Now it's simple to understand the consol present that says
the price of the consol p is equal to c over r.
You can just return that, turn it around.
It says the yield to maturity on a consol is c over p, and
that's kind of obvious, right?
If the consol is paying a 3 pound coupon, and it's selling for
200 pounds, I say what is the yield to maturity on it?
Well it's 3 pounds divided by 200 pounds.
In that case it would be, if it was 3% yield to maturity, I'm sorry if it
was a 3% coupon issued, it's now paying one and
a half percent yield to maturity because the price has gone up.
This is an important point with bonds.
The coupon is fixed at the time the bond is issued but
the market price of the bond changes through time so
if the British government issued a 3 pound consol for
100 pounds and that consol is selling for £200 today,
the yield to maturity is down to 1.5% instead of 3%.
But this is no fault of the British government, they are true to their word.
They are paying the consol as promised, it's the market that does it so
bonds are risky, they have market risk even if there is no default risk.
If you buy a consol, you know you won't live forever.
The British government may live forever but you won't, so
you're going to want to sell the coupon at some point.
The British government does not guarantee the rate that you will get,
the price you will get for selling your consol.
So, there's market risk for our consol and for
any debt instrument, long term debt instrument.
By the way, if a bank or a company or
a government were to issue a usually companies don't issue
consols because nobody believes they'll last forever.