Duration & YTM

Just a question on Duration…

A high coupon = Low duration (because you are receiving high cash payments so less risk)

A long maturity = High duration (Longer to wait until you get your principal back… more risk)

I understand those 2 clearly.

Here’s where it gets a little unclear for me.

A high market yield = high duration - why?

A low YTM = a high Duration - why?

Thanks

I wrote an article on this that may help: http://financialexamhelp123.com/macaulay-duration-modified-duration-and-effective-duration/. Look under Macaulay Duration, I detail the effects of time to maturity, coupon rate, and YTM. The Reader’s Digest version is that at high YTM the cash flows far into the future have nearly zero present value, so they don’t affect the duration much; at low YTM, the cash flows far into the future have much higher present values, so they affect the duration a lot more.

If you’d like more visual representation, draw a typical price-yield curve, and notice that the slope is very steep (downward) when YTM is low, and nearly flat when YTM is high. (Yes, I know that modified or effective duration isn’t the slope of that curve – it’s the slope of the ln(price)-yield curve; for visualization the simpler curve works just fine. Don’t send letters.)

S2000. You are a hero.

Aw, shucks.