Investment Course - 2005

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Investment Course - 2005

• Day Three
• Fixed-Income Analysis and Portfolio Strategies

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The Role of Fixed-Income Securities in the
Financial Markets and Portfolio Management
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U.S. Chilean Yield Curves Feb 2004 Feb 2005
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U.S. Yield Curve and Credit Spreads February 2005
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Historical Data on U.S. Credit Spreads
Rating-Class Average Yields
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Historical Data on U.S. Credit Spreads Spreads
over Treasury
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Latin American Long-Term Credit Ratings February
2005
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Par vs. Spot Yield Curves
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Par vs. Spot Yield Curves (Cont.)

• A par value yield curve summarizes the yields for
  coupon-bearing instruments where the coupon rate
  is equal to the yield-to-maturity. Assuming that
  the above example is based a collection of
  Eurobonds (i.e., bonds that pay an annual
  coupon), the 10 yield for the three-year
  instrument can be interpreted as the average
  annual return that the investor can expect if he
  or she
• (i) Holds the bond until maturity,
• (ii) Reinvests all intermediate cash flows
  (i.e., the first two coupons) at the same 10
  rate for the remaining time until maturity.
• A spot, or zero coupon, yield curve summarizes
  the yields for non-coupon-bearing instruments
  (i.e., pure discount bonds). These yields can
  therefore be interpreted as more of a "pure"
  return since there is no concern about having to
  reinvest intermediate coupon cash flows. For
  example, if the above yield curve corresponded to
  zero coupon securities, the 10, three-year yield
  would represent the average annual price
  appreciation in the bond if it were held to
  maturity.

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U.S. Par and Spot Yield Curves February 2005
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Par vs. Spot Yield Curves (cont.)
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Implied Spot Yield Curves
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Implied Spot Yield Curves (cont.)
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Implied Spot Yield Curves (cont.)
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Implied Spot Yield Curves (cont.)
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Implied Forward Rates
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Implied Forward Rates (cont.)
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Implied Forward Rates (cont.)
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Implied Forward Rates (cont.)
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Uses for Implied Forward Rates

• Predictions of Future Spot Rates This assumes
  that investors set yield curves with unbiased
  expectations, which is seldom true. Generally,
  implied forward rates are upward-biased
  predictions of future spot rates because of
  liquidity premiums attached to yields of
  longer-term maturity bonds relative to
  shorter-term instruments
• Maturity Choice Decisions Helps fixed-income
  investors decide on appropriate maturity
  structure for a bond portfolio by quantifying the
  reinvestment rate embedded in longer-term
  securities compared to shorter-term ones
• Pricing Interest Rate Derivatives Sets the
  arbitrage boundaries for the rates attached to
  actual forward agreements (e.g., bond futures,
  interest rate swaps)

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U.S. Implied Forward Rates February 2005
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Basics of Bond Valuation

• Bonds are simply loans from bondholder to issuer
  (e.g., firm or government). Just like loans,
  bonds require interest payments and repayment of
  principal (also called face value or par) at a
  pre-specified future date. Interest payments are
  called coupon payments and bond principal
  repayments are usually non-amortizing (i.e., paid
  all at once at maturity)
• The current market value of a fixed-income bond
  is the present value of its future coupon and
  principal cash flows. In theory, the interest
  rates used to discount those future cash flows
  are the zero-coupon (or pure discount) rates
  corresponding to the dates of each cash flow.

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Basics of Bond Valuation (cont.)

• Consider a five-year, 9 (annual coupon payment)
  Eurobond. The market value of the bond, 103.99
  ( of par value), can be obtained by calculating
  the present value of each scheduled cash flow
  using a sequence of zero-coupon rates
  commensurate with the riskiness of the bond.

Period Cash Flow Zero-Coupon Rate Present Value
1 9 6.00 8.49
2 9 7.00 7.86
3 9 7.50 7.24
4 9 7.80 6.66
5 109 8.13 73.74
Value 103.99
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Basics of Bond Valuation (cont.)

• The yield to maturity (y) of the bond is the
  constant interest rate per period that solves the
  following equation
• The yield-to-maturity is the internal rate of
  return of all cash flows. It is the rate such
  that the present values of the cash flows, each
  discounted by that same rate, exactly equal the
  market value of the bond. The yield to maturity
  of this bond turns out to be 8.00.

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Basics of Bond Valuation (cont.)
Period Cash Flow Yield-to- Maturity Present Value
1 9 8.00 8.33
2 9 8.00 7.72
3 9 8.00 7.14
4 9 8.00 6.62
5 109 8.00 74.18
Value 103.99

• The yield to maturity is a statistic about the
  rate of return on the bond that includes both the
  coupon cash flows as well as any inevitable
  capital gain or loss if the bond is held to
  maturity (a gain if the bond is purchased at a
  discount below par value, a loss if the bond is
  purchased at a premium above par value).
• Therefore, it contains more information than the
  current yield, which is simply the coupon rate
  divided by the current price, e.g., 9 ? 103.99
  .0865 . The current yield of 8.65 overstates
  the investors rate of return since it neglects
  the capital loss.

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Basics of Bond Valuation (cont.)

• Notice that the yield to maturity can be
  interpreted as a "weighted average" of the
  sequence of zero-coupon rates, with most of the
  weight placed on the last cash flow since that is
  when the principal is redeemed, in that both
  deliver the same present value
• Clearly, the yield to maturity must lie within
  the range of the zero-coupon rates.

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Current Coupon, Premium, and Discount Bonds

• A Current Coupon (or Par-Value) Bond is one for
  which the current market price equals the face
  value. In that case, the coupon rate (C/F) will
  equal the current yield (C/P), which will equal
  the yield-to-maturity (y).
• P F ltgt C/F C/P y
• The bond is priced at par value since its coupon
  rate is "fair" in that it equals the current
  market interest rate as represented by the
  yield-to-maturity.
• A Premium Bond has a current market price that
  exceeds the face value. In this case, the coupon
  rate will be higher than the current yield, which
  in turn will be higher than the
  yield-to-maturity.
• P gt F ltgt C/F gt C/P gt y
• The bond is priced at a premium above par value
  since its coupon rate is "high" given current
  market rates. A par-value, current coupon bond
  would have a lower coupon rate, so the premium
  represents the value of the "excessive" coupon
  cash flows. In fact, the amount of the premium
  is the present value of the annuity represented
  by the difference between the coupon rate and the
  bond's yield, discounted at that yield.
• A Discount Bond has a current market price that
  is less than the face value. The coupon rate
  will be less than the current yield, which will
  be less than the yield-to-maturity.
• P lt F ltgt C/F lt C/P lt y
• The bond is priced at a discount below par value
  since its coupon rate is "low" given current
  market rates. The amount of the discount is the
  present value of the annuity represented by the
  difference between the yield and the coupon rate.
  For example, a zero-coupon bond will usually be
  at a deep discount to par value.

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Current Coupon, Premium, and Discount Bonds
(cont.)

• Example Calculate the yield-to-maturity
  statistic on a seven-year, 6-3/4 Treasury note
  priced at 98.125. Assume that a semi-annual
  coupon payment has just been made so that exactly
  14 periods remain until the principal is refunded
  at maturity.
• Algebraically, the yield is the solution y to
  the following equation
• Solving for the periodic yield (i.e., y/2) on a
  financial calculator (such as the HP 12C) obtains
  3.5472 100 FV, 14 n, 3.375 PMT, -98.125 PV, i .
  3.5472.
• The annualized yield-to-maturity would then be
  reported as y 7.0944 (i.e., 3.5472 x 2).

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Interpreting Bond Information Chile Govt 5.50
of January 2013
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Interpreting Bond Information ENDESA 8.35 of
August 2013
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ENDESA 8.350 Bond of August 13 (cont.)
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Sources of Bond Risk

• Primary
• Default Will the borrower honor its promise to
  repay?
• Interest Rate How will changing market
  conditions affect the value of the bond?
• Price risk component
• Reinvestment risk component
• Secondary
• Call Will the borrower refinance the loan under
  conditions that are disadvantageous to investor?
• Liquidity How easily can bond be bought or sold?
• Tax Will changes in the tax code affect bond
  values?

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Bond Yields, Pricing, and Volatility

• Theorem 1 Bond prices are inversely related to
  bond yields.
• Implication When market rates fall, bond
  prices rise, and vice versa.
• Theorem 2 Generally, for a given coupon rate,
  the longer is the term to maturity, the greater
  is the percentage price change for a given shift
  in yields. (The maturity effect)
• Implication Long-term bonds are riskier than
  short-term bonds for a given shift in yields, but
  also have more potential for gain if rates fall.
• Theorem 3 For a given maturity, the lower is
  the coupon rate, the greater is the percentage
  price change for a given shift in yields. (The
  coupon effect)
• Implication Low-coupon bonds are riskier than
  high-coupon bonds given the same maturity, but
  also have more potential for gain if rates fall.
• Theorem 4 For a given coupon rate and maturity,
  the price increase from a given reduction in
  yield will always exceed the price decrease from
  an equivalent increase in yield. (The convexity
  effect)

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Bond Yields, Pricing, and Volatility (cont.)

• Implication There are potential gains from
  structuring a portfolio to be more convex (for a
  given yield and market value) since it will
  outperform a less convex portfolio in both a
  falling yield market as well as a rising yield

Price
Convex Price-Yield Curve
Yield
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Bond Yields, Pricing, and Volatility Example

• Consider the following bonds
• Initial Prices

Bond Coupon Maturity Initial Yield
A 8 5 yrs 10
B 5 20 8
C 8 20 8
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Bond Yields, Pricing, and Volatility Example
(cont.)

• Prices after yields increase by 50 bp
• Percentage price changes
• Bond A (906.43 - 924.18) / (924.18) -1.92
  (least)
• Bond B (668.78 - 705.46) / (705.46) -5.20
  (most)

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Bond Yields, Pricing, and Volatility Example
(cont.)

• Question Where would Bond D, which has a coupon
  rate of 6 and a maturity of 19 years, fit into
  this price sensitivity spectrum? (Assume its
  initial yield is also 8.)
• Initial
• After
• So, percentage change
• Bond D (768.31 - 807.93) / (807.93) -4.90

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Motivating the Concept of Bond Duration
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Motivating the Concept of Bond Duration (cont.)
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Calculating the Duration Statistic

• The duration of a bond is a weighted average of
  the payment dates, using the present value of the
  relative cash payments as the weights
• This statistic is the Macaulay duration, named
  after Frederick Macaulay who first developed it,
  and can be interpreted as the point in the life
  of the bond when the average cash flow is paid.

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Calculating the Duration Statistic Example

• Consider a five-year, 12 annual payment bond
  having a face value of 1,000. Suppose that the
  bond is priced at a premium to yield 10 (p.a.).
  The price of the bond is 1,075.82 and the
  Macaulay duration is 4.074
• or

Year Cash Flow PV at 10 PV/Price Yr x (PV/Pr)
1 120 109.09 0.1014 0.1014
2 120 99.17 0.0922 0.1844
3 120 90.16 0.0838 0.2514
4 120 81.96 0.0762 0.3047
5 1120 695.43 0.6464 3.2321
1075.82 1.0000 4.074 yrs
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Calculating the Duration Statistic Closed-Form
Equation
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Duration as a Measure of Price Volatility

• Basic Price-Yield Elasticity Relationship
• Convert to Volatility Prediction Equation
• Prediction Equation in Modified Form ( price
  change)

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Duration as a Measure of Price Volatility (cont.)

• Convert to dollar (or cash) sensitivity
• DMV -(Mod D)( Dy)(MV)
• Sensitivity to a one bp yield change (i.e., Dy
  0.0001)
• DMV -(Mod D)(0.0001)(MV) Basis Point
  Value BPV

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Duration as a Measure of Price Volatility (cont.)
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Duration and Price Volatility Example

• Consider again the five-year, 12 coupon bond
  with a yield to maturity of 10
• Macaulay D 4.074
• Modified D 3.704 ( 4.074 / 1.1)
• This means that an increase in yields of 100 bp
  will change the bonds price by approximately
  3.7 in opposite direction
• Basis Point Value 0.0398 (3.704)(.0001)(107.
  582)
• This means that a one bp change in yields will
  cause the bonds price to move by about 4 cents
  per 100 of par value (which would correspond to
  a 40 cent movement for a bond with a par value of
  1000)

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Duration Example ENDESA 8.350 of 2013
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Duration of a Bond Portfolio
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LVACL Corporate Bond Index Description
Performance
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Example of Portfolio Duration LVACL Corporate
Bond Index
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Example of Portfolio Duration MBA Investment
Fund Endowment Portfolio
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Bond Convexity An Overview
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Using Bond Convexity in Estimating Price
Volatility
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Using Bond Convexity in Estimating Price
Volatility (cont.)
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Convexity Trades An Example(Source R.
Dattareya and F. Fabbozi)

• Consider the following hypothetical U.S. Treasury
  bonds
• Consider two different bond portfolios
• Bullet Portfolio 100 of Bond C
• Barbell Portfolio 50.2 of Bond A, 49.8 of Bond
  B
• Notice the following
• Duration of Barbell (.502)(4.005)(.498)(8.882)
  6.434
• Same as Bullet Portfolio
• Convexity of Barbell (.502)(19.82)(.498)(124.17)
  71.7846
• Greater than Bullet Portfolio

Bond Coupon Maturity (yrs) Invoice Price Yield Dollar Duration Dollar Convexity
A 8.50 5 100 8.50 4.005 19.8164
B 9.50 20 100 9.50 8.882 124.1702
C 9.25 10 100 9.25 6.434 55.4506
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Relative Performance (Bullet Rtn Barbell Rtn)
Over Six-Month Period
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Embedded Bond Options and Negative Convexity
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Embedded Bond Options and Negative Convexity
(cont.)
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Callable Bond Example SBC 6.28 of October
2010-04
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Callable Bond Example SBC 6.28 of October
2010-04
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Callable Bond Example ENTEL 7.00 of January
2010-04
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Overview of Bond Portfolio Strategies
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Overview of Bond Portfolio Strategies (cont.)
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Overview of Bond Portfolio Strategies (cont.)
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Overview of Bond Portfolio Strategies (cont.)
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Overview of Bond Portfolio Strategies (cont.)
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Examples of Typical Yield Curve Shifts
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Active Bond Trades Examples
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Bond Swaps

• Another type of active trade is a bond swap.
  This involves liquidating a current position and
  simultaneously buying a different issue in its
  place with similar attributes, but a chance of
  improved returns.
• Notable examples of bond swaps include
• Pure Yield Pickup Swaps Swapping out of a
  low-coupon bond into a comparable higher-coupon
  bond to realize an automatic and instantaneous
  increase in current yield and yield to maturity.
• Substitution Swaps Swapping comparable bonds
  that are trading at different yields based on
  the premise that the credit market is temporarily
  out of balance.
• Tax Swaps Trades motivated by prevailing tax
  codes and accumulated capital gains in a
  portfolio (e.g., selling a bond with a capital
  loss to offset one with a capital gain).

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Bond Swap Example

• Evaluate the following pure yield pickup swap
  You are currently holding a 20-year, Aa-rated,
  9.0 percent coupon bond priced to yield 11.0
  percent.
• As a swap candidate, you are considering a
  20-year, Aa-rated, 11.0 percent coupon bond
  priced to yield 11.5 percent
• You can assume that all cash flows are reinvested
  at 11.5 percent.

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Bond Swap Example Solution
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Overview of Bond Portfolio Strategies (cont.)
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(No Transcript)
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The Mechanics of Bond Immunization
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The Mechanics of Bond Immunization (cont.)
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The Mechanics of Bond Immunization (cont.)
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Overview of Bond Portfolio Strategies (cont.)
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Overview of Bond Portfolio Strategies (cont.)
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Overview of Bond Portfolio Strategies (cont.)
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Overview of Bond Portfolio Strategies (cont.)
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An Overview of Equity Alternatives

• As we have seen, debt and equity securities are
  the fundamental cornerstones of the capital
  markets. They represent the most prevalent
  securities that companies use to raise external
  funds and that investors purchase to hold in
  their portfolios.
• Often, however, there will be cases when either
  investors or issuers will want to do a
  transaction involving securities with an
  equity-like payoff structure, but they may choose
  not (or otherwise be unable) to use plain
  vanilla equity directly. Some reasons why
  conventional stock shares may not be appropriate
  even when an equity payoff is desired include
• A corporation seeking to raise additional capital
  may find the market for its common stock to be
  unreceptive, perhaps due to other recent
  issuances.
• An institutional investor may be restricted from
  holding equity directly but can purchase a debt
  instrument with a equity-like principal payoff at
  maturity.
• A company may be able to lower the present cost
  of a debt financing by structuring a bond
  contract that allows investors the right to
  convert the debt into common equity at a future
  date.
• We will look at two alternative forms of equity
  along these lines (i) convertible securities,
  and (ii) structured notes

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Notion of Convertible Bonds

• A convertible bond can be viewed as a
  pre-packaged portfolio containing two distinct
  securities (i) a regular bond and (i) an option
  to exchange the bond for a pre-specified number
  of shares of the issuing firms common stock.
  Thus, a convertible bond represents a hybrid
  investment involving elements of both the debt
  and equity markets.
• The option involved can be viewed as either a put
  (i.e., the investor has the right to sell the
  bond back to the issuer and receive a fixed
  number of shares) or a call (i.e., the investor
  can buy a fixed number of shares from the issuing
  company, paid for with the bond).
• From the investors standpoint, there are both
  advantages and disadvantages to this packaging.
  Specifically, while buyer receives equity-like
  returns with a guaranteed terminal payoff equal
  to the bonds face value, he or she must also pay
  the option premium, which is embedded in the
  price of the security.
• Conversely, the issuer of a convertible bond
  increases the companys leverage while providing
  a potential source of equity financing in the
  future. This arrangement may be particularly
  useful as a means for low-rated issuers to borrow
  money more cheaply in the present than with a
  straight debt issue while creating a potential
  demand for their shares if future conditions are
  favorable.

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Convertible Bond Example Cypress Semiconductor

• As an example of how one such issue is structured
  and priced, consider the 4.00 percent coupon
  convertible subordinated notes (sub cv nt)
  maturing in February of 2005 issued by a
  NYSE-traded company, Cypress Semiconductor
  Corporation (CY). Cypress Semiconductor designs,
  develops, manufactures and markets a broad line
  of high-performance digital and mixed-signal
  integrated circuits for a range of markets,
  including data communications, telecommunications,
  computers and instrumentation systems.
• The Bloomberg screen on the next slide shows the
  issues CUSIP identifier, contract terms and
  default rating, (i.e., B1), and indicates that
  this bond pays interest semi-annually on February
  1 and August 1. The bond issue has 283 million
  outstanding and is callable at 101 percent of
  par.
• At the time of this report (i.e. February 2001),
  the listed price of the convertible was 92
  percent of par and the price of Cypress
  Semiconductor common stock was 27.375 per share.

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CY Convertible Bond Example (cont.)
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CY Convertible Bond Example (cont.)

• As spelled out at the top of this display, each
  1,000 face value of this bond can be converted
  into 21.6216 shares of Cypress Semiconductor
  common stock. This statistic is called the
  instruments conversion ratio. At the current
  share price of 27.375, an investor exercising
  her conversion option would have received only
  591.89 ( 27.375 ? 21.6216) worth of stock, an
  amount considerably below the current market
  value of the bond.
• In fact, the conversion parity price (i.e. the
  common stock price at which immediate conversion
  would make sense) is equal to 42.55, which is
  the bond price of 920 divided by the conversion
  ratio of 21.6216. The prevailing market price of
  27.375 is far below this parity level, meaning
  that the conversion option is currently out of
  the money. Of course, if the conversion parity
  price ever fell below the market price for the
  common stock, an astute investor could buy the
  bond and immediately exchange it into stock with
  a greater market value.

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CY Convertible Bond Example (cont.)

• Most convertible bonds are also callable by the
  issuer. Of course, a firm will never call a bond
  selling for less than its call price (which is
  the case with the Cypress Semiconductor note). In
  fact, firms often wait until the bond is selling
  for significantly more than its call price before
  calling it. If the company calls the bond under
  these conditions, investors will have an
  incentive to convert the bond into the stock that
  is worth more than they would receive from the
  call price this situation is referred to as
  forcing conversion.
• Two other factors also increase the investors
  incentive to convert their bonds. First, some
  instruments have conversion prices that step up
  over time according to a predetermined schedule.
  Since a stepped up conversion price leads to a
  lower number of shares received, it becomes more
  likely that investors will exercise their option
  just before the conversion price increases.
  Second, a firm can help to encourage conversion
  by increasing the dividends on the stock, thereby
  making the income generated by the shares more
  attractive relative to the income from the bond.

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CY Convertible Bond Example (cont.)

• Another important characteristic when evaluating
  convertible bonds is the payback or break-even
  time, which measures how long the higher interest
  income from the convertible bond (compared to the
  dividend income from the common stock) must
  persist to make up for the difference between the
  price of the bond and its conversion value (i.e.,
  the conversion premium). The calculation is as
  follows
• For instance, the annual coupon yield payment on
  the Cypress Semiconductor convertible bond is
  40, while the firms dividend yield is zero.
  Thus, assuming you sold the bond for 920 and used
  the proceeds to purchase 33.607 shares (
  920/27.375) of Cypress Semiconductor stock, the
  payback period would be

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CY Convertible Bond Example (cont.)

• It is also possible to calculate the combined
  value of the investors conversion option and
  issuers call feature that are embedded in the
  note. In the Cypress Semiconductor example, with
  a market price of 920, the convertibles
  yield-to-maturity can be calculated as the
  solution to
• or y 6.29 percent. This computation assumes 8
  semi-annual coupon payments of 20 ( 40 ? 2).
  Since the yield on a Cypress Semiconductor debt
  issue with no embedded options and the same (B1)
  credit rating and maturity was 8.5 percent, the
  present value of a straight fixed-income
  security with the same cash flows would be
• This means that the net value of the combined
  options is 69.94, or 920 minus 850.06. Using
  the Black-Scholes valuation model, it is easily
  confirmed that a four-year call option to buy one
  share of Cypress Semiconductor stock which does
  not pay a dividend at an exercise price of
  42.55 (i.e. the conversion parity value) is
  equal to 6.35. Thus the value of the investors
  conversion option which allows for the
  acquisition of 21.6216 shares must be 137.26
  ( 21.6216 ? 6.35). This means that the value of
  the issuers call feature under these conditions
  must be 67.32 ( 137.26 69.94).

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Illustrating Convertible Bond Valuation
91
Notion of Structured Notes

• Generally speaking, structured notes are debt
  issues that have their principal or coupon
  payments linked to some other underlying
  variable. Examples would include bonds whose
  coupons are tied to the appreciation of an equity
  index such as the SP 500 or a zero-coupon bond
  with a principal amount tied to the appreciation
  of an oil price index.
• There are several common features that
  distinguish structured notes from regular
  fixed-income securities, two of which are
  important for our discussion. First, structured
  notes are designed for (are targeted to) a
  specific investor with a very particular need.
  That is, these are not "generic" instruments, but
  products tailored to address an investor's
  special constraints, which are often themselves
  created by tax, regulatory, or institutional
  policy restrictions.
• Second, after structuring the financing to meet
  the investor's needs, the issuer will typically
  hedge that unique exposure with swaps or
  exchange-traded derivatives. Inasmuch as the
  structured note itself most likely required an
  embedded derivative to create the desired payoff
  structure for the investor, this unwinding of the
  derivative position by the issuer generates an
  additional source profit opportunity for the bond
  underwriter.

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Overview of the Structured Note Market
93
Equity Index-Linked Note Example MITTS

• In July of 1992, Merrill Lynch Co. raised USD
  77,500,000 by issuing 7,750,000 units of an SP
  500 Market Index Target-Term Security, or "MITTS"
  for short, at a price of USD 10 per unit. These
  MITTS units had a maturity date of August 29,
  1997, making them comparable in form to a
  five-year bond even though they traded on the New
  York Stock Exchange. Indeed, Merrill Lynch
  issued them as a series of Senior Debt Securities
  making no coupon payments prior to maturity.
• At maturity, a unit holder received the original
  issue price plus a "supplemental redemption
  amount," the value of which depended on where the
  Standard Poor's 500 index settled relative to a
  predetermined initial level. Given that this
  supplemental amount could not be less than zero,
  the total payout to the investor at maturity can
  be written
• where the initial SP value was specified as
  412.08.

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MITTS Example (cont.)

• From the preceding description, recognize that
  the MITTS structure combines a five-year,
  zero-coupon bond with an SP index call option,
  both of which were issued by Merrill Lynch.
  Thus, the MITTS investor essentially owns a
  "portfolio" that is (i) long in a bond and (ii)
  long in an index call option position.
• This particular security was designed primarily
  for those investors who wanted to participate in
  the equity market but, for regulatory or taxation
  reasons, were not permitted to do so directly.
  For example, the manager of a fixed-income mutual
  fund might be able to enhance her return
  performance by purchasing this "bond" and then
  hoping for an appreciating stock market.
• Notice that the use of the call option in this
  design makes it fairly easy for Merrill Lynch to
  market to its institutional customers in that it
  is a "no lose" proposition the worst-case
  scenario for the investor in that she simply gets
  her money back without interest in five years.
  (Of course, the customer does carry the company's
  credit risk for this period.) Thus, at
  origination the MITTS issue had no downside
  exposure to stock price declines.

95
MITTS Example (cont.)

• The call option embedded in this structure is
  actually a partial position. To see this, we can
  rewrite the option portion of the note's
  redemption value as
• Thus, given that a regular index call option
  would have a terminal payoff of Max0, (Final SP
  X), where X is the strike price, the
  derivative in the MITTS represents 2.79 of this
  amount.

96
MITTS Example (cont.)

• On February 28, 1996, the closing price for the
  MITTS issue was USD 15.625, while the SP 500
  closed at 644.75. Further, the semi-annually
  compounded yield of a zero-coupon (i.e.,
  "stripped") Treasury bond on this date was 5.35.
  
• Assuming a credit spread of 30 basis points to be
  appropriate for Merrill Lynch's credit rating
  (i.e., A and A1 by Standard Poor's and
  Moody's, respectively) and the remaining time to
  maturity (i.e., one-and-a-half years, or three
  half-years), the bond portion of the MITTS issue
  should be worth
• This means that the investor is paying 6.43 (
  15.63 - 9.20) for the embedded index call.

97
MITTS Example (cont.)

• Without reproducing the full calculations, it is
  interesting to note that the theoretical value on
  February 28, 1996 of an SP index call option
  expiring on August 29, 1997 with an exercise
  price of 412.08 is 243.19.
• Thus, since the MITTS option feature represents
  0.0279 of this amount, the call option embedded
  in the MITTS issue is worth 6.78 ( 243.19 x
  0.0279). Thus, on this particular date the MITTS
  issue was priced in the market below its
  theoretical value, presenting investors with a
  potential buying opportunity depending on their
  transaction costs. In fact, the embedded call is
  actually priced below the index options
  intrinsic value of 6.49 ( 644.75 412.08 x
  0.0279), making the issue that much more
  attractive to investors.

98
MITTS Example (cont.)

• This MITTS transaction can be illustrated as
  follows

Max(0, SPX Rtn)
10
August 1992
February 1996
August 1997
Zero-Coupon Bond
9.20
10
SPX Index Call Option
6.43
99
Additional Structured Note Examples
100
Additional Structured Note Examples (cont.)