In a non-mathematical way, and before our next lecture on actually calculating convexity, we try to explain why convexity has to be taken into account, particularly for large interest rate moves in either direction.
At the limit, interest rates moving down have a proportionally larger and larger effect on bond prices. Similarly, interest rates moving up have a proportionally smaller and smaller effect on bond prices.
Taken together at the limit of infinitely small interest rate moves, these two effects create convexity in the bond price, when measured against changing interest rates.
The flat-sloped tangential line of Modified Duration will then tend to underestimate price moves up, when interest rates move down, and will tend to overestimate price moves down, when interest rates move up.
This is the calculus principle behind convexity.
In our next lecture, we will actually calculate convexity.
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