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Fundamentals of Bond Valuation

A bond's cash flows are known in advance, so valuation is pure discounting. The only question is the rate.

P=∑t=1nC(1+r)t+F(1+r)nP = \sum_{t=1}^{n}\frac{C}{(1+r)^t} + \frac{F}{(1+r)^n}

Price and yield are the same statement

This is the point to internalise: quoting a price and quoting a yield are two ways of saying the same thing. Given one, the other follows.

Yield to maturity is the discount rate that makes the formula produce the observed price. It is an internal rate of return, and there is no closed form, so it is solved numerically.

Three relationships follow immediately and are worth knowing on sight:

  • Price above face means the coupon exceeds the yield, so the bond trades at a premium.
  • Price below face means the coupon is below the yield, a discount.
  • Price equal to face means coupon equals yield, trading at par.

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