1. Figuring out the Assured Returns
Chapter 12
BOND PRICES AND YIELDS
Figuring out the Assured Returns

2. OUTLINE
Changes in Bond Market
Bond Characteristics
Bond Prices
Bond Yields
Risks in Bonds
Rating of Bonds
The Yield Curve
Explaining the Term Structure
Determinants of Interest Rates
Analysis of Convertible Bonds

3. CHANGES IN DEBT MARKET THEN NOW
• PLAIN VANILLA BONDS • BONDS WITH COMPLEX FEATURES
• STABLE & ADMINISTERED • VOLATILE & MARKET- INTEREST RATES DETERMINED INTEREST RATES
• SIMPLISTIC MEASURES OF • PRECISE MEASURES OF RETURN & LIFE RETURN & LIFE
• RULES OF THUMB • ANALYTICAL METHODS
• FEW PLAYERS • MORE PLAYERS
• PASSIVE APPROACH • RELATIVELY MORE ACTIVE APPROACH
• ILLIQUID MARKET • LIQUID MARKET ?
• ABSENCE OF A REFERENCE • EMERGENCE OF A REFERENCE RATE RATE

4. BOND CHARACTERISTICS A BOND IS AN IOU. IT IS DESCRIBED IN TERMS OF:
PAR VALUE
COUPON RATE
MATURITY DATE
GOVERNMENT BONDS ALSO CALLED GOVERNMENT
SECURITIES (G-SECS) OR GILT-EDGED SECURITIES.
THESE ARE GENERALLY MEDIUM TO LONG-TERM
BONDS ISSUED BY RBI ON BEHALF OF THE
GOVERNMENT OF INDIA AND STATE GOVERNMENTS.
CORPORATE BONDS OR CORPORATE DEBENTURES ARE
DEBT INSTRUMENTS ISSUED BY COMPANIES

5. TYPES OF BONDS
STRAIGHT BONDS
ZERO COUPON BONDS.
FLOATING RATE BONDS
BONDS WITH EMBEDDED OPTIONS
COMMODITY-LINKED BONDS

6. BOND PRICING (VALUATION)
n C M P =  t= (1+r)t (1+r)n
2n C/ M P =  t= (1+r/2)t (1+r/2)2n

7. BOND PRICING
A RS.600 FACE VALUE BOND CARRIES A COUPON RATE OF 12 PERCENT P.A. PAYABLE SEMI-ANNUALLY. THE BOND IS REDEEMBALE AT PAR AFTER 5 YEARS. IF INVESTORS REQUIRE A RETURN OF 9% PER HALF-YEAR PERIOD, WHAT WILL BE THE PRICE OF THE BOND P0 =  t= (1.09)t (1.09)10
= 36 x x = RS
1 – F P = C r (1+r)n
36 x x = 1
(1+r)n

8. PRICE - YIELD RELATIONSHIP
YEILD
PRICE CHANGES WITH TIME VALUE OF BOND PREMIUM BOND: rd = 11% A PAR VALUE BOND: rd = 13% B DISCOUNT BOND: rd = 15%
YEARS TO MATURITY

9. BOND PRICE THEOREMS
1. BOND PRICES & YIELDS MOVE IN OPPOSITE DIRECTIONS
2. BOND PRICES ARE MORE SENSITIVE TO YIELD CHANGES THE LONGER THEIR MATURITIES
3. THE PRICE SENSITIVITY OF BONDS TO YIELD CHANGES INCREASES AT A DECREASING RATE WITH MATURITY
4. HIGH COUPON BOND PRICES ARE LESS SENSITIVE TO YIELD CHANGES THAN LOW COUPON BOND PRICES
5. WITH A CHANGE IN YIELD OF A GIVEN NUMBER OF BASIS POINTS, THE ASSOCIATED PERCENT GAIN IS LARGER THAN THE PERCENT LOSS.

10. BOND YIELDS • CURRENT YIELD ANNUAL INTEREST PRICE
• YIELD TO MATURITY C C C M P = … (1+r) (1+r)2 (1+r)n (1+r)n
, =  t= (1+r)t (1+r) AT r = % … RHS = AT r = % … RHS = YTM = 13% + (14% - 13%) = 13.2% C + (M - P) / n YTM ≃ M P • YIELD TO CALL n* C M* P =  t= (1+r)t (1+r)n

11. YTM
• SOMEONE WHO INVESTS IN A COUPON - PAYING BOND WILL EARN THE YTM PROMISED ON THE PURCHASE DATE IF AND ONLY IF ALL OF THE FOLLOWING THREE CONDITIONS ARE FULFILLED
• THE BOND IS HELD UNTIL IT MATURES RATHER THAN BEING SOLD AT A PRICE WHICH DIFFERS FROM ITS FACE VALUE BEFORE ITS MATURITY
• THE BOND DOES NOT DEFAULT
• ALL CASHFLOWS ARE RE-INVESTED AT AN INTEREST RATE EQUAL TO THE PROMISED YTM

12. REALISED YIELD TO MATURITY
FUTURE VALUE OF BENEFITS
(1+r*)5 = 2032 / 850 = r* = OR 19 PERCENT

13. RISKS IN BOND INVESTMENT
• INTEREST RATE RISK INTEREST BOND (MARKET RISK) RATE PRICE
• REINVESTMENT INTEREST RATE ON RISK INTERIM CASH FLOW
• DEFAULT RISK ISSUER MAY DEFAULT (CREDIT RISK)
• INFLATION RISK PURCHASING POWER RISK
• CALL RISK ISSUER MAY RECALL THE BONDS
• EXCHANGE RATE RISK A NON-RUPEE DENOMINATED BOND
• LIQUIDITY RISK MARKETABILITY RISK
• EVENT RISK ISSUER’S ABILITY.. CHANGE UNEXPECTEDLY (a) A NATURAL ACCIDENT OR (b) .. CORP. RESTR’G

14. DEBT RATING WHAT IS IT ? WHAT IT ‘IS NOT’ ? HOW IS IT DONE ?
PROBABILITY OF TIMELY PAYMENT OF INTEREST & PRINCIPAL BY A BORROWER
WHAT IT ‘IS NOT’ ?
NOT A RECOMMENDATION
NOT A GENERAL EVAL’N OF THE ISSUING ORGANISATION
NOT A ONE-TIME EVALUAT’N CREDIT RISK . . VALID ENTIRE LIFE
HOW IS IT DONE ?
INDUSTRY & BUS ANALYSIS. FINANCIAL ANALYSIS
QUANTITATIVE RATING MODELS
VALUE OF RATINGS ?
RATING SCENARIO ?

15. FUNCTIONS OF DEBT RATING
DEBT RATINGS (OR DEBT RATING FIRMS) ARE SUPPOSED TO :
PROVIDE SUPERIOR INFORMATION
OFFER LOW-COST INFORMATION
SERVE AS A BASIS FOR A PROPER RISK-RETURN TRADEOFF.
IMPOSE HEALTHY DISCIPLINE ON CORPORATE BORROWERS.
LEND GREATER CREDENCE TO FINANCIAL AND OTHER REPRESENTATIIONS.
FACILITATE THE FORMULATION OF PUBLIC POLICY GUIDELINES ON INSTITUTIONAL INVESTMENT.

16. CREDIT RATING CRISIL’S RATING SYMBOLS
AAA : HIGHEST SAFETY
AA : HIGH SAFETY
A : ADEQUATE SAFETY
BBB : LOW SAFETY
BB : INADEQUATE SAFETY
B : HIGH RISK
C : SUBSTANTIAL RISK
D : IN DEFAULT
KEY FACTORS CONSIDERED IN CREDIT RATING
INDUSTRY & BUSINESS ANALYSIS FINANCIAL ANALYSIS
• GROWTH RATE & REL’N WITH THE ECONOMY • EARNING POWER
• INDUSTRY RISK CHARACTERISTICS • BUSINESS & FINANCIAL RISKS
• STRUCTURE OF INDUSTRY & NATURE • ASSET PROTECTION OF COMPETITION
• COMPETITIVE POSITION OF THE ISSUER • CASH FLOW ADEQUACY
• MANAGERIAL CAPABILITY OF THE ISSUER • FINANCIAL FLEXIBILITY
• QUALITY OF ACCOUNTING

17. THE YIELD CURVE YIELD CURVE
THE YIELD CURVE., OR THE TERM STRUCTURE OF INTEREST RATES, SHOWS HOW YTM IS RELATED TO TERM TO MATURITY FOR BONDS THAT ARE SIMILAR IN ALL RESPECTS, EXPECTING MATURITY.
YIELD CURVE
YIELD TO MATURITY (YTM)
14.0
13.0
12.0
TERM TO MATURITY (YRS)

18. TYPES OF YIELD CURVE YTM A. UPWARD SLOPING YTM B. DOWNWARD SLOPING
TERM TERM
YTM C. FLAT YTM D. HUMPED

19. ILLUSTRATIVE DATA FOR GOVERNEMNT SECURITIES
Face Value Interest Rate Maturity (years) Current Price Yield to maturity
100, ,
100, ,
100, ,
100, ,
100, ,

20. FORWARD RATES
• ONE - YEAR TB RATE = r1 = (1 + r1)
• 2 - YEAR GOVT. SECURITY = r2 = (1.124) (1.124) (1 + r2)
• 3 - YEAR GOVT. SECURITY = (1.124) (1.124) ( ) (1.124) (1.1289) (1 + r3)
r3 =

21. FORWARD RATES
4-YEAR GOVERNMENT SECURITY

22. FORWARD RATES

23. EXPLAINING THE TERM STRUCTURE
EXPECTATIONS THEORY
LIQUIDITY PREFERENCE THEORY
PREFERRED HABITAT THEORY
MARKET SEGMENTATION THEORY

24. EXPECTATIONS THEORY
SHAPE …. YIELD CURVE … DEPENDS ON .. EXPECTATIONS … THOSE WHO PARTICIPATE … MARKET
(1 + tRn) = [ (1 + tR1) (1 + t+1R1) … (1 + t+n-1Rn)]1/n
YIELD CURVE EXPLANATION
ASCENDING SHORT-TERM RATES RISE IN FUTURE
DESCENDING SHORT-TERM RATES … FALL IN FUTURE
HUMPED SHORT-TERM RATES … RISE …. FALL
FLAT SHORT-TERM RATES . . UNCHANGED IN FUTURE

25. LIQUIDITY PREFERENCE THEORY
FORWARD RATES SHOULD INCORPORATE INTEREST RATE EXPECTATIONS AS WELL AS A RISK (OR LIQUIDITY) PREMIUM
(1 + tRn) = [ (1 + tR1) (1 + t+1R1+L2) … (1 + t+n-1Rn +Ln)]1/n
AN UPWARD-SLOPING YIELD CURVE SUGGESTS THAT FUTURE INTEREST RATES WILL RISE (OR WILL BE FLAT) OR EVEN FALL IF THE LIQUIDITY PREMIUM INCREASES FAST ENOUGH TO COMPENSATE FOR THE DECLINE IN THE FUTURE INTEREST RATES

26. PREFERRED HABITAT THEORY MARKET SEGMENTATION THEORY
INVESTORS PREFER TO MATCH THE MATURITY OF INVESTMENT TO THEIR INVESTMENT OBJECTIVE
BORROWERS . . TOO
IF MISMATCH … INDUCEMENT TO SHIFT
MARKET SEGMENTATION THEORY
EXTREME FORM OF PREFERRED HABITAT THEORY

27. DETERMINANTS OF INTEREST RATES
INFLATION RATE
REAL GROWTH RATE
TIME PREFERENCE
SHORT-TERM RISK-FREE RATE
DEFAULT PREMIUM
BUSINESS RISK
FINANCIAL RISK
COLLATERAL
MATURITY PREMIUM
FUTURE EXPECTATIONS
LIQUIDITY PREFERENCE
PREFERRED HABITAT
INTEREST RATE
SPECIAL FEATURES
CALL/PUT FEATURE
CONVERSION FEATURE
OTHER FEATURES

28. VALUATION OF CONVERTIBLE BONDS
VALUE OF THE STRAIGHT CONVERSION OPTION
CONVERTIBLE = MAX BOND VALUE VALUE
BOND VALUE ,
A. STRAIGHT DEBT VALUE B. CONVERSION VALUE C. VALUE OF CONVERTIBLE BOND
FIRM VALUE FIRM VALUE FIRM VALUE
VA L U E O F CONV E R T I B L E BOND S
CONVERT I ON VALUE
S TRA I GHT DEBT VALUE

29. SUMMING UP
The debt market in India has registered an impressive growth
particularly since mid-1990s and has been accompanied by
increasing complexity in instruments,interest rates, methods of
analysis, and so on
The value of a noncallable, nonconvertible bond is:
n C M
P = 
t =1 (1+ r)t (1 + r)n
The commonly employed yield measures are : current yield, yield
to maturity (YTM), yield to call, and realised yield to maturity.
The YTM of a bond is the discount rate that makes the present
value of the cash flows receivable from owning the bond equal to
the price of the bond.

30. Bonds are subject to diverse risks, such as interest rate risk,
inflation risk, real interest rate risk, default risk, call risk, and
liquidity risk.
Default risk or credit risk is reflected in credit rating of debt
instruments.
The term structure of interest rates, popularly called the yield
curve, shows how yield is related to maturity.
Three principal explanations have been offered to explain the term
structure of interest rates : expectations theory, liquidity
preference theory, and preferred habitat theory.
The interest rate is determined by four factors : short-term risk-
free interest rate, maturity premium, default premium, and
special features.
Convertible bonds may be viewed as a debenture – warrant
package.