Why Coupon-to-Yield Ratios Fail for Short-Maturity Bond Pricing

Summary

The note evaluates whether a bond index price can be approximated by dividing average coupon yield by yield to maturity. It explains that this ratio is appropriate in the limiting case of a bond with infinite maturity, where price is tied to coupon divided by yield. That relationship does not generally hold for bonds with finite maturities.

A one-year annual-pay bond provides a counterexample: its price depends on both coupon and principal repayment, discounted by the yield, so the simple ratio can be substantially inaccurate. The answer therefore cautions against using coupon yield divided by yield to maturity as a general basis for estimating bond index price returns. It does not quantify an error tolerance for an index; actual results depend on maturity structure, coupon timing, and the index's composition.

Key ideas

• Coupon divided by yield is a limiting approximation for an infinite-maturity bond.
• Finite-maturity bond prices also reflect repayment of principal at maturity.
• A short-dated bond can be poorly represented by the coupon-to-yield ratio.
• Index price-return estimates need maturity and cash-flow information beyond average coupon and yield.

Tags

# Bond yield to maturity vs current interest yield


# Bond yield to maturity vs current interest yield












How close is yield to maturity usually to current interest yield? Can I use yield to maturity to approximate current interest yield of a bond index?

I am trying to calculate bond index price returns and I only have yield to maturity and average coupon yield. Can I just divide average coupon yield by yield to maturity to get a "reasonable" approximation of bond index price, to get price returns with ~10% error?

## Answer by dm63 (score 4)

https://quant.stackexchange.com/a/34663

Not really. For infinite maturity bonds we have $Price = coupon/yield$ so your approximation is actually correct. However for short dated bonds it is not a good approximation. For example , a 1 year annual pay bond gives $Price=(1+coupon)/(1+yield)$ which is very poorly approximated by $coupon/yield$.

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