Library/CFA (Chartered Financial Analyst)/JuiceNotes 2024 Fixed Income/Fixed-Income Bond Valuation: Prices and Yields

Fixed-Income Bond Valuation: Prices and Yields

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Bond Valuation Fundamentals10 min

This section establishes the core concepts of bond pricing. A bond represents a loan where the issuer pays a coupon rate on the face value and repays the principal at maturity. The market value is determined by discounting these future cash flows at the market discount rate or Yield to Maturity (YTM). The YTM represents the expected total return if the bond is held to maturity, assuming full payments are made and coupons are reinvested at the same rate. The section also highlights the inverse relationship between bond prices and yields: as yields rise, prices fall, and vice versa. It introduces the concept of 'convexity,' where the price-yield relationship is curved rather than linear.

Key Points

Market Value = PV of future cash flows discounted at YTM.
Inverse relationship between price and yield.
Convexity: Price increase for a yield drop is larger than price decrease for a yield rise.
YTM assumptions: Hold to maturity, no default, reinvestment at YTM.

Pricing Conventions and Matrix Pricing8 min

This section differentiates between Full Price (Dirty) and Flat Price (Clean). The full price includes accrued interest and is the actual transaction price, while the flat price is the quoted price used to avoid misleading trends caused by interest accrual. Matrix pricing is introduced as a technique to value illiquid bonds by interpolating yields from comparable liquid bonds (benchmarks) based on maturity and credit quality.

Key Points

Full Price = Flat Price + Accrued Interest.
Quoted prices are typically Flat Prices.
Matrix pricing uses linear interpolation of comparable bonds.
Used when current market prices are unavailable.

Yield Measures and Spreads12 min

This section covers various yield metrics. It explains periodicity, distinguishing between annual and semiannual compounding (bond equivalent yield). It defines spreads used to assess credit and liquidity risk: G-spread (over government bonds), I-spread (over swap rates), and Z-spread (constant spread over the entire spot curve). It also introduces Option-Adjusted Spread (OAS) for callable bonds, which removes the value of the embedded option from the Z-spread.

Key Points

Bond Equivalent Yield usually assumes semiannual periodicity.
G-spread uses government bond yields as a benchmark.
I-spread uses swap rates as a benchmark.
Z-spread is the static spread added to the spot curve.
OAS = Z-spread - Option Value.

Floating Rate and Money Market Valuation10 min

The final section addresses floating-rate notes (FRNs) and money market instruments. FRN coupons adjust based on a reference rate (MRR) plus a quoted margin. The bond trades at a premium or discount depending on whether the quoted margin is higher or lower than the market's required margin. Money market instruments are quoted using either discount rates (e.g., T-bills, CP) or add-on rates (e.g., CDs, Repos). The section details how to convert between these conventions to compare yields effectively.

Key Points

FRN Price depends on Quoted Margin vs Required Margin.
Money market yields: Discount vs Add-on.
Discount Rate uses Face Value as the denominator.
Add-on Rate uses Principal (Price) as the denominator.

Questions

Question 1

What does the Yield to Maturity (YTM) of a fixed-rate bond represent?

Fixed-Income Bond Valuation: Prices and Yields

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