Yield types

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 include:

• Interest rate (coupon)

• Purchase price

• Length of time until maturity

The interest rate (coupon) and a bond’s 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 when a 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 coupon rate. You typically won’t calculate nominal yield in practice, 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 returns 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)

No matter what happens to the bond’s market price, this bond pays $40 per year.

The nominal yield is a fixed rate over the life of the bond. Unlike the other yields we’ll cover, market price is not part of the calculation. When you’re given bond information, the nominal yield is usually the first percentage you’ll see.

Current yield

Let’s add one detail to the previous example.

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

If this bond is bought at $800 (discount), the investor’s overall return will be higher than the 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) back to par ($1,000) at maturity. That extra $200 increases the overall return, so the yield will be above 4%.

In the preferred stock chapter, we discussed current yield, which is also important for bonds. Current yield is:

• annual income divided 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%). This leads to a key relationship:

For discount bonds, current yield is always higher than the coupon.

Although current yield is important for the exam, it has a major limitation as an investing tool: it doesn’t account for time.

Yield is an annualized measure of overall return. For a discount bond, part of the return comes from the $200 discount. But that $200 is earned over the life of the bond. A one-year bond and a 30-year bond shouldn’t have the same annualized return from the discount - and current yield doesn’t capture that difference.

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

Now let’s see how current yield works for premium bonds (bonds trading above par).

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. That loss reduces the investor’s overall return, so yields on premium bonds are 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:

For premium bonds, current yield is always lower than the coupon.

Current yield is an approximate yield that can appear on the Series 65 exam, but it’s not the most complete measure of return. The next two yields are more useful because they incorporate time.

Yield to maturity (YTM)

Yield to maturity and yield to call formulas are difficult to memorize and typically are not heavily 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) 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
• Annualized discount: the total discount ($1,000 − $800 = $200) spread over 10 years → $200/10 = $20 per year
• Average bond value: the average of price and par → ($800 + $1,000)/2 = $900

Because the investor earns both coupon interest and the discount over time, the YTM (6.7%) is higher than the coupon (4%).

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: the premium ($1,100 − $1,000 = $100) spread over 10 years → $100/10 = $10 per year
• Because the premium is a loss over time, it’s subtracted from the coupon income.
• Average bond value: ($1,100 + $1,000)/2 = $1,050

Since the investor loses the premium over time, the YTM (2.9%) is lower than the coupon (4%).

Sidenote

"Basis"

You may encounter a test question that refers to YTM as “basis.” This is just another way to say yield to maturity. For example:

A 5% bond trades on a 7% basis

This means a bond with a 5% coupon (nominal yield) is trading at a price that produces a 7% yield to maturity. A higher YTM than coupon implies the bond is trading at a discount.

Yield to call (YTC)

Yield to call (YTC) applies only to callable bonds. If a bond isn’t callable, YTC doesn’t exist.

YTC is the bond’s overall rate of return assuming the bond is called on the first call date (as soon as it’s eligible).

The YTC formula is similar to the YTM formula, but it uses:

• the call price instead of par (if different)
• the years to call instead of years to maturity

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 a $200 discount.
• If the bond is held to maturity, that $200 is earned over 10 years.
• If the bond is called in 5 years, the investor earns that same $200 in half the time, which 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 why:

• The investor will lose a $100 premium.
• If the bond is held to maturity, that $100 loss is spread over 10 years.
• If the bond is called in 5 years, the investor loses the $100 sooner, which lowers the annualized return.

Key points

Nominal yield

• $\text{NY}=\frac{\text{Annual income}}{\text{Par}}$
• Measures the interest paid annually to investor
• Never changes over the life of the bond
• Also known as:
  • Coupon
  • Interest rate
  • Stated rate

Current yield

• $\text{CY}=\frac{\text{Annual income}}{\text{Market price}}$
• Measures overall rate of return based on the current market price
• Discount bonds CY > coupon
• Premium bonds CY < coupon

Yield to maturity (YTM)

• Measures overall rate of return if the bond is held to maturity
• Discount bonds YTM > coupon
• Premium bonds YTM < coupon

Yield to call (YTC)

• Measures overall rate of return if the bond is held until called
• Discount bonds YTC > coupon
• Premium bonds YTC < coupon