How do government bond yields work?

Question

Let's take the following quote from Bloomberg:

Russian government bonds rose, pushing the yield to the lowest level in almost three weeks, as inflation data boosted speculation the central bank may restart interest-rate cuts next year.

Why does the rising price of a bond pushes it's yield down? Because of the bond's risk going lower and bond's bringing back therefore lower returns?

Or take another example, from FT:

The prices of both countries’ bonds plummeted amid fraught negotiations, and yields hit a peak of 48 per cent in Ukraine in April, and 20.47 per cent in Greece in July.

Here we see that risk associated with the bonds in question has skyrocketed, and thus bonds' returns has skyrocketed, too. Am I right?

Now, I assume that bonds' price is determined by the market (issued by a state, traded at the market). Is that correct?

Then who determines bonds' yields? I mean, isn't it fixed? Or - in the FT quote above - they are talking about the yields for the new bonds issued that particular month?

Thank you.

Answer 1

Why does the rising price of a bond pushes it's yield down?

The bond price and its yield are linked; if one goes up, the other must go down. This is because the cash flows from the bond are fixed, predetermined. The market price of the bond fluctuates. Now what if people are suddenly willing to pay more for the same fixed payments? It must mean that the return, i.e. the yield, will be lower.

Here we see that risk associated with the bonds in question has skyrocketed, and thus bonds' returns has skyrocketed, too. Am I right?

The default risk has increased, yes.

Now, I assume that bonds' price is determined by the market (issued by a state, traded at the market). Is that correct?

Correct, as long as you are talking about the market price.

Then who determines bonds' yields? I mean, isn't it fixed? Or - in the FT quote above - they are talking about the yields for the new bonds issued that particular month?

The yield is not fixed - the cash flows are. Yield is the internal rate of return. See my answer above to your first question.

Answer 2

Imagine a $1,000 face value bond paying 10% interest semi-annually. That means every 6 months there is $50 being paid.

Now, if the price of that bond doubled to $2,000, what is the yield? It is still paying $50 every 6 months but now sports a 5% yield as the price went up a great deal.

Similarly, if the price of the bond was cut in half to $500, now it is yielding 20% because it is still paying out the $50 every 6 months.

The dollar figure is fixed. What percentage of the price it is can vary and that is why there is the inverse relationship between prices and yields.

Note that the length of the bond isn't mentioned here where while usually longer bonds will have higher yields, there can be inverted yield curves as well as calls on some bonds. Also, inflation-indexed and convertible bonds could have different calculations used as principal adjustments or possible conversion to stock can change a perception on the overall return.