Why government bonds fluctuate so much, even though interest rates don't change that often?

Question

Why do government bond prices fluctuate on a daily basis on the bond market?

I can understand the fluctuation of corporate bonds because they are tied to the credit worthiness of the company and bad company news can shake bondholders' confidence.

But government bonds are backed by the full faith & credit of the government (U.S for example). So, wouldn't that only leave the interest rate as the other parameter? If interest rates are not changing on a daily basis, why do government bonds fluctuate on a daily basis?

Obviously I am over-simplifying the relationship between interest rate and bond price, but I cannot pinpoint how, exactly. What am I missing?

Answer 1

Long term gov't bonds fluctuate in price with a seemingly small interest rate fluctuation because many years of cash inflows are discounted at low rates. This phenomenon is dulled in a high interest rate environment.

For example, just the principal repayment is worth ~1/3, P * 1/(1+4%)^30, what it will be in 30 years at 4% while an overnight loan paying an unrealistic 4% is worth essentially the same as the principal, P * 1/(1+4%)^(1/365).

This is more profound in low interest rate economies because, taking the countries undergoing the present misfortune, one can see that their overnight interest rates are double US long term rates while their long term rates are nearly 10x as large as US long term rates. If there were much supply at the longer maturities which have been restrained by interest rates only manageable by the highly skilled or highly risky, a 4% increase on a 30% bond is only about a 20% decline in bond price while a 4% increase on a 4% bond is a 50% decrease.

The easiest long term bond to manipulate quantitatively is the perpetuity

p = i / r

where p is the price of the bond, i is the interest payment per some arbitrary period usually 1 year, and r is the interest rate paid per some arbitrary period usually 1 year. Since they are expressly linked, a price can be implied for a given interest rate and vice versa if the interest payment is known or assumed.

At a 4% interest rate, the price is

p = i / 4% = i / 0.04 = 25 * i  

At 4.04%, the price is

p = i / 4.04% = i / 0.0404 = 24.8 * i

, a 1% increase in interest rates

4.04% / 4% = 101%

and a 0.8% decrease in price

( 24.8 * i ) / ( 25 * i ) = 24.8 / 25 = 0.992%

.

Longer term bonds such as a 30 year or 20 year bond will not see as extreme price movements.

The constant maturity 30 year treasury has fluctuated between 5% and 2.5% to ~3.75% now from before the Great Recession til now, so prices will have more or less doubled and then reduced because bond prices are inversely proportional to interest rates as generally shown above.

At shorter maturities, this phenomenon is negligible because future cash inflows are being discounted by such a low amount. The one month bill rarely moves in price beyond the bid/ask spread during expansion but can be expected to collapse before a recession and rebound during.