How Bond Maturity Changes Convexity at the Same Yield and Price
Summary
Bonds can share a price and yield while having different convexities because their maturities and cash flow timing differ. The examples contrast a bond close to maturity with a much longer bond and describe how a flat yield curve can also produce equal prices and yields alongside different convexity and DV01.
Greater convexity does not automatically make a bond more attractive in every market setting. The discussion suggests expressing views on yield curve shape by pairing bonds with different convexities, while recognizing that relative performance depends on rate movements and investor views. It offers intuition rather than quantitative valuation analysis, and its brief examples do not account for other bond features or trading costs.
Key ideas
- Bonds with equal prices and yields can have different convexities when their maturities differ.
- A longer maturity generally means greater sensitivity to changes in rates.
- Convexity is not universally attractive; its value depends on the market regime and investor view.
- Relative convexity positions can target changes in yield curve shape while reducing exposure to parallel shifts.
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# Can two bonds have same yield and price but different convexity? # Can two bonds have same yield and price but different convexity? In the market, if there are two bonds that have the same yield and price, then the higher convexity bonds will be more attractive. However, this would mean the market would increase the price of the attractive bonds. If the cash flows don't change, this means the yield will go down on the higher convex bond. Given this, does this mean it is impossible to have two bonds with the same yield and different convexities if the cash flows are the same? In the lieu of the changing coupons, time to maturity, will the market always bring down yields (increase prices)? ## Answer by dm63 (score 5) https://quant.stackexchange.com/a/42646 To directly answer the question: bond A= one day to maturity , price 100, yield 2%. Bond B: 10 years to maturity, price 100 yield 2%. This is perfectly possible. Bond B has greAter convexity but it also has substantially more risk. ## Answer by PlantFox (score 1) https://quant.stackexchange.com/a/42645 It is possible for equivalent bonds to have different convexity. Remember, convexity is calculated from duration. Duration is a measure of time / sensitivity (regular / modified). Both convexity and duration relate to time. Convexity is the true sensitive of future cashflows whereas duration is the approximated. If you really want to get in the weeds, you discount each periods cashflow by not the yield of the bond ,but each tenor's yield along a curve. Intuitively when rates fall or rise the bond with more time left to maturity will react more because you are discounting more future cash flows. The key part here is maturity. It is not impossible to have two bonds with equivalent price/yield. A simple example is a sovereign yield curve that is completely flat. Each bond would have the same price and yield , but the convexity would differ hence DV01s would differ. Now to answer your question about market behavior. Well it depends on the market participants views. Convexity is not always viewed as attractive. From a trading/investing prospective you might spread the lower convexity against the higher convexity. Each handles a different regime. If rates are rising, you could long the low convexity and short the high convexity or in falling rate environments, short the low convexity and long the high convexity. The main goal of these strategies is to trade the shape of the yield curve removing the parallel shifts. Please let me know if that answers your question.
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