 # duration vs rate duration

Vol. 5 p270 It explained duration a bit here: “… Duration estimates the % price change for 100 pbs change in yield. As can be seen, duration is a measure of the price sensitivity of a bond to a change in yield”. p286 Summary “Duration is a measure of interest rate risk; it measures the price sensitivity of a bond to interest rate changes.” So one is talking about duration in relation of change in yield and the other is talking about it in relation of change in interest rate. Which should I refer to? I vaguely know there are some nuances btwn them, I’m just not there yet. Can someone explain? Rate duration is the % value change of the bond porfolio in response to one maturity’s yield change assuming all other maturities’ yields unchanged. What’s the relationship of duration and rate duration? Is rate duration a special case of duration?

Yes interest rate is in fact the yield. Do not confuse interest rates with coupon rate. The coupon rate does not change at all. Interest rates do change which in bond markets they call them yield. I may need to go back to the book and look at it but i think duration rate is the rate of change in bond price due to duration effect ( I may be wrong on this one, i do not have the book with me to look at it.

Thx. It’s not duration rate - it’s rate duration. Market interest rate is different than the bond’s interest rate? And are the terms of bond’s interest rate and bond’s yield interchangeable? So the bond’s interest rate is the one required by market?

hyang Wrote: ------------------------------------------------------- > Thx. It’s not duration rate - it’s rate duration. > > Market interest rate is different than the bond’s > interest rate? And are the terms of bond’s > interest rate and bond’s yield interchangeable? So > the bond’s interest rate is the one required by > market? For a “plain vanilla” coupon bond, the bond’s coupon rate is contractual, and fixed at issue. It’s really another way to define the coupon payment (i.e. Coupon Payment = Par Value * Coupon Rate). The yield is the market interest rate (or discount rate) implied by the current price of the bond. The market price is the present value of the cash flows promised by the issuer (i.e the coupon payments and par value at maturity), discounted at a risk-appropriate interest rate. Calculating the “yield” involves “driving the process in reverse” (i.e. finding the discount rate that results in the current market price). It’s equivalent to the IRR of the bond.

Thanks, busprof. I may have to complete the study of the entire section of fixed income to better understand this. For now I realized “interest rate” could have various meanings depending on the context.

The rate duration (or usually key rate duration) is the change in the bond’s price relative to a change in the a single market interest rate and usually this would be a risk-free rate (but a risky rate makes sense too, but you would need to explain that). This could be important in, say, mortgage backed securities where securities are not very sensitive to low key rates (e.g., 1 year) because nobody refinances because 1-yr rates drop. Edit: You can get a duration if you know all the key rate durations but not the other way around. Give me a duration and a couple of key rate durations, I might be able to get you a different key rate duration…

Thanks, Joey. Key rate duration is the rate duration in respect to a change in a key maturity sector. I think this is more advanced topic in Level II. Duration measures the price sensitivity of a bond to interest rate changes. So you are saying “interest rate” here refers to the risk-free market interest rate. It’s the same one you often hear from the news such as “Fed lowered interest rate half point again” etc. And this interest rate is obviously different than the bond’s interest rate which sometimes is also called “yield”, right? My mind was trying to figure out the interplay of risk-free market interest rate; bond’s interest rate/yield and bond’s coupon rate…