Fixed Income Investments - Arbitrage-free Valuation Approach

Under a traditional approach to valuing a bond, it is typical to view the security as a single package of cash flows, discounting the entire issue with one discount rate. Under the arbitrage-free valuation approach, the issue is viewed, instead, as various zero-coupon bonds that should be valued individually and added together to determine value. The reason this is the correct way to value a bond is that it does not allow a risk-free profit to be generated by "stripping" the security and selling the parts at a higher price than purchasing the security in the market.

As an example, a five-year bond that pays semi-annual interest would have 11 separate cash flows, and be valued using the appropriate yield on the curve that matches its maturity. So the markets implement this approach by determining the theoretical rate the U.S. Treasury would have to pay on a zero-coupon treasury for each maturity. The investor then determines the value of all the different payments using the theoretical rate and adds them together. This zero-coupon rate is the treasury spot rate. The value of the bond based on the spot rates is the arbitrage-free value.

Determining Whether a Bond is Under or Over Valued
What you need to be able to do is value a bond like we have done before using the more traditional method of applying one discount rate to the security. The twist here, however, is that instead of using one rate, you will use whatever rate the spot curve has that coordinates with the proper maturity. You will then add the values up as you did previously to get the value of the bond. You will then be given a market price to compare to the value that you derived from your work. If the market price is above your figure, then the bond is undervalued and you should buy the issue. If the market price is below your price, then the bond is overvalued and you should sell the issue.

How Does a Dealer Generate Arbitrage Profits?
A dealer has the ability to strip a security or to take apart the cash flows that make up the bond. These Treasury strips can be sold to investors. So if the market price of a Treasury security is less than the value using the arbitrage-free valuation, a dealer will buy the security, strip the bond and then sell the Treasury strips at a higher amount than the purchase price for the whole bond.

On the other hand, if the market price is more than the value using the arbitrage-free valuation, the dealer will buy the strips, make the bond "whole" and sell it at a higher price than that of the purchased strips.

Typical Yield Measures


Related Articles
  1. Bonds & Fixed Income

    What are Treasury STRIPS?

    STRIPS is an acronym that stands for Separate Trading of Registered Interest and Principal Securities.
  2. Bonds & Fixed Income

    Introduction To STRIPS

    STRIPS provide an alternative form of bond for fixed-income investors who need definite cash flows at specific times. Read the article to find out how.
  3. Options & Futures

    20 Investments: Zero-Coupon Securities

    What Is It? A zero-coupon security, or "stripped bond", is basically a regular coupon-paying bond without the coupons. The process of "stripping" or "zeroing" a bond is usually done by a brokerage ...
  4. Bonds & Fixed Income

    Find The Right Bond At The Right Time

    Find out which bonds you should be investing in and when you should be buying them.
  5. Bonds & Fixed Income

    How To Evaluate Bond Performance

    Learn about how investors should evaluate bond performance. See how the maturity of a bond can impact its exposure to interest rate risk.
  6. Bonds & Fixed Income

    Understanding Bond Prices and Yields

    Understanding this relationship can help an investor in any market.
  7. Home & Auto

    How To Choose The Right Bond For You

    Bond investing is a stable and low-risk way to diversify a portfolio. However, knowing which types of bonds are right for you is not always easy.
  8. Investing

    Advising FAs: Explaining Bonds to a Client

    Most of us have borrowed money at some point in our lives, and just as people need money, so do companies and governments. Companies need funds to expand into new markets, while governments need ...
  9. Bonds & Fixed Income

    How To Invest In Corporate Bonds

    Understand the basics of corporate bonds to increase your chances of positive returns.
  10. Retirement

    Analyzing The Best Retirement Plans And Investment Options: Bonds

    What they are: Debt securities in which you lend money to an issuer (such as a corporation or government) in exchange for interest payments and the future repayment of the bond’s face value. ...
RELATED TERMS
  1. Rational Pricing

    A financial theory that contends that the market prices of assets ...
  2. Coupon Stripping

    The separation of a bond's periodic interest payments from its ...
  3. Bond Valuation

    A technique for determining the fair value of a particular bond. ...
  4. Discount Bond

    A bond that is issued for less than its par (or face) value, ...
  5. Interest Only (IO) Strips

    The interest portion of mortgage, Treasury or bond payments, ...
  6. Bond Discount

    The amount by which the market price of a bond is lower than ...
RELATED FAQS
  1. What is a stripped bond?

    The quick answer to this question is that a stripped bond is a bond that has had its main components broken up into a zero-coupon ... Read Answer >>
  2. What determines the price of a bond in the open market?

    Learn more about some of the factors that influence the valuation of bonds on the open market, and why bond prices and yields ... Read Answer >>
  3. How does an investor make money on a zero coupon bond?

    Learn about investing in zero-coupon bonds, exactly how they work as an investment vehicle, and their advantages and disadvantages ... Read Answer >>
  4. How is convertible bond valuation different than traditional bond valuation?

    Read about bond valuation, particularly the differences between how a traditional bond is valued and how a convertible bond ... Read Answer >>
  5. Why do interest rates tend to have an inverse relationship with bond prices?

    At first glance, the inverse relationship between interest rates and bond prices seems somewhat illogical, but upon closer ... Read Answer >>
  6. What happens to the price of a premium bond as it approaches maturity?

    Learn how bonds trade in regard to premiums and discounts, and how bond prices shift closer to par value as bonds approach ... Read Answer >>
Hot Definitions
  1. White Squire

    Very similar to a "white knight", but instead of purchasing a majority interest, the squire purchases a lesser interest in ...
  2. MACD Technical Indicator

    Moving Average Convergence Divergence (or MACD) is a trend-following momentum indicator that shows the relationship between ...
  3. Over-The-Counter - OTC

    Over-The-Counter (or OTC) is a security traded in some context other than on a formal exchange such as the NYSE, TSX, AMEX, ...
  4. Quarter - Q1, Q2, Q3, Q4

    A three-month period on a financial calendar that acts as a basis for the reporting of earnings and the paying of dividends.
  5. Weighted Average Cost Of Capital - WACC

    Weighted average cost of capital (WACC) is a calculation of a firm's cost of capital in which each category of capital is ...
  6. Basis Point (BPS)

    A unit that is equal to 1/100th of 1%, and is used to denote the change in a financial instrument. The basis point is commonly ...
Trading Center