Yield types

We first discussed the concept of yield in the preferred stock chapter. The concept is the same for bonds; yield measures the overall return of an investment. With bonds, there are several factors that determine bond yields. These factors include:

• Interest rate (coupon)

• Purchase price

• Length of time until maturity

While the interest rate of a bond and its yield sound like they’re the same thing, they are not (except for the nominal yield, which is discussed below). The interest rate represents the amount of annual interest paid by the issuer to the bondholder. Yield represents the overall rate of return of the bond. The bond’s interest rate factors into the yield, but the interest rate and yield will be different if the bond is bought 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 way to refer to the interest rate (coupon). You will likely never do a calculation to find the nominal yield, but you may be asked what the formula is.

For example:

A $1,000 par, 4% bond

$\text{Nominal yield}=\frac{\text{Annual\hspace{0.33em}income}}{\text{Par}}$

$\text{Nominal\hspace{0.33em}yield}=\frac{\text{\$40}}{\text{\$1,000}}$

$\text{Nominal\hspace{0.33em}yield}=4\%$

As you can see, we went through a calculation only to find the 4% that was originally provided to us. The nominal yield is based on two factors, both of which never change over the life of the bond. This bond has a $1,000 par value and pays $40 annually to its bondholder, regardless of what happens in the market.

The nominal yield is a fixed, unaffected rate throughout the life of the bond. Unlike all the other yields we’ll discuss, the bond’s market price is not a factor. If you are given information on a bond, the nominal yield is always the first % referenced.

Current yield

Let’s add some information to the example we used in the last section.

A $1,000 par, 4% bond bought for $800

If this bond is bought at $800 (discount), the bond’s overall rate of return will be higher than the interest rate of the bond. How do we know this? The investor is earning two separate forms of return:

Coupon

• Pays the investor $40 annually

Discount

• Investor earns $200 over the life of the bond

The investor is receiving 4% of par ($1,000) annually, but they’re also benefiting from the difference between the purchase price and the maturity value (par). The extra $200 return adds to their overall return (yield), so we can assume it’s something above 4%.

In the preferred stock chapter, we discussed the current yield, which is also an important yield for bonds. As a reminder, the current yield is found by dividing the annual income by the market price of the security.

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

Can you figure it out?

As you can see, the current yield reflects a higher yield than the interest rate of the bond. Therefore, you can always assume the current yield for discount bonds will always be higher than the coupon.

Although the current yield is an important yield that must be known for the exam, it’s not a terribly effective yield to utilize as an investor. Why? Because the current yield does not factor in time.

You’ve probably heard the term “time is money.” This couldn’t be more true with bonds. When time is not a factor in a yield, the yield is not really telling the full story. Yield is an annualized number that represents the annual overall return to the investor.

A large component of this bond’s return is the discount, which gives the investor an additional $200 over the life of the bond. Shouldn’t there be a difference in the annualized return if the bond had a one-year maturity as compared to a 30-year maturity? Yes, there should be!

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

Let’s also discuss how current yield works with premium bonds. As a reminder, premium bonds trade in the market at prices above par ($1,000).

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

The investor purchasing this bond will receive $40 a year in interest from the issuer. They’ll lose money over the life of the bond by buying it at a premium because bonds mature at par. Paying $1,100 for a bond that will mature at $1,000 results in a $100 loss at maturity. Because of this dynamic, yields of premium bonds will always 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?

When the coupon is coupled with the loss of the premium, we find that the investor’s current yield reflects a more accurate rate of return than the coupon. Therefore, you can always assume the current yield for premium bonds will always be lower than the coupon.

Current yield is only an approximate yield that shouldn’t be taken too seriously in the real world, but can show up on the Series 66 exam. The next two yields we’ll discuss are more applicable in the investing world.

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 the current yield, the yield to maturity (YTM) does factor in time. In fact, the YTM assumes the investor buys the bond and holds it until the bond’s maturity. Let’s look at an example:

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

$$\begin{gathered} \begin{array}{rl}\mathrm{ytm}& =\frac{C+\frac{F-P}{n}}{\frac{F+P}{2}}\\ \mathrm{ytm}& =\frac{40+\frac{1000-800}{10}}{\frac{1000+800}{2}}\\ \mathrm{ytm}& =\frac{40+20}{900}\\ \mathrm{ytm}& =6.7\%\end{array} \\ \begin{array}{rl}\text{where:}& \\ C& =\text{coupon\hspace{0.33em}interest payment}\\ F& =\text{face\hspace{0.33em}value (par)}\\ P& =\text{price}\\ n& =\text{years to\hspace{0.33em}maturity}\end{array} \end{gathered}$$

The YTM is not the easiest formula to work through, so let’s break it down. The annual income is $40, based on the 4% coupon. The annualized discount is found by dividing the overall discount ($200) by the number of years until maturity (10). Remember, the discount is equal to the difference between the market price ($800) and par ($1,000). From there, find the average between the market price ($800) and par ($1,000).

We see this yield (6.7%) is higher than the coupon (4%). The trend remains the same; bonds bought at discounts have yields higher than their coupon because the bond’s discount is providing them with extra return.

Let’s look at how YTM looks with a premium bond.

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

$$\begin{gathered} \begin{array}{rl}\mathrm{ytm}& =\frac{C-\frac{P-F}{n}}{\frac{F+P}{2}}\\ \mathrm{ytm}& =\frac{40-\frac{1,100-1,000}{10}}{\frac{1,000+1,100}{2}}\\ \mathrm{ytm}& =\frac{40-10}{1050}\\ \mathrm{ytm}& =2.9\%\end{array} \\ \begin{array}{rl}\text{where:}& \\ C& =\text{coupon\hspace{0.33em}rate}\\ F& =\text{face\hspace{0.33em}value (par)}\\ P& =\text{price}\\ n& =\text{years to\hspace{0.33em}maturity}\end{array} \end{gathered}$$

The annual income of the bond is $40, based on its 4% coupon. The annualized premium is found by dividing the premium ($100) by the number of years to maturity (10 years). Instead of adding, we subtract the annualized premium because the investor is losing money over time. The average value of the bond is found by adding the market value ($1,100) to the par value ($1,000), and dividing by 2.

We see the trend again with premium bonds. When purchased at a market price above par, the YTM is lower than the bond’s coupon.

Sidenote

"Basis"

You may encounter a test question referencing YTM as “basis.” This is simply just another way of saying the same thing. For example:

A 5% bond trades on a 7% basis

This translates to a 5% coupon (nominal yield) bond is trading at a price that reflects a 7% yield to maturity. If you’re comfortable with yields at this point, you should know this means the bond is trading at a discount.

Yield to call (YTC)

Yield to call (YTC) only applies to callable bonds. If a bond is not callable, YTC does not exist. It represents a bond’s overall rate of return if held until the bond is callable. Essentially, we’re assuming the bond will be called as soon as it’s eligible.

The YTC formula is similar to the YTM formula, but there are some differences. Calculating YTC is also 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)?

$$\begin{gathered} \begin{array}{rl}\mathrm{ytc}& =\frac{C+\frac{CP-MP}{t}}{\frac{CP+MP}{2}}\\ \mathrm{ytc}& =\frac{40+\frac{1000-800}{5}}{\frac{1000+800}{2}}\\ \mathrm{ytc}& =\frac{40+40}{900}\\ \mathrm{ytc}& =8.9\%\end{array} \\ \begin{array}{rl}\text{where:}& \\ C& =\text{coupon\hspace{0.33em}rate}\\ CP& =\text{call\hspace{0.33em}price}\\ MP& =\text{market\hspace{0.33em}price}\\ t& =\text{years to\hspace{0.33em}call}\end{array} \end{gathered}$$

Again, we see the yield we calculated (8.9%) is higher than the coupon (4%). Also, the YTC (8.9%) is higher than the YTM (6.7%). Why is that?

Remember, this investor is earning a discount of $200 over the life of the bond. If the bond is held to maturity, it will take the investor 10 years to earn the $200 discount. If the bond is called in 5 years, the customer earns the $200 5 years earlier than expected, which increases their annualized rate of return.

Let’s take a look at YTC with 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)?

$$\begin{gathered} \begin{array}{rl}\mathrm{ytc}& =\frac{C-\frac{MP-CP}{t}}{\frac{CP+MP}{2}}\\ \mathrm{ytc}& =\frac{40-\frac{1,100-1,000}{5}}{\frac{1,000+1,100}{2}}\\ \mathrm{ytc}& =\frac{40-20}{1050}\\ \mathrm{ytc}& =1.9\%\end{array} \\ \begin{array}{rl}\text{where:}& \\ C& =\text{coupon\hspace{0.33em}rate}\\ CP& =\text{call\hspace{0.33em}price}\\ MP& =\text{market\hspace{0.33em}price}\\ t& =\text{years\hspace{0.33em}to call}\end{array} \end{gathered}$$

We see the yield we calculated (1.9%) is lower than the coupon (4%). Also, the YTC (1.9%) is lower than the YTM (2.9%). Why is that? Remember, this customer is losing a premium of $100 over the life of the bond. If the bond is held to maturity, it will take the investor 10 years to lose the $100 premium. If the bond is called in 5 years, the customer loses the $100 5 years earlier than expected, which decreases their annualized rate of return.

Key points

Benefits of common stock

• Capital appreciation
• Income from cash dividends
• Hedge against inflation

Capital appreciation

• Investment value rises above the cost
• Also known as:
  • Growth
  • Capital gains

Unrealized capital gain

• Current gain on an investment
• Investment has not been sold
• Gains at risk if the market declines

Realized capital gain

• Locked-in gain on an investment
• Investment has been sold
• Gains are not at risk

Growth stock

• Company with expanding business model
• Typical for smaller companies
• High capital appreciation potential
• Little or no dividend potential

Income

• Dividend payments from common stock
• Paid by larger, successful companies

Dividend payout ratio

• $\text{DPR}=\frac{\text{annual dividend per\hspace{0.33em}share}}{\text{annual earnings per share}}$

Value stock

• Company with a “bargain” stock price
• Usually well-established businesses
• Commonly pay cash dividends

Diversification

• Investing in multiple asset classes and investments
• Cannot diversify out of systematic risk

Systematic risk

• Occurs when an event or circumstance negatively affects the entire market

Market risk

• An investment is negatively affected by a general downturn in the stock market

Inflation risk

• Also known as purchasing power risk
• General prices rise more than expected
• Common stock tends to outpace inflation over long-term periods

Non-systematic risk

• Affects specific investment or sector
• Can be reduced by diversification

Financial risk

• High debt levels negatively affect company performance

Business risk

• Products or services in low demand due to competition or mismanagement

Regulatory risk

• Potential or current government regulation negatively affects an investment

Liquidity risk

• Also known as marketability risk
• Inability to sell a security without dropping the price dramatically

Concentration risk

• Lack of diversification
• Amplifies relevant non-systematic risks

Common stock typical investors

• Younger, risk-tolerant investors
• Long time horizons
• Seeking capital appreciation or income

Key points

Nominal yield

• $\text{NY}=\frac{\text{Annual\hspace{0.33em}income}}{\text{Par}}$
• 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

• $\text{CY}=\frac{\text{Annual\hspace{0.33em}income}}{\text{Market price}}$
• 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 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