Confused about Duration & Convexity?
I haven't taken the fixed income class yet so I'm just learning this stuff by myself. I've came across many different definitions of duration and convexity, and I was hoping someone can tell me which one is right.
Definitions I got for duration:
- amount of time it takes to recover the cost of the bond
- sensitivity of the bond's price to interest rates
- amount of time it takes to get half of the PV of the bond's cash flows
Definitions I got for convexity:
- second derivative of duration
- measures the curvature of the yield/price curve
- sensitivity of bond's duration to interest rates
So which one is right? More importantly, if I'm asked this in an interview (e.g. define duration and convexity), what answer should I give them? Thanks guys.
2nd one is correct for duration. 2nd and 3rd are correct for convexity.
Where the hell are you finding these other definitions?
The simplest way to explain the concepts in an interview is to walk through how the formulas are derived using a tailor series expansion with f(x) representing the price of a bond with respect to interest rate.
Once you understand this, the rest will begin to make a lot more sense.
Well actually, a more intuitive explanation is that:
Duration is the amount of time to recover the cost of the bond and therefore it is a measure of risk for a bond. Duration isn't a measure of sensitivity but a bond with longer duration would also be more sensitive to interest rates. For example you must have learned that a 30 year bond (a bond with a longer duration) would be more sensitive to interest rate changes (due to the term-structure of interest rates). Its similar to how between two bonds holding everything the same the one with a higher coupon rate would be less interest rate sensitive.
Hope that helped!
This is retarded and incorrect. This is why high school students should not attempt to answer questions.
If you are asked in an interview about duration, do not say it "is the amount of time to recover the cost of the bond"....idiotic.
I was trying to give an intuitive answer asshole, its the same concept as weighted average time to repayment which is the definition of Macaulay's Duration for a Bond straight from Bodie's Investment. The duration definition that was given in this forum is the Modified Duration which is the Macaulay's Duration over 1 + YTM / # of coupon periods of the year. The modified duration which show how much duration changes for each percentage change in yield. Both are classified as duration. In an interview, the interviewer would probably specify which duration he/she would want you to define, the Macaulay, Modified, Spread, Keyrate, Effective, Bear-Bull. The definition I was giving was for the most common type of duration.
I don't usually argue on the internet as it is pointless, achieves nothing, and is a complete waste of time. I thought I'd made an exception for scum like you who are single-handedly destroying the forum. Why don't you try to actually contribute to the topic instead of attacking other users.
Think of it like this: duration is the linear relationship between prices and interest rates. If interest rates rise by 1% and you have a ten year duration, your bond price will fall by about 10%. Duration works best for small changes in interest rates.
Convexity: the real relationship between rates and prices is not linear and the convexity measure tells you how curved the relationship is and measures the change in duration for a change in rates. So, if you have a duration of 10 years, if rates fall by 1%, the bond price will increase by something more than 10% and will fall by something less than 10% if rates rise by 1%, for any bond that has positive convexity
One question I have seen some people ask in interviews is 'where do you encounter negative convexity'? It happens in a large part of the bond market. I can tell you if you have trouble figuring it out, but try to figure it out before just Googling it.
I would suggest you run some figures to understand the concepts more clearly. Price a bond at various interest rates and see how that compares to the prices you got by estimating the price changes by using duration.
Duration, Convexity and Immunization (Originally Posted: 01/17/2018)
If a bond trader structures his portfolio to take advantage of positive convexity but wants immunizes his portfolio to have zero duration, what is the exposure if the interest rate has no effect or does it? Unlike Options, I can take advantage of the volatility but with bonds, it's not the case. So any insights would help?
Thanks for the convexity def. I always thought duration was a much easier concept to grasp. To OP, I guess for convexity, your 3rd listed def would be the closest.
Waiting for the usual responders. Brings out popcorn
lower coupon bonds have higher convexity...so you could go long a 30yr zero coupon, such as the Nov 2047 principle strip, vs short a 30yr coupon bond (for simplicity, lets use the Nov 2047 30yr bond). Even after you hedge out the majority of the curve component of the 30yr zero (using 2yr, 5yr, 10yr, 20yr notes and coupon benchmark bonds), you can be long convexity, and will be flat duration. Its a very small component of your PnL....but its there. even bigger will be coup-prin spread exposure. Again, pretty small compared to everything else...but non-zero.
However, in a low rates environment such as we are currently in, this is not where the majority of your PnL will come from. Thats RV
Isn’t it mostly a mbs versus treasuries trade?
You can do a flattener, if you desire positive convexity with no outright duration... Obv, you will be taking curve risk in such a case.
There are some other, more fanciful ways of doing this stuff, but they would probably involve weirder concoctions
One way to intuitively think about convexity is this: imagine you have a bond with a ten year duration and interest rates rise by 10%. Your simple linear estimate of the price change using duration would be that the bond price decreased by 100%, which is clearly not true.
Duration and Convexity (Originally Posted: 10/10/2017)
I understand that actual bond prices are convex and that duration is graphically a straight line between price changes and interest rate changes which equates to the first derivative of the bond. What I don't get is when using duration to forecast changes in a bonds price, why does the forecast become less accurate given a greater change in interest rates? Also, why do interest rate increases seem to have less of an affect on duration and convexity than interest rate decreases?
Hi Bruce Wayne, any of these threads helpful:
More suggestions...
Fingers crossed that one of those helps you.
If you are a math/physics guy, duration is the equivalent of speed and convexity is the equivalent of acceleration. First derivative (in the mathematical sense) of the px of bond wrt interest rates vs second derivative.
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