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Why Yield to Maturity Requires a Price

Article Quant Q&A · Author: Kosta S.
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Summary

The document explains why yield to maturity cannot be computed for a loan portfolio without a price or present value. YTM is a way to express the relationship between a bond’s price and its promised cash flows as a yield, which can help compare instruments with differing maturities or coupon rates. It is therefore derived from price rather than an independent measure that can be calculated from cash flows alone.

For loans that do not trade and have no observable market quote, a valuation input is still needed to produce a yield. The questioner proposes the present value of the mortgage as the available price, and the answer confirms the need for a price but does not discuss how that present value should be estimated or whether it represents a market value. As a result, the note clarifies the conceptual requirement for YTM while leaving valuation methodology, loan prepayments, defaults, and other cash-flow uncertainties outside its scope.

Key ideas

  • Yield to maturity is a transformation of price and promised cash flows.
  • A market quote is not the only possible price input, but some price or valuation is required.
  • A present value can serve as an input only if the analyst has established how it is determined.
  • The discussion does not specify how to value illiquid loans or adjust their cash flows.

Tags

Fixed income
Full text
# YTM of a Fixed-Income Loan?


# YTM of a Fixed-Income Loan?












I'm quite confused regarding the computation of a YTM.

I got a Portfolio of Single Loans 30Y(like a MBS) which are not traded and hence do not have a market price. Now I want to compute the YTM in the usual manner but as far as I know in order to do so I need a (market) price, which does not exist in my case. The only price I could get is the Present Value of the Mortgage?

Thanks,

KS

## Answer by Chris Taylor (score 1)

https://quant.stackexchange.com/a/35192

Yes, you need a market price to compute the yield to maturity. The YTM is just another way of expressing price that puts different bonds (e.g. with different maturities or coupon rates) onto something approaching the same footing. Since it is a transformation of price, you can't calculate it without knowing the price.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.