive bond's cash flows (in years)
- Modified Duration = Macaulay Duration / (1 + YTM/m) — % price change per 1% yield change
- Convexity correction: actual price change = (−Modified Duration × ΔY) + (½ × Convexity × ΔY²)
- Credit spread = yield of corporate bond − yield of comparable maturity government bond
- Investment grade: BBB−/Baa3 and above; High yield (junk): BB+/Ba1 and below
Bond Pricing
A bond's price is the present value of all its future cash flows:
Price = Σ [Coupon / (1+YTM)^t] + [Face Value / (1+YTM)^n]
For a semi-annual bond: use semi-annual coupon = Annual Coupon / 2, and semi-annual YTM = YTM / 2, and n = years × 2.
Example: 5% annual coupon, 3-year bond, face value ₹1,000, YTM = 6%:
- Year 1: 50 / 1.06 = 47.17
- Year 2: 50 / 1.06² = 44.50
- Year 3: 50 / 1.06³ = 41.98 + 1000/1.06³ = 839.62
- Price = 47.17 + 44.50 + 41.98 + 839.62 = ₹973.27 (discount bond — coupon < YTM)
Price-Yield Relationship
- When YTM = Coupon rate: Price = Face Value (par bond)
- When YTM > Coupon rate: Price < Face Value (discount bond)
- When YTM < Coupon rate: Price > Face Value (premium bond)
Yield Measures
- YTM (Yield to Maturity): Discount rate equating PV of cash flows to price. Assumes coupons reinvested at YTM and held to maturity.
- Yield to Call (YTC): YTM calculated to the call date at call price — relevant for callable bonds in falling rate environments.
- Current Yield: Annual Coupon / Current Price. Simple but ignores capital gain/loss and reinvestment income.
- Effective Yield: For bonds with embedded options, uses option-adjusted spread (OAS) instead of YTM.
Duration
Macaulay Duration
The weighted average time (in years) to receive all cash flows, where weights = PV of each cash flow / Total Price.
Zero-coupon bond: Macaulay Duration = Maturity (all cash flow at end)
Coupon bond: Macaulay Duration < Maturity
Modified Duration
Modified Duration = Macaulay Duration / (1 + YTM/m)
where m = compounding periods per year.
Interpretation: If Modified Duration = 5, then a 1% rise in yield → approximately 5% price decline.
% Change in Price ≈ −Modified Duration × ΔYield
Example: Bond with Modified Duration = 7. Yield rises 0.50%: Price change ≈ −7 × 0.005 = −3.5%
Dollar Duration (DV01)
DV01 (Dollar Value of a Basis Point) = Modified Duration × Price × 0.0001
Used in portfolio hedging — tells you $ change in bond value per 1bp yield move.
Convexity
Duration is a linear approximation of price-yield relationship. Convexity captures the curvature.
More accurate price change = (−Modified Duration × ΔY) + (½ × Convexity × ΔY²)
Positive convexity is desirable: for a given yield move, price rises more than duration predicts and falls less. Higher convexity bonds command a premium.
Callable bonds have negative convexity at low yield levels (price is capped by call price even as yields fall).
Credit Analysis
Credit Rating Framework
| S&P/Fitch | Moody's | Category |
|---|---|---|
| AAA, AA, A, BBB | Aaa, Aa, A, Baa | Investment Grade |
| BB, B | Ba, B | Speculative / High Yield |
| CCC, CC, C, D | Caa, Ca, C | Distressed / Default |
Four Cs of Credit Analysis
- Capacity: Ability to repay — EBITDA coverage, leverage ratios, free cash flow generation
- Collateral: Asset quality — liquidation value in default scenario
- Covenants: Debt covenants protecting bondholders (maintenance covenants, incurrence covenants)
- Character: Management quality, track record, governance
Credit Spread Analysis
Credit Spread = Bond YTM − Risk-Free Rate (comparable government bond)
Spread reflects: Default risk premium + Liquidity premium
In recessions, spreads widen dramatically (flight to quality). In expansion, spreads narrow.
Frequently asked questions
What is the difference between Macaulay and Modified Duration?
Macaulay Duration is the weighted average time (in years) to receive all bond cash flows — it's a time measure. Modified Duration = Macaulay Duration / (1 + YTM/m) — it's a price sensitivity measure, telling you the % price change for a 1% yield change. For exam questions: if asked for price impact of a yield change, use Modified Duration. If asked for weighted average time to cash flows, use Macaulay Duration.
Why does bond price fall when yields rise?
Existing bond coupons are fixed. When new bonds are issued at higher yields, existing bonds paying lower coupons become less attractive — their prices must fall to make their effective yield (YTM) competitive with new issues. This is the fundamental price-yield inverse relationship. Think of it this way: if you paid ₹1,000 for a 5% coupon bond and new 1-year bonds are offering 7%, no one will pay ₹1,000 for your 5% bond — they'll only pay enough that their total return (coupon + price discount) equals 7%.
Written by Arpan Das.
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