1. Relationship Between Price and YTM
One of the most critical things to understand about bonds is the relationship
between the price of a bond and the yield to maturity of a
bond. The more you pay for a bond today or any investment for
that matter, the lower your overall return or yield will be.
So the higher the price of a bond, the lower the YTM. Conversely,
the lower the price of the bond, the higher the overall return or
yield will be. In other words, there is an inverse relationship between
the price of a bond and its yield to maturity.
We can demonstrate this back in Excel. So here I am,
back looking at my 5% annual coupon bond, the annual coupon is 5%,
and The yield to maturity is currently 6% which gives us a price
of 95.79. I want to demonstrate this in this relationship by decreasing
the yield to maturity. If I decrease the yield to maturity,
the price to the bond should increase. So let's decrease it to 5%
and the price of the bond goes up to 100.
Again, if I decrease the yield to maturity from 5% down to 4%,
that price in the bond should go up, and it does go up
to 104.45. So using this model, we can very clearly see the inverse
relationship between bond prices and the yield to maturity.
As we've just seen, if the YTM of this five year annual bond
was 6%, this is more than the coupon rate of 5%. In other
words, the investor is getting an extra return over and above the income
or coupon that this bond is providing. This extra return comes from the
gain of buying the bond at a discount of 95.79 today,
but receiving the par value of $100 on the maturity date.
If the YTM was at 5%, the YTM and the coupon are equal,
this means that the overall return is equal to the income of the
bond, and there is no capital gain or loss if the bond is held
to maturity. In other words, the bond is trading at par and its
price is $100. If the YTM of this five year annual bond was
4%, this is less than the coupon rate of 5%.
In other words, the investor is getting an overall return which is less
than the income or coupon that this bond is providing.
This lower return comes from the fact that the investor is buying the
bond at a premium at 104.45 today, but only receiving the par value
of $100 on the maturity date. Remember, there is an inverse relationship
between the price of a bond and its yield to maturity.
2. Let's practice!