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.

Introduction

Price vs. value

Time value of money

Computing a bond's future value

Computing a bond's present value

Bond valuation

Laying out the bond's cash flows

Discounting bond cash flows with a known yield

Convert your code into a function

Convert your code into a bond valuation function

Introduction and Plain Vanilla Bond Valuation

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.

Price-yield relationship

Credit ratings

The yield on the Moody's Baa index

Value the 5% bond using the Baa yield you found

Plotting the price/yield relationship

Components of yield

Risk-free yield

Plotting US Treasury yields

Plotting the investment grade spread

Estimating the yield of a bond

Finding a bond's yield

Use uniroot function to find YTM

Yield to Maturity

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.

Bond price volatility and the price value of a basis point

Price value of a basis point

Calculate PV01 of a 10% bond

Duration

Duration of a zero-coupon bond

Calculate approximate duration for a bond

Estimating effect on bond price using duration

Convexity

Calculate approximate convexity for a bond

Estimating effect of convexity on bond price

Estimating the bond price using duration and convexity

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.

Summarizing the main lessons

Find AAA bond yields as of September 30, 2016

Alternative cash flow vector code

Duration and convexity

Direction of price change

Calculate duration

Calculate convexity measure

The estimated price change using duration and convexity

Congratulations!

Comprehensive Example

After this course on quantitative finance with R, you will be able to use R to develop a model to value a fixed interest rate bond, estimate and analyze a bond's yield (i.e., a measure of the opportunity cost of bond investors), and model techniques used to protect bond portfolios from changes in interest rates. Why value bonds? Bonds are securities issued by governments or corporations that pay interest over a fixed schedule and are the most well-known type of fixed income securities. The US fixed income market is 1.5x larger than the US stock market, but, unlike stocks, most fixed income instruments, including bonds, trade very infrequently. Consequently, a bond's price may be a less reliable indicator of its value and analytical techniques are necessary when analyzing and valuing bonds.

Importing and Managing Financial Data in R

Learn to use R to develop models to evaluate and analyze bonds as well as protect them from interest rate changes.

Bond Valuation and Analysis in R

Angewandte Finanzen in R

Quantitativer Analyst  in R

Price vs. value

Bond Valuation and Analysis in R

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