Bond Yield Question

Q:
I was wondering if you could explain bond yields to me. I'm a little confused as to exactly what they are. I was used to thinking of it as the interest rate that you would get on a comparable asset, but in the helpful hints it talks about a Wall Street Journal table and it talks about how different bonds have different yields. So what exactly is a bond yield, and how does it differ from a coupon payment?

A:
Simply put, the yield on a bond is the value of i that makes the PDV calculation work out for the given price. It is also the yield on a comparable asset since efficient markets enforce the idea that returns on comparable assets must be equal.

In general, different bonds have different yields because they are not actually comparable. Consider the following situation- would you be indifferent between holding a 5% coupon Delta Air Lines bond or a 5% coupon General Electric bond, if they were the same price? (I use this example because Delta is performing poorly and filing for bankruptcy protection for the 800th time) If you would not be, then the two bonds are not comparable. Because Delta has a higher default risk, you would need to be compensated for that in order to be willing to purchase the bond. The way you are compensated is through a lower price, or equivalently, a higher yield.

If a bond is trading at face value, the yield is equal to the coupon rate. However, the coupon rate is stated as a percentage of face value, so it never changes. On the other hand, yield moves around as the price of the bond changes. Consider a bond that never expires with a 5% coupon. If the bond is trading at $100, you clearly get 5% return per year. If the bond is trading below $100, say at $90, you are actually getting a yearly return of $5/$90, which is greater than 5%. Thus your yield goes up. The opposite is true if the bond is trading above $100. (I use the consol example because then I don't have to worry about the return of the face value complicating the yield calculation.)