Duration and Change in Yields

CFA Level I
#1

I know that the general rule is that if market yield rates increase, duration decreases. However, none of the reading that I’ve been doing explains why that happens. I’m so confused. In my mind, a higher market yield would imply a lower present value of future bond associated cash flows and therefore a higher duration. Please help!

#2

think of price-yield curve, it a convex shaped curve, price is more indifferent toward yield change than it is when yields are low.

#3

Think of duration (interest rate risk) as the slope of the price yield profile. As you move to the right (higher yields) the sloper get flatter (moves towards zero), which indicates lower sensitivity to changes in interest rates.

#4

The price yield curve has a convex shape. The Intrest rate risk cannot be easily determined if the slope of yield curve is non-linear so to get a linear relationship between Bond value and yield a new term DURATION is introduced. Duration is termed as price sensitivity of a bond to change it yield.The approx percentage is asumed to be constant for a rise or decline in the yield.In short the Duration can be assumed as the slope of the linear relation between bond value and yield.As the slope is constant for a given line the value of duration remains the same for a specified yield curve. The statement “Market yield rates increase duration decreases.” implies that when the market yield increases Bond value decreases(linearly) i.e duration. Hope that this solves your problem and not complicate it further…

#5

That cleared it up, thanks!

#6

So…still a little mixed up with maturity-to-duration If maturity has high interest rate sensitivity but a low duration… - How is maturity reflected in the price/yield curve? Would a high-yielding, 30-year CMO have a high duration or a low duration?

#7

another way to think about it is to think of duration as the point that makes the left side equal to the right side. http://www.investopedia.com/university/advancedbond/advancedbond5.asp the scale is a good picture. imagine 2 cash flows. 100 today and 100 5 years from now. midpoint (proxy for duration) is at 2.5. if yields increase, the 100 5 years from now becomes smaller and the midpoint moves to the left.

#8

Thanks for the link homie !!!