Calculate convexity measure

Recall from Chapter Three that duration does not adequately adjust for the convex nature of the relationship between price and yield. To improve the estimate of the bond price based on duration, we can add a term based on the convexity measure.

In Chapter Three, you learned that the approximate formula for convexity is:

$$(P(up) + P(down) - 2 * P) / (P * \Delta y^2)$$

where \(P\) is the price of the bond, \(P(up)\) is the price of the bond when yields increase, \(P(down)\) is the price of the bond when yields decrease, and \(\Delta y\) is the expected change in yield.

You have calculated the objects px, px_up, and px_down previously and all three objects are available in your workspace. For this exercise, assume the expected change in yield is 1%. Calculate the convexity measure, the estimated percentage change in price due to convexity, and the estimated dollar effect on price due to convexity.

This exercise is part of the course

Bond Valuation and Analysis in R

Exercise instructions

Use the formula above with px, px_up, and px_down to calculate convexity. Save this to convexity.
Use convexity and your knowledge about change in yield to calculate and view the percentage effect of convexity on price (convexity_pct_change).
Use convexity to calculate and view the dollar effect of convexity on price (convexity_dollar_change).

Hands-on interactive exercise

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

# Calculate convexity measure
convexity <-

# Calculate percentage effect of convexity on price
convexity_pct_change <-
convexity_pct_change

# Calculate dollar effect of convexity on price
convexity_dollar_change <-
convexity_dollar_change

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 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

Current Exercise

Exercise 9: The estimated price change using duration and convexity Exercise 10: Congratulations!