1. Bond Valuation and Risk8

2. Chapter 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

3. Bond 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

4. Bond 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

5. Bond 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

6. Bond 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 C C
C + Par +
+ …
PV =
(1+ i)1
(1+ i)2
(1+ i)n

7. Bond 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%

8. Bond 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

9. Bond 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

10. Bond 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)

11. Re-work the above problem assuming semiannual compoundingPV
PMT FV 6 ? 50
1000

12. Re-work the above problem assuming semiannual compoundingPV
PMT FV 6
950.82 50
1000

13. Relationships Between Coupon Rate, Required 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

14. Relationships Between Coupon Rate, Required 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

15. Relationships Between Coupon Rate, Required 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

16. Relationships Between Coupon Rate, Required 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

17. a a Exhibit 8.4 20-Y ear Bond 10-Y ear Bond 5-Y ear Bond
1,800
1,600
20-Y
ear Bond
1,400
10-Y
ear Bond
1,200
5-Y
ear Bond
1,000
800
600
400
200 5 8 10 12 15 20
Required Return (Percent)

18. Relationships Between Coupon Rate, Required 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

19. Explaining 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

20. Explaining 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

21. Explaining 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

22. Exhibit 8.8 a U.S. Fiscal Policy U.S. Monetary Policy U.S. Economic
Conditions
Issuer’s
Industry
Conditions
Issuer’s
Unique
Conditions
Long-T
erm
Risk-Free
Interest Rate (T
reasury
Bond Rate)
Risk
Premium
of Issuer
Required
Return
on the
Bond
Bond Price

23. Sensitivity of Bond Prices to Interest Rate Movements
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

24. Sensitivity of Bond Prices to Interest Rate Movements
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.

25. Sensitivity of Bond Prices to Interest Rate Movements
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

26. Sensitivity of Bond Prices to Interest Rate Movements
Calculate the bond elasticity:
Bond elasticity or price sensitivity to changes in
interest rates approaches the limit at –1 for zero-coupon
bonds. Price sensitivity is lower for coupon
bonds. The inverse relationship between k and p
causes the negative numbers

27. Sensitivity of Bond Prices to Interest Rate Movements
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

28. Sensitivity of Bond Prices to Interest Rate Movements
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

29. Sensitivity of Bond Prices to Interest Rate Movements
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

30. Sensitivity of Bond Prices to Interest Rate Movements
Modified duration is an easily calculated approximate of the duration measure
DUR* is a linear approximation of DUR which measures
the convex relationship between bond yields and prices

31. Bond Investment Strategies Used by Investors
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

32. Bond Investment Strategies Used by Investors
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

33. Bond Investment Strategies Used by Investors
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

34. Bond Investment Strategies Used by Investors
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

35. Foreign Exchange Rates and Interest Rates
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

36. Diversifying 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