Can someone please assist me here. I have memozied all the rules of duration and they all make sense other than the following:
“Higher market yields means lower interest rate risk”
Can someone please explain why this is the case, I just can not get my head around why this is the case.
Thanks guys
My understanding is because of the non linearity of the price /yield relationship. SInce this relationship is convex, after a certain level, increase in interest rates will have a (diminishing)marginal effect on price. Convexity almost acts like a floor. I hope this helps.
i was thinking about it: Duration basically tells us when the cash flows are being received… the higher the YTM means a higher discount rate and makes the bulk principle or face value less… thus increasing duration
That is one way to interpret it, however, how would you then explain negative duration in the case of an MBS. Though it is commonly used as a measure of time it may be more appropriate to use it as a measure of price sensitivity. For eg, a duration of 3 could be explained as the price sensitivity of a Zero with a TTM of 3 years. You get your cake and it too! In this manner, you are better positioned to estimate interest rate risk. My 2c.
The price-yield profile is convex. At high yeilds the slope (or duration) of the curve is flatter (lower). Lower duration means lower interest rate risk.
For a given percentage change in interest rate there is a lower percentage change in price change at high yields. This is because the slope is flatter at high yields. If you draw along the curve at high yields you can see for a given change, the price of the bond does not change that much.
Interest rate risk is associated with the percentage change in price with 1% (100 bps) change in yield. Bonds with higher market yields have less price sensitivity to changes in interest rates. For this reason the zero coupon bonds have greater price sensitivity. Consider this example. Suppose a 6% 20-year bond selling to yield 6%. A rise in yield required by the investor to 6.5% will cause the price of the bond to fall from 100 to 94.4479 which is 5.55% whereas another bond with same maturity (20 years) and 9% coupon paying selling to yield 6%, a rise in yield required by the investor to 6.5% will case the price of the bond to fall from 134.6722 to 127.7605 which is 5.13%. Since the second bond was paying 9% coupon, higher market yield, its price sensitivity to change in interest rate is less as compared to the bond which was paying 6% coupon. Hope its helpful.
Hope this would be useful. Duration is the slope of the line Price (Y axis) Vs Yield (X Axis). i.e. Change in Price for a Change in Yield, hence duration is called measure of interest rate risk. This is convex to the origin and decreases from left to right. Consider the left portion of the convex graph (closer to the origin). Here we see that Change in price is higher than the Change in yield i.e. slope is higher; hence Duartion or interest rate risk is higher. Now move far towards right - away from the origin. Here Change in price is far lower than the Change in yield - thus the slope is lower meaning low interest rate risk. Therefroe we can say that the rate at which it falls decreases as you move from left to right. So the duration is lower at higher yields while it is higher when the yield is low. To put the same thing in other words, the sensitivity of bond prices to change in interest rates is higher when the interest rates are low as compared to when interest rates are high. Mathematically too, Increases in market yield rates cause a decrease in the present value factors of each cashflow. Since Duration is a product of the present value of each cashflow and time, higher yield rates also lower Duration. Therefore Duration varies inversely with yield rates.
It may help to think about duration in simpler terms: it is, in essence, the time to recoup your investment. This is oversimplification, but still gets the point across. There are other things that you have to account for, but it is easier to remember about duration in this regard. The bond with the highest coupon, highest yield, and shortest maturity has the lowest duration.