Statement:
Straight bonds have positive effective convexity: the increase in the value of an option-free bond is higher when rates fall than the decrease in value when rates increase by an equal amount.
Is this simply because when rates rise the price of a straight cannot go below 0?
I understand it like this, dy/dx(so the second order) for a rectangular hyperbola curve is higher as x moves towards zero.
Draw the yield curve.
Zilch
dude, English please. Just a simple explanation will suffice.
No, its because the curve between value of a straight bond and rates is like the shape of hyperbola (Looks somewhat like this , ignore the points).
Just assume a level of interest rate and the corresponding value. Now increase/decrease the interest rate by same amount. You will be able to understand that the increase in the value is higher when rates fall than the decrease in value when rates increase.
Convexity is second order sensitivity wrt int rate d2p/di2 . And Price vs Yield curve is a rectangular hyperbolic.
if you draw a yield curve you will see dp ( or change in price) is higher for the same amount of change in interest rate ( di) for lower values of i .Hence from a same interest rate point if you traverse same distance to right and to left change in price will be higher when you traverse towards left. That means price sensitivity of a straight bond is higher if int rate decreases.
Not exactly.
Bear in mind that modified duration does not give the slope of the price/yield curve; i.e., it does not give the (total) price change for a small change in yield. It gives the _ percentage _ price change for a small change in yield. It’s the slope of the ln(price)/yield curve.
Similarly, (modified) convexity does not give the change in the slope of the price/yield curve; it gives the change in the slope of the ln(price)/yield curve, or the change in the _ percentage _ price change.
Once again, this isn’t true.
It’s a reasonable way to visualize the price/yield curve (as long at you realize that the vertical asymptote occurs at a yield of −100%, not at a yield of 0% as people often draw it), but it isn’t remotely an hyperbola.
Essentially, yes.
(Properly, it isn’t that the constraint that the price must be positive causes the positive convexity, it’s that the effect of discounting causes both the positive convexity and the nonnegative price constraint.)
Thank you Magician. 
My pleasure.
Did you really have to use the terms rectangular hyperbolic…? lol
