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Fundamentals of the bond Fundamentals of the bond Valuation Process Valuation Process The Value of a Bond. The Value of a Bond.

Fundamentals of the bond Valuation Process

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Fundamentals of the bond Valuation Process. The Value of a Bond. Computing Bond Yields. Yield Measure Purpose. Nominal Yield. Measures the coupon rate. Current yield. Measures current income rate. Promised yield to maturity. - PowerPoint PPT Presentation

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Page 1: Fundamentals of the bond Valuation Process

Fundamentals of the bond Valuation Fundamentals of the bond Valuation ProcessProcess

The Value of a Bond.The Value of a Bond.

Page 2: Fundamentals of the bond Valuation Process

Computing Bond YieldsComputing Bond Yields

Yield Measure PurposeYield Measure PurposeNominal 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

Realized (horizon) yield

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.

Page 3: Fundamentals of the bond Valuation Process

Rates of ReturnRates of Return

Approximate Promised YieldApproximate Promised Yield

APY = APY = C + (Par – Market Price)/ NMaruityC + (Par – Market Price)/ NMaruity

.60 ( Market Price) + .4 (Par).60 ( Market Price) + .4 (Par)

  Yield to Call:Yield to Call:

AYC = AYC = C + (Call Price – Market Price)/ NCallC + (Call Price – Market Price)/ NCall

.60 ( Market Price) + .4 (Call Price).60 ( Market Price) + .4 (Call Price)

Approximate Realized YieldApproximate Realized Yield

ARY = ARY = C + (Realized Price – Market Price)/ NC + (Realized Price – Market Price)/ NRealize Realize .60 ( Market .60 ( Market Price) + .4 (Realize Price)Price) + .4 (Realize Price)

Page 4: Fundamentals of the bond Valuation Process

Corporate Bond QuotesCorporate Bond Quotes

Cur Cur NetNet Bonds Yld Vol Close Bonds Yld Vol Close ChgChg

ATT 8ATT 811//8 8 22 7.7 52 10522 7.7 52 10533//8 8 + + 11//44

Issued by AT&T8.125% coupon rate; matures in 2022

Current yield = coupon/market price = 7.7%

52 of these bonds traded that day

The closing price was 105 3/8% of par which was up 1/4 from the prior day

Page 5: Fundamentals of the bond Valuation Process

Term Structure of Interest RatesTerm Structure of Interest Rates

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

Page 6: Fundamentals of the bond Valuation Process

Maturity

Yield

c

Maturity

Yield

a

Yield

Maturityb

Maturity

Yield

d

Normal

Figure 12-1 Term Structure of Interest Figure 12-1 Term Structure of Interest RatesRates

Page 7: Fundamentals of the bond Valuation Process

The Movement of Interest Rates The Movement of Interest Rates (cont.)(cont.)

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

Investors demand higher returns from longer-Investors demand higher returns from longer-term securities.term securities.

Page 8: Fundamentals of the bond Valuation Process

The Movement of Interest Rates The Movement of Interest Rates (cont.)(cont.)

Market Segmentation Theory focuses on Market Segmentation Theory focuses on the demand side of the market.the demand side of the market.– Banks tend to prefer Short Term liquid Banks tend to prefer Short Term liquid

securities to match the nature of their securities to match the nature of their deposits.deposits.

– Life insurance companies invest in Long-Term Life insurance companies invest in Long-Term bonds to match their Long-Term obligations.bonds to match their Long-Term obligations.

Page 9: Fundamentals of the bond Valuation Process

10 20 30

8% 127.18% 139.59% 145.25%

10 112.46 117.16 118.93

12 100.00 100.00 100.00

14 89.41 86.55 85.96

Source: Reprinted by permission from the Thorndike Encyclopedia of Banking and f inancial tables, 1981. Copyright ©1981, Warren, Gorham and Lamont Inc. 210 South Street, boston MA. All rights reserved.

Bond Value table

Yield to Maturity

Coupon Rate 12 percentNumber of Years

Page 10: Fundamentals of the bond Valuation Process

Investment Strategy: Interest-Investment Strategy: Interest-Rate Considerations Rate Considerations

Bond Pricing RulesBond Pricing Rules

– 1.1. Bond prices and interest rates are Bond prices and interest rates are

inversely related.inversely related.

– 2.2. Prices of long-term bonds are more Prices of long-term bonds are more

sensitive to a change in yields to maturity sensitive to a change in yields to maturity

than short-term bonds.than short-term bonds.

– 3.3. Bond price sensitivity increases at a Bond price sensitivity increases at a

decreasing rate as maturity increases.decreasing rate as maturity increases.

Page 11: Fundamentals of the bond Valuation Process

Investment Strategy: Interest-Rate Investment Strategy: Interest-Rate Considerations (cont.)Considerations (cont.)

– 4. Bond prices are more sensitive to a decline in 4. Bond prices are more sensitive to a decline in market YTM than to a rise in YTM.market YTM than to a rise in YTM.

– 5. Prices of low-coupon bonds are more sensitive to 5. Prices of low-coupon bonds are more sensitive to a change in YTM than high coupon bonds.a change in YTM than high coupon bonds.

– 6. Bond prices are more sensitive when YTM is low 6. Bond prices are more sensitive when YTM is low than when YTM is high.than when YTM is high.

– 7. Margin trading magnifies profits and losses of 7. Margin trading magnifies profits and losses of bond investments by a factor of 1/(margin bond investments by a factor of 1/(margin requirement).requirement).

Page 12: Fundamentals of the bond Valuation Process

What Determines the What Determines the Price Volatility for BondsPrice Volatility for Bonds

Five observed behaviorsFive observed behaviors1. Bond prices move inversely to bond yields (interest rates)1. Bond prices move inversely to bond yields (interest rates)2. For a given change in yields, longer maturity bonds post 2. For a given change in yields, longer maturity bonds post

larger price changes, thus bond price volatility is directly larger price changes, thus bond price volatility is directly related to maturityrelated to maturity

3. Price volatility increases at a diminishing rate as term to 3. Price volatility increases at a diminishing rate as term to maturity increasesmaturity increases

4. Price movements resulting from equal absolute increases or 4. Price movements resulting from equal absolute increases or decreases in yield are not symmetricaldecreases in yield are not symmetrical

5. Higher coupon issues show smaller percentage price 5. Higher coupon issues show smaller percentage price fluctuation for a given change in yield, thus bond price fluctuation for a given change in yield, thus bond price volatility is inversely related to couponvolatility is inversely related to coupon

Page 13: Fundamentals of the bond Valuation Process

What Determines the What Determines the Price Volatility for BondsPrice Volatility for Bonds

The maturity effectThe maturity effect

The coupon effectThe coupon effect

The yield level effectThe yield level effect

Some trading strategiesSome trading strategies

Page 14: Fundamentals of the bond Valuation Process

The Duration MeasureThe Duration Measure

Since price volatility of a bond varies Since price volatility of a bond varies inversely with its coupon and directly with inversely with its coupon and directly with its term to maturity, it is necessary to its term to maturity, it is necessary to determine the best combination of these determine the best combination of these two variables to achieve your objectivetwo variables to achieve your objective

A composite measure considering both A composite measure considering both coupon and maturity would be beneficialcoupon and maturity would be beneficial

Page 15: Fundamentals of the bond Valuation Process

The Duration MeasureThe Duration Measure

Developed by Frederick R. Macaulay, 1938Developed by Frederick R. Macaulay, 1938

Where:Where:

tt = = time period in which the coupon or principal payment occurs time period in which the coupon or principal payment occurs

CCtt = = interest or principal payment that occurs in period interest or principal payment that occurs in period tt

i i = = yield to maturity on the bondyield to maturity on the bond

price

)(

)1(

)1(

)(

1

1

1

n

tt

n

tt

t

n

tt

t CPVt

i

Ci

tC

D

Page 16: Fundamentals of the bond Valuation Process

Characteristics of DurationCharacteristics of DurationDuration of a bond with coupons is always less than its Duration of a bond with coupons is always less than its term to maturity because duration gives weight to these term to maturity because duration gives weight to these interim paymentsinterim payments– A zero-coupon bond’s duration equals its maturityA zero-coupon bond’s duration equals its maturity

There is an inverse relation between duration and There is an inverse relation between duration and couponcouponThere is a positive relation between term to maturity and There is a positive relation between term to maturity and duration, but duration increases at a decreasing rate with duration, but duration increases at a decreasing rate with maturitymaturityThere is an inverse relation between YTM and durationThere is an inverse relation between YTM and durationSinking funds and call provisions can have a dramatic Sinking funds and call provisions can have a dramatic effect on a bond’s durationeffect on a bond’s duration

Page 17: Fundamentals of the bond Valuation Process

Modified Duration and Bond Price Modified Duration and Bond Price VolatilityVolatility

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

m

YTM1

durationMacaulay duration modified

Where:

m = number of payments a year

YTM = nominal YTM

Page 18: Fundamentals of the bond Valuation Process

Duration and Bond Price VolatilityDuration and Bond Price VolatilityBond price movements will vary proportionally with Bond price movements will vary proportionally with modified duration for small changes in yieldsmodified duration for small changes in yields

An estimate of the percentage change in bond prices An estimate of the percentage change in bond prices equals the change in yield time modified durationequals the change in yield time modified duration

iDP

P

mod100

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

Page 19: Fundamentals of the bond Valuation Process

Trading Strategies Using DurationTrading Strategies Using Duration

Longest-duration security provides the maximum Longest-duration security provides the maximum price variationprice variationIf you expect a decline in interest rates, increase If you expect a decline in interest rates, increase the average duration of your bond portfolio to the average duration of your bond portfolio to experience maximum price volatilityexperience maximum price volatilityIf you expect an increase in interest rates, reduce If you expect an increase in interest rates, reduce the average duration to minimize your price declinethe average duration to minimize your price declineNote that the duration of your portfolio is the Note that the duration of your portfolio is the market-value-weighted average of the duration of market-value-weighted average of the duration of the individual bonds in the portfoliothe individual bonds in the portfolio

Page 20: Fundamentals of the bond Valuation Process

Matched-Funding TechniquesMatched-Funding Techniques

Immunization StrategiesImmunization Strategies– A portfolio manager (after client consultation) A portfolio manager (after client consultation)

may decide that the optimal strategy is to may decide that the optimal strategy is to immunize the portfolio from interest rate immunize the portfolio from interest rate changeschanges

– The immunization techniques attempt to The immunization techniques attempt to derive a specified rate of return during a given derive a specified rate of return during a given investment horizon regardless of what investment horizon regardless of what happens to market interest rateshappens to market interest rates

Page 21: Fundamentals of the bond Valuation Process

Immunization StrategiesImmunization Strategies

Components of Interest Rate RiskComponents of Interest Rate Risk– Price RiskPrice Risk– Coupon Reinvestment RiskCoupon Reinvestment Risk

Page 22: Fundamentals of the bond Valuation Process

Classical ImmunizationClassical Immunization

Immunization is neither a simple nor a Immunization is neither a simple nor a passive strategypassive strategy

An immunized portfolio requires frequent An immunized portfolio requires frequent rebalancing because the modified duration rebalancing because the modified duration of the portfolio always should be equal to of the portfolio always should be equal to the remaining time horizon (except in the the remaining time horizon (except in the case of the zero-coupon bond)case of the zero-coupon bond)

Page 23: Fundamentals of the bond Valuation Process

Classical ImmunizationClassical Immunization

Duration characteristicsDuration characteristics– Duration declines more slowly than term to Duration declines more slowly than term to

maturity, assuming no change in market maturity, assuming no change in market interest ratesinterest rates

– Duration changes with a change in market Duration changes with a change in market interest ratesinterest rates

– There is not always a parallel shift of the yield There is not always a parallel shift of the yield curvecurve

– Bonds with a specific duration may not be Bonds with a specific duration may not be available at an acceptable priceavailable at an acceptable price