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Textbook
1. Common stock
2. Preferred stock
3. Bond fundamentals
3.1 Review
3.2 Trading
3.3 Yield types
3.4 Yield relationships
3.5 Suitability
4. Corporate debt
5. Municipal debt
6. US government debt
7. Investment companies
8. Alternative pooled investments
9. Options
10. Taxes
11. The primary market
12. The secondary market
13. Brokerage accounts
14. Retirement & education plans
15. Rules & ethics
16. Suitability
17. Wrapping up
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3.4 Yield relationships
Achievable Series 7
3. Bond fundamentals

Yield relationships

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Discount bond yield relationships

Let’s look at a summary of our discount bond example from the previous sections.

A 10 year, $1,000 par, 4% bond is trading at $800. The bond is callable at par after 5 years.

  • Coupon = 4%

  • Current yield = 5%

  • YTM = 6.7%

  • YTC = 8.9%

The order of these yields is no coincidence. In fact, every discount bond will exhibit the same relationship between the yields. The coupon will be the lowest rate, followed by the current yield, then the YTM, and last the YTC. You could spend time calculating each yield separately, or you can utilize a beloved visual with bonds: the bond see-saw.

Bond see-saw discount

As you can see, the bond see-saw is a quick way of determining the relationship between a bond’s price and its yields. Many test-takers commit the bond see-saw to memory and write it out on their scratch paper when they take the exam. By doing this, you can avoid doing most of the calculations we just went through.

NASAA is more concerned that you know the relationship between the yields (which is lower or higher) than your ability to calculate these yields. While you certainly can be required to calculate current yield, the order of the yields and their relationships are more important topics to master. Plus, knowing the order of yields will help you eliminate wrong answers to yield calculation questions.

Premium bond yield relationships

Let’s continue using our premium bond example from the previous sections.

A 10 year, $1,000 par, 4% bond is trading at $1,100. The bond is callable at par after 5 years.

  • Coupon = 4%

  • Current yield = 3.6%

  • YTM = 2.9%

  • YTC = 1.9%

Again, the order of these yields is no coincidence. In fact, every premium bond will exhibit the same relationship between the yields. The YTC will be the lowest rate, followed by the YTM, then the current yield, and last the coupon. You could spend time calculating each yield separately, or you can utilize the bond see-saw.

Bond see-saw premium

As we witnessed with discount bonds, the bond see-saw gives us a great visual representation of the yields. Now, we have the price side pointed upward, as premium bonds are purchased at prices above par. Remember the specific order of the yields on the see-saw and yield-based questions will be easy to answer!

Yield for par bonds

We’ve gone through how prices affect yields for bonds purchased at discounts and premiums. What if a bond is purchased at par ($1,000)? We won’t need to go into much detail, because this concept is fairly simple. When a bond is purchased at par, all of the yields are equal to the coupon.

The investor isn’t making or losing any money through the purchase price of their bond. If the bond is bought at par ($1,000), it will mature at par ($1,000). The only return the investor is realizing is the coupon. For a bond purchased at its par value, the see-saw looks like this:

Bond see-saw par

As you can see, the coupon is at the same level as the current yield, YTM, and YTC. If you see a question on par bond yields, keep it simple. All of them are the same.

The bond see-saw

Yield is a very important concept on the Series 7 exam, and hopefully, the bond see-saw helps visualize the relationship between bond prices, interest rate changes, and the yields. We’ve looked at the see-saw through the lens of a discount bond, premium bond, and par bond. Let’s take a look at all of them together:

Bond see-saw par

If you’re going to utilize a “dump sheet,” it’s highly recommended that this be a part of it. A dump sheet is a list of visual items that are written out on your scratch paper after you start your exam. Many students memorize concepts like the bond see-saw in order to rewrite them for the exam and rely on it for yield questions.

I’ve also seen a lot of successful test-takers use acronyms, like this:

CYM Call

  • CY = Current Yield

  • M = yield to Maturity

  • Call = yield to Call

Whatever will help you commit these terms to memory is encouraged. It doesn’t matter how you remember it, as long as you remember it!

Yield to worst

Two yields are typically provided when a bond quote is given to investors (and also disclosed on trade confirmations). First, the bond’s nominal yield (coupon) is disclosed, which provides insight into the security’s interest payments. Second, the bond’s yield to worst is furnished, which represents the lower of the YTM or YTC. Providing an investor with the worst of these two yields gives them a “worst-case scenario.” Let’s go through the two general scenarios.

If a callable bond is bought at a discount, the investor is provided the YTM. An investor would make a higher annualized return if a discount bond is redeemed sooner as they would earn the discount faster. For example, let’s assume a 20 year bond that is callable in 10 years at par is purchased for 90 ($900). The investor would earn the $100 discount faster if the bond is called before maturity, resulting in a higher annualized return. The YTM assumes the discount bond is held to maturity, which reflects the discount being gained slower and the lowest possible yield (unless the bond defaults).

If a callable bond is bought at a premium, the investor is provided the YTC. An investor would make a higher annualized return if a premium bond is held to maturity as they would lose the premium slower. For example, let’s assume a 20 year bond that is callable in 10 years at par is purchased for 110 ($1,100). The investor would lose the $100 premium slower if the bond is held to maturity, resulting in a higher annualized return. The YTC assumes the premium bond is called at the first possible date, which reflects the premium being lost faster and the lowest possible yield (unless the bond defaults).

No YTC exists if a bond is not callable. Therefore, the YTM is always provided when quoting a non-callable bond.

Assuming a bond is callable, here’s the “yield to worst” summary:

  • Discount bonds = YTM is quoted
  • Premium bonds = YTC is quoted
Key points

Discount bond yield relationships

  • Current yield, YTM, and YTC are higher than the coupon
  • Order of all yields (lowest to highest)
    • Nominal yield (coupon)
    • Current yield
    • Yield to maturity (YTM)
    • Yield to call (YTC)

Premium bond yield relationships

  • Current yield, YTM, and YTC are lower than the coupon
  • Order of all yields (lowest to highest)
    • Yield to call (YTC)
    • Yield to maturity (YTM)
    • Current yield
    • Nominal yield (coupon)

Par bond yield relationships

  • All yields are the same

Yield to worst

  • Lower of YTM or YTC provided in callable bond quotes
  • Discount bonds = YTM is quoted
  • Premium bonds = YTC is quoted

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