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Fixed IncomeModule 3 of 5

Fixed-Income Bond Valuation

4

Concepts

4

Formulas

1

Decisions

3

Quiz Questions

Key Concepts

4 concepts covered in this module.

Bond Pricing

PV of future cash flows discounted at YTM. Premium: coupon > YTM. Discount: coupon < YTM. Par: coupon = YTM.

Spot Rates

Yields on zero-coupon bonds. Used to discount each cash flow at the appropriate maturity rate.

Forward Rates

Future short-term rates implied by spot rates. No-arbitrage condition links spot and forward rates.

Flat vs Full Price

Full (dirty) price = Flat (clean) price + Accrued interest. Quoted price is usually clean.

Formulas

4 essential formulas for this module.

Bond Price (YTM)

P = Σ C/(1+y)t + FV/(1+y)n

Where: y = YTM per period

Bond Price (Spot Rates)

P = C/(1+S1) + C/(1+S2)² + ... + (C+FV)/(1+Sn)n

Where: St = spot rate for maturity t

Accrued Interest

AI = Coupon × (Days since last coupon / Days in coupon period)

Where: Linear interpolation between coupon dates

Full Price

Full Price = Clean Price + Accrued Interest

Where: What the buyer actually pays

Decision Frameworks

1 decision frameworks to guide your analysis.

When does a bond trade at premium/discount?

  • Premium: coupon rate > market yield (investors pay extra for higher coupons)
  • Discount: coupon rate < market yield
  • Par: coupon rate = market yield

Mind Map

Visual overview of how concepts connect in this module.

Bond Valuation
Pricing
PV of cash flows
YTM discount
Spot rate discount
Premium/Par/Discount
Yield Curve
Spot rates
Forward rates
Par rates
Yield spreads
Price Concepts
Clean (flat) price
Dirty (full) price
Accrued interest
Day count conventions
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Bond Pricing

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Answer
PV of future cash flows discounted at YTM. Premium: coupon > YTM. Discount: coupon < YTM. Par: coupon = YTM.
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Fixed-Income Cash Flows and Types

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Interest Rate Risk and Duration