Change in Yield and Duration

I Appear to have forgotten everything about fixed income.

If yields are expected to fall, the price will rise and therefore we should move to higher duration bonds right? As evidenced by % Change in P = -D X Change in Y

Let us assume we have a portfolio and we expect yields to fall by 50bps. Current D =2 and a higher D bond of 4

Change in P = -2 * -0.5 = 1

Change in P = -4 * -0.5 = 2

Hence, the higher D gave the better return in a falling rate environment.

If we are to look at this conversely and assume that yields will RISE, would we therefore want to switch to a lower D bond As the example above shows -2 loss over -1 loss with higher D.

Can someone also explain intuition please!

If yields fall, bond prices rise. Higher duration bonds (Long Term 30 yr Tsy (3%) will go up by a higher amount vs lower (Short Term T-Bill (1.79%) duration bond. If you believe rates will sink, would you want to lock in a long bond @ 3% for 30 yrs or purchase a 1 year T-Bill which yields 1.79% and will only yield lower since Interest rates are in a downtrend. (Also keep in mind the value of those coupon payments will go up since you’re discounting them @ a lower rate)

On the other hand, if rates are shooting up (Yields & Bond prices are inversely related) the Long Bond ( Higher Duration) will fall much harder vs a short term T-Bill. Investors locked into a 3% for 30 years will want out if it means that they could get 5% on short term bonds. They will dump the long bond (prices will go down) and purchase the short term one. (Also keep in mind the value of those coupon payments will go down since you’re discounting them @ a higher rate)

Alex: that sounds a lot like reasoning, not intuition.

:wink:

If you owned a bond that was paying 3% today, but tomorrow you could buy a bond that pays 5% for the same price, would your 3% bond be worth more or less tomorrow?

Less because you’d be crazy to not swap for the higher return. Intuitive?