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When people say "yield curve", do they mean yield/time curve, or yield/price curve?

It seems that most of the time, people refer to yield/time curve, as wikipedia suggests. Though sometimes, people seem to use this term referring to yield/price curve, often when talking about the convexity, like here in investopedia.

What is the right definition?

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Usually yield/time is the standard context for definition of a yield curve, with yields being derived from prices (of interest rate instruments) for certain maturities (times). The investopedia article you are referencing is all about the yield/price connection (since duration and convexity represent first and second order "price" sensitivity measures to "rate" changes) - so that is why you shouldn't view that article as the default context for yield curve lingo.

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