Convexity of bonds
Hello Folks,
I am reading on convexity of bonds and I am confused on a few of the concepts.
A bond with greater convexity is less affected by interest rates than a bond with less convexity. Also, bonds with greater convexity will have a higher price than bonds with a lower convexity, regardless of whether interest rates rise or fall.
In general, the higher the coupon rate, the lower the convexity of a bond. Zero-coupon bonds have the highest convexity.
So does this mean we want bonds that have low convexity correct? Because they have higher coupon rates, lower duration and low price volatility compared to zero bonds who have higher convexity and more price volatility?
Please share your thoughts.
That's the idea but remember it depends on the dynamics of the portfolio and how the specific bond fits into the parameters.
From what I learned, you definitely want a bond with high convexity.
Low coupon, high duration, high convexity.
Convexity is good. Why? Because you get more bang for your buck. If interest rates come down, bond price increases.
However, a high convexity bond will increase in price higher than a bond with low convexity.
....
That is the graph I was trying to look for. The clue is to see what happens to the bond price of the bond with higher convexity.
longer maturity bonds have higher convexity, why? (Originally Posted: 10/07/2012)
Hi,
I can't seem to get the intuition, why longer maturity bonds have higher convexity than shorter maturity bonds.
Let's take treasuries. Why a longer duration treasury (say 30yr) will have a higher convexity than a 10yr treasury?
Imagine you have two non-callable bonds. One is a 10 year bond, the other 30. Both have a 5% coupon and the yield curve is perfectly flat (any maturity bond requires a 5% yield). Tomorrow the required yield goes down to 4% (still flat). In order to trade at a 4% yield, the price on the 30 year bond will go up more (a lot more actually) than the 10 year bond. Basically you will benefit from the higher coupon for longer so the price is more sensitive to interest rate movements.
Really stupid question on convexity (Originally Posted: 10/08/2012)
Can someone confirm or deny that this Investopedia definition is incorrect: http://www.investopedia.com/terms/c/convexity.asp#axzz28jtXFEk5
How can the relationship between a bond's price and its yield be anything but fixed? When a bond's price goes down, it's yield goes up (reflecting more risk).
I thought convexity had something to do with the second derivative of yield or some shit like that (hence why I was looking it up)
Thanks
It is most certainly correct. It is the second derivative of the price of the bond with respect to interest rates (duration is the first). When the price of a bond increases, yield decreases. And vis-a-vis. But that relationship is not linear, as duration assumes. It is non-linear, like the graph on investopedia shows.
Can you help me understand this please. I thought a yield was Coupon Payment / Price (that's what Investopedia says: http://www.investopedia.com/terms/c/currentyield.asp#axzz28jtXFEk5).
What determines P is a factor of risk, what determines PMT is a given.
The graph in the original link graphs P against Y, but Y is a function of P and PMT...?
If the source ends in "pedia," you don't question it.
College 101
What about uncylcopedia?
You realize that if something has a second-derivative then the first derivative will not demonstrate a linear relationship, right? (Assuming the second derivative is not a constant.)
Coupon payment / Price is your current yield, not your yield to maturity. When people say "yield" they probably mean YTM. You are not even looking up the right term! YTM takes into account the price of the bond and assumes that you also are able to reinvest all your coupons. The simple math is this: a 5-year bond that pays 10% coupons and is selling at $90 will have a yield to maturity of ~13%. You get a 10% coupon for $90 invested, which is a 11.1% current yield, plus you are collecting $10 over the next 5 years, which is $2 per year, or 2% of par.
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