Why do government bonds prices fluctuate? [duplicate]

Question

I've heard that bond yields go up if interest rates also go up, which to me makes sense for corporate bonds since if interest rates go up company prices could fall since people spend less and companies give higher yield bonds to compensate and help fund their business.

Now why would this be the case for government bonds? Why would the government issue higher yield bonds?

My guess is that the FED raises interest rates now people spend less and the government is running short of cash so they start issuing higher yield bonds.

Answer 1

Just to clarify terms, yield and coupon are different. Yield is a function of both the coupon and the price of the bond. The coupon of a bond is fixed (for this example; there are floating-rate bonds but they behave differently). But as the price goes down, the yield goes up, because you're paying less for the same monetary amount. The yield is determined by the market that buys and sells these bonds. The issuer will sat a coupon rate that's close to what they think the yield is in the market, but they don't "set" the yield.

Which to me makes sense for company bonds not government bonds since if interest rates go up company prices could fall since people spend less and companies give higher yield bonds to compensate.

That's not why yields go down when rates go up.

Say the government issued a bond that pays 4% interest. It sells for face value (par), which means that the bond's yield is 4% (when a bond sells at par, the yield is simply its coupon rate).

Later, "interest rates" go up and the government issues another bond that pays a 5% coupon to match the market. It also sells at face value for a yield of 5%.

Now, you want to buy one of those bonds. You can either buy the bond that pays a 5% coupon for face value, or you can buy the original bond that pays a 4% coupon. Obviously you would pay less for the bond that pays a 4% coupon, so it's value (and hence its yield) goes down.

The idea for corporate bonds is the same, but their bonds can also be affected by market forces to the extent that those forces increase the company's chances of going bankrupt, increasing the risk of their bonds and lowering their value. But that affect is typically not as big as the effect of interest rates. Market forces affect the company's stock prices much more than bond prices. Unless the company defaults, the cash you get from owning the bond is fixed regardless of the profit a company makes.

Answer 2

The government issues higher yield bonds because it has to.

Government bonds have a nominal value and yearly interest payment. For example, in an environment where a 10-year interest rate is 4.5%, the government most likely chooses a yearly interest payment of 4.5%. This means that when the government borrows $1 million, it has to pay back $1 million at the end of the 10-year period. (In theory, it might be possible for a government to for example choose 0% yearly interest payment, in which case a bond paying back $1 million at end of 10-year period will be sold at a price of 1000000/1.045^10 = $675564.17 so the government can't get million dollars for a million-dollar bond if there are no yearly interest payments)

As for old bonds, the discounted value of the bond changes if interest rates change. So for example if a bond was recently issued at 3.5% interest rate, at this rate the discounted present value is (in GNU Octave notation):

sum(0.035*1000000./1.035.^[1:10]) + 1000000/1.035^10 = 1000000

However, if the interest rate suddenly jumps to 4.5% overnight, then the new value of the bond is:

sum(0.035*1000000./1.045.^[1:10]) + 1000000/1.045^10 = 920872.82

So although you get 3.5% yearly interest payments, the 1% difference in yield is from the fact that you can purchase the bond for $920872.82 and get $1000000 back at the end of the 10-year period.

Note that if you purchase a 10-year bond at interest rate of 3.5% and then the rate jumps to 4.5%, your investment is worth only 92% of what it used to be before that interest rate jump. You made an immediate 8% loss, therefore.

This is why I never purchased (and still haven't purchased) bonds when the interest rates were low. Maybe if the 10-year rate in Europe rises to 4.5% I will reconsider. I also made sure to protect all my loans against interest rate rise whenever such protection was available from the bank.

Recently, bond values have dropped as much as stock values! That's due to interest rate rise reducing their value (and equivalently, increasing their future yield).