Fundamentals of the bond Valuation Process

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Fundamentals of the bond Valuation Process

• The Value of a Bond.

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Computing Bond Yields

• Yield Measure Purpose

Nominal Yield
Measures the coupon rate
Current yield
Measures current income rate
Promised yield to maturity
Measures expected rate of return for bond held to
maturity
Promised yield to call
Measures expected rate of return for bond held to
first call date
Measures expected rate of return for a bond
likely to be sold prior to maturity. It
considers specified reinvestment assumptions and
an estimated sales price. It can also measure
the actual rate of return on a bond during some
past period of time.
Realized (horizon) yield
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Rates of Return

• Approximate Promised Yield
• APY C (Par Market Price)/ NMaruity
• .60 ( Market Price) .4 (Par)
•  Yield to Call
• AYC C (Call Price Market Price)/ NCall
• .60 ( Market Price) .4 (Call Price)
• Approximate Realized Yield
• ARY C (Realized Price Market Price)/
  NRealize .60 (
  Market Price) .4 (Realize Price)

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Corporate Bond Quotes

• Cur
  Net
• Bonds Yld Vol Close Chg
• ATT 81/8 22 7.7 52 1053/8 1/4

Issued by ATT
52 of these bonds traded that day
8.125 coupon rate matures in 2022
Current yield coupon/market price 7.7
The closing price was 105 3/8 of par which was
up 1/4 from the prior day
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Term Structure of Interest Rates

• The relationship between maturity and interest
  rates. It is also known as the Yield Curve.
• Expectations Hypothesis suggests that the
  long-term rate is an average of the expectations
  of the future short-term rates over the
  applicable time horizon.
• Reinforced by borrower/lender strategies.

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Figure 12-1 Term Structure of Interest Rates
Normal
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The Movement of Interest Rates (cont.)

• Liquidity Preference Theory states that the shape
  of the yield curve is upward sloping. Investors
  will pay a higher price for short-term securities
  because they are more easily turned into cash
  without the risk of large price changes.
• Investors demand higher returns from longer-term
  securities.

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The Movement of Interest Rates (cont.)

• Market Segmentation Theory focuses on the demand
  side of the market.
• Banks tend to prefer Short Term liquid securities
  to match the nature of their deposits.
• Life insurance companies invest in Long-Term
  bonds to match their Long-Term obligations.

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Investment Strategy Interest-Rate
Considerations

• Bond Pricing Rules
• 1. Bond prices and interest rates are inversely
  related.
• 2. Prices of long-term bonds are more sensitive
  to a change in yields to maturity than
  short-term bonds.
• 3. Bond price sensitivity increases at a
  decreasing rate as maturity increases.

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Investment Strategy Interest-Rate
Considerations (cont.)

• 4. Bond prices are more sensitive to a decline
  in market YTM than to a rise in YTM.
• 5. Prices of low-coupon bonds are more sensitive
  to a change in YTM than high coupon bonds.
• 6. Bond prices are more sensitive when YTM is
  low than when YTM is high.
• 7. Margin trading magnifies profits and losses
  of bond investments by a factor of 1/(margin
  requirement).

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What Determines the Price Volatility for Bonds

• Five observed behaviors
• 1. Bond prices move inversely to bond yields
  (interest rates)
• 2. For a given change in yields, longer maturity
  bonds post larger price changes, thus bond price
  volatility is directly related to maturity
• 3. Price volatility increases at a diminishing
  rate as term to maturity increases
• 4. Price movements resulting from equal absolute
  increases or decreases in yield are not
  symmetrical
• 5. Higher coupon issues show smaller percentage
  price fluctuation for a given change in yield,
  thus bond price volatility is inversely related
  to coupon

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What Determines the Price Volatility for Bonds

• The maturity effect
• The coupon effect
• The yield level effect
• Some trading strategies

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The Duration Measure

• Since price volatility of a bond varies inversely
  with its coupon and directly with its term to
  maturity, it is necessary to determine the best
  combination of these two variables to achieve
  your objective
• A composite measure considering both coupon and
  maturity would be beneficial

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The Duration Measure

• Developed by Frederick R. Macaulay, 1938
• Where
• t time period in which the coupon or
  principal payment occurs
• Ct interest or principal payment that occurs in
  period t
• i yield to maturity on the bond

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Characteristics of Duration

• Duration of a bond with coupons is always less
  than its term to maturity because duration gives
  weight to these interim payments
• A zero-coupon bonds duration equals its maturity
• There is an inverse relation between duration and
  coupon
• There is a positive relation between term to
  maturity and duration, but duration increases at
  a decreasing rate with maturity
• There is an inverse relation between YTM and
  duration
• Sinking funds and call provisions can have a
  dramatic effect on a bonds duration

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Modified Duration and Bond Price Volatility

• An adjusted measure of duration can be used to
  approximate the price volatility of a bond

Where m number of payments a year YTM
nominal YTM
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Duration and Bond Price Volatility

• Bond price movements will vary proportionally
  with modified duration for small changes in
  yields
• An estimate of the percentage change in bond
  prices equals the change in yield time modified
  duration

Where ?P change in price for the bond P
beginning price for the bond Dmod the modified
duration of the bond ?i yield change in basis
points divided by 100
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Trading Strategies Using Duration

• Longest-duration security provides the maximum
  price variation
• If you expect a decline in interest rates,
  increase the average duration of your bond
  portfolio to experience maximum price volatility
• If you expect an increase in interest rates,
  reduce the average duration to minimize your
  price decline
• Note that the duration of your portfolio is the
  market-value-weighted average of the duration of
  the individual bonds in the portfolio

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Matched-Funding Techniques

• Immunization Strategies
• A portfolio manager (after client consultation)
  may decide that the optimal strategy is to
  immunize the portfolio from interest rate changes
• The immunization techniques attempt to derive a
  specified rate of return during a given
  investment horizon regardless of what happens to
  market interest rates

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Immunization Strategies

• Components of Interest Rate Risk
• Price Risk
• Coupon Reinvestment Risk

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Classical Immunization

• Immunization is neither a simple nor a passive
  strategy
• An immunized portfolio requires frequent
  rebalancing because the modified duration of the
  portfolio always should be equal to the remaining
  time horizon (except in the case of the
  zero-coupon bond)

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Classical Immunization

• Duration characteristics
• Duration declines more slowly than term to
  maturity, assuming no change in market interest
  rates
• Duration changes with a change in market interest
  rates
• There is not always a parallel shift of the yield
  curve
• Bonds with a specific duration may not be
  available at an acceptable price