We first discussed the concept of yield in the preferred stock chapter. The idea is the same for bonds: yield measures the overall return of an investment.

With bonds, several factors affect yield. These factors include:

• Interest rate (coupon)

• Purchase price

• Length of time until maturity

The interest rate (coupon) and yield sound similar, but they aren’t the same thing (except for nominal yield, discussed below). The interest rate is the annual interest the issuer pays the bondholder. The yield is the bond’s overall rate of return. The coupon is part of the yield, but the two will differ if the bond is purchased at a discount or a premium.

We’ll discuss the following yields in this chapter:

• Nominal yield
• Current yield
• Yield to maturity (YTM)
• Yield to call (YTC)

Nominal yield

The nominal yield is another name for the bond’s interest rate (coupon). You typically won’t calculate nominal yield, but you may be asked to identify the formula.

For example:

A $1,000 par, 4% bond

$\text{Nominal yield}=\frac{\text{Annual income}}{\text{Par}}$

$\text{Nominal yield}=\frac{\text{\$40}}{\text{\$1,000}}$

$\text{Nominal yield}=4\%$

As you can see, the calculation simply confirms the 4% coupon that was given. Nominal yield depends on two values that don’t change over the life of the bond:

• Par value ($1,000)
• Annual interest paid ($40)

This bond pays $40 per year regardless of what happens to its market price.

The nominal yield is fixed throughout the life of the bond. Unlike the other yields we’ll discuss, market price is not part of the nominal yield calculation. When you’re given bond information, the nominal yield is usually the first percentage shown.

Current yield

Let’s add one detail to the example from the last section.

A $1,000 par, 4% bond bought for $800

If this bond is bought for $800 at a (discount), the bond’s overall return will be higher than its 4% coupon. That’s because the investor earns return from two sources:

Coupon

• Pays the investor $40 annually

Discount

• Investor earns $200 over the life of the bond

The investor receives 4% of par ($1,000) each year, and also benefits from the bond moving from the purchase price ($800) up to par ($1,000) at maturity. That extra $200 increases the overall return (yield), so the yield must be above 4%.

In the preferred stock chapter, we discussed current yield, which is also important for bonds. Current yield is found by dividing annual income by the security’s current market price.

A $1,000 par, 4% bond bought for $800. What’s the current yield?

Can you figure it out?

The current yield (5%) is higher than the coupon (4%). That leads to a key relationship to remember: the current yield for discount bonds will always be higher than the coupon.

Current yield is important for the exam, but it has a major limitation: it doesn’t factor in time.

You’ve probably heard “time is money.” That’s especially true with bonds. Yield is an annualized measure of overall return, and a big part of a discount bond’s return comes from the discount. A $200 discount spread over 1 year is very different from a $200 discount spread over 30 years, but current yield doesn’t capture that difference.

Here’s a video breakdown of a practice question on current yield:

Let’s also see how current yield works with premium bonds. Premium bonds trade above par ($1,000).

A $1,000 par, 4% bond bought for $1,100

The investor still receives $40 per year in interest. However, because bonds mature at par, paying $1,100 for a bond that matures at $1,000 creates a $100 loss at maturity. Because of this, yields on premium bonds will be lower than the coupon.

A $1,000 par, 4% bond bought for $1,100. What is the current yield?

Can you figure it out?

The current yield (3.6%) is lower than the coupon (4%). Another key relationship follows: the current yield for premium bonds will always be lower than the coupon.

Current yield is an approximate measure that can appear on the Series 7 exam, but it’s not the most useful yield for real-world bond analysis. The next two yields are more practical because they incorporate time.

Yield to maturity (YTM)

Yield to maturity and yield to call formulas are difficult to memorize and typically are not tested. Exam questions are more likely to focus on the relationships of the yields, which is best depicted on the bond see-saw (discussed at the end of this chapter). Additionally, it’s possible a test question focuses on the components of these yield formulas. Don’t spend a significant amount of time focusing on the math related to these yields.

Unlike current yield, yield to maturity (YTM) (also called a bond’s basis) does factor in time. YTM assumes the investor buys the bond and holds it until maturity.

A 10 year, $1,000 par, 4% bond is trading at $800. What is the yield to maturity (YTM)?

$$\begin{gathered} \begin{array}{rl}\mathrm{ytm}& =\frac{C+\frac{F-P}{n}}{\frac{F+P}{2}}\\ \mathrm{ytm}& =\frac{40+\frac{1000-800}{10}}{\frac{1000+800}{2}}\\ \mathrm{ytm}& =\frac{40+20}{900}\\ \mathrm{ytm}& =6.7\%\end{array} \\ \begin{array}{rl}\text{where:}& \\ C& =\text{coupon interest payment}\\ F& =\text{face value (par)}\\ P& =\text{price}\\ n& =\text{years to maturity}\end{array} \end{gathered}$$

This formula is easier to understand if you separate it into parts:

• Annual income ©: $40 from the 4% coupon on $1,000 par
• Annualized discount: total discount ($1,000 − $800 = $200) divided by years to maturity (10), which is $20 per year
• Average value in the denominator: the average of par and market price, $\frac{1,000+800}{2}=900$

The result (6.7%) is higher than the coupon (4%). The pattern is the same as before: discount bonds have yields above the coupon because the discount adds to the investor’s return.

Now compare that to a premium bond.

A 10 year, $1,000 par, 4% bond is trading at $1,100. What is the yield to maturity (YTM)?

$$\begin{gathered} \begin{array}{rl}\mathrm{ytm}& =\frac{C-\frac{P-F}{n}}{\frac{F+P}{2}}\\ \mathrm{ytm}& =\frac{40-\frac{1,100-1,000}{10}}{\frac{1,000+1,100}{2}}\\ \mathrm{ytm}& =\frac{40-10}{1050}\\ \mathrm{ytm}& =2.9\%\end{array} \\ \begin{array}{rl}\text{where:}& \\ C& =\text{coupon rate}\\ F& =\text{face value (par)}\\ P& =\text{price}\\ n& =\text{years to maturity}\end{array} \end{gathered}$$

Here’s what’s happening:

• Annual income: $40 from the coupon
• Annualized premium: total premium ($1,100 − $1,000 = $100) divided by 10 years, which is $10 per year
• We subtract the annualized premium because it represents a loss over time (the bond matures at par)
• The denominator is the average of market price and par: $\frac{1,100+1,000}{2}=1,050$

The YTM (2.9%) is lower than the coupon (4%). Again, the pattern holds: premium bonds have yields below the coupon because the premium reduces the investor’s return.

Yield to call (YTC)

Yield to call (YTC) applies only to callable bonds. If a bond is not callable, YTC does not exist. YTC represents the bond’s overall return if it’s held until the call date, assuming the issuer calls the bond as soon as it’s eligible.

The YTC formula is similar to the YTM formula, but it uses the call date and call price instead of maturity and par. Calculating YTC is generally less important for the exam than calculating YTM.

A 10 year, $1,000 par, 4% bond is trading at $800. The bond is callable at par after 5 years. What is the yield to call (YTC)?

$$\begin{gathered} \begin{array}{rl}\mathrm{ytc}& =\frac{C+\frac{CP-MP}{t}}{\frac{CP+MP}{2}}\\ \mathrm{ytc}& =\frac{40+\frac{1000-800}{5}}{\frac{1000+800}{2}}\\ \mathrm{ytc}& =\frac{40+40}{900}\\ \mathrm{ytc}& =8.9\%\end{array} \\ \begin{array}{rl}\text{where:}& \\ C& =\text{coupon rate}\\ CP& =\text{call price}\\ MP& =\text{market price}\\ t& =\text{years to call}\end{array} \end{gathered}$$

The YTC (8.9%) is higher than the coupon (4%), and it’s also higher than the YTM (6.7%). The reason is timing: the investor earns the same $200 discount, but earns it sooner.

• Held to maturity: the $200 discount is earned over 10 years
• Called in 5 years: the $200 discount is earned over 5 years

Earning the discount faster increases the annualized return.

Now look at a premium bond.

A 10 year, $1,000 par, 4% bond is trading at $1,100. The bond is callable at par after 5 years. What is the yield to call (YTC)?

$$\begin{gathered} \begin{array}{rl}\mathrm{ytc}& =\frac{C-\frac{MP-CP}{t}}{\frac{CP+MP}{2}}\\ \mathrm{ytc}& =\frac{40-\frac{1,100-1,000}{5}}{\frac{1,000+1,100}{2}}\\ \mathrm{ytc}& =\frac{40-20}{1050}\\ \mathrm{ytc}& =1.9\%\end{array} \\ \begin{array}{rl}\text{where:}& \\ C& =\text{coupon rate}\\ CP& =\text{call price}\\ MP& =\text{market price}\\ t& =\text{years to call}\end{array} \end{gathered}$$

The YTC (1.9%) is lower than the coupon (4%), and it’s also lower than the YTM (2.9%). Again, timing explains the difference:

• Held to maturity: the $100 premium is lost over 10 years
• Called in 5 years: the $100 premium is lost over 5 years

Losing the premium sooner reduces the annualized return.