Relative Bond Valuation Using Discount Factors and Replication

Summary

The document considers how to compare the relative value of zero-coupon bonds and a coupon bond when their yields to maturity appear equal. Its central point is that the three bonds form a replication relationship: given prices for two instruments, cash flows and discount factors determine the fair value of the third. The supplied calculation discounts the coupon bond’s cash flows using spot discount factors and compares that value with its quoted price.

The conclusion is relative rather than absolute: under the assumed discount factors and prices, the coupon bond can be described as cheap versus the zero-coupon bonds. Equal yield to maturity alone does not establish which bond is mispriced, since YTM compresses cash flows at different dates into one rate. The comparison depends on the discount curve and the accuracy and comparability of the quoted prices; the brief discussion does not provide a broader arbitrage analysis or address transaction costs.

Key ideas

• Discount each bond cash flow using the spot discount factor for its payment date to estimate value.
• Coupon and zero-coupon bonds can be linked by replication of their cash flows.
• A bond can be cheap relative to another set of bonds without being cheap in an absolute sense.
• Equal yields to maturity do not by themselves imply equal relative value when cash-flow timing differs.

Tags

# Between these bonds, how to find out which is one pricey (Higher valuation) and cheap (Lower valuation)?


# Between these bonds, how to find out which is one pricey (Higher valuation) and cheap (Lower valuation)?












Trying to understand, how to find out which of these bonds are cheap and which are expensive?

The current spot rate is 8.167%. How do I go about finding the cheap vs expensive bonds especially when YTM is same?

## Answer by dm63 (score 2, accepted)

https://quant.stackexchange.com/a/70232

These 3 bonds form a triangle - given the price of two of them, you can calculate the third. So your calc is correct, but all you can conclude is that the coupon bond is cheap relative to the zero coupon bonds.

## Answer by nsivakr (score 0)

https://quant.stackexchange.com/a/70231

Is this correct?

Using discount factors, the 8% coupon bond should be trading at ( 8 * .96154) + ( 108 * .85734) = $100.285

Since it is trading only at $100, the coupon paying bond is cheaper and zero coupon bonds are trading at higher premium.

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