RISKS ASSOCIATED WITH BONDSRISKS ASSOCIATED WITH BONDSRISKS ASSOCIATED WITH BONDSRISKS ASSOCIATED WITH BONDS

RISKS RELATED TO BONDSRISKS RELATED TO BONDSRISKS RELATED TO BONDSRISKS RELATED TO BONDS

– Interest Rate Risk

– Maturity Risk

– Coupon Rate Risk

– Reinvestment Risk

– Default Risk

– Credit Spread Risk

– Downgrade Risk

– Event Risk

– Interest Rate Risk

– Maturity Risk

– Coupon Rate Risk

– Reinvestment Risk

– Default Risk

– Credit Spread Risk

– Downgrade Risk

– Event Risk

INTEREST RATE RISKINTEREST RATE RISKINTEREST RATE RISKINTEREST RATE RISK

The price on a typical bond will change in the opposite direction to changes in the market yields.

When the interest rates rises, the bond´s price will fall; when interest rates fall, bond´s prices will rise.

The risk an investor faces is that the price of a bond will decline if market interest rates rise.

The price on a typical bond will change in the opposite direction to changes in the market yields.

When the interest rates rises, the bond´s price will fall; when interest rates fall, bond´s prices will rise.

The risk an investor faces is that the price of a bond will decline if market interest rates rise.

INTEREST RATE RISKINTEREST RATE RISKINTEREST RATE RISKINTEREST RATE RISK

Which bonds have and error in their reported price?Which bonds have and error in their reported price?

Bond/Issuer Coupon Rate Maturity (Years) Market Rate Price (% of Par)A 7.75% 16 6.00% 114.02%B 6.75% 4 7.00% 99.14%C 0.00% 10 5.00% 102.10%D 5.50% 20 5.90% 104.15%E 8.50% 18 8.50% 100.00%F 4.50% 6 4.00% 96.50%G 6.25% 25 6.25% 103.45%

MATURITY RISKMATURITY RISKMATURITY RISKMATURITY RISK

• All other factors constant, the longer the bond´s maturity, the greater the bond´s price sensitivity to changes in market rates.

• All other factors constant, the longer the bond´s maturity, the greater the bond´s price sensitivity to changes in market rates.

COUPON RATE RISKCOUPON RATE RISKCOUPON RATE RISKCOUPON RATE RISK

• All other factors constant, the lower the coupon rate, the greater the bond´s price sensitivity to changes in market rates.

• All other factors constant, the lower the coupon rate, the greater the bond´s price sensitivity to changes in market rates.

MATURITY AND COUPON RATE MATURITY AND COUPON RATE RISKRISKMATURITY AND COUPON RATE MATURITY AND COUPON RATE RISKRISK

A report shows that the market yield for the bonds below are the same. Which bond has the greatest interest rate risk and which has the least interest rate risk?

A report shows that the market yield for the bonds below are the same. Which bond has the greatest interest rate risk and which has the least interest rate risk?

Bond/Issuer Coupon Rate Maturity (Years)A 5.25% 15B 6.50% 12C 4.75% 20D 8.50% 10

MARKET YIELD RISKMARKET YIELD RISKMARKET YIELD RISKMARKET YIELD RISK

• If two bonds have the same characteristics, the one trading at a lower market rate is more sensitive to changes in the market rate.

• Price sensitity is higher when the level of market rates is low, and price sensitivity is lower when the level of market rates is high.

• If two bonds have the same characteristics, the one trading at a lower market rate is more sensitive to changes in the market rate.

• Price sensitity is higher when the level of market rates is low, and price sensitivity is lower when the level of market rates is high.

MARKET YIELD RISKMARKET YIELD RISKMARKET YIELD RISKMARKET YIELD RISK

• Which of the following bonds has the greatest market yield risk?

• Which one has the lowest credit rating?

• Which of the following bonds has the greatest market yield risk?

• Which one has the lowest credit rating?

Bond/Issuer Coupon Rate Maturity Market RateA 6.5% 12 7.00%B 6.5% 12 8.00%C 6.5% 12 9.00%

REINVESTMENT RISKREINVESTMENT RISKREINVESTMENT RISKREINVESTMENT RISK

• Reinvestment Risk is the possibility that the proceeds from payments of interest and principal will be reinvested at a lower market rates than the original invesment.

• Which of the following bonds has higher reinvestment risk?

• Reinvestment Risk is the possibility that the proceeds from payments of interest and principal will be reinvested at a lower market rates than the original invesment.

• Which of the following bonds has higher reinvestment risk?

Bond/Issuer Coupon Rate Maturity Market RateA 0.0% 5 5.00%B 8.0% 5 12.00%C 10.0% 5 10.00%

DEFAULT RISKDEFAULT RISKDEFAULT RISKDEFAULT RISK

• Risk that the issuer will fail to satisfy the terms of the obligation with respect to the timely payment of interest and principal

• Default Rate is the percentage of a population of bonds that is expected to default .

• Recovery Rate is the percentage of a default investment that can be recovered.

• Risk that the issuer will fail to satisfy the terms of the obligation with respect to the timely payment of interest and principal

• Default Rate is the percentage of a population of bonds that is expected to default .

• Recovery Rate is the percentage of a default investment that can be recovered.

DOWNGRADE RISKDOWNGRADE RISKDOWNGRADE RISKDOWNGRADE RISK

• A credit rating is an indicator of the potencial default risk associated with a bond

• A credit rating is an assessment of an issuer´s ability to meet the payment of principal and interest in accordance with the term of indenture.

• Bond market can be divided in:– Investment grade AAA, AA, A and BBB– Non-Investment grade Below BBB

• A credit rating is an indicator of the potencial default risk associated with a bond

• A credit rating is an assessment of an issuer´s ability to meet the payment of principal and interest in accordance with the term of indenture.

• Bond market can be divided in:– Investment grade AAA, AA, A and BBB– Non-Investment grade Below BBB

DOWNGRADE RISKDOWNGRADE RISKDOWNGRADE RISKDOWNGRADE RISK

Rating Agencies following up the “credit quality” of bonds can reassign a different credit rating.

An improvement in the credit quality is rewarded with a better credit rating, and it´s referred to as an UPGRADE.

A deterioration in the credit quality is penalized by the assignment of a lower credit rating, and it´s referred to as a DOWNGRADE.

Rating Agencies following up the “credit quality” of bonds can reassign a different credit rating.

An improvement in the credit quality is rewarded with a better credit rating, and it´s referred to as an UPGRADE.

A deterioration in the credit quality is penalized by the assignment of a lower credit rating, and it´s referred to as a DOWNGRADE.

CREDIT SPREAD RISKCREDIT SPREAD RISKCREDIT SPREAD RISKCREDIT SPREAD RISK

• Credit Spread Risk (or Yield Spread Risk) is the Risk Premium for a “bond rating class” is referred to

• Recall that risk premium is the yield above the risk-free rate to compensate for the additional risk taken.

• Credit Spread Risk is measured in basis points

• Credit spread risk changes with industry, sector, and economic fluctuations.

• An anticipated downgrading increases the credit spread and results in a decline of the bond´s price

• Credit Spread Risk (or Yield Spread Risk) is the Risk Premium for a “bond rating class” is referred to

• Recall that risk premium is the yield above the risk-free rate to compensate for the additional risk taken.

• Credit Spread Risk is measured in basis points

• Credit spread risk changes with industry, sector, and economic fluctuations.

• An anticipated downgrading increases the credit spread and results in a decline of the bond´s price

RateFreeRiskYTMRiskSpreadCredit

EVENT RISKEVENT RISKEVENT RISKEVENT RISK

• Deterioration on the ability of an issuer to make interest and principal payments due to unexpected events outside of the issuer controloutside of the issuer control.

– Natural disaster– Takeovers – Regulatory Changes

• Deterioration on the ability of an issuer to make interest and principal payments due to unexpected events outside of the issuer controloutside of the issuer control.

– Natural disaster– Takeovers – Regulatory Changes

YIELD CURVE (Term StructureYIELD CURVE (Term Structureof Interest Rates)of Interest Rates)

YIELD CURVE (Term StructureYIELD CURVE (Term Structureof Interest Rates)of Interest Rates)

Yield CurveYield CurveYield CurveYield Curve

• plot of maturity vs. yield (spot rates)

• slope of curve indicates relationship between maturity and yield.

• A spot rate is the rate used to discount a “single”

expected future cash flow.

• plot of maturity vs. yield (spot rates)

• slope of curve indicates relationship between maturity and yield.

• A spot rate is the rate used to discount a “single”

expected future cash flow.

Yield Curve: An ExampleYield Curve: An ExampleYield Curve: An ExampleYield Curve: An Example

Term (years) Interest Rate (%) 0.25 3.62

2.00 4.34

5.00 5.07

10.00 5.54

30.00 5.86

Term (years) Interest Rate (%) 0.25 3.62

2.00 4.34

5.00 5.07

10.00 5.54

30.00 5.86

n

n

1tt r)(1

Pr)(1Pi

Bond Price

n321 r)(1PPi

...r)(1Pi

r)(1Pi

r)(1Pi

Bond Price

CF1 = i x P

CF2= i x P CF3 = i x P CFn = i x P + P

t = 1 t = 2 t = 2 t = n…

t = 0

Bond Price = ?

BOND VALUATION

P = Principali = coupon rater = market rate (market yield)i x P = Coupon Payment

flat yield curveflat yield curveflat yield curveflat yield curve

• yields similar for all maturities• yields similar for all maturities

maturity

yield

upward sloping yield cuveupward sloping yield cuveupward sloping yield cuveupward sloping yield cuve

• yields rise w/ maturity (common)• yields rise w/ maturity (common)

maturity

yield

downward sloping (inverted) yield downward sloping (inverted) yield curvecurvedownward sloping (inverted) yield downward sloping (inverted) yield curvecurve

• yield falls w/ maturity (rare)• yield falls w/ maturity (rare)

maturity

yield

humped humped humped humped

• intermediate yields are highest

• May 2000• intermediate yields are highest

• May 2000

maturity

yield

BOND VALUATION TRADITIONAL APPROACHBOND VALUATION TRADITIONAL APPROACHBOND VALUATION TRADITIONAL APPROACHBOND VALUATION TRADITIONAL APPROACH

Traditional approach to bond valuation is to discount every cash flow of a fixed income security using the same interest rate or discount rate.

Traditional approach to bond valuation is to discount every cash flow of a fixed income security using the same interest rate or discount rate.

nn yP

yC

yC

yC

Value)1()1()1()1( 21

nn y

Py

Cy

Cy

CValue

)1()1()1()1( 21

where: C = coupon paymentP = principal paymenty = market yield (typically Yield to Maturity,YTM)n = number of periods over life of bond

BOND AS A PACKAGE OF ZEROES COUPON BONDSBOND AS A PACKAGE OF ZEROES COUPON BONDSBOND AS A PACKAGE OF ZEROES COUPON BONDSBOND AS A PACKAGE OF ZEROES COUPON BONDS

• Any bond can be thought of as a package of zero-coupon bonds.

• Another way to view a 4-year, every 6 months, 6% coupon bond is as a package of zero-coupon bonds.

The 4-year security should be viewed as a package of 8 zero-coupon instruments that mature every six months for the next four years.

• Any bond can be thought of as a package of zero-coupon bonds.

• Another way to view a 4-year, every 6 months, 6% coupon bond is as a package of zero-coupon bonds.

The 4-year security should be viewed as a package of 8 zero-coupon instruments that mature every six months for the next four years.

PC

C C

CC

C

C

C

DETERMINING SPOT RATESDETERMINING SPOT RATESDETERMINING SPOT RATESDETERMINING SPOT RATES

• A spot rate is the rate used to discount a “single” expected future cash flow.

• Suppose you observe the following data for three government bonds (default risk close to zero) :

• In order to find the spot rates from this data, we need to “strip” the coupons from the bonds.

• A spot rate is the rate used to discount a “single” expected future cash flow.

• Suppose you observe the following data for three government bonds (default risk close to zero) :

• In order to find the spot rates from this data, we need to “strip” the coupons from the bonds.

Maturity YTM Coupon Rate Price(% of par)1 Year 3.6% 0.0% 96.64%

2 Years 3.8% 3.8% 100%3 Years 4.0% 4.0% 100%

Cash flow timeline from the stripped cash flows is as follows:

Cash flow timeline from the stripped cash flows is as follows:

0 1 2 3

1-year bond

2-year bond

3-year bond

-96.6463

-100.000

-100.000

+4

+3.8

+100

+104+4

+103.8

Maturity YTM Coupon Rate Price(% of par)1 Year 3.6% 0.0% 96.64%

2 Years 3.8% 3.8% 100%3 Years 4.0% 4.0% 100%

DETERMINING SPOT RATESDETERMINING SPOT RATESDETERMINING SPOT RATESDETERMINING SPOT RATES

• Since these bonds all have the same issuer, all cash flows received at t=1, must be discounted at the same rate.

• The 1-year zero coupon bond has only one cash flow, we can use its YTM as the discount factor for other t=1 cash flows, i.e. use 3.62% as the one-year spot rate Z1. (Z1 = 3.62%)

• NOTE: This approach to create a theoretical spot rate curve is called bootstrapping.

• Since these bonds all have the same issuer, all cash flows received at t=1, must be discounted at the same rate.

• The 1-year zero coupon bond has only one cash flow, we can use its YTM as the discount factor for other t=1 cash flows, i.e. use 3.62% as the one-year spot rate Z1. (Z1 = 3.62%)

• NOTE: This approach to create a theoretical spot rate curve is called bootstrapping.

DETERMINING SPOT RATESDETERMINING SPOT RATESDETERMINING SPOT RATESDETERMINING SPOT RATES

• We can use the one-year spot rate to discount the cash flows for the 2-year bond as follows:

100.000 = 3.8/(1 + Z1)1 + 103.8/(1 + Z2)2

100.000 = 3.8/(1.0362)1 + 103.8/(1 + Z2)2

100.000 – 3.93756 = 103.8/(1 + Z2)2

96.06244 = 103.8/(1 + Z2)2

1.080547194 = (1 + Z2)2

1.03949372 = 1 + Z2

Z2 = 3.949372%

• We can use the one-year spot rate to discount the cash flows for the 2-year bond as follows:

100.000 = 3.8/(1 + Z1)1 + 103.8/(1 + Z2)2

100.000 = 3.8/(1.0362)1 + 103.8/(1 + Z2)2

100.000 – 3.93756 = 103.8/(1 + Z2)2

96.06244 = 103.8/(1 + Z2)2

1.080547194 = (1 + Z2)2

1.03949372 = 1 + Z2

Z2 = 3.949372%

DETERMINING SPOT RATESDETERMINING SPOT RATESDETERMINING SPOT RATESDETERMINING SPOT RATES

• We can use the one- and two-year spot rates to discount the cash flows for the 3-year bond as follows:

100.000 = 4/(1 + Z1)1 + 4/(1 + Z2)2 + 104/(1 + Z3)3

100.000 = 4/(1.0362)1 + 4/(1.03949372)2 + 104/(1 + Z3)3

1.125079487 = (1 + Z3)3

Z3 = 4.0066406%

• We can use the one- and two-year spot rates to discount the cash flows for the 3-year bond as follows:

100.000 = 4/(1 + Z1)1 + 4/(1 + Z2)2 + 104/(1 + Z3)3

100.000 = 4/(1.0362)1 + 4/(1.03949372)2 + 104/(1 + Z3)3

1.125079487 = (1 + Z3)3

Z3 = 4.0066406%

DETERMINING SPOT RATESDETERMINING SPOT RATESDETERMINING SPOT RATESDETERMINING SPOT RATES

VALUING BONDS WITH SPOT RATESVALUING BONDS WITH SPOT RATESVALUING BONDS WITH SPOT RATESVALUING BONDS WITH SPOT RATES

• We can use the spot rates to value other bonds issued by the same entity or by adding a credit spread to value bonds issued by another entity.

• Recall, Z1 = 3.62%, Z2 = 3.949%, Z3 = 4.007%

• Use these spots rates to calculate the value of a three-year, annual-pay, 5% coupon bond with the same risk characteristics as the previous bond.

Bond Value = 5/(1 + Z1)1 + 5/(1 + Z2)2 + 105/(1 + Z3)3

102.778 = 5/(1.0362)1 + 5/(1.03949)2 + 105/(1.04007)3

• We can use the spot rates to value other bonds issued by the same entity or by adding a credit spread to value bonds issued by another entity.

• Recall, Z1 = 3.62%, Z2 = 3.949%, Z3 = 4.007%

• Use these spots rates to calculate the value of a three-year, annual-pay, 5% coupon bond with the same risk characteristics as the previous bond.

Bond Value = 5/(1 + Z1)1 + 5/(1 + Z2)2 + 105/(1 + Z3)3

102.778 = 5/(1.0362)1 + 5/(1.03949)2 + 105/(1.04007)3

PLEASE DO NOT FORGET WEDNESDAY 9thMID-TERM EXAM9PM TO 10:30PM

PLEASE DO NOT FORGET WEDNESDAY 9thMID-TERM EXAM9PM TO 10:30PM