Estimating the bond price using duration and convexity

In an earlier exercise, you calculated the dollar change due to duration of 8.5459 and convexity of 0.5826. You stored these two values in duration_dollar_change and convexity_dollar_change, respectively.

Recall that the price of the bond is $100, which is stored in the object px. In this exercise, you will be asked to calculate the estimated change in price based on duration and convexity and calculate the estimated new price of the bond when yields decrease by 1%.

Suppose you know that the bond's duration leads to a price effect of 8.5459, which we will store in the object duration_dollar_change. Suppose we also know that the bond's convexity leads to a price effect of 0.5826, which we will store in the object convexity_dollar_change. In this exercise, you will add the duration and convexity effects to arrive at the estimated bond price.

This exercise is part of the course

Bond Valuation and Analysis in R

Exercise instructions

Estimate change in price (price_change) due to duration and convexity. To do this, combine the duration_dollar_change with convexity_dollar_change.
Estimate price based on duration and convexity. This formula should have similarities to your formula for price_change, but should incorporate the bond's current price (px).

Hands-on interactive exercise

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

# Estimate change in price
price_change <- ___ + ___

# Estimate price
price <- ___ + ___ + ___

Edit and Run Code

This exercise is part of the course

Bond Valuation and Analysis in R

IntermediateSkill Level

5.0+

Start Course for Free

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

Current Exercise

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!