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  3. Bond Valuation and Analysis in R
  • 1

    Introduction and Plain Vanilla Bond Valuation

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    The fixed income market is large and filled with complex instruments. In this course, we focus on plain vanilla bonds to build solid fundamentals you will need to tackle more complex fixed income instruments. In this chapter, we demonstrate the mechanics of valuing bonds by focusing on an annual coupon, fixed rate, fixed maturity, and option-free bond.

  • 2

    Yield to Maturity

    Estimating Yield To Maturity - The YTM measures the expected return to bond investors if they hold the bond until maturity. This number summarizes the compensation investors demand for the risk they are bearing by investing in a particular bond. We will discuss how one can estimate YTM of a bond.

  • 3

    Duration and Convexity

    Interest rate risk is the biggest risk that bond investors face. When interest rates rise, bond prices fall. Because of this, much attention is paid to how sensitive a particular bond's price is to changes in interest rates. In this chapter, we start the discussion with a simple measure of bond price volatility - the Price Value of a Basis Point. Then, we discuss duration and convexity, which are two common measures that are used to manage interest rate risk.

  • 4

    Comprehensive Example

    We will put all of the techniques that the student has learned from Chapters One through Three into one comprehensive example. The student will be asked to value a bond by using the yield on a comparable bond and estimate the bond's duration and convexity.

Initializing

Ubung

Calculate approximate duration for a bond

A useful approximation of the duration formula is called the approximate duration, which is given by $$(P(down) - P(up)) / (2 * P * \Delta y)$$

where \(P\) is the price of the bond, \(P(down)\) is the price of the bond if yield decreases, \(P(up)\) is the price of the bond if yield increases, and \(\Delta y\) is the expected change in yield.

The full duration formula is more complex. If you're interested, you can refer to the "Fixed Income" chapter of my book as a reference for that formula.

In this exercise, you will calculate the approximate duration of a bond with $100 par value, 10% coupon rate, 20 years to maturity, 10% yield to maturity, and a 1% expected change in yield. To make this calculation, use your familiar bondprc() function, which has been preloaded in the workspace.

Anweisungen

100 XP
  • Use bondprc() to calculate the bond price today given 10% yield. Save this to px and then view px.
  • Use another call to bondprc() to calculate the bond price (px_up) if the yield increases by 1%.
  • Use a third call to bondprc() to calculate the bond price (px_down) if the yield decreases by 1%.
  • Use your three objects (px, px_up, px_down) to calculate the approximate duration assuming a 1% change in yields.