Plotting the price/yield relationship

Although there is an inverse relationship between price and yield, this relationship is not linear. This means that changes in price due to change in yield could differ substantially depending on whether the yield goes up or down. We will revisit this important concept when we discuss the concept of convexity in Chapter Three and how an adjustment is necessary to account for this curved relationship between a bond's price and yield. For now, just keep in mind that this inverse relationship is non-linear.

In this exercise, you will assume that you have a bond with $100 par value, 10% coupon rate, and 20 years to maturity. Note that this is different from the bond you've been working with to this point! Your goal is to value this bond at different levels of yield using your bondprc() function, which is available in your workspace.

This exercise is part of the course

Bond Valuation and Analysis in R

Exercise instructions

Create the vector prc_yld from 2% (0.02) to 40% (0.40) by increments of 1% (0.01) by using the seq() function.
Use data.frame() to convert prc_yld to a data frame.
Use the pre-written for loop with bondprc() to calculate bond price at different yield levels in prc_yld. Try to understand the behavior of the loop.
Your prc_yld object now contains a column for yield (prc_yld) and a column for price (price). Plot this object using the pre-written code to see the relationship between price and yield to maturity (YTM).

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Generate prc_yld
prc_yld <- seq(___, ___, ___)

# Convert prc_yld to data frame
prc_yld <- data.frame(___)

# Calculate bond price given different yields
for (i in 1:nrow(prc_yld)) {
     prc_yld$price[i] <- bondprc(100, 0.10, 20, prc_yld$prc_yld[i])  
}

# Plot P/YTM relationship
plot(___,
     type = "l",
     col = "blue",
     main = "Price/YTM Relationship")

Edit and Run Code

This exercise is part of the course

Bond Valuation and Analysis in R

IntermediateSkill Level

5.0+

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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.

Exercise 1: Introduction Exercise 2: Price vs. value Exercise 3: Time value of money Exercise 4: Computing a bond's future value Exercise 5: Computing a bond's present value Exercise 6: Bond valuation Exercise 7: Laying out the bond's cash flows Exercise 8: Discounting bond cash flows with a known yield Exercise 9: Convert your code into a function Exercise 10: Convert your code into a bond valuation function

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.

Exercise 1: Price-yield relationship Exercise 2: Credit ratings Exercise 3: The yield on the Moody's Baa index Exercise 4: Value the 5% bond using the Baa yield you found Exercise 5: Plotting the price/yield relationship

Current Exercise

Exercise 6: Components of yield Exercise 7: Risk-free yield Exercise 8: Plotting US Treasury yields Exercise 9: Plotting the investment grade spread Exercise 10: Estimating the yield of a bond Exercise 11: Finding a bond's yield Exercise 12: Use uniroot function to find YTM

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.

Exercise 1: Bond price volatility and the price value of a basis point Exercise 2: Price value of a basis point Exercise 3: Calculate PV01 of a 10% bond Exercise 4: Duration Exercise 5: Duration of a zero-coupon bond Exercise 6: Calculate approximate duration for a bond Exercise 7: Estimating effect on bond price using duration Exercise 8: Convexity Exercise 9: Calculate approximate convexity for a bond Exercise 10: Estimating effect of convexity on bond price Exercise 11: Estimating the bond price using duration and convexity

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.

Exercise 1: Summarizing the main lessons Exercise 2: Find AAA bond yields as of September 30, 2016 Exercise 3: Bond valuation Exercise 4: Alternative cash flow vector code Exercise 5: Duration and convexity Exercise 6: Direction of price change Exercise 7: Calculate duration Exercise 8: Calculate convexity measure Exercise 9: The estimated price change using duration and convexity Exercise 10: Congratulations!