Investment Analysis and Portfolio Management

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					Investment Analysis and
Portfolio Management
   Lecture 8
   Gareth Myles
Lecture Notes

  Lecture on Thursday 26th
  No class on Monday 30th
  Lecture on Thursday 3rd
Risk-Free Security

  Risk-free: a security with a known return
  Typically taken to be US/UK short-term bonds
        These have little risk of default
        Payments guaranteed but there is some price risk
        Latter minimized if inflation can be forecast
Bonds

  A bond is a promise to make certain payments
  On the maturity date the final payment is made
  The principal is the face value of the bond
  There are two distinct categories of bond
        (a) Pure discount bond: a bond which provides one
         final payment equal to the principal
        (b) Coupon bond: provides a series of payments
         throughout the life of the bond plus a final payment
         equal to the principal
Bonds
    Periodic coupon payments
        Coupons are typically made semi-annually or
         annually
        The final payment is coupon plus principal
    A bond is callable if the final payment may be
     made earlier than maturity.
        The bond will be called if its issuer finds it
         advantageous to do so
        If it is advantageous for the issuer it is usually not
         so for the holder
        Callable bonds must offer a better return than non-
         callable
Bonds
  If a Treasury note or bond is non-callable it is
   effectively a portfolio of pure discount bonds
  For example assume the bond has a maturity
   of two years
        The coupon in year 1 is a pure discount bond
        The coupon plus principal in year 2 is a second
         pure discount bond
    Coupon stripping is the process of selling each
     coupon as an individual asset
        Can have the advantage of allowing investors to
         purchase assets whose timing of payments best
         matches their needs
Ratings and Default

    Bonds have some chance of default.
        This varies across bonds (government bonds
         safest, corporate bonds can be very risky)
    Bonds are rated by likelihood of default
        The two most famous rating agencies are: (1)
         Standard and Poor's (2) Moody's
        The categories used in these ratings systems are:
          (1) Investment Grade Aaa – Baa (2) Speculative
            Grade Ba – below
        The lowest category of bonds are known as junk
         bonds
Ratings and Default

    For corporate bonds, better ratings are
     associated with:
        Lower financial leverage
        Smaller variation in earnings
        Larger asset base
        Profitability
        Lack of subordination
    The possibility of default implies that a risk
     premium is offered
Yield-to-Maturity

  This is the most common measure of the
   return on a bond
  It allows for comparisons between bonds with
   different structures of payments
  Definition
   “The interest rate (with interest compounded at
   a specified interval) that if paid on the amount
   invested would allow the investor to receive all
   the payments of the security”
Examples

  Bond A
  Matures in 1 year, at that time pays £1000
  Present price £934.58
  Yield-to-maturity satisfies
          1  rA 934 .58  1000  rA  7%
    Or
                             1000
                   934 .58 
                             1  rA
Examples

  Bond B
  Matures in 2 years, at that time pays £1000
  Present price £857.34
  Yield-to-maturity satisfies

          1  rB 1  rB 857 .34   1000  rB  8%
    Or
                                  1000
                      857 .34 
                                1  rB 2
Examples
   Bond C
   Coupon of £50 each year, matures in 2 years, at
    that time pays £1050
   Present price £946.93
   This is equivalent to investing £946.93, remove
    £50 after 1 year
   Yield-to-maturity satisfies
      1  rC 1  rC 946 .53  50   1050  rC  7.975 %
   Or                       50     1050
                 946 .93        
                           1  rC 1  rC 2
Spot Rates

    The spot rate is the interest rate associated
     with a spot loan
        An immediate loan with capital and interest repaid
         at a specified date.
        Generally a spot contract is a contract to buy now
    Bonds A and B in the previous examples
     satisfy this description so for these bonds

                 spot rate = yield-to-maturity
Spot Rates

    In general for a pure discount bond the spot
     rate St satisfies
                                  Mt
                          Pt 
                               1  St t


    Where
        Pt = market price of a security that matures in t
         years
        Mt = maturity value
Spot Rates

    For a coupon bond like C the problem is how
     to adjust for coupon
    This is done by observing
                    C        C            M2
             P2                    
                  1  S1 1  S 2 2
                                       1  S 2 2

    P2 = market price
    C = coupon payment
    M2 = maturity value
Spot Rates

    The spot rates have to be found sequentially
        S1 from a bond maturing in one year
        S2 from a bond maturing in two years
        S3 from a bond maturing in three years
  This process is called bootstrapping
  It can be continued for bonds of all life times
Spot Rates

    Example
        Three bonds have face values of $1000
        A pure discount bond with price $909.09
        A coupon bond with coupon payment $40, a
         maturity of 2 years and a price of $880.45
        A coupon bond with coupon of $60, maturity of 3
         years and price of $857.73
  The spot rate S1 is given by
                 909.09 = 1000/(1+ S1)
  So S1 = 0.1 (10%)
Spot Rates

  Using the fact that S1 = 0.1, S2 is determined by
          880.45 = 40/1.1 + 1040/(1+ S2)2
  So
                   S2 = 0.11 (11%)
  Finally, using S1 and S2, S3 solves
   857.73 = 60/1.1 + 60/(1.11)2 + 1060/(1+ S3)3
  This gives
                   S3 = 0.12 (12%)
Discount Factors

  Discount factors are used to discount
   payments to find the present value of future
   payments
  Let d t be the present value of £1 in t years
  Then

                             1
                    dt 
                         1  St t
Discount Factors

  These discount factors can be used to find the
   present value of any security
  Given a payment Ct in t the price is

                         n
                   P   d t Ct
                        t 1
Discount Factors

  Example
  Assume d 1 = 0.9346 and d 2 = 0.8573
  Consider a security that pays £70 in 1 years
   time and £1070 in 2 years time
  The price is


     P  0.9346  70  0.85731070  £982.73
Forward Rates

  The forward rate is the link between spot rates
   for different years
  Consider £1 to be paid in 2 years
  In 1 year's time, this is worth
                             1
                          1  f1, 2
  f1,2   is the forward rate between years 1 and 2
Forward Rates

    The present value of the £1 in two years is
                        1
                     1  f1, 2       1
                               
    Or              1  S1      1  S2 2

                     1  f1,2   
                                  1  S2 2
                                    1  S1
    The forward rate can be interpreted as the
     interest rate that is charged on a loan to be
     made in 1 years time if the contract is written
     today
Forward Rates

    In general the forward rate between years t - 1
     and t is defined by


                                   1  S t  t
                1  f t 1,t   
                                 1  S t 1 t 1
Forward Rates and Discount
Factors
    The link between these is given by the relation


                                   1
                dt 
                       1  St 1  1  ft ,t 1 
                                  t 1
Yield Curve
  The yield curve shows Yield-to-
   the yield-to-maturity for Maturity
   Treasury securities of
   various maturities at a
   particular date
  In practice securities do
   not lie exactly on this
   line
        Tax treatment
                                        Time to
        Callability                    Maturity
Term Structure
    A similar graph can be constructed using spot
     rates on the vertical axis
        This is called the term structure of interest rates
  Spot rates are more fundamental than yield-to-
   maturity
  The following question are raised by the term
   structure
        i. Why do rates vary with time?
        ii. Should the term structure slope up or down?
Term Structure

  Although the term structure can slope either
   way periods in which it slope upwards are
   more common than periods in which it slopes
   down
  There are theories that try to explain this
        Liquidity preference
        Preferred habitat

				
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posted:8/6/2011
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