# Duration - error

Schweser p. 126 book 3 “Due to the linear nature of duration, which makes it overestimate the increase or decrease in the value of the portfolio, the convexity effect must also be considered.” Shouldn’t this read underestimate rather than overestimate? Positive convexity on a bullet is a good thing. There is nothing in the errata. Please explain why I am an idiot.

Actually, the linear nature of duration causes its use to underestimate the increase in value due to declining interest rates and overestimate the decline in price due to increasing interest rates (assuming positive convexity). It helps to picture the graph of duration and convexity.

I was thinking the exact thing as McLeod

underestimates the increase in price and overestimates the decrease in price. that is why when adjusting for positive convexity you always add something to the price calculated by duration. right?

Because “overestimates the DECREASE in price” means that the price is actually higher than what duration predicts (it went to far).

Yeah. I can see that with the graph McLeod. So you agree the statement is incorrect as written?

I am with you guys on this one. But I had to draw the graph to see it. That makes it pretty easy to see.

Yeah, whoever wrote that probably wasn’t really thinking about what they were saying. Duration is the first derivative of the price / interest rate relationship while convexity is the second derivative. As such, duration underestimates the curvature of the real relationship.

Nothing like some Level 1 concepts to throw more confusion into the mix. I agree, duration underestimates price increases, overestimates price decreases. Unless I need to go back to Start, do not pass go, do not collect \$200.

Here is a quote from the Secret Sauce book Pg 149. “Duration alone underestimates the increase in price form a decrease in interest rates and overestimates the decrease in price form an increase in interest rates.”

perfect.