Discount Bonds

Par value is what is returned to the bondholder at maturity and what the coupon rate is multiplied against. But, bonds are not bank deposits. Rather, they are securities trading on a secondary market. Among other factors, a bond's market price fluctuates in response to changes in interest rates. If a bondholder has a bond that pays a nominal yield of 8%, what is the bond worth when interest rates in general climb to 10%?

Not as much. If you had something that paid you 8%, when you knew you could be receiving more like 10%, how would you feel about the bond?

Not too good. But, when interest rates fall to 6%, suddenly that 8% bond looks good, right? It's all relative.
 
Current Yield
When we take a bond's market price into consideration, we're looking at current yield. Current yield (CY) takes the annual interest paid by the bond and divides it by what an investor would have to pay for the bond.
Current Yield = Annual Interest / Market Price

So, let's say after an investor buys an 8% bond, interest rates rise, knocking down the market price to just $800. What is the current yield if that happens?
$80/$800 gives us a current yield of 10%.

Did the bond's market price just drop, or did its current yield rise? Those are two ways of saying the same thing.

Yield answers the question, "How much do I get every year compared to what I pay to get it?" If interest rates rise to 10%, suddenly this bond that pays only 8% isn't worth as much.

The only motivation for buying this 8% bond is if an investor could get it at a discount. And, if she can get the $80 that the bond pays in annual interest for just $800, isn't she getting 10% on her money? That's why we say her current yield is 10%, higher than the nominal yield that never, ever changes.

Rates and yields up, price down. Rates are what new bonds pay. Yields are what existing bonds offer, after we factor in their market price.

A discount bond is a bond trading below par value. When you see a current yield higher than the coupon rate of the bond, you're looking at a discount bond. An 8% bond with a 10% current yield, for example, must be a discount bond. An 8% bond with a 6% current yield would not be a discount bond. As we'll see in a minute, it would, in fact, be a "premium bond."

Yield to Maturity
Yield to maturity (YTM) is the return an investor gets if she holds the bond to maturity. It is sometimes called basis and represents the only yield that really matters to an investor.

It factors in all the coupon payments and the difference between the market price paid for the bond and the par value received at maturity.

At maturity, an investor receives the par value, which is $1,000. If the investor puts down only $800 to buy the bond and receives $1,000 when the bond matures, doesn't she receive more at maturity than she paid?

She does, and that's why her yield to maturity is even higher than her current yield. She gets all the coupon payments, plus an extra $200 when the bond matures. If you see a yield-to-maturity higher than the coupon rate or the current yield, you're looking at a discount bond. For example, a bond with a 4% nominal yield trading at a 5.50 basis or yield to maturity is a discount bond.

Yield to Call
Like homeowners, sometimes issuers get tired of making interest payments that seem too high. That's why many bonds are issued as callable, meaning after a certain period the issuer can buy the bonds back from investors at a stated price.

A bond that matures in 10 or 20 years is often callable in just 5 years. If a bond is trading at a discount, rates have risen. Therefore, it is unlikely such a bond would be called. But, if it were called, the investor would make his gain faster than if he had to wait until maturity. That's why yield to call (YTC) is the highest of all for a discount bond.

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