bond valuation and analysis - amazon s3 · 2018-03-01 · bond valuation & analysis what you...
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![Page 1: Bond Valuation and Analysis - Amazon S3 · 2018-03-01 · Bond Valuation & Analysis What You Should Know Introduction to R Intermediate R No prior experience with financial analysis](https://reader033.vdocuments.us/reader033/viewer/2022041619/5e3dd8b09c8fa8718c592ad7/html5/thumbnails/1.jpg)
BOND VALUATION AND ANALYSIS
Bond Valuation and Analysis
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Bond Valuation & Analysis
The Fixed Income Market Is Large…
$0
$5,000
$10,000
$15,000
$20,000
$25,000
$30,000
$35,000
$40,000
$45,000
2007 2008 2009 2010 2011 2012 2013 2014 2015
OustandingDebt/M
arketCapita
lization(US$inbillion
s)
USFixedIncomeMarket
USStockMarket
$40trillion
$25trillion
$32trillion
$20trillion
Sources: BonddatafromtheSecuritiesIndustryandFinancialMarketsAssociation;StockdatafromtheWorldBank.
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Bond Valuation & Analysis
Layout of the Course● Chapter 1: Bond Valuation
● Chapter 2: Estimating Yield to Maturity
● Chapter 3: Duration and Convexity
● Chapter 4: Comprehensive Example
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Bond Valuation & Analysis
What You Should Know● Introduction to R
● Intermediate R
● No prior experience with financial analysis necessary!
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Bond Valuation & Analysis
About me● Advise clients on valuation
and other financial issues primarily related to litigation
● Previously taught investments, investment management, and corporate finance
● Author of Analyzing Financial Data and Implementing Financial Models Using R
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BOND VALUATION AND ANALYSIS
See you in the course!
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BOND VALUATION AND ANALYSIS
Welcome to the Course!
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Bond Valuation & Analysis
About me● Advise clients on valuation
and other financial issues related to litigation
● Author of Analyzing Financial Data and Implementing Financial Models Using R
![Page 9: Bond Valuation and Analysis - Amazon S3 · 2018-03-01 · Bond Valuation & Analysis What You Should Know Introduction to R Intermediate R No prior experience with financial analysis](https://reader033.vdocuments.us/reader033/viewer/2022041619/5e3dd8b09c8fa8718c592ad7/html5/thumbnails/9.jpg)
Bond Valuation & Analysis
Bonds● Debt instrument
● Repay borrowed amount + interest
● Allows us to focus on fundamental concepts of bond valuation
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Bond Valuation & Analysis
Characteristics of a Bond - I● Issuer: The entity that borrows the money
● Corporations
● Governments
● Municipalities
● Principal: The amount borrowed
● Also called par value or face value
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Bond Valuation & Analysis
Characteristics of a Bond - II● Coupon Rate: The amount of interest issuer
agrees to pay
● Annually, semi-annually, or quarterly
● Fixed or floating rate
● Maturity Date: Date when principal amount is returned to investor
● Some bonds do not mature
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Bond Valuation & Analysis
Characteristics of a Bond - III● Embedded Options
● Could affect bond’s cash flow profile - i.e., can change amount and timing of cash flow
● For example, callable bond
● Issuer can buyback bond earlier than maturity at a pre-agreed price
● More complex analysis required
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Bond Valuation & Analysis
The Bond We Will Use● Annual coupons
● Fixed rate
● Fixed maturity
● No embedded options
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Bond Valuation & Analysis
Price vs. Value● We will use the terms “price” and “value”
interchangeably, but there are distinctions:
● Price: Amount paid to acquire asset
● Value: How much the asset is worth
● For actively traded assets, price may be considered the best estimate of value
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BOND VALUATION AND ANALYSIS
Let’s practice!
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BOND VALUATION AND ANALYSIS
Time Value of Money
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Bond Valuation & Analysis
Time Value of Money (TVM)● $1 today is worth more than $1 tomorrow
● Suppose you won $10,000 in a game, what would you choose?
● Receive the $10,000 today?
● Receive the $10,000 one year from now?
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Bond Valuation & Analysis
Future Value● The future value is the value of $1 at some point in the future
● Prefer $1 today, so would have to be compensated to agree to receive the cash flow in the future
● Future value (fv) one and two years from now can be calculated as:
> fv1 <- pv * (1 + r) > fv2 <- pv * (1 + r) * (1 + r)
present value
interest rate
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Bond Valuation & Analysis
Present Value● Reverse logic of future values
● The value of $1 in the future is worth less today
● So you will be willing to take less than $1 today instead of waiting to receive $1 one or two years from now
● This can be calculated as follows:
> pv <- fv1 / (1 + r) > pv <- fv2 / ((1 + r) * (1 + r))
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Bond Valuation & Analysis
TVM Applied To Bonds● We can apply this Time Value of Money concept to bonds
● Example:
● $100 par value, 5% coupon rate (= $5),5 years to maturity
● Price = $100 today
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Bond Valuation & Analysis
Bond Investors’ Trade-Off
$5 $5 $5 $5$105
CF out - $ 100
CF in
Year 0 1 2 3 4 5
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Bond Valuation & Analysis
Comparing Cash Flows
$5 $5 $5 $5$105
CF out - $ 100
CF in
Year 0 1 2 3 4 5
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BOND VALUATION AND ANALYSIS
Let’s practice!
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BOND VALUATION AND ANALYSIS
Bond Valuation
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Bond Valuation & Analysis
Bond Valuation● In this course, we will consider the following
simple bond:
● Fixed Annual Coupon Rate
● Fixed Maturity Date
● Option-free
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Bond Valuation & Analysis
Value of an Asset● The value of an asset = present value of expected future
cash flows
● Cash flows: discounted at the appropriate risk-adjusted discount rate
V = CFt(1+ y)tt=1
T
∑
Cash Flows
Discount Rate
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Bond Valuation & Analysis
Laying Out a Bond’s Cash Flows● Prior to maturity, the investor receives coupon
payments
V = Ct
(1+ y)t+ CT + P(1+ y)Tt=1
T −1
∑Coupon Payment
Discount Rate or Yield
Principal Repayment
V = Ct
(1+ y)t+ CT + P(1+ y)Tt=1
T −1
∑
● At maturity, the investor receives the last coupon payment and the par value
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Bond Valuation & Analysis
Creating a Cash Flow Vector
> cf <- c(c1, c2, c3, c4, c5, . . . )
V = Ct
(1+ y)t+ CT + P(1+ y)Tt=1
T −1
∑V = Ct
(1+ y)t+ CT + P(1+ y)Tt=1
T −1
∑
coupon payment coupon + principal
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Bond Valuation & Analysis
Converting to Data Frame● So we can add additional columns, we need to convert
the cash flow vector into a data frame
● Use the data.frame() command
> cf <- data.frame(cf)
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Bond Valuation & Analysis
Creating a Time Index● Each cash flow occurs at a certain period of time
● The unit of the periods will be in years
● We create a variable that creates a time index
> cf$t <- c(1, 2, 3, 4, 5, . . . )
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Bond Valuation & Analysis
Calculating the PV Factors● To discount the cash flows, we need a “discount rate”
● For bonds, the discount rate is called a “yield”
● We create a present value factor used for discounting
> cf$pv_factor <- 1 / (1 + y)^cf$t
> pv_factor <- 1 / (1 + .10)^2 > pv_factor [1] 0.8264463
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Bond Valuation & Analysis
PV of Cash Flows● We calculate each cash flow’s present value
> sum(cf$pv)
> cf$pv <- cf$cf * cf$pv_factor
● The sum of the present values of the bond’s cash flow is equal to the bond’s value
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BOND VALUATION AND ANALYSIS
Let’s practice!
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BOND VALUATION AND ANALYSIS
Converting Your Code Into Function
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Bond Valuation & Analysis
Bond Valuation Function● We will value many bonds in this course
● Steps described in prior chapter will be repeated
● We will create the bondprc() function to simplify calculations
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Bond Valuation & Analysis
Steps in Bond Valuation - I● Generalize these inputs:
● p for par value,
● r for coupon rate,
● "m for time to maturity,
● y for yield
● We also make some of the code more generic
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Bond Valuation & Analysis
Steps in Bond Valuation - II
● rep(x, y) - repeats y times the value of x
● x = p * r = coupon payment
● y = ttm - 1 = bond’s time to maturity minus one year
● p * (1 + r) = principal + final coupon payment
> cf <- c(rep(p * r, ttm - 1), p * (1 + r))
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Bond Valuation & Analysis
Steps in Bond Valuation - III
● Create time index used for discounting
● rownames() of “cf” vector is equal to 1, 2, 3, 4, until the “"m” of bond
● as.numeric() needed to ensure values are read as numbers
> cf <- data.frame(cf)
> cf$t <- as.numeric(rownames(cf))
● Convert to data frame so we can add variables to the data (same as last section)
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Bond Valuation & Analysis
Steps in Bond Valuation - IV
● Calculate PV Factor
> cf$pv_factor <- 1 / (1 + y)^cf$t
> cf$pv <- cf$cf * cf$pv_factor
> sum(cf$pv)
● Calculate PV of each cash flow
● Sum PV to arrive at bond’s value
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Bond Valuation & Analysis
Wrap the Code● Create the bondprc() function
● This will take as inputs p, r, "m, and y
bondprc <- function(p, r, ttm, y){ cf <- c(rep(p * r, ttm - 1), p * (1 + r)) cf <- data.frame(cf) cf$t <- as.numeric(rownames(cf)) cf$pv_factor <- 1 / (1 + y)^cf$t cf$pv <- cf$cf * cf$pv_factor sum(cf$pv) }
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BOND VALUATION AND ANALYSIS
Let’s practice!