BONDS

Loan is an IOU between two specific entities

Bond is also a loan but Bond is an IOU between an entity and the

population in general This can now be traded in an exchange

What is the advantage

Fixed-Income Market Participants Issuers1048707Governments1048707Corporations1048707Commercial

Banks1048707States1048707Municipalities1048707SPVs Intermediaries1048707Primary Dealers1048707Other

Dealers1048707Investment Banks1048707Credit-rating Agencies Investors1048707Governments1048707Pension

Funds1048707Insurance Companies1048707Commercial Banks1048707Mutual Funds1048707Foreign Institutions1048707Individuals

Industry Overview

Bond Perspectives

Needs Rupees Borrower Issuer or seller Debtholder Cost of borrowing

Interest Paid (Expense) ndash generates tax benefit (Svgs)

Cost of Debt = Rd or Kd After-tax cost = Rd (1-t)

Has Rupees Lender Buyer or Investor Bondholder Creditor Requires return to

invest rupees in bonds based on risk Interest Received

(earned) (Revenue) - pay tax on it

Capital Appreciation4

DEBT ASSET

Par value Face amount paid at maturity Assume $1000

Coupon interest rate Stated interest rate Multiply by par value to get rupees of lsquointerestrsquo Generally fixed

5

Key Features of a Bond

(Morehellip)

Maturity Years until bond must be repaid Declines

Issue date Date when bond was issued Default risk Risk that issuer will not make

interest or principal payments

6

Characteristics of Bonds Bonds debt securities that pay a rate of interest

based upon the face amount or par value of the bond

Price changes as market interest changes

Interest payments are commonly semiannual

Bond investors receive full face amount when bonds mature

Zero coupon bonds ndash no periodic payment (no interest reinvestment rate) Originally sold at a discount

Pure Discount Bond No coupons single payment of principal at maturity Bond trades at a ldquodiscountrdquo to face value Also known as zero-coupon bonds Valuation is straightforward application of PV

P0 = F (1+r)t

Note (P0 r F) is ldquoover-determinedrdquo given two the third is determined

Now What If r Varies Over Time Different interest rates from one year to the next Denote by rt the spot rate of interest in year t

Zero coupon bond

Suppose a zero coupon bond pays Rs 1000 (face value) exactly five years from now What is the price or value today if the interest rate on similar bonds is 9

Example

Yield to maturity ndash It is the return you can expect if you hold the bond to maturity

What is the YTM of a 10 year zero coupon bond with a face value of Rs 1000 and a current price of Rs 42241

The price is given face value is given the question is what is the rate of return built into this

YTM

What makes a YTM of a zero coupon government bond risk free(let us ignore inflation risk)

VALUE in finance is not what you say But what people perceive whatrsquos going to

happen

Now try semi annual compounding

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Loan is an IOU between two specific entities

Bond is also a loan but Bond is an IOU between an entity and the

population in general This can now be traded in an exchange

What is the advantage

Fixed-Income Market Participants Issuers1048707Governments1048707Corporations1048707Commercial

Banks1048707States1048707Municipalities1048707SPVs Intermediaries1048707Primary Dealers1048707Other

Dealers1048707Investment Banks1048707Credit-rating Agencies Investors1048707Governments1048707Pension

Funds1048707Insurance Companies1048707Commercial Banks1048707Mutual Funds1048707Foreign Institutions1048707Individuals

Industry Overview

Bond Perspectives

Needs Rupees Borrower Issuer or seller Debtholder Cost of borrowing

Interest Paid (Expense) ndash generates tax benefit (Svgs)

Cost of Debt = Rd or Kd After-tax cost = Rd (1-t)

Has Rupees Lender Buyer or Investor Bondholder Creditor Requires return to

invest rupees in bonds based on risk Interest Received

(earned) (Revenue) - pay tax on it

Capital Appreciation4

DEBT ASSET

Par value Face amount paid at maturity Assume $1000

Coupon interest rate Stated interest rate Multiply by par value to get rupees of lsquointerestrsquo Generally fixed

5

Key Features of a Bond

(Morehellip)

Maturity Years until bond must be repaid Declines

Issue date Date when bond was issued Default risk Risk that issuer will not make

interest or principal payments

6

Characteristics of Bonds Bonds debt securities that pay a rate of interest

based upon the face amount or par value of the bond

Price changes as market interest changes

Interest payments are commonly semiannual

Bond investors receive full face amount when bonds mature

Zero coupon bonds ndash no periodic payment (no interest reinvestment rate) Originally sold at a discount

Pure Discount Bond No coupons single payment of principal at maturity Bond trades at a ldquodiscountrdquo to face value Also known as zero-coupon bonds Valuation is straightforward application of PV

P0 = F (1+r)t

Note (P0 r F) is ldquoover-determinedrdquo given two the third is determined

Now What If r Varies Over Time Different interest rates from one year to the next Denote by rt the spot rate of interest in year t

Zero coupon bond

Suppose a zero coupon bond pays Rs 1000 (face value) exactly five years from now What is the price or value today if the interest rate on similar bonds is 9

Example

Yield to maturity ndash It is the return you can expect if you hold the bond to maturity

What is the YTM of a 10 year zero coupon bond with a face value of Rs 1000 and a current price of Rs 42241

The price is given face value is given the question is what is the rate of return built into this

YTM

What makes a YTM of a zero coupon government bond risk free(let us ignore inflation risk)

VALUE in finance is not what you say But what people perceive whatrsquos going to

happen

Now try semi annual compounding

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Fixed-Income Market Participants Issuers1048707Governments1048707Corporations1048707Commercial

Banks1048707States1048707Municipalities1048707SPVs Intermediaries1048707Primary Dealers1048707Other

Dealers1048707Investment Banks1048707Credit-rating Agencies Investors1048707Governments1048707Pension

Funds1048707Insurance Companies1048707Commercial Banks1048707Mutual Funds1048707Foreign Institutions1048707Individuals

Industry Overview

Bond Perspectives

Needs Rupees Borrower Issuer or seller Debtholder Cost of borrowing

Interest Paid (Expense) ndash generates tax benefit (Svgs)

Cost of Debt = Rd or Kd After-tax cost = Rd (1-t)

Has Rupees Lender Buyer or Investor Bondholder Creditor Requires return to

invest rupees in bonds based on risk Interest Received

(earned) (Revenue) - pay tax on it

Capital Appreciation4

DEBT ASSET

Par value Face amount paid at maturity Assume $1000

Coupon interest rate Stated interest rate Multiply by par value to get rupees of lsquointerestrsquo Generally fixed

5

Key Features of a Bond

(Morehellip)

Maturity Years until bond must be repaid Declines

Issue date Date when bond was issued Default risk Risk that issuer will not make

interest or principal payments

6

Characteristics of Bonds Bonds debt securities that pay a rate of interest

based upon the face amount or par value of the bond

Price changes as market interest changes

Interest payments are commonly semiannual

Bond investors receive full face amount when bonds mature

Zero coupon bonds ndash no periodic payment (no interest reinvestment rate) Originally sold at a discount

Pure Discount Bond No coupons single payment of principal at maturity Bond trades at a ldquodiscountrdquo to face value Also known as zero-coupon bonds Valuation is straightforward application of PV

P0 = F (1+r)t

Note (P0 r F) is ldquoover-determinedrdquo given two the third is determined

Now What If r Varies Over Time Different interest rates from one year to the next Denote by rt the spot rate of interest in year t

Zero coupon bond

Suppose a zero coupon bond pays Rs 1000 (face value) exactly five years from now What is the price or value today if the interest rate on similar bonds is 9

Example

Yield to maturity ndash It is the return you can expect if you hold the bond to maturity

What is the YTM of a 10 year zero coupon bond with a face value of Rs 1000 and a current price of Rs 42241

The price is given face value is given the question is what is the rate of return built into this

YTM

What makes a YTM of a zero coupon government bond risk free(let us ignore inflation risk)

VALUE in finance is not what you say But what people perceive whatrsquos going to

happen

Now try semi annual compounding

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Bond Perspectives

Needs Rupees Borrower Issuer or seller Debtholder Cost of borrowing

Interest Paid (Expense) ndash generates tax benefit (Svgs)

Cost of Debt = Rd or Kd After-tax cost = Rd (1-t)

Has Rupees Lender Buyer or Investor Bondholder Creditor Requires return to

invest rupees in bonds based on risk Interest Received

(earned) (Revenue) - pay tax on it

Capital Appreciation4

DEBT ASSET

Par value Face amount paid at maturity Assume $1000

Coupon interest rate Stated interest rate Multiply by par value to get rupees of lsquointerestrsquo Generally fixed

5

Key Features of a Bond

(Morehellip)

Maturity Years until bond must be repaid Declines

Issue date Date when bond was issued Default risk Risk that issuer will not make

interest or principal payments

6

Characteristics of Bonds Bonds debt securities that pay a rate of interest

based upon the face amount or par value of the bond

Price changes as market interest changes

Interest payments are commonly semiannual

Bond investors receive full face amount when bonds mature

Zero coupon bonds ndash no periodic payment (no interest reinvestment rate) Originally sold at a discount

Pure Discount Bond No coupons single payment of principal at maturity Bond trades at a ldquodiscountrdquo to face value Also known as zero-coupon bonds Valuation is straightforward application of PV

P0 = F (1+r)t

Note (P0 r F) is ldquoover-determinedrdquo given two the third is determined

Now What If r Varies Over Time Different interest rates from one year to the next Denote by rt the spot rate of interest in year t

Zero coupon bond

Suppose a zero coupon bond pays Rs 1000 (face value) exactly five years from now What is the price or value today if the interest rate on similar bonds is 9

Example

Yield to maturity ndash It is the return you can expect if you hold the bond to maturity

What is the YTM of a 10 year zero coupon bond with a face value of Rs 1000 and a current price of Rs 42241

The price is given face value is given the question is what is the rate of return built into this

YTM

What makes a YTM of a zero coupon government bond risk free(let us ignore inflation risk)

VALUE in finance is not what you say But what people perceive whatrsquos going to

happen

Now try semi annual compounding

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Par value Face amount paid at maturity Assume $1000

Coupon interest rate Stated interest rate Multiply by par value to get rupees of lsquointerestrsquo Generally fixed

5

Key Features of a Bond

(Morehellip)

Maturity Years until bond must be repaid Declines

Issue date Date when bond was issued Default risk Risk that issuer will not make

interest or principal payments

6

Characteristics of Bonds Bonds debt securities that pay a rate of interest

based upon the face amount or par value of the bond

Price changes as market interest changes

Interest payments are commonly semiannual

Bond investors receive full face amount when bonds mature

Zero coupon bonds ndash no periodic payment (no interest reinvestment rate) Originally sold at a discount

Pure Discount Bond No coupons single payment of principal at maturity Bond trades at a ldquodiscountrdquo to face value Also known as zero-coupon bonds Valuation is straightforward application of PV

P0 = F (1+r)t

Note (P0 r F) is ldquoover-determinedrdquo given two the third is determined

Now What If r Varies Over Time Different interest rates from one year to the next Denote by rt the spot rate of interest in year t

Zero coupon bond

Suppose a zero coupon bond pays Rs 1000 (face value) exactly five years from now What is the price or value today if the interest rate on similar bonds is 9

Example

Yield to maturity ndash It is the return you can expect if you hold the bond to maturity

What is the YTM of a 10 year zero coupon bond with a face value of Rs 1000 and a current price of Rs 42241

The price is given face value is given the question is what is the rate of return built into this

YTM

What makes a YTM of a zero coupon government bond risk free(let us ignore inflation risk)

VALUE in finance is not what you say But what people perceive whatrsquos going to

happen

Now try semi annual compounding

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Maturity Years until bond must be repaid Declines

Issue date Date when bond was issued Default risk Risk that issuer will not make

interest or principal payments

6

Characteristics of Bonds Bonds debt securities that pay a rate of interest

based upon the face amount or par value of the bond

Price changes as market interest changes

Interest payments are commonly semiannual

Bond investors receive full face amount when bonds mature

Zero coupon bonds ndash no periodic payment (no interest reinvestment rate) Originally sold at a discount

Pure Discount Bond No coupons single payment of principal at maturity Bond trades at a ldquodiscountrdquo to face value Also known as zero-coupon bonds Valuation is straightforward application of PV

P0 = F (1+r)t

Note (P0 r F) is ldquoover-determinedrdquo given two the third is determined

Now What If r Varies Over Time Different interest rates from one year to the next Denote by rt the spot rate of interest in year t

Zero coupon bond

Suppose a zero coupon bond pays Rs 1000 (face value) exactly five years from now What is the price or value today if the interest rate on similar bonds is 9

Example

Yield to maturity ndash It is the return you can expect if you hold the bond to maturity

What is the YTM of a 10 year zero coupon bond with a face value of Rs 1000 and a current price of Rs 42241

The price is given face value is given the question is what is the rate of return built into this

YTM

What makes a YTM of a zero coupon government bond risk free(let us ignore inflation risk)

VALUE in finance is not what you say But what people perceive whatrsquos going to

happen

Now try semi annual compounding

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Characteristics of Bonds Bonds debt securities that pay a rate of interest

based upon the face amount or par value of the bond

Price changes as market interest changes

Interest payments are commonly semiannual

Bond investors receive full face amount when bonds mature

Zero coupon bonds ndash no periodic payment (no interest reinvestment rate) Originally sold at a discount

Pure Discount Bond No coupons single payment of principal at maturity Bond trades at a ldquodiscountrdquo to face value Also known as zero-coupon bonds Valuation is straightforward application of PV

P0 = F (1+r)t

Note (P0 r F) is ldquoover-determinedrdquo given two the third is determined

Now What If r Varies Over Time Different interest rates from one year to the next Denote by rt the spot rate of interest in year t

Zero coupon bond

Suppose a zero coupon bond pays Rs 1000 (face value) exactly five years from now What is the price or value today if the interest rate on similar bonds is 9

Example

Yield to maturity ndash It is the return you can expect if you hold the bond to maturity

What is the YTM of a 10 year zero coupon bond with a face value of Rs 1000 and a current price of Rs 42241

The price is given face value is given the question is what is the rate of return built into this

YTM

What makes a YTM of a zero coupon government bond risk free(let us ignore inflation risk)

VALUE in finance is not what you say But what people perceive whatrsquos going to

happen

Now try semi annual compounding

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Pure Discount Bond No coupons single payment of principal at maturity Bond trades at a ldquodiscountrdquo to face value Also known as zero-coupon bonds Valuation is straightforward application of PV

P0 = F (1+r)t

Note (P0 r F) is ldquoover-determinedrdquo given two the third is determined

Now What If r Varies Over Time Different interest rates from one year to the next Denote by rt the spot rate of interest in year t

Zero coupon bond

Suppose a zero coupon bond pays Rs 1000 (face value) exactly five years from now What is the price or value today if the interest rate on similar bonds is 9

Example

Yield to maturity ndash It is the return you can expect if you hold the bond to maturity

What is the YTM of a 10 year zero coupon bond with a face value of Rs 1000 and a current price of Rs 42241

The price is given face value is given the question is what is the rate of return built into this

YTM

What makes a YTM of a zero coupon government bond risk free(let us ignore inflation risk)

VALUE in finance is not what you say But what people perceive whatrsquos going to

happen

Now try semi annual compounding

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Suppose a zero coupon bond pays Rs 1000 (face value) exactly five years from now What is the price or value today if the interest rate on similar bonds is 9

Example

Yield to maturity ndash It is the return you can expect if you hold the bond to maturity

What is the YTM of a 10 year zero coupon bond with a face value of Rs 1000 and a current price of Rs 42241

The price is given face value is given the question is what is the rate of return built into this

YTM

What makes a YTM of a zero coupon government bond risk free(let us ignore inflation risk)

VALUE in finance is not what you say But what people perceive whatrsquos going to

happen

Now try semi annual compounding

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Yield to maturity ndash It is the return you can expect if you hold the bond to maturity

What is the YTM of a 10 year zero coupon bond with a face value of Rs 1000 and a current price of Rs 42241

The price is given face value is given the question is what is the rate of return built into this

YTM

What makes a YTM of a zero coupon government bond risk free(let us ignore inflation risk)

VALUE in finance is not what you say But what people perceive whatrsquos going to

happen

Now try semi annual compounding

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

What makes a YTM of a zero coupon government bond risk free(let us ignore inflation risk)

VALUE in finance is not what you say But what people perceive whatrsquos going to

happen

Now try semi annual compounding

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Now try semi annual compounding

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

The most common type of Bond is a coupon bond

They pay periodic coupons and a larger face value at maturity

All payments are explicitly stated in the IOU contract

Coupon Bond

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

WARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations

The coupon rate merely tells us what cash flow the bond will produce

Since the coupon rate is listed as a this misconception is quite common

Bonds

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

A Rs1000 par value bond bearing a coupon rate of 12 percent will mature after 6 years What is the value of the bond if the discount rate is 16 percent

Simple problems

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Suppose a government bond has a 10 coupon a face value of Rs 1000 and 10 years to maturity What is the price of the bond if similar bonds yield a annual return of 10 What if the similar bond yield 8 or 12

Find out the absolute and percentage difference in both the cases

Example ndash very important

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

The relation between maturity and the YTM of government bonds

Typical relation Why Some idea of risk

Yield Curve

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Expectations theory Liquidity preference theory Inflation premium theory

19

Theories of Interest Rate Structure

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

According to the expectations theory of interest rates investment opportunities with different time horizons should yield the same return

20

Expectations Theory

22 1 1 2

1 2

(1 ) (1 )(1 )

where the forward rate from time 1 to time 2

R R f

f

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)

Example

An investor can purchase a two-year CD at a rate of 5 percent Alternatively the investor can purchase two consecutive one-year CDs The current rate on a one-year CD is 475 percent

According to the expectations theory what is the expected one-year CD rate one year from now

21

Expectations Theory (contrsquod)

• BONDS
• Slide 2
• Industry Overview
• Bond Perspectives
• Key Features of a Bond
• Slide 6
• Characteristics of Bonds
• Zero coupon bond
• Example
• YTM
• Slide 11
• Now try semi annual compounding
• Coupon Bond
• Bonds
• Simple problems
• Example ndash very important
• Slide 17
• Yield Curve
• Theories of Interest Rate Structure
• Expectations Theory
• Expectations Theory (contrsquod)