7 Writing Service đã đạt HD với Bond Portfolio Mid-term của BAFI3271 bằng cách:

1. Tiếp cận đề

Assignment 1 của BAFI3271 là bài foundational về bond mathematics. Trước khi bạn có thể quản lý bond portfolio (như A3), bạn phải master bond pricing, yield concepts, duration và convexity. Bài thường có cấu trúc 3-4 parts:

  • Bond pricing under different yield environments
  • Yield to Maturity (YTM) và Yield to Call (YTC) calculations
  • Duration và Convexity computation
  • Yield curve analysis và term structure

Bài này có khá nhiều tính toán nhưng không phải pure math exercise. Marker muốn thấy bạn understand intuition behind formulas. Tại sao bond price và yield inverse related? Tại sao long-term bonds có duration cao hơn? Tại sao convexity is desirable feature?

Hướng dẫn cùng ngành Finance:

2. Outline chuẩn HD

Section 1: Bond Pricing Fundamentals

  • Price as PV of future cash flows: P = Σ C/(1+y)^t + F/(1+y)^n
  • Coupon rate vs yield: premium, par, discount bonds
  • Clean price vs dirty price (accrued interest treatment)
  • Price tables for various coupon/yield combinations
  • Price-yield curve (downward sloping, convex)

Section 2: Yield Measures

  • Yield to Maturity (YTM): single discount rate equating PV to price
  • Current Yield = annual coupon / price (incomplete measure)
  • Yield to Call (YTC) for callable bonds
  • Yield to Worst (lower of YTM, YTC) for callable bonds
  • Realized yield (assumes specific reinvestment rates)
  • Comparison across yields: when each is appropriate

Section 3: Duration

  • Macaulay Duration: weighted avg time to receive cash flows
  • Modified Duration = Macaulay / (1 + y)
  • Effective Duration for bonds with embedded options
  • Price approximation: ΔP/P ≈ minus Modified Duration x Δy
  • Duration of zero-coupon bond = maturity
  • Duration of perpetuity = (1 + y) / y
  • Portfolio duration = weighted avg of individual durations

Section 4: Convexity

  • Convexity formula and interpretation
  • Second-order Taylor approximation: ΔP/P ≈ minus D x Δy + 0.5 x C x (Δy)^2
  • Why convexity is desirable (asymmetric payoff)
  • Convexity adjustment for large yield changes

Section 5: Yield Curve Analysis

  • Spot rates vs forward rates
  • Bootstrap method to derive spot curve from coupon bonds
  • Forward rate calculation: (1+f) = (1+s_n+1)^(n+1) / (1+s_n)^n
  • Yield curve shape: normal, flat, inverted, humped
  • Theories: Pure Expectations, Liquidity Preference, Market Segmentation

3. Theory cần nắm

Bond Pricing Mechanism

Bond price = present value of all future cash flows. Coupon payments are annuity, face value is single cash flow at maturity. When yield rises, denominator (1+y)^t increases, present value falls, price decreases. When yield falls, opposite. This inverse relationship is fundamental. Magnitude depends on duration: long-duration bonds more sensitive to yield changes.

Yield to Maturity Logic

YTM is single discount rate that, when applied to all future cash flows, gives current market price. YTM assumes: (1) bond held to maturity, (2) all coupons reinvested at YTM. Both assumptions often violated in practice. Realized yield differs from YTM if interest rates change during holding period (reinvestment risk).

Duration Intuition

Macaulay duration = weighted average time to receive cash flows, with weights = present values. Zero-coupon bond duration = maturity (only one cash flow). Coupon bond duration < maturity (cash flows distributed). Higher coupon = lower duration. Higher yield = lower duration (later cash flows discounted more heavily, lose weight). Modified duration approximates % price change for 1% yield change.

Convexity Intuition

Duration assumes linear price-yield relationship. Actually, relationship is convex. Convexity adjustment captures curvature. Convexity good for investor: when yields fall, prices rise more than duration predicts; when yields rise, prices fall less than duration predicts. Asymmetric favorable. Higher convexity bonds preferred all else equal, often demand lower yield.

Term Structure Theories

Pure Expectations: forward rates = expected future spot rates. Yield curve shape reflects rate expectations only. Liquidity Preference: investors prefer short-term bonds (less risk), demand premium for long-term. Adds liquidity premium increasing with maturity, biasing yield curve upward. Market Segmentation: different investors have different maturity preferences (pension funds prefer long, banks prefer short). Supply-demand at each maturity drives rates.

Inverted Yield Curve Signal

When short rates exceed long rates, yield curve inverts. Historically reliable recession predictor (US 2-10 year inversion preceded most recessions). Implies market expects rate cuts ahead, typically because economy slowing. Mention current yield curve state: as of late 2025/early 2026, US curve normalizing after extended inversion 2022-2024.

4. Tips làm bài

Tip 1: Build pricing function in Excel. Create cell function: input coupon rate, face value, periods, yield. Output: price using PV formula. Test by reproducing textbook examples. This becomes your engine for all subsequent questions.

Tip 2: YTM calculation needs Solver or Goal Seek. YTM solves implicitly: given price, find y. Excel YIELD function works but understand mechanics. Use Goal Seek: set price cell to actual price, change yield cell. Or Solver with constraint. Show iteration process in your work.

Tip 3: Duration table for multiple bonds. Format:

  • Bond A (3% coupon, 5Y): Macaulay 4.71, Modified 4.55, Convexity 24.8
  • Bond B (5% coupon, 10Y): Macaulay 8.02, Modified 7.74, Convexity 75.2
  • Bond C (zero, 7Y): Macaulay 7.00, Modified 6.76, Convexity 49.2

Then explain patterns: zero-coupon highest duration for given maturity, longer maturity higher duration, lower coupon higher duration.

Tip 4: Sensitivity table for price changes. Show predicted price change using duration only vs duration plus convexity, for yield shocks of plus/minus 50bps, 100bps, 200bps. Compare to actual recalculated prices. As shock size grows, convexity adjustment becomes more important. Visual evidence why convexity matters.

Tip 5: Bootstrap spot curve from coupon bonds. If given 1Y, 2Y, 3Y coupon bonds prices, derive 1Y, 2Y, 3Y spot rates. Method: 1Y spot from 1Y bond directly. For 2Y bond, use 1Y spot to discount first coupon, solve for 2Y spot to make PV equal price. Iterate forward. Show all steps.

Tip 6: Forward rate interpretation. 1Y forward rate 2 years from now = market's implied expectation of 1Y rate at that time. Use forwards to compare strategies: roll over 1Y bonds vs buy 3Y bond. If forward rates accurate, returns should equalize (Pure Expectations).

Tip 7: Connect to current monetary policy. Discuss current yield curve shape and what it implies. "As of early 2026, the Australian yield curve has normalized from inversion experienced 2023-2024, with 10Y AGB yielding around 4.2% versus 3M bills at 4.0%, implying market expects RBA on hold near term." Make analysis current.

Tip 8: Discussion of immunization preview. Even though A1 doesn't require immunization (that's A3), mention how duration concept enables immunization: by matching portfolio duration to liability duration, you neutralize interest rate risk. This shows you see the bigger picture, integrating with later assignments.

Nếu bạn cần mình giúp tính YTM, build duration table, hoặc làm trọn bài BAFI3271 A1 này. chỉ cần inbox 7 Writing Service. Bond math là specialty bọn mình làm rất nhiều cho RMIT students.

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