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Financial Markets and Institutions6th Edition
PowerPoint Slides for:PowerPoint Slides for:
By Jeff Madura
CHAPTER
88Bond Valuation
and Risk
Copyright© 2002 Thomson Publishing. All rights reserved.
Chapter ObjectivesChapter Objectives
Demonstrate how bond market prices are established and influenced by interest rate movements
Identify the factors that affect bond prices Explain how the sensitivity of bond prices to
interest rates is dependent on particular bond characteristics
Explain the benefits of diversifying the bond portfolio internationally
Copyright© 2002 Thomson Publishing. All rights reserved.
Bond Valuation ProcessBond Valuation Process
Bonds are debt obligations with long-term maturities issued by governments or corporations to obtain long-term funds
Commonly purchased by financial institutions that wish to invest funds for long-term periods
Bond price (value) = present value of cash flows to be generated by the bond
Copyright© 2002 Thomson Publishing. All rights reserved.
Bond Valuation ProcessBond Valuation Process
Impact of the Discount Rate on Bond Valuation Discount rate = market-determined yield that
could be earned on alternative investments of similar risk and maturity
Bond prices vary inversely with changes in market interest rates Cash flows are contractual and remain the same each
period Bond prices vary to provide the new owner the market
rate of return
Copyright© 2002 Thomson Publishing. All rights reserved.
Bond Risks and PricesBond Risks and Prices
Higher risk Higher discount rates Lower bond prices
Lower risk Lower discount rates Higher bond prices
Note Inverse Relationship
Between Risk, required returns
and Bond Prices
Copyright© 2002 Thomson Publishing. All rights reserved.
Bond Valuation ProcessBond Valuation Process
Bond Price = present value of cash flows discounted at the market required rate of return C = Coupon per period (PMT) Par = Face or maturity value (FV) i = Discount rate (i) n = Compounding periods to maturity
PV = C
(1+ i)1+
(1+ i)2 (1+ i)nC C + Par+ …
Copyright© 2002 Thomson Publishing. All rights reserved.
Bond Valuation ProcessBond Valuation Process
Consider a $1000, 10% coupon (paid annually) bond that has three years remaining to maturity. Assume the prevailing annualized yield on other bonds with similar risk is 12 percent. Calculate the bond’s value. The expected cash flows of a coupon bond
includes periodic interest payments, and… A final $1000 payoff at maturity Discounted at the market rate of return of 12%
Copyright© 2002 Thomson Publishing. All rights reserved.
Bond Valuation ProcessBond Valuation Process
PV = $100/(1+.12)1 + $100/(1+.12)2 + $1100/(1+.12)3
= $951.97
N I PV PMT FV
3 12 ? 100 1000
Copyright© 2002 Thomson Publishing. All rights reserved.
Bond Valuation ProcessBond Valuation Process
PV = $100/(1+.12)1 + $100/(1+.12)2 + $1100/(1+.12)3
= $951.97
N I PV PMT FV
3 12 –951.97 100 1000
Copyright© 2002 Thomson Publishing. All rights reserved.
Bond Valuation ProcessBond Valuation Process
Valuation of Bonds with Semiannual Payments Most bonds pay interest semiannually Double the number of compounding periods (N)
and halve the annual coupon amount (PMT) and the discount rate (I)
Copyright© 2002 Thomson Publishing. All rights reserved.
Re-work the above problem assuming semiannual compounding
N I PV PMT FV
6 6 ? 50 1000
Copyright© 2002 Thomson Publishing. All rights reserved.
Re-work the above problem assuming semiannual compounding
N I PV PMT FV
6 6 950.82 50 1000
Copyright© 2002 Thomson Publishing. All rights reserved.
Relationships Between Coupon Rate, Relationships Between Coupon Rate, Required Return, and Bond PriceRequired Return, and Bond Price
No periodic coupon Pays face value at maturity Trade at discount from face value No reinvestment risk Considerable price risk
Zero-Coupon Bonds
Copyright© 2002 Thomson Publishing. All rights reserved.
Relationships Between Coupon Rate, Relationships Between Coupon Rate, Required Return, and Bond PriceRequired Return, and Bond Price
Discount bonds are bonds priced below face value; premium bonds above face value
Discounted bond Coupon < Market rates Rates have increased since issuance Adverse risks factors that may have occurred
Price risk—depends on maturity Default risk may have increased Fisher effect of higher expected inflation
Copyright© 2002 Thomson Publishing. All rights reserved.
Relationships Between Coupon Rate, Relationships Between Coupon Rate, Required Return, and Bond PriceRequired Return, and Bond Price
Premium bond Coupon > Market Rates decreased since issuance Favorable risk experience
Price risk—depends on maturity Default risk might have decreased as economic activity
has increased Low inflation expectations
Copyright© 2002 Thomson Publishing. All rights reserved.
Relationships Between Coupon Rate, Relationships Between Coupon Rate, Required Return, and Bond PriceRequired Return, and Bond Price
Long-term bond prices are more sensitive to given changes in market rates than short-term bonds
Changes in rates compounded many times for later coupon and maturity value, impacting price (PV) significantly
Short-term securities have smaller price movements
Bond Maturity and Price Variability
Copyright© 2002 Thomson Publishing. All rights reserved.
Exhibit 8.4Exhibit 8.4
0 5 8 10 12 15 200
1,800
1,600
1,400
1,200
1,000
800
600
400
200
5-Year Bond10-Year Bond20-Year Bond
Required Return (Percent)
Copyright© 2002 Thomson Publishing. All rights reserved.
Relationships Between Coupon Rate, Relationships Between Coupon Rate, Required Return, and Bond PriceRequired Return, and Bond Price
Low coupon bond prices more sensitive to change in interest rates
PV of face value at maturity a major proportion of the price
Coupon Rates and Price Variability
Copyright© 2002 Thomson Publishing. All rights reserved.
Explaining Bond Price MovementsExplaining Bond Price Movements
The price of a bond should reflect the present value of future cash flows discounted at a required rate of return
The required return on a bond is primarily determined by Prevailing risk-free rate Risk premium
Copyright© 2002 Thomson Publishing. All rights reserved.
Explaining Bond Price MovementsExplaining Bond Price Movements
Factors that affect the risk-free rate Changes in returns on real investment
Financial investment an alternative to real investment Opportunity cost of financial investment is the returns
available from real investment Federal Government deficits/surplus position
Inflationary expectations Consumer price index Federal Reserve monetary policy position Oil prices and other commodity prices Exchange rate movements
Copyright© 2002 Thomson Publishing. All rights reserved.
Explaining Bond Price MovementsExplaining Bond Price Movements
Factors that affect the credit or default risk premium Strong economic growth
High level of cash flows Investors bid up bond prices; lower default premium
Weak economic growth Lower profits and cash flows Impact on specific industries varied Investors flee from risky bonds to Treasury bonds Bond prices fall; default premiums increase
Copyright© 2002 Thomson Publishing. All rights reserved.
Exhibit 8.8Exhibit 8.8
U.S.FiscalPolicy
U.S.Monetary
Policy
Long-TermRisk-Free
Interest Rate(TreasuryBond Rate)
RiskPremiumof Issuer
U.S.Economic
Conditions
Issuer’sIndustry
Conditions
Issuer’sUnique
Conditions
RequiredReturnon theBond
Bond Price
Copyright© 2002 Thomson Publishing. All rights reserved.
Sensitivity of Bond Prices to Interest Rate Sensitivity of Bond Prices to Interest Rate MovementsMovements
Bond Price Elasticity = Bond price sensitivity for any % change in market interest rates
Bond Price Elasticity = (% Change In Price)/(% Change In Interest Rates)
Increased elasticity means greater price risk
Copyright© 2002 Thomson Publishing. All rights reserved.
Sensitivity of Bond Prices to Interest Rate Sensitivity of Bond Prices to Interest Rate MovementsMovements
Calculate the price sensitivity of a zero-coupon bond with 10 years until maturity if interest rates go from 10% to 8%. First, calculate the price of the bond for both rates
When k = 10%, PV = ? When k = 8%, PV = ? Hint: Remember zero-coupon or no PMT in this
calculation The price of a zero-coupon bond is the present value of
a single future value cash flow.
Copyright© 2002 Thomson Publishing. All rights reserved.
Sensitivity of Bond Prices to Interest Rate Sensitivity of Bond Prices to Interest Rate MovementsMovements
Calculate the price sensitivity of a zero-coupon bond with 10 years until maturity if interest rates go from 10% to 8%. First, calculate the price of the bond for both rates
When k = 10%, PV = $386 When k = 8%, PV = $463
Copyright© 2002 Thomson Publishing. All rights reserved.
Sensitivity of Bond Prices to Interest Rate Sensitivity of Bond Prices to Interest Rate MovementsMovements
Calculate the bond elasticity:
997.
%10%10%8
386$386$463$
kpercent
PpercentPe
Bond elasticity or price sensitivity to changes in interest rates approaches the limit at –1 for zero-coupon
bonds. Price sensitivity is lower for couponbonds. The inverse relationship between k and p
causes the negative numbers
Copyright© 2002 Thomson Publishing. All rights reserved.
Sensitivity of Bond Prices to Interest Rate Sensitivity of Bond Prices to Interest Rate MovementsMovements
Price-Sensitive Bonds Longer maturity—more price variation for a
change in interest rates Lower coupon rate bonds are more price sensitive
(the PV is a greater % of current value) Zero-coupon bonds most sensitive, approaching –
1 price elasticity Greater for declining rates than for increasing
rates
Copyright© 2002 Thomson Publishing. All rights reserved.
Sensitivity of Bond Prices to Interest Rate Sensitivity of Bond Prices to Interest Rate MovementsMovements
Measure of bond price sensitivity Measures the life of bond on a PV basis Duration = Sum of discounted, time-weighted cash
flows divided by price
Duration
Copyright© 2002 Thomson Publishing. All rights reserved.
Sensitivity of Bond Prices to Interest Rate Sensitivity of Bond Prices to Interest Rate MovementsMovements
The longer a bond’s duration, the greater its sensitivity to interest rate changes
The duration of a zero-coupon bond = bond’s term to maturity
The duration of any coupon bond is always less than the bond’s term to maturity
Duration
Copyright© 2002 Thomson Publishing. All rights reserved.
Sensitivity of Bond Prices to Interest Rate Sensitivity of Bond Prices to Interest Rate MovementsMovements
Modified duration is an easily calculated approximate of the duration measure
)1(*
k
DURDUR
DUR* is a linear approximation of DUR which measuresthe convex relationship between bond yields and prices
Copyright© 2002 Thomson Publishing. All rights reserved.
Bond Investment Strategies Used by Bond Investment Strategies Used by InvestorsInvestors
Create bond portfolio that will generate income that will match their expected periodic expenses
Used to provide retirement income from savings accumulation
Estimate cash flow needs then select bond portfolio that will generate needed income
Matching Strategy
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Bond Investment Strategies Used by Bond Investment Strategies Used by InvestorsInvestors
Funds are allocated evenly to bonds in several different maturity classes
Example: ¼ funds invested in bonds with 5 years until maturity, ¼ in10-year bonds, ¼ in 15-year bonds, and ¼ in 20-year bonds
Investor receives average return of yield curve over time as maturing bonds are reinvested
Laddered Strategy
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Bond Investment Strategies Used by Bond Investment Strategies Used by InvestorsInvestors
Allocated funds to short-term bonds and long-term bonds
Short-term bonds provide liquidity from maturity Long-term bonds provide higher yield (assuming
up-sloping yield curve)
Barbell Strategy
Copyright© 2002 Thomson Publishing. All rights reserved.
Bond Investment Strategies Used by Bond Investment Strategies Used by InvestorsInvestors
Funds are allocated in a manner that capitalizes on interest rate forecasts
Example: if rates are expected to decline, move into longer-term bonds
Problems: High transaction costs because of higher trading Difficulty in forecasting interest rates
Interest Rate Strategy
Copyright© 2002 Thomson Publishing. All rights reserved.
Foreign Exchange Rates and Interest Foreign Exchange Rates and Interest RatesRates
Country interest rate differences reflect expected future spot foreign exchange rates
Expected future spot foreign exchange rates (forward forex rates) reflect expected inflation differences between countries
Expected return on foreign bond portfolio related to return on bonds adjusted for expected changes in forex rates
Copyright© 2002 Thomson Publishing. All rights reserved.
Diversifying Bonds InternationallyDiversifying Bonds Internationally
Investor may diversify by: Credit risk Country risk Foreign exchange risk Interest rate risk
Seek lower total variability of returns per level of risk assumed