Bonds

1
Bonds

• Chapter 9 and 10

2
Why Buy Bonds?

• Attractive to investors seeking steady income and
  aggressive investors seeking capital gains
• Promised yield to maturity is known at the time
  of purchase
• Can eliminate risk that a rise in rates decreases
  bond price by holding to maturity
• Diversification

3
WHY ARE BONDS VIABLE INVESTMENT ALTERNATIVES?

• YIELD ON T-BONDS AND SP 500 DIVIDEND YIELD

4
The Case Against Buying Bonds

• Dont hold bonds unless investing strictly for
  income
• Capital appreciation negative
• Alternative a combination of cash investments
  and stocks
• Investors should consider whether they could
  build better portfolios that do not include bonds

5
Are bonds important?

• Bond analysis is relevant for
• Pension funds that have major investments in
  fixed income securities
• In order to understand basics of discounting
• At individual level closely related to mortgages
  etc.

6
Market Value of a Bond

• Present Value of the Future Expected Cash Flows
  discounted by the
• Required Rate of Return

7
Required Rate of Return

• Required Rate of Return on a Particular Bond is a
  Function of
• Real Risk Free Rate
• Inflation Risk
• Credit Risk
• Interest Rate Risk
• Call Risk
• Liquidity Risk
• Foreign Exchange Risk

8
Bond Basics

• Indenture
• Bond contract specifying the terms of the bond.
• Terms that must be specified
• Bond Date
• Stated Rate
• Interest Date(s)
• Maturity Date
• Maturity Value
• Selected Optional Terms
• Callable
• Convertible

9
How are the cash flows being sold specified?

• The bond terms specify the cash flows.
• Two types of cash flows
• Annuity
• Single Sum
• Annuity being sold is the periodic interest
  payments.
• SR X MV X 1/ interest pmts. per year
• Single sum is the maturity value

10
What is the value of the bonds sold?

• The value of the bonds is measured at the present
  value of the two types of cash flows being sold.
• The cash flows are discounted (present value
  determined) using the market rate of interest.

11
Bond ExampleMarket Rate Stated Rate

• Terms
• Stated Rate 10
• Bond date June 1, 1997
• Maturity value 100,000
• Interest dates May 31 and Nov. 30
• Maturity Date May 31, 1999
• Information determined outside contract
• Market rate of interest 10
• Issue date Bond date

12
Bond Value CalculationStep One

• Determine the cash flows associated with the bond
  issue

13
Bond Value CalculationStep One

• Determine the cash flows associated with the bond
  issue

14
Bond Valuation Step Two

• Determine the Present Value of the cash flows
  determined in step one.
• Calculate the Market Rate per interest payment
  period
• Annual Market rate / interest Pmts. per Yr.

15
Bond Valuation Step Two

• Determine the Present Value of the cash flows
  determined in step one.
• Calculate the Market Rate per interest payment
  period
• Annual Market rate / interest Pmts. per Yr.
• 10 / 2 5 semi-annual rate
• Calculate the PV of each cash flow.

16
Bond Valuation Step Two

• Determine the Present Value of the cash flows
  determined in step one.
• Calculate the Market Rate per interest payment
  period
• Annual Market rate / interest Pmts. per Yr.
• 10 / 2 5 semi-annual rate
• Calculate the PV of each cash flow.

17
(No Transcript)
18
Various Yield Measures You Need Know and Price
Volatility

• YTMYield to maturity
• YTCYield to call
• RCYRealized compound yield.
• Price Changes

19
Yield to Maturity

• Solve for YTM

For A Zero Coupon Bond
Investors Earn Yield to Maturity Only if Hold
to maturity Reinvest at the market rate
purchased to yield.
20
(No Transcript)
21
Yield to Call

• Yield to a specified call date and call price
• Substitute number of periods until first call
  date for and call price for face value

22
(No Transcript)
23
(No Transcript)
24
Is the YTM the same as The Compound Annual Return
on Investment?

• Only if the periodic cash flows from the
  investment are reinvested at the rate the bonds
  were originally purchased to return.
• In other words, if the RIR (reinvestment rate)
  YTM (yield to maturity) then,
• RCY (Realized Compound Yield) YTM
• Note, the RCY is the same as the Geometric return
  we previously calculated.

25
Realized Compound Yield

• Rate of return actually earned on a bond given
  the reinvestment of the coupons at varying rates
• Can only be calculated after investment period is
  over
• Horizon return analysis
• Bond returns based on assumptions about
  reinvestment rates

26
RIR YTM
RIR YTM RCY YTM
27
RIR gt YTM
RIR gt YTM RCY gt YTM
28
RIR lt YTM
RIR lt YTM RCY lt YTM
29
Bond Price Changes

• What happens to FMV when interest rates change?

30
Bond Price Changes

• Holding maturity constant, a rate decrease will
  raise prices a greater percent than a
  corresponding increase in rates will lower prices

Price
Market yield
31
Measuring Bond Price Volatility Duration

• Important considerations
• Different effects of yield changes on the prices
  and rates of return for different bonds
• Maturity inadequate measure of a bonds economic
  lifetime
• A measure is needed that accounts for both size
  and timing of cash flows

32
Sensitivity to Rate Changes

• Maturity differences.

33
Whats the only difference between the two bond?
Bond 2 is more volatile.
Bond 2 maturity gt Bond 1 maturity
34
Maturity and Price Volatility Given a Rate Change
2.68
4.83
35
Sensitivity to Rate Changes

• Coupon Rate Differences.

36
Whats the only difference between the two bond?
Bond 1 is more volatile.
Bond 2 Coupon gt Bond 1 Coupon
37
Summary of Volatility to Rate Changes

• Greater Maturity, Greater Volatility to rate
  changes.
• Lower Coupon, Greater Volatility to rate Changes.

38
Duration

• A measure of a bonds lifetime, stated in years,
  that accounts for the entire pattern (both size
  and timing) of the cash flows over the life of
  the bond
• The weighted average maturity of a bonds cash
  flows
• Weights determined by present value of cash flows

39
Calculating Duration

• Need to time-weight present value of cash flows
  from bond
• Duration depends on three factors
• Maturity of the bond
• Coupon payments
• Yield to maturity

40
(No Transcript)
41
Duration Used to Estimate Volatility

• Higher the duration, the greater the volatility
  of the bond to rate changes
• Need to calculate a Modified duration to estimate
  the volatility.

42
Estimating Price Changes Using Duration

• Modified duration DD/(1r/2)
• Dcan be used to calculate the bonds percentage
  price change for a given change in interest rates

43
(No Transcript)
44
Duration Relationships

• Duration increases with time to maturity but at a
  decreasing rate
• For coupon paying bonds, duration is always less
  than maturity
• For zero coupon-bonds, duration equals time to
  maturity
• Duration increases with lower coupons
• Duration increases with lower yield to maturity

45
Why is Duration Important?

• Allows comparison of effective lives of bonds
  that differ in maturity, coupon
• Used in bond management strategies particularly
  immunization
• Measures bond price sensitivity to interest rate
  movements, which is very important in any bond
  analysis

46
Convexity

• Refers to the degree to which duration changes as
  the yield to maturity changes
• Price-yield relationship is convex
• Duration equation assumes a linear relationship
  between price and yield
• Convexity largest for low coupon, long-maturity
  bonds, and low yield to maturity

47
Duration Conclusions

• To obtain maximum price volatility, investors
  should choose bonds with the longest duration
• Duration is additive
• Portfolio duration is just a weighted average
• Duration measures volatility which isnt the only
  aspect of risk in bonds

48
Risk Structure of Rates

• Yield spreads
• Relationship between yields and the particular
  features on various bonds

49
Bond Yield Spread

• Attributes that affect a bonds value
• Time to maturity
• Term structure
• Coupon rate
• Call provisions
• Tax status
• Marketability
• Default probability

50
Call provisions

• A provision in some bond indentures that permits
  an issuer to retire some or all of the bonds in a
  particular issue prior to maturity date stated

51
Call provisions 2

• Issuer may find it advantageous to call existing
  bond
• if market interest rate is lower, then replace
  existing bonds with lower rate bonds
• Callable bonds have lower price

52
Tax structure

• Taxation affects bond prices and yields
• low-coupon bonds selling at a discount provide
  return in
• coupon payments
• gains from price appreciation
• taxes on appreciation may be deferred until bond
  sale or maturity (US)
• discount bonds have a tax advantage

53
Marketability

• Refers to the ability of the investor to resell
• Bid-ask spread is one indicator of marketability
• the higher the spread, the less marketable
• Bonds that are actively traded should have a
  lower YTM.

54
Default probabilities

• Some bond issuers may default (Mexican debt
  crisis)
• Probability of default important in pricing
• Bond ratings provided by professional services
• Moodys Investors Services, Inc.
• Standard Poors Corporate ratings

55
Ratings

• Ratings go from AAA to D
• Categories
• investment grade usually the bonds in the top
  four ratings (B or higher)
• BB or lower are called speculative/junk bonds
• Lower ratings promise higher yields

56
Ratings 2

• Better ratings are generally associated with
• larger financial leverage
• larger firm size
• larger and steadier profits
• large cash flows
• lack of subordination to other debt series

57
(No Transcript)
58
The Term Structure of Interest Rates

• Term structure of interest rates
• Relationship between time to maturity and yields
• Yield curves
• Graphical depiction of the relationship between
  yields and time for bonds that are identical
  except for maturity
• Default risk held constant

59

• Yield Curve

60
(No Transcript)
61
Term Structure of Interest Rates

• Upward-sloping yield curve
• typical, interest rates rise with maturity
• Downward-sloping (or inverted) yield curves
• Unusual, predictor of recession?
• Term structure theories
• Explanations of the shape of the yield curve and
  why it changes shape over time

62
Pure Expectations Theory

• Long-term rates are an average of current
  short-term rates and those expected to prevail
  over the long-term period
• Average is geometric rather than arithmetic
• If expectations otherwise, the shape of the yield
  curve will change
• Forward rates are rates that are expected to
  prevail in the future

63
Liquidity Preference Theory

• Rates reflect current and expected short rates,
  plus liquidity risk premiums
• Liquidity premium to induce long term lending
• Implies long-term bonds should offer higher
  yields
• Interest rate expectations are uncertain

64
Preferred Habitat Theory

• Investors have preferred maturities
• Borrowers and lenders can be induced to shift
  maturities with appropriate risk premium
  compensation
• Shape of yield curve reflects relative supplies
  of securities in each sector
• Most market observers are not firm believers in
  any one theory

65
Passive Bond Strategies

• Investors do not actively seek out trading
  possibilities in an attempt to outperform the
  market
• Bond prices fairly determined
• Risk is the portfolio variable to control
• Investors do assess default and call risk
• Diversify bond holdings to match preferences

66
Passive Bond Strategies

• Buy and hold
• Choose most promising bonds that meet the
  investors requirements
• No attempt to trade in search of higher returns
• Indexing
• Attempt to match performance of a well known bond
  index
• Indexed bond mutual funds

67
Immunization

• Used to protect a bond portfolio against interest
  rate risk
• Price risk and reinvestment risk cancel
• Price risk results from relationship between bond
  prices and rates
• Reinvestment risk results from uncertainty about
  the reinvestment rate for future coupon income

68
Immunization

• Risk components move in opposite directions
• Favorable results on one side can be used to
  offset unfavorable results on the other
• Portfolio immunized if the duration of the
  portfolio is equal to investment horizon
• Like owning zero-coupon bond

69
Active Bond Strategies

• Requires a forecast of changes in interest rates
• Lengthen (shorten) maturity of bond portfolio
  when interest rates are expected to decline
  (rise)
• Horizon analysis
• Projection of bond performance over investment
  horizon given reinvestment rates and future yield
  assumptions

70
Active Bond Strategies

• Identify mispricing among bonds then swap
• Substitution swap, yield pickup swap, rate
  anticipation swap, sector swap
• Interest rate swaps
• Exchange a series of cash flows
• Convert from fixed- to floating-rate
• Primarily used to hedge interest rate risk

71
Building a Fixed-Income Portfolio

• If conservative investor
• View bonds as fixed-income securities that will
  pay them a steady stream of income with little
  risk
• Buy and hold Treasury securities
• Conservative investor should consider
• Maturity, reinvestment risk, rate expectations,
  differences in coupons, indirect investing

72
Building a Fixed Income Portfolio

• If aggressive investor
• View bonds as source of capital gains arising
  from changes in interest rates
• Treasury bonds can be bought on margin to further
  magnify gains (or losses)
• Seek the highest total return
• International bonds
• Direct or indirect investment
  

73
Immunization

• Example

74
Bond A
75
Bond B
76
Bond A and B if Reinvestment Rate YTM
77
Bond B if Reinvestment Rate lt YTM
78
Bond A if Reinvestment Rate lt YTM