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Bond Analysis Notes

Term Structure of Interest Rates

  • Bond Yield Curve/Term Structure: Based on economic outlook or bond market dynamics, the term structure can assume various shapes.

  • Types of Curves:

    • Par Curve (YTM): A sequence of YTM that prices a bond back to par or its current market price for various time intervals.

    • Spot Curve: Sequence of YTM on zero coupon bonds (zero rates). Viewed as risk-free (credit risk) and used for bond valuations.

    • Forward Rate Curve: Implied forward rates calculated from spot rates. Links return from shorter-term bonds to longer-term bonds.

Yield to Maturity (YTM)

  • Formula: YTM is mathematically related to spot rates through the no arbitrage principle. The bond's value equals the sum of PVs of cash flows discounted by their corresponding spot rates.

  • Expectations: YTM is not the expected return unless:

    • The bond is held to maturity.

    • All coupons are reinvested at the original YTM.

  • Limitations of YTM: Poor estimator of expected returns if:

    • Interest rates are volatile.

    • The yield curve is steeply sloped.

    • The bond has significant default risk or embedded options.

  • Realized Return: Actual return based on actual reinvestment rates during the bond's holding period.

Bootstrapping

  • Definition: A method to construct a zero coupon curve from prices of coupon-bearing instruments (bonds/swaps).

  • Process:

    1. Use market observable Par Rates to build zero-coupon rates.

    2. Example Calculation:

      • 1-Year Par Rate (NACA) = 5%

    3. Calculate discount factors for successive periods using the bootstrapping formula.

Spot Rates and Forward Rates

  • Relation: An upward sloping spot curve implies the forward curve lies above while a downward sloping spot curve implies the opposite.

  • Forward Rate Calculation:

    • Example of calculating forward rates using spot rates:

      • If Spot Rate (Year 1) = 9% and (Year 2) = 10%, express using the formula.

Yield Curve Factor Models

  • Factors Affecting the Yield Curve:

    • Level, Steepness, Curvature

  • Implication of Changes:

    • Shifts in yields impact bond pricing and sensitivity to interest rates.

  • Macroeconomic Variables: Inflation and monetary policies explain variance in bond yields;

    • Short to medium-term yields respond to inflation, while long-term yields react more to monetary policy.

Yield Spread Analysis

  • G-Spread: Spread over corresponding government bond rates (e.g., 10-year Corporate bond YTM minus 10-year Government bond YTM).

  • Z-Spread: Spread added to the entire benchmark spot rate curve to equal the bond's price based on PV of its cash flows.

  • OAS: Option adjusted spread considering embedded options in callable bonds.

Summary

  • Understanding yield curves and spreads helps in making informed decisions regarding bond valuation and investment strategy. Proper analysis of the relationships among different curves is vital for evaluating market conditions and making investment decisions.