BONDS
Feb 15, 2016
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)