Fixed Income Investments - Spot Rates and Bond Valuation

On some occasions, such as with non-U.S. government bonds which pay annual interest compared to semi-annual interest in the U.S., an adjustment needs to be made in order to compare their yields.
The computation is as follows:

Formula 14.11

Bond-equivalent yield of an annual-pay bond = 2[(1 + yield on annual-pay bond) to the .5 power - 1]

Assume that the YTM on an annual-pay bond is 8%.

Bond-equivalent yield = 2 [(1 + .08) to the .5 power - 1]
= 2 [.03923]
= .078461 = 7.95%

Look Out!

The bond equivalent yield will always be less than the annual-yield.

Now if you want to convert the bond equivalent yield of a U.S. bond into an annual-pay bond the calculations are as follows:

Formula 14.12

Yield on annual-pay basis = [(1 + yield on bond-equivalent basis/2)2-1

The yield of a U.S. bond quoted on a bond-equivalent basis of 8%:

Yield on annual-pay basis = [(1 + 8/2 to the 2nd power) -1]
= [(1.04) to the 2nd power - 1]
= .0816 = 8.16%

Look Out!

The yield on an annual-pay basis is always greater than the yield on a bond-equivalent basis. This is because of compounding.

Example: Computing the Value of a Bond Using Spot Rates
Suppose you have a bond that matures in 1.5 years that has a coupon rate of 8% and the spot curve is 5% for six months, 5.25% for 1 year and 5.50% for 1.5 years.

Bond price = 40/ (1.05) + 40 / (1.0525) to the second power + 1040 / (1.055) to the third power.
Bond Price = 38.09 + 36.12 + 931.06
Bond Price = 1005.27

This can be applied to any maturity; all you need to do is to continue theformula out to that maturity to discover the price of the bond.

Example: Compute the Theoretical Treasury Spot Rate Curve Using Bootstrapping
Again let's look at an example to get through this LOS. We have a six month annualized yield of 4% and similarly of the 1 year Treasury Security the rate is 4.40%. Given these two rates we can compute the 1.5 year theoretical spot rate of a zero coupon bond. For our example let's use a coupon of 6% with them selling at par.

First let's get the cash flows:
0.5 year = .06 x $100 x .5 = 3.00
1.0 year = .06 x $100 x .5= 3.00
1.5 year = .06 x $100 x .5 = 3.00 +100(par value) = 103

On to the next step:

3.00/ 1.02 + 3 / (1.02) to the second power + 103 / (1 +x3) to the third power = 100
2.94+ 2.88 + 103 / (1 + x3 ) to the third power = 100
103/ (1 +x3) to the third power = 94.18
(1 + x3) to the third power = 103 /94.18

Limitations of the Nominal Spread
As we discussed earlier, a nominal spread is the spread between a non-treasury bond's yield and the yield to maturity on the comparable Treasury security in terms of maturity. For example, if an IBM is trading at a YTM or 6.25% and the comparable Treasury is at 5%, then the nominal spread is 125 basis points. This spread measure takes into consideration the extra credit risk, option risk and any liquidity risk that may be associated with the non-treasury security.

Even though this is a quick and dirty way to describe the yield difference, it has two drawbacks. They are:

1. For bond bonds, the yield does not take into consideration the term structure of spot rates.
2. In the case of callable/puttable bonds, expected interest-rate volatility may change the cash flows of the non-treasury security.

Differentiating Between Spreads
Related Articles
  1. Financial Advisors

    Tips on Passing the CFA Level I on Your First Attempt

    Obtain valuable tips and helpful study instructions that can help you pass the Level 1 Chartered Financial Analyst exam on your first attempt.
  2. Financial Advisors

    Putting Your CFA Level I on Your Resume

    Learn techniques for emphasizing your CFA Level I status in the Skills and Certifications or Professional Development section of your resume.
  3. Professionals

    Investment Analyst: Career Path and Qualifications

    Learn how to prepare for a career as an investment analyst, and read more about how many professionals in the field progress during their careers.
  4. Professionals

    CAIA Vs. CFA: How Are They Different?

    Find out how the CAIA and CFA designations differ, including which professionals should seek either title based on their career ambitions.
  5. Professionals

    Equity Investments: CFA Level II Tutorial

    Chapter 1: Equity Valuation: Its Applications and Processes Chapter 2: Return Concepts for Equity Valuation Chapter 3: Industry Analysis With Porter's 5 Forces
  6. Professionals

    What To Expect On The CFA Level III Exam

    The Chartered Financial Analyst Level III exam, which is only offered in June, is the last in the series of three tests that CFA candidates must pass.
  7. Professionals

    What To Expect On The CFA Level I Exam

    Becoming a chartered financial analyst requires the passing of three grueling exams covering an array of topics.
  8. Options & Futures

    The Alphabet Soup of Financial Certifications

    We decode the meaning of the many letters that can follow the names of financial professionals.
  9. Professionals

    How to Ace the CFA Level I Exam

    Prepare to ace the CFA Level 1 exam by studying systematically.
  10. Personal Finance

    How To Choose A Financial Advisor

    Many advisors display similar skillsets that can make distinguishing between them difficult. The following guidelines can help you better understand their qualifications and services.
  1. Personal Financial Advisor

    Professionals who help individuals manage their finances by providing ...
  2. CFA Institute

    Formerly known as the Association for Investment Management and ...
  3. Security Analyst

    A financial professional who studies various industries and companies, ...
  4. Chartered Financial Analyst - CFA

    A professional designation given by the CFA Institute (formerly ...
  1. What are the differences between a Chartered Financial Analyst (CFA) and a Certified ...

    The differences between a Chartered Financial Analyst (CFA) and a Certified Financial Planner (CFP) are many, but comes down ... Read Full Answer >>
  2. How do I become a Chartered Financial Analyst (CFA)?

    According to the CFA Institute, a person who holds a CFA charter is not a chartered financial analyst. The CFA Institute ... Read Full Answer >>
  3. What types of positions might a Chartered Financial Analyst (CFA) hold?

    The types of positions that a Chartered Financial Analyst (CFA) is likely to hold include any position that deals with large ... Read Full Answer >>
  4. Who benefits the most from prepaid expenses?

    Prepaid expenses benefit both businesses and individuals. Prepaid expenses are the types of expenses that are bought or paid ... Read Full Answer >>
  5. If I am looking to get an Investment Banking job. What education do employers prefer? ...

    If you are looking specifically for an investment banking position, an MBA may be marginally preferable over the CFA. The ... Read Full Answer >>
  6. Can I still pass the CFA Level I if I do poorly in the ethics section?

    You may still pass the Chartered Financial Analysis (CFA) Level I even if you fare poorly in the ethics section, but don't ... Read Full Answer >>
Hot Definitions
  1. Take A Bath

    A slang term referring to the situation of an investor who has experienced a large loss from an investment or speculative ...
  2. Black Friday

    1. A day of stock market catastrophe. Originally, September 24, 1869, was deemed Black Friday. The crash was sparked by gold ...
  3. Turkey

    Slang for an investment that yields disappointing results or turns out worse than expected. Failed business deals, securities ...
  4. Barefoot Pilgrim

    A slang term for an unsophisticated investor who loses all of his or her wealth by trading equities in the stock market. ...
  5. Quick Ratio

    The quick ratio is an indicator of a company’s short-term liquidity. The quick ratio measures a company’s ability to meet ...
  6. Black Tuesday

    October 29, 1929, when the DJIA fell 12% - one of the largest one-day drops in stock market history. More than 16 million ...
Trading Center