1.6. Qaracter Functional Training - Fixed Income 2024.pdf
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About This Presentation
Finance
Slide Content
Training with
Fixed Income
Assets
Madrid, January 2023
©Qaracter,2024todoslosderechosreservados 1
Fixed Income
Assets
Madrid, January 2023
©Qaracter,2024todoslosderechosreservados 1
Index
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•Fixed income financial assets are securitiesthat promise the investor the future receipt of certain cash flows until a
certain amortization or maturity date.
•These fixed income securities represent loans that issuers of these securities receive from investors.
•Most important elementsof fixed income assets:
✓Nominal: Constitutes the principal of each of these loans (securities) and on which the future periodic
payments (coupons) are calculated.
✓Coupon: Amount of periodic interest payments (monthly, quarterly, annually, etc.) determined in the issue.
✓Amortization or maturity date: Future date on which the life of the fixed income security ends and the
security amortization occurs.
✓Amortization: Principal capital refund on the maturity date.
•Fixed income financial assets are securitiesthat promise the investor the future receipt of certain cash flows until a
certain amortization or maturity date.
•These fixed income securities represent loans that issuers of these securities receive from investors.
•Most important elementsof fixed income assets:
✓Nominal: Constitutes the principal of each of these loans (securities) and on which the future periodic
payments (coupons) are calculated.
✓Coupon: Amount of periodic interest payments (monthly, quarterly, annually, etc.) determined in the issue.
✓Amortization or maturity date: Future date on which the life of the fixed income security ends and the
security amortization occurs.
✓Amortization: Principal capital refund on the maturity date.
4 ©Qaracter,2024todoslosderechosreservados
•Other elements that characterize some bonds or obligations from others:
oConsidering the price or value at which these are issued or the value at which these are amortized:
✓At par
✓Below par ("at discount")
✓Above par ("at a premium")
•Fixed income asset types:
oSecurities with periodic coupon payments:
✓Bonds
✓Obligations
✓Index-linked bonds (tips)
oSecurities without coupon payments:
✓Zero coupon bonds (strips)
✓Commercial papers
✓Treasury bills
•Other elements that characterize some bonds or obligations from others:
oConsidering the price or value at which these are issued or the value at which these are amortized:
✓At par
✓Below par ("at discount")
✓Above par ("at a premium")
•Fixed income asset types:
oSecurities with periodic coupon payments:
✓Bonds
✓Obligations
✓Index-linked bonds (tips)
oSecurities without coupon payments:
✓Zero coupon bonds (strips)
✓Commercial papers
✓Treasury bills
5 ©Qaracter,2024todoslosderechosreservados
•Represent debtissued by big companies and governments (fixed income securities):
✓Bonds have 3 or 5 maturity years.
✓Obligations have 10, 15, 30 or 50 maturity years.
•Providepayment of nominal value at maturity (end life of fixed income security) plus the fixed and periodic interest
payment called coupon (expressed as a % of nominal).
•Couponis fixed at the beginning of the issuance.
•Coupon interest types can be fixed during the fixedincome security life or variables(linked to some interest index
type, such as Euribor or Libor).
•The price is often expressed as a nominal percentage.
•The price is expressed netted of accrued interest net, what is known as ex-coupon, in other words, the bond price
is separated from the accrued coupon value.
•If the company does not pay the interest, the lenders can demand the repayment of the debt. The interest payment
provides protection to the lender.
Bond / Obligations characteristics:
•Represent debtissued by big companies and governments (fixed income securities):
✓Bonds have 3 or 5 maturity years.
✓Obligations have 10, 15, 30 or 50 maturity years.
•Providepayment of nominal value at maturity (end life of fixed income security) plus the fixed and periodic interest
payment called coupon (expressed as a % of nominal).
•Couponis fixed at the beginning of the issuance.
•Coupon interest types can be fixed during the fixedincome security life or variables(linked to some interest index
type, such as Euribor or Libor).
•The price is often expressed as a nominal percentage.
•The price is expressed netted of accrued interest net, what is known as ex-coupon, in other words, the bond price
is separated from the accrued coupon value.
•If the company does not pay the interest, the lenders can demand the repayment of the debt. The interest payment
provides protection to the lender.
Bond / Obligations characteristics:
6 ©Qaracter,2024todoslosderechosreservados
•The issuanceis carried out via auctionor syndication:
✓Underwriting (syndicated): Similar to equity public offerings. The issuer contracts a financial institutions
syndicate that undertakes to provide the required funds volume (underwriting).
✓Competitive auctions: Minor importance in the Spanish financial system.
•Other bond types:
✓Subordinated issuances (coupon attached to conditions).
✓Zero coupon
✓Issuances convertible into shares
✓Floating coupon linked to Euribor (Floating Rate Notes)
✓Structured (index-linked)
✓Mortgage certificates: Bonds secured by loans from the issuing bank.
•The issuanceis carried out via auctionor syndication:
✓Underwriting (syndicated): Similar to equity public offerings. The issuer contracts a financial institutions
syndicate that undertakes to provide the required funds volume (underwriting).
✓Competitive auctions: Minor importance in the Spanish financial system.
•Other bond types:
✓Subordinated issuances (coupon attached to conditions).
✓Zero coupon
✓Issuances convertible into shares
✓Floating coupon linked to Euribor (Floating Rate Notes)
✓Structured (index-linked)
✓Mortgage certificates: Bonds secured by loans from the issuing bank.
7 ©Qaracter,2024todoslosderechosreservados
•Basic instrument of bank financing.
•The bank "packages" a set of loans from its balance sheet, with a certain seniority and collateral. The bank places this
bundle of assets in a Securitization Fund.
•The Securitization Fund pays the bank for these assets through the funds obtained from the securitization bonds
issuances. The loans of a same fund have different levels of risk (and profitability): AAA, AA, A...
•Their disproportionate expansion in the US for low-quality assets has been one of the causes of the economic crisis.
Securitization Bonds
•Basic instrument of bank financing.
•The bank "packages" a set of loans from its balance sheet, with a certain seniority and collateral. The bank places this
bundle of assets in a Securitization Fund.
•The Securitization Fund pays the bank for these assets through the funds obtained from the securitization bonds
issuances. The loans of a same fund have different levels of risk (and profitability): AAA, AA, A...
•Their disproportionate expansion in the US for low-quality assets has been one of the causes of the economic crisis.
Securitization Bonds
Index
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•Assume a fixed income asset that pays in each time period (t=1, 2, 3, ...n) a predetermined Cash Flow (CF). It can be
represented like this:
•Price or value can be calculated through the discounting of all the promised future cash flows:
•r
1,r
2,…r
Nare called the spot interest rates for each period.
Valuation of Bonds and Obligations with non-constant coupons
•Assume a fixed income asset that pays in each time period (t=1, 2, 3, ...n) a predetermined Cash Flow (CF). It can be
represented like this:
•Price or value can be calculated through the discounting of all the promised future cash flows:
•r
1,r
2,…r
Nare called the spot interest rates for each period.
Valuation of Bonds and Obligations with non-constant coupons
10 ©Qaracter,2024todoslosderechosreservados
•Assume a fixed income asset that pays in each time period (t=1, 2, 3...n) a coupon equal to C, and amortized at par.
Can be represented as follows:
•Theoretical price can be calculated with the following formula:
Valuation of Bonds and Obligations with constant coupons (C)
•Assume a fixed income asset that pays in each time period (t=1, 2, 3...n) a coupon equal to C, and amortized at par.
Can be represented as follows:
•Theoretical price can be calculated with the following formula:
Valuation of Bonds and Obligations with constant coupons (C)
11 ©Qaracter,2024todoslosderechosreservados
•Cash flows at the end of each year over the remaining life of the bond (today = year 2021)
Practical example: Treasury obligation with €1000 as nominal value, 6%
annual coupon and maturity of 5 years.
•How much an investor will be willing to pay for this obligation?
•Let’s learn how to value an obligation: Assume that the investor has the alternative to deposit money at the following
maturities and interest rates (assuming that can lend and borrow at the same rates):A 1 AÑOA 2 AÑOSA 3 AÑOSA 4 AÑOSA 5 AÑOS
6,50% 7,00% 7,25% 7,50% 7,70% 2022 2023 2024 2025 2026
60 60 60 60 1060
•Cash flows at the end of each year over the remaining life of the bond (today = year 2021)
Practical example: Treasury obligation with €1000 as nominal value, 6%
annual coupon and maturity of 5 years.
•How much an investor will be willing to pay for this obligation?
•Let’s learn how to value an obligation: Assume that the investor has the alternative to deposit money at the following
maturities and interest rates (assuming that can lend and borrow at the same rates):A 1 AÑOA 2 AÑOSA 3 AÑOSA 4 AÑOSA 5 AÑOS
6,50% 7,00% 7,25% 7,50% 7,70% 2022 2023 2024 2025 2026
60 60 60 60 1060
12 ©Qaracter,2024todoslosderechosreservados
•How much money would have to deposit today to obtain the same income that the obligation offers and on the
same dates? Clearly we are asking about the actual value (VA) of those future payments that the obligation makes at
the corresponding interest rates:
•In other words, the investor would have to lend €933.8 today.
•If this is the only investment alternative the obligation price will be the exposed.
•Suppose the obligation price was €900. How could the investor make money without any risk?
✓Investor could buy the obligation and borrow the prior amounts to those maturities and at the corresponding
interest rates (€56.34 for one year, €52.41 for two years, etc.).
•How much money would have to deposit today to obtain the same income that the obligation offers and on the
same dates? Clearly we are asking about the actual value (VA) of those future payments that the obligation makes at
the corresponding interest rates:
•In other words, the investor would have to lend €933.8 today.
•If this is the only investment alternative the obligation price will be the exposed.
•Suppose the obligation price was €900. How could the investor make money without any risk?
✓Investor could buy the obligation and borrow the prior amounts to those maturities and at the corresponding
interest rates (€56.34 for one year, €52.41 for two years, etc.).
13 ©Qaracter,2024todoslosderechosreservados
•After the first year, the investor will have to pay back €60 for the €56.34 1-year loan. But since the obligation has
been purchased, the investor will have the €60 that needs to repay his debt.
•In the same way, coupons and the nominal of the obligation can be used to repay the rest of the debt. In this way net
payment or collection will be exactly zero.
•However, today the investor has paid €900 for the obligation and received €933, in other words, the investor had
€33 as net cash inflow with no risk.
•Many investors will identify this business opportunity and will want to buy the obligation. This increased demand on
the obligation will increase the price. Until when? Till the strategy is no longer attractive, in other words, until the
obligation price is equal to the present value of future payments at current market interest rates (€933.8).
•In the practice, this processes happen almost instantaneously, so risk-free opportunities to make money (called
arbitrage opportunities) are difficult to find due to the high competition level in the financial markets.
•After the first year, the investor will have to pay back €60 for the €56.34 1-year loan. But since the obligation has
been purchased, the investor will have the €60 that needs to repay his debt.
•In the same way, coupons and the nominal of the obligation can be used to repay the rest of the debt. In this way net
payment or collection will be exactly zero.
•However, today the investor has paid €900 for the obligation and received €933, in other words, the investor had
€33 as net cash inflow with no risk.
•Many investors will identify this business opportunity and will want to buy the obligation. This increased demand on
the obligation will increase the price. Until when? Till the strategy is no longer attractive, in other words, until the
obligation price is equal to the present value of future payments at current market interest rates (€933.8).
•In the practice, this processes happen almost instantaneously, so risk-free opportunities to make money (called
arbitrage opportunities) are difficult to find due to the high competition level in the financial markets.
14 ©Qaracter,2024todoslosderechosreservados
•Financial assets market is at equilibrium when prices are equal to the present value of their future payments
considering the return offered by similar financial investments in terms of maturity and risk level.
•The obligation equilibrium price is equal to the present value of its future payments:
•Obligation is sold at 93.3% of its nominal value.
•Rarely obligation price matches with its nominal value. Let’s think the obligation price changes every day:
✓Discount factors change over the time.
✓Interest rates change.
•Financial assets market is at equilibrium when prices are equal to the present value of their future payments
considering the return offered by similar financial investments in terms of maturity and risk level.
•The obligation equilibrium price is equal to the present value of its future payments:
•Obligation is sold at 93.3% of its nominal value.
•Rarely obligation price matches with its nominal value. Let’s think the obligation price changes every day:
✓Discount factors change over the time.
✓Interest rates change.
15 ©Qaracter,2024todoslosderechosreservados
•Calculation of Half-yearly cash flows and the actual value (VA):
Practical example: Calculate the price of an obligation with a nominal
value of €1000, maturity of 5 years, if it pays a coupon of 6% per year
every six months and the semi-annual interest rate of an alternative
investment is 3.20%.
•Considering it’s a constant coupon, formula for an annuity with 10 periods can be used:
•Obligation price is 983.11. That is 98.31% of nominal value.
•Calculation of Half-yearly cash flows and the actual value (VA):
Practical example: Calculate the price of an obligation with a nominal
value of €1000, maturity of 5 years, if it pays a coupon of 6% per year
every six months and the semi-annual interest rate of an alternative
investment is 3.20%.
•Considering it’s a constant coupon, formula for an annuity with 10 periods can be used:
•Obligation price is 983.11. That is 98.31% of nominal value.
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•As we have seen, the obligation price is calculated as exposed below:
•The discount rates r
1, r
2, … r
Nare denominated spot rates at different maturities.
•These discount rates constitute the Temporary Structure of Interest Rates (relation between interest rates and
maturities).
•As we reviewed, these are the interest rates of alternative investments. Risk plays a decisive role, so it is important if
the issuer is the state or a company.
•As we have seen, the obligation price is calculated as exposed below:
•The discount rates r
1, r
2, … r
Nare denominated spot rates at different maturities.
•These discount rates constitute the Temporary Structure of Interest Rates (relation between interest rates and
maturities).
•As we reviewed, these are the interest rates of alternative investments. Risk plays a decisive role, so it is important if
the issuer is the state or a company.
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•Constant coupons and amortization at par:
•Corporate debt: discount rates should be higher, because this debt type has a higher risk level.
•Constant coupons and amortization at par:
•Corporate debt: discount rates should be higher, because this debt type has a higher risk level.
18 ©Qaracter,2024todoslosderechosreservados
•Zero coupon bonds (STRIP) (Separated Trading of Interest and Principal):
Practical example: Evaluate today 1-1-2021 a strip with $10,000 of
nominal value and maturity on 1-1-2026. Bond is repayable at par (with a
premium of 20%), and the 5-year interest rate type is 4.5%.
•Zero coupon bonds (STRIP) (Separated Trading of Interest and Principal):
Practical example: Evaluate today 1-1-2021 a strip with $10,000 of
nominal value and maturity on 1-1-2026. Bond is repayable at par (with a
premium of 20%), and the 5-year interest rate type is 4.5%.
19 ©Qaracter,2024todoslosderechosreservados
Practical example: Calculate the price today (16-11-2021) of a Spanish
Treasury bond of 1000€ nominal value, yearly coupon 3.25% and
maturity 16-11-2026 if it is amortized at 110% and spot interest rates at 1,
2, 3, 4 and 5 years are 3%, 3.5%, 4%, 4.5% and 5.25%, respectively:
Practical example: Calculate the price today (16-11-2021) of a Spanish
Treasury bond of 1000€ nominal value, yearly coupon 3.25% and
maturity 16-11-2026 if it is amortized at 110% and spot interest rates at 1,
2, 3, 4 and 5 years are 3%, 3.5%, 4%, 4.5% and 5.25%, respectively:
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•Bonds price is exposed as a percentage of nominal value and net of accrued interest, what is known as ex-coupon or
clean price, in other words, the bond price and the value of the accrued coupon are shown separately.
•If the bond is sold between two coupon payments, a certain amount of accrued interest has been accumulated, so
the price increases and then falls when coupon is distributed.
•However, the bond price also changes when discount rates change due to changes in interest rates or changes in
credit quality. This is what traders in markets are interested in, so they only need clean prices.
Accrued Coupon
•Bonds price is exposed as a percentage of nominal value and net of accrued interest, what is known as ex-coupon or
clean price, in other words, the bond price and the value of the accrued coupon are shown separately.
•If the bond is sold between two coupon payments, a certain amount of accrued interest has been accumulated, so
the price increases and then falls when coupon is distributed.
•However, the bond price also changes when discount rates change due to changes in interest rates or changes in
credit quality. This is what traders in markets are interested in, so they only need clean prices.
Accrued Coupon
21 ©Qaracter,2024todoslosderechosreservados
•Dirty price = Clean price + Accrued coupon
•Accrued coupon is calculated by multiplying the value of the next coupon x number of days that have elapsed in the
coupon period, divided by the total number of days in the coupon period.
Practical example: Calculate the accrued coupon on 1 October for a bond
with Nominal=1000€ that pays 7% annual coupon every 1 December.
•Dirty price = Clean price + Accrued coupon
•Accrued coupon is calculated by multiplying the value of the next coupon x number of days that have elapsed in the
coupon period, divided by the total number of days in the coupon period.
Practical example: Calculate the accrued coupon on 1 October for a bond
with Nominal=1000€ that pays 7% annual coupon every 1 December.
22 ©Qaracter,2024todoslosderechosreservados
•Let's be investors for a moment... where does the return of the obligations come from?
✓Nominal value purchased at a discount
✓Interest Regular collection (coupons)
•Example: Return on zero coupon bond
•VN=1000 €, term 6 months, emission price 977 €.
•Half-yearly yield 2.354%.
•Effective annual yield 4.76
•Let's be investors for a moment... where does the return of the obligations come from?
✓Nominal value purchased at a discount
✓Interest Regular collection (coupons)
•Example: Return on zero coupon bond
•VN=1000 €, term 6 months, emission price 977 €.
•Half-yearly yield 2.354%.
•Effective annual yield 4.76
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•Perpetual income: Perpetual income is any income that consists in an infinite term succession.
•This income type has not a final value but it is possible to calculate the present value with a positive rate, since the
contribution of distant terms in time tends to zero.
•There are two types of perpetual incomes depending on the maturity term, which can be distinguished because the
formula that has to be used for their calculation will differ:
•Prepayable (or advanced): terms are at the beginning of each period.
•Postpayable(or past due): terms are at the end of each period.
•Perpetual income: Perpetual income is any income that consists in an infinite term succession.
•This income type has not a final value but it is possible to calculate the present value with a positive rate, since the
contribution of distant terms in time tends to zero.
•There are two types of perpetual incomes depending on the maturity term, which can be distinguished because the
formula that has to be used for their calculation will differ:
•Prepayable (or advanced): terms are at the beginning of each period.
•Postpayable(or past due): terms are at the end of each period.
24 ©Qaracter,2024todoslosderechosreservados
•Prepayable Perpetual Income:
✓What would be the actual value of a pre-payable perpetual income of €800 per month, with 0.75% discount
rate per month?
Practical examples:
✓Result: 107,466.67 €.
•PostpayablePerpetual Income:
✓What would be the actual value of a postpayableperpetual income of €500 per year, with 10% discount rate
per year?
✓Result: 5,000 €.
•Prepayable Perpetual Income:
✓What would be the actual value of a pre-payable perpetual income of €800 per month, with 0.75% discount
rate per month?
Practical examples:
✓Result: 107,466.67 €.
•PostpayablePerpetual Income:
✓What would be the actual value of a postpayableperpetual income of €500 per year, with 10% discount rate
per year?
✓Result: 5,000 €.
Index
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•Short-term financial assets are securitiesissued by the state, regional governments, corporations and financial
institutions with the purpose of short-term financing (assets with a maturity of no more than one year or, in some
cases, up to 18 months).
•All these assets have the same financial approach, simple financial transactions in which:
✓The provision is the capital initially provided to the issuer and called CASH.
✓The compensation is the capital returned by the issuer and is usually referred as NOMINAL.
•Short-term financial assets are securitiesissued by the state, regional governments, corporations and financial
institutions with the purpose of short-term financing (assets with a maturity of no more than one year or, in some
cases, up to 18 months).
•All these assets have the same financial approach, simple financial transactions in which:
✓The provision is the capital initially provided to the issuer and called CASH.
✓The compensation is the capital returned by the issuer and is usually referred as NOMINAL.
•Depending on the type of issuer, short-term financial assets are classified as follows:
•TheMarketsin which short-term financial assets are issued are as follows:
27 ©Qaracter,2024todoslosderechosreservados
Issuers Assets
Public Treasury Treasury bills
Non-financial corporations Commercial paper
Banks Interbank deposits
Assets Markets
Treasury bills Short-term public debt
Commercial paper Corporate assets
Interbank Deposits Assets of banking financial intermediaries
•TheMarketsin which short-term financial assets are issued are as follows:
27 ©Qaracter,2024todoslosderechosreservados
Issuers Assets
Public Treasury Treasury bills
Non-financial corporations Commercial paper
Banks Interbank deposits
Assets Markets
Treasury bills Short-term public debt
Commercial paper Corporate assets
Interbank Deposits Assets of banking financial intermediaries
28 ©Qaracter,2024todoslosderechosreservados
•Short-term fixed-income securities have been issued by the Public Treasury since 1987 and represented exclusively
by account entries.
•Treasury bills are issued by auction, conducted by the Spanish Bank every two weeks. The minimum amount of each
request (VN) is 1000 euros and requests for higher amounts must be multiples of 1000 euros.
•Public Treasury currently issues Treasury bills with maturities of 6, 12 and 18 months.
•Treasury bills are securities issued at discount, so their acquisition price is lower than the amount that investor will
receive on amortization. The difference between the amortization value of the bill (1000 euros) and the purchase
price will be the interest or yield generated by the Treasury bill.
Treasury bills
•Short-term fixed-income securities have been issued by the Public Treasury since 1987 and represented exclusively
by account entries.
•Treasury bills are issued by auction, conducted by the Spanish Bank every two weeks. The minimum amount of each
request (VN) is 1000 euros and requests for higher amounts must be multiples of 1000 euros.
•Public Treasury currently issues Treasury bills with maturities of 6, 12 and 18 months.
•Treasury bills are securities issued at discount, so their acquisition price is lower than the amount that investor will
receive on amortization. The difference between the amortization value of the bill (1000 euros) and the purchase
price will be the interest or yield generated by the Treasury bill.
Treasury bills
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•To calculate the Treasury bill price, the maturity of the operation must be taken in consideration, as the
capitalization law to be used is different, distinguishing two cases:
✓Simple capitalization, if the maturity is less than 376 days.
✓Compound capitalization, if the maturity is longer than 376 days.
•These securities are fully liquid and guaranteed. The investor can either wait for the amortization date or sell them in
the secondary market at any time prior to maturity.
•In the second case, the yield will be determined by the market price at the time of sale, so the investor does not
know at the time of purchase what the final profit will be.
•To calculate the Treasury bill price, the maturity of the operation must be taken in consideration, as the
capitalization law to be used is different, distinguishing two cases:
✓Simple capitalization, if the maturity is less than 376 days.
✓Compound capitalization, if the maturity is longer than 376 days.
•These securities are fully liquid and guaranteed. The investor can either wait for the amortization date or sell them in
the secondary market at any time prior to maturity.
•In the second case, the yield will be determined by the market price at the time of sale, so the investor does not
know at the time of purchase what the final profit will be.
30 ©Qaracter,2024todoslosderechosreservados
Practical example: Imagine you buy a 12-month Treasury bill at the last
Treasury auction, where the price was €958.5 and you receive €1000 at
maturity. What is the yield on that security? ()
%..r
;r.
340430
100015958
=
=+ %65.80865.0
;1000
360
180
15.958
=
=
+
r
r
•What if the bill was for 6-month?
•The Treasury General Directorate uses “Base 360”.
Practical example: Imagine you buy a 12-month Treasury bill at the last
Treasury auction, where the price was €958.5 and you receive €1000 at
maturity. What is the yield on that security? ()
%..r
;r.
340430
100015958
=
=+ %65.80865.0
;1000
360
180
15.958
=
=
+
r
r
•What if the bill was for 6-month?
•The Treasury General Directorate uses “Base 360”.
31 ©Qaracter,2024todoslosderechosreservados
•Treasury bills are placed in the primary market through auctions.
•Trading takes place on the book-entry market. Physical securities no longer exist since 1987.
•Book-entry trading are a securities representation in which these ones are identified through entry in special
accounting registers, usually computerized.
•Facilitates the holding and transfer of public debt securities on secondary markets, facilitating financing of the State
and introducing elements that contribute to increase the efficiency of the financial market, improving management
and sfacilitating the trading of financial assets issued by the State.
•Treasury bills are placed in the primary market through auctions.
•Trading takes place on the book-entry market. Physical securities no longer exist since 1987.
•Book-entry trading are a securities representation in which these ones are identified through entry in special
accounting registers, usually computerized.
•Facilitates the holding and transfer of public debt securities on secondary markets, facilitating financing of the State
and introducing elements that contribute to increase the efficiency of the financial market, improving management
and sfacilitating the trading of financial assets issued by the State.
32 ©Qaracter,2024todoslosderechosreservados
•Normally (regular auctions) auctions take place:
✓12 and 18-month bills: every two weeks.
✓6-month bills: every 4 weeks.
✓Bonds and State Obigations: once a month, except for 30-year obligations which are auctioned every two
months.
•Outside this established periodicity special auctions may be scheduled.
•Two request types (bids) could be made at auctions:
✓Competitive bids: participant has to indicate nominal amount that want to purchase and at what price wants
to purchase it, expressed as percentage of nominal value.
✓Non-competitive bids: Is only necessary to indicate the nominal amount to be purchased. The average price
to be paid for the securities will be the weighted average price resulting from the auction. Non-competitive
bids are the most suitable for a small investor, in this way ensure that the bid is accepted and will receive
interest with the average auction price.
Treasury bill auctions
•Normally (regular auctions) auctions take place:
✓12 and 18-month bills: every two weeks.
✓6-month bills: every 4 weeks.
✓Bonds and State Obigations: once a month, except for 30-year obligations which are auctioned every two
months.
•Outside this established periodicity special auctions may be scheduled.
•Two request types (bids) could be made at auctions:
✓Competitive bids: participant has to indicate nominal amount that want to purchase and at what price wants
to purchase it, expressed as percentage of nominal value.
✓Non-competitive bids: Is only necessary to indicate the nominal amount to be purchased. The average price
to be paid for the securities will be the weighted average price resulting from the auction. Non-competitive
bids are the most suitable for a small investor, in this way ensure that the bid is accepted and will receive
interest with the average auction price.
Treasury bill auctions
33 ©Qaracter,2024todoslosderechosreservados
•Once the requests have been received and submitting bids deadline for each auction has closed, will be determined,
after ranking the competitive bids from highest to lowest price offered:
✓The nominal volume or cash that wants to issue in the auction and the minimum price accepted.
✓All bids whose offered prices equal or higher than the minimum price accepted shall be automatically awarded
and the others rejected.
✓With the competitive bids accepted, will proceed to determine weighted average price (PMP) (a weighted
arithmetic average of prices and nominals of the accepted competitive bids) expressed as percentage of
nominal value.
•Once the requests have been received and submitting bids deadline for each auction has closed, will be determined,
after ranking the competitive bids from highest to lowest price offered:
✓The nominal volume or cash that wants to issue in the auction and the minimum price accepted.
✓All bids whose offered prices equal or higher than the minimum price accepted shall be automatically awarded
and the others rejected.
✓With the competitive bids accepted, will proceed to determine weighted average price (PMP) (a weighted
arithmetic average of prices and nominals of the accepted competitive bids) expressed as percentage of
nominal value.
34 ©Qaracter,2024todoslosderechosreservados
•The price to be paid for securities will be:
✓For all requests whose offered price is higher or equal to the PMP, the award price will be average price.
✓For all bids whose bid price is less than the PMP and higher or equal to the minimum accepted price, the
award price will be the bid price.
✓Non-competitive bids will be accepted in their totality as long as competitive bid has been accepted. The
award price for these securities will be the PMP.
•The price to be paid for securities will be:
✓For all requests whose offered price is higher or equal to the PMP, the award price will be average price.
✓For all bids whose bid price is less than the PMP and higher or equal to the minimum accepted price, the
award price will be the bid price.
✓Non-competitive bids will be accepted in their totality as long as competitive bid has been accepted. The
award price for these securities will be the PMP.
35 ©Qaracter,2024todoslosderechosreservados
Practical example: The Treasury issues a bill for 12-months for 850
million euros as nominal amount and with mature of 364 days later.
•In the non-competitive stager the requests increase to 150 million.
•Competitive bids received were:
OfferedPrice
Requested
Nominal
(millioneuros)
95,250 % 125
95,235 % 200
95,220 % 170
95,210 % 205
95,205 % 250
95,200 % 300
Practical example: The Treasury issues a bill for 12-months for 850
million euros as nominal amount and with mature of 364 days later.
•In the non-competitive stager the requests increase to 150 million.
•Competitive bids received were:
OfferedPrice
Requested
Nominal
(millioneuros)
95,250 % 125
95,235 % 200
95,220 % 170
95,210 % 205
95,205 % 250
95,200 % 300
36 ©Qaracter,2024todoslosderechosreservados
•Total nominal amount to be allotted is €850 million.
•Non-competitive offers are allotted in full.
•The remaining €700 million (850-150 million) is obtained from accepted competitive offers, in which way the
Treasury will select the highest offered priced and rejecting the rest.
•The minimum accepted price was 95.210%, rejecting offers lower than that price.
•Then with the accepted competitive offers the weighted average price (PMP) is calculated:
OfferedPrice
Requested
Nominal
(million
euros)
Allocated
Nominal
Accumulat
ed
95.250 % 125 125
95.235 % 200 325
95.220 % 170 495
95.210 % 205 700%227.95
700
205*21.95170*22.95200*235.95125*25.95
=
+++
=PMP
PMP
•Total nominal amount to be allotted is €850 million.
•Non-competitive offers are allotted in full.
•The remaining €700 million (850-150 million) is obtained from accepted competitive offers, in which way the
Treasury will select the highest offered priced and rejecting the rest.
•The minimum accepted price was 95.210%, rejecting offers lower than that price.
•Then with the accepted competitive offers the weighted average price (PMP) is calculated:
OfferedPrice
Requested
Nominal
(million
euros)
Allocated
Nominal
Accumulat
ed
95.250 % 125 125
95.235 % 200 325
95.220 % 170 495
95.210 % 205 700%227.95
700
205*21.95170*22.95200*235.95125*25.95
=
+++
=PMP
PMP
37 ©Qaracter,2024todoslosderechosreservados
•Prices at which bills are finally allocated are:
•Obtained cash is 809.32 million for a nominal value of 850, resulting in an average auction price of:
OfferedPrice
Allocated
Price
Requested
Nominal
(million
euros)
No compet 95.227 150
95.250% 95.227 125
95.235 95.227 200
95.220 95.22 170
95.210 95.21 205
475328099521020595220170952270475 ..*.*.* =++ 952140
32809850
.
.*
=
=
p
p
•Prices at which bills are finally allocated are:
•Obtained cash is 809.32 million for a nominal value of 850, resulting in an average auction price of:
OfferedPrice
Allocated
Price
Requested
Nominal
(million
euros)
No compet 95.227 150
95.250% 95.227 125
95.235 95.227 200
95.220 95.22 170
95.210 95.21 205
475328099521020595220170952270475 ..*.*.* =++ 952140
32809850
.
.*
=
=
p
p
38 ©Qaracter,2024todoslosderechosreservados
•The effective interest rates type (yields) correspond to the different prices are different depending on the allocated
price:
•Calculations of these interest rates have been:
OfferedPrice Profitability
95.227 4.957
95.227 4.957
95.22 4.964
95.21 4.975%957.4;100
360
364
1227.95 ==
+ ii
•The effective interest rates type (yields) correspond to the different prices are different depending on the allocated
price:
•Calculations of these interest rates have been:
OfferedPrice Profitability
95.227 4.957
95.227 4.957
95.22 4.964
95.21 4.975%957.4;100
360
364
1227.95 ==
+ ii
39 ©Qaracter,2024todoslosderechosreservados
•The non-financial companies act also as issuers in the monetary markets, even the issuances volume is smaller
compared with the amounts of the state.
•The commercial paper is an unconditional payment promise issued by big non-financial corporations. As financial
instrument it has existed for many years but its negotiation as an asset in organized markets in Spain dates from
1982.
•Commercial papers are negotiable at discount with a functionality very similar to Treasury bills.
•Issuers are usually large non-financial companies (example: Renfe, Telefónica), but the higher risk compared to
Treasury bills will provide a higher return.
•Secondary market where commercial paper is traded is AIAF (Financial Intermediaries Association). AIAF exposes in
its circular 2/94, for the calculation of the TIR, that simple capitalization is used if maturity<376 and compound
capitalization if maturity>376 days. And all this with a 365 base.
Commercial Papers
•The non-financial companies act also as issuers in the monetary markets, even the issuances volume is smaller
compared with the amounts of the state.
•The commercial paper is an unconditional payment promise issued by big non-financial corporations. As financial
instrument it has existed for many years but its negotiation as an asset in organized markets in Spain dates from
1982.
•Commercial papers are negotiable at discount with a functionality very similar to Treasury bills.
•Issuers are usually large non-financial companies (example: Renfe, Telefónica), but the higher risk compared to
Treasury bills will provide a higher return.
•Secondary market where commercial paper is traded is AIAF (Financial Intermediaries Association). AIAF exposes in
its circular 2/94, for the calculation of the TIR, that simple capitalization is used if maturity<376 and compound
capitalization if maturity>376 days. And all this with a 365 base.
Commercial Papers
40 ©Qaracter,2024todoslosderechosreservados
Practical example: An investor acquires a commercial paper from
company XXX for 12 months and a nominal value of 1000 euros, paying a
price of 980.02 euros. If the amortization is made in 364 days, calculate
its rentability.
•As the maturity is less than 376 days, simple capitalization is used.%.)(. 04421000364
365
102980 ==
+ r
r
Practical example: An investor acquires a commercial paper from
company XXX for 12 months and a nominal value of 1000 euros, paying a
price of 980.02 euros. If the amortization is made in 364 days, calculate
its rentability.
•As the maturity is less than 376 days, simple capitalization is used.%.)(. 04421000364
365
102980 ==
+ r
r
41 ©Qaracter,2024todoslosderechosreservados
Practical example: An investor bought a commercial paper with a
nominal value of €3000 and maturity of 270 days with a discount rate of
2.2% (commercial discount and base 360).
•Calculate the price that investor pays for the commercial paper.
•Calculate the return on the investment in simple capitalization and base 365.
•If investor wants to sell this commercial paper for €2,960, what will be the sale date if the investor wants to obtain a
return of at least 2.25%?
Practical example: An investor bought a commercial paper with a
nominal value of €3000 and maturity of 270 days with a discount rate of
2.2% (commercial discount and base 360).
•Calculate the price that investor pays for the commercial paper.
•Calculate the return on the investment in simple capitalization and base 365.
•If investor wants to sell this commercial paper for €2,960, what will be the sale date if the investor wants to obtain a
return of at least 2.25%?
42 ©Qaracter,2024todoslosderechosreservados
•Firstly, we have to calculate the cash paid for the commercial paper. If the discount is 2.2%.
•Regarding the calculation of the investment return, we can say that we invest 2950.5 € today in order to receive
3000 € in 270 days. Equalizing both capitals and applying the simple capitalization law we have that:
•If commercial paper wants to be sold for €2,960 at date t, in order to have a return equal to 2.25%, the equation will
be:€5.2950)270(
360
022.0
13000 =
−=E días 522960
365
02250
152950 ==
+ tt)(
.
.
•Firstly, we have to calculate the cash paid for the commercial paper. If the discount is 2.2%.
•Regarding the calculation of the investment return, we can say that we invest 2950.5 € today in order to receive
3000 € in 270 days. Equalizing both capitals and applying the simple capitalization law we have that:
•If commercial paper wants to be sold for €2,960 at date t, in order to have a return equal to 2.25%, the equation will
be:€5.2950)270(
360
022.0
13000 =
−=E días 522960
365
02250
152950 ==
+ tt)(
.
.
Index
43©Qaracter,2024todoslosderechosreservados
43©Qaracter,2024todoslosderechosreservados
44 ©Qaracter,2024todoslosderechosreservados
•When price is calculated, we discount each payment at a different spot rate.
•Now, we need to find a single discount rate that applied to all flows, gives us exactly the price: this is the Yield to
Maturity (YTM)or return to maturity.
•To calculate the TIR we need the price, the maturity and the payments.
•The TIR measures the return that will be earned on a bond if it is purchased now and kept to maturity.
Yield to maturity
•When price is calculated, we discount each payment at a different spot rate.
•Now, we need to find a single discount rate that applied to all flows, gives us exactly the price: this is the Yield to
Maturity (YTM)or return to maturity.
•To calculate the TIR we need the price, the maturity and the payments.
•The TIR measures the return that will be earned on a bond if it is purchased now and kept to maturity.
Yield to maturity
45 ©Qaracter,2024todoslosderechosreservados
•So, instead of discounting each payment at a different spot rate, we would have a single discount rate that gives the
same actual value: YTM or Yield to Maturity.
•YTM can be interpreted as the compound return rate that would be earned over the bond life under the assumption
that coupons are reinvested at that same rate and the bond is kept till the maturity.
•YTM is a complete and complex measure of the security return and is associated to each fixed income asset, being
affected by:
✓Security issue: At par, below par or above par.
✓Security amortization: At par, below par or above par.
✓Coupons: Coupon rate, monthly, half-yearly or annual frequency.
•So, instead of discounting each payment at a different spot rate, we would have a single discount rate that gives the
same actual value: YTM or Yield to Maturity.
•YTM can be interpreted as the compound return rate that would be earned over the bond life under the assumption
that coupons are reinvested at that same rate and the bond is kept till the maturity.
•YTM is a complete and complex measure of the security return and is associated to each fixed income asset, being
affected by:
✓Security issue: At par, below par or above par.
✓Security amortization: At par, below par or above par.
✓Coupons: Coupon rate, monthly, half-yearly or annual frequency.
46 ©Qaracter,2024todoslosderechosreservados
•We have to find a discount rate or average interest rate that equals the theoretical price to the actual value of its
cash flows.
Practical example: Calculate the maturity return of 2-year bond with a
nominal value of €1000 and coupon of 4%, which has a market price of
€963.69. The bond is amortized at par.
•We have to find a discount rate or average interest rate that equals the theoretical price to the actual value of its
cash flows.
Practical example: Calculate the maturity return of 2-year bond with a
nominal value of €1000 and coupon of 4%, which has a market price of
€963.69. The bond is amortized at par.
47 ©Qaracter,2024todoslosderechosreservados
•The Excel YTM function calculates the Yield to Maturity for periodic cash flows (in the same time frame: monthly,
half-yearly, yearly).
Practical example: Suppose currently there is an Interest Rate Term Structure
increasing with a one-year interest rate of 5% and two-year interest rate of 6%.
Calculate the yield to maturity of a government bond of €1000 nominal, paying
a coupon of 4%, with a maturity of two years and amortizing at par.
•YTM is 5.98%
•The Excel YTM function calculates the Yield to Maturity for periodic cash flows (in the same time frame: monthly,
half-yearly, yearly).
Practical example: Suppose currently there is an Interest Rate Term Structure
increasing with a one-year interest rate of 5% and two-year interest rate of 6%.
Calculate the yield to maturity of a government bond of €1000 nominal, paying
a coupon of 4%, with a maturity of two years and amortizing at par.
•YTM is 5.98%
48 ©Qaracter,2024todoslosderechosreservados
•Note that the YTM does not have to match with the discount rate of any particular flow. YTM is an average summary
of all of them.
•Is the YTM the true bond return? Not exactly.
✓YTM assumes that, as coupons are received, these ones are reinvested at an equal interest rate to the YTM for
the remaining life of the bond.
✓However, there is no guarantee that coupons can be reinvested at the YTM if the interest rates at different
maturities change.
✓So if interest rates are increasing, the final return eventually will be higher than the YTM suggests.
✓If rates are decreasing, the final return eventually will be lower than the YTM.
•Note that the YTM does not have to match with the discount rate of any particular flow. YTM is an average summary
of all of them.
•Is the YTM the true bond return? Not exactly.
✓YTM assumes that, as coupons are received, these ones are reinvested at an equal interest rate to the YTM for
the remaining life of the bond.
✓However, there is no guarantee that coupons can be reinvested at the YTM if the interest rates at different
maturities change.
✓So if interest rates are increasing, the final return eventually will be higher than the YTM suggests.
✓If rates are decreasing, the final return eventually will be lower than the YTM.
49 ©Qaracter,2024todoslosderechosreservados
•YTM and the investment actual return could be different.
•In zero coupon bonds this reinvestment risk does not exist and the YTM matches with the actual return earned.
•In order to valuate bonds, YTM of bonds with coupons are not going to be used, neither of corporate fixed income,
but the spot interest rates of zero-coupon bonds issued by the highest credit quality institutions.
•YTM and the investment actual return could be different.
•In zero coupon bonds this reinvestment risk does not exist and the YTM matches with the actual return earned.
•In order to valuate bonds, YTM of bonds with coupons are not going to be used, neither of corporate fixed income,
but the spot interest rates of zero-coupon bonds issued by the highest credit quality institutions.
Index
50©Qaracter,2024todoslosderechosreservados
50©Qaracter,2024todoslosderechosreservados
51 ©Qaracter,2024todoslosderechosreservados
•Although there is a common idea that fixed income assets are risk-free, we will show that this idea is wrong. Fixed
income assets are affected by different risk types:
✓Default Risk
✓Interest Rate Risk
Default Risk
•Refers to the possibility that issuer will not comply with its future payment obligations.
•In other words, that the issuer will not pay the corresponding coupon or will not return the principal at maturity.
•Logically, this default risk is higher when the credit quality of the issuer of the fixed income security is worse. For this
reason, investors will demand a higher return on securities issued by entities with worse credit quality.
•Although there is a common idea that fixed income assets are risk-free, we will show that this idea is wrong. Fixed
income assets are affected by different risk types:
✓Default Risk
✓Interest Rate Risk
Default Risk
•Refers to the possibility that issuer will not comply with its future payment obligations.
•In other words, that the issuer will not pay the corresponding coupon or will not return the principal at maturity.
•Logically, this default risk is higher when the credit quality of the issuer of the fixed income security is worse. For this
reason, investors will demand a higher return on securities issued by entities with worse credit quality.
52 ©Qaracter,2024todoslosderechosreservados
•The negotiable bonds quality can be established taking into account obligations rating provided by credit rating
agencies (Moody's, Standard and Poor's, etc.).
•Moody's rates the highest quality obligations as Aaa.
•Obligations rated Baa or higher are known as qualified investment. Many banks are not allowed to invest unless the
investment is rated as qualified.
•Obligations below Ba are known as junk bonds.
•There is a close relationship between the obligation rating and its performance.
•The negotiable bonds quality can be established taking into account obligations rating provided by credit rating
agencies (Moody's, Standard and Poor's, etc.).
•Moody's rates the highest quality obligations as Aaa.
•Obligations rated Baa or higher are known as qualified investment. Many banks are not allowed to invest unless the
investment is rated as qualified.
•Obligations below Ba are known as junk bonds.
•There is a close relationship between the obligation rating and its performance.
53 ©Qaracter,2024todoslosderechosreservados
Aaa
Bonds that have the highest quality and lowest risk. Known as glit edged. The interest
payments are secured by an extensive and stable margin, as the principal payment.
AAA
Aa
High quality bonds. Together with Aaabonds are known as high-grade bonds. The security
level of these bonds is not as high as Aaabonds.
AA
A
Bonds of a medium-high level. The factors that guarantee the principal and interest are
adequate, but there are elements that may add some risk.
A
Baa
Bonds known as medium-grade. Interest and principal payments seem adequate at
present but there should be some elements that suggest long-term mistrust. They have
speculative characteristics.
BBB
Ba
Interest and principal payment protection is very moderate. These ones have speculative
elements as their future cannot be considered certain.
BB
B
Bonds that lack desirable investment characteristics. Interest and principal payment
guarantee, as well as fulfillment of other terms of the contract are small in the long term.
B
Caa Bonds with poor credit rating and high risk. Issuers could default. CCC
Ca Highly speculative bonds. Issuers are usually in default. CC
C Bonds of insolvent issuers with poor prospects of fulfilling their obligations. C
Moody’s
Standard and Poor’s
Aaa
Bonds that have the highest quality and lowest risk. Known as glit edged. The interest
payments are secured by an extensive and stable margin, as the principal payment.
AAA
Aa
High quality bonds. Together with Aaabonds are known as high-grade bonds. The security
level of these bonds is not as high as Aaabonds.
AA
A
Bonds of a medium-high level. The factors that guarantee the principal and interest are
adequate, but there are elements that may add some risk.
A
Baa
Bonds known as medium-grade. Interest and principal payments seem adequate at
present but there should be some elements that suggest long-term mistrust. They have
speculative characteristics.
BBB
Ba
Interest and principal payment protection is very moderate. These ones have speculative
elements as their future cannot be considered certain.
BB
B
Bonds that lack desirable investment characteristics. Interest and principal payment
guarantee, as well as fulfillment of other terms of the contract are small in the long term.
B
Caa Bonds with poor credit rating and high risk. Issuers could default. CCC
Ca Highly speculative bonds. Issuers are usually in default. CC
C Bonds of insolvent issuers with poor prospects of fulfilling their obligations. C
Moody’s
Standard and Poor’s
54 ©Qaracter,2024todoslosderechosreservados
•Interest rate risk refers to the possibility that the valueof a fixed income securities portfolio (or a single fixed
income security) would decrease as a result of a rise of the market interest rates.
•Bond price and interest rate relationship:
✓This is an inverse relationship.
✓The price of a bond is a decreasing function of the interest rate applied.
Interest rate risk
•Interest rate risk refers to the possibility that the valueof a fixed income securities portfolio (or a single fixed
income security) would decrease as a result of a rise of the market interest rates.
•Bond price and interest rate relationship:
✓This is an inverse relationship.
✓The price of a bond is a decreasing function of the interest rate applied.
Interest rate risk
55 ©Qaracter,2024todoslosderechosreservados
•These price variations in a bond portfolio are known as bond volatility. And it must be analyzed of what factors it
depends.
•We should not forget that interest rate risk only affects or benefits when the bond owner wants to get rid of it
before maturity.
•What does the sensitivity of a bond’s price depend on (taking into account the changes in the interest type levels)?
•Until the 1960s
✓It was thought that the sensitivity was a function of bond life.
✓The further away from maturity, the more sensitive.
✓However, it was identified that bonds with the same maturity could have different sensitivity to changes in
interest rates, for example, if the coupons were different.
•These price variations in a bond portfolio are known as bond volatility. And it must be analyzed of what factors it
depends.
•We should not forget that interest rate risk only affects or benefits when the bond owner wants to get rid of it
before maturity.
•What does the sensitivity of a bond’s price depend on (taking into account the changes in the interest type levels)?
•Until the 1960s
✓It was thought that the sensitivity was a function of bond life.
✓The further away from maturity, the more sensitive.
✓However, it was identified that bonds with the same maturity could have different sensitivity to changes in
interest rates, for example, if the coupons were different.
56 ©Qaracter,2024todoslosderechosreservados
•It is known that bond’s price sensitivity to changes in interest rates depends on the bond's DURATION:
•Duration is the weighted average life of a security (expressed in years).
•It is the weighted average of the maturities of the cash flows generated by that security, where the weights are
the proportion that each CF represents in the total value of the security.
Since the 1970s
•"P" is the price of the security.
•"Cs" is each of the future
payments.
Duration of
MACAULAY
•It is known that bond’s price sensitivity to changes in interest rates depends on the bond's DURATION:
•Duration is the weighted average life of a security (expressed in years).
•It is the weighted average of the maturities of the cash flows generated by that security, where the weights are
the proportion that each CF represents in the total value of the security.
Since the 1970s
•"P" is the price of the security.
•"Cs" is each of the future
payments.
Duration of
MACAULAY
57 ©Qaracter,2024todoslosderechosreservados
•Constant coupon bond
•Zero coupon bond
✓Its duration matches with its maturity
•Factors on which the security duration depends:
✓Time to maturity (T): If the time to maturity increases, the duration increases.
✓Coupon amount (C): If the amount of paid coupons increases, the duration decreases.
✓Level of interest rates (y): If the level of interest rates or YTM increases, the duration decreases.
•Constant coupon bond
•Zero coupon bond
✓Its duration matches with its maturity
•Factors on which the security duration depends:
✓Time to maturity (T): If the time to maturity increases, the duration increases.
✓Coupon amount (C): If the amount of paid coupons increases, the duration decreases.
✓Level of interest rates (y): If the level of interest rates or YTM increases, the duration decreases.
58 ©Qaracter,2024todoslosderechosreservados
•It is the slope of the curve relating the bond price and the interest rate.
•It is equal to the Modified Duration (DM).
Volatility
•It is the slope of the curve relating the bond price and the interest rate.
•It is equal to the Modified Duration (DM).
Volatility
59 ©Qaracter,2024todoslosderechosreservados
•The Macaulay duration will be:
Practical example: Calculation of the duration of a bond with 1000 € nominal which
will be amortized after 3 years, giving 50 € coupon one year after issue, another 50 €
coupon two years after issue and another 50 € coupon three years after issue. At the
same time (third year) it will be amortized, taking a discount rate of 6%.
•The Macaulay duration will be:
Practical example: Calculation of the duration of a bond with 1000 € nominal which
will be amortized after 3 years, giving 50 € coupon one year after issue, another 50 €
coupon two years after issue and another 50 € coupon three years after issue. At the
same time (third year) it will be amortized, taking a discount rate of 6%.
60 ©Qaracter,2024todoslosderechosreservados
•Credit derivatives are bilateral agreements that allow the present credit risk to be isolated into an instrument
and transferred.
•Conventional derivatives depend on a market price. Credit derivatives depend on the event of default, which has
to be very well defined in the contract terms.
•Four reasons that justify the use of credit derivatives:
✓The reference entity does not need to be informed about a credit derivative written on its debt.
✓Credit derivatives allow short positions to be taken (increasing its value when the borrower's credit quality
deteriorates) in instruments with credit risk.
✓Allow arbitrage trading using different markets, assets, maturities, ratings, time zones, currencies, etc.
✓Banks can use credit derivatives in order to reduce capital buffer required by Basilea for credit risk.
•Credit derivatives are bilateral agreements that allow the present credit risk to be isolated into an instrument
and transferred.
•Conventional derivatives depend on a market price. Credit derivatives depend on the event of default, which has
to be very well defined in the contract terms.
•Four reasons that justify the use of credit derivatives:
✓The reference entity does not need to be informed about a credit derivative written on its debt.
✓Credit derivatives allow short positions to be taken (increasing its value when the borrower's credit quality
deteriorates) in instruments with credit risk.
✓Allow arbitrage trading using different markets, assets, maturities, ratings, time zones, currencies, etc.
✓Banks can use credit derivatives in order to reduce capital buffer required by Basilea for credit risk.
61 ©Qaracter,2024todoslosderechosreservados
•The bond holder has the risk that 100% of bond's
value will be reduced by a given percentage, which
is defined as (1-R), where R is equal to the
Recovery Ratio.
•The protection buyer pays an annual premium
(CDS spread) to ensure that will receive 100% of
its bond in case the firm fails.
•In the event of a default, the protection seller will
pay the face value of bond multiplied by 1-R (LGD,
Loss Given Default) or you can physically keep the
bond in exchange for its face value.
Credit Default Swaps (CDS)
Protection
buyer
Protection
buyer
Reference
debt
•The bond holder has the risk that 100% of bond's
value will be reduced by a given percentage, which
is defined as (1-R), where R is equal to the
Recovery Ratio.
•The protection buyer pays an annual premium
(CDS spread) to ensure that will receive 100% of
its bond in case the firm fails.
•In the event of a default, the protection seller will
pay the face value of bond multiplied by 1-R (LGD,
Loss Given Default) or you can physically keep the
bond in exchange for its face value.
Credit Default Swaps (CDS)
Protection
buyer
Protection
buyer
Reference
debt
62 ©Qaracter,2024todoslosderechosreservados
•The CDS premium reflects the annual amount we must pay to sell the CDS. A premium of 0.0050 (50 basis points)
means that if we want to insure against the credit risk of a bond with a face value of $10 million, we must pay
$50,000 per year.
CDS Spread (or premium):
Company
Average
Rating
CDS 1 year
CDS 3
years
CDS 5
years
BBVA AA 0.0075 0.0089 0.0110
Iberdrola A 0.0045 0.0069 0.0084
Gas NaturalBBB 0.0067 0.0100 0.0116
Repsol YPFBBB 0.0062 0.0092 0.0111
TelefónicaBBB 0.0041 0.0063 0.0081
•Some considerations that influence the premium:
✓The CDS premium is higher for longer maturities.
✓The CDS premium tends to be higher for
companies with poorer credit ratings.
✓The CDS premium tends to be higher for
companies with small estimated recovery rates.
Companies in non-traditional sectors, with many
intangible assets, tend to have lower recovery
rates and therefore, pay a higher CDS premium.
✓The CDS premium is usually higher for unsecured
debt than for secured debt.
✓The CDS premium tends to be higher for
recessionary periods, because there tend to be
higher default rates and lower recovery rates.
•The CDS premium reflects the annual amount we must pay to sell the CDS. A premium of 0.0050 (50 basis points)
means that if we want to insure against the credit risk of a bond with a face value of $10 million, we must pay
$50,000 per year.
CDS Spread (or premium):
Company
Average
Rating
CDS 1 year
CDS 3
years
CDS 5
years
BBVA AA 0.0075 0.0089 0.0110
Iberdrola A 0.0045 0.0069 0.0084
Gas NaturalBBB 0.0067 0.0100 0.0116
Repsol YPFBBB 0.0062 0.0092 0.0111
TelefónicaBBB 0.0041 0.0063 0.0081
•Some considerations that influence the premium:
✓The CDS premium is higher for longer maturities.
✓The CDS premium tends to be higher for
companies with poorer credit ratings.
✓The CDS premium tends to be higher for
companies with small estimated recovery rates.
Companies in non-traditional sectors, with many
intangible assets, tend to have lower recovery
rates and therefore, pay a higher CDS premium.
✓The CDS premium is usually higher for unsecured
debt than for secured debt.
✓The CDS premium tends to be higher for
recessionary periods, because there tend to be
higher default rates and lower recovery rates.
Index
63©Qaracter,2024todoslosderechosreservados
63©Qaracter,2024todoslosderechosreservados
64 ©Qaracter,2024todoslosderechosreservados
•They are framed as two purchase and sale transactions of opposite sign carried out at two different moments in
time, where the seller undertakes to repurchase the securities within a certain period of time and for a fixed
price fixed to the first buyer.
•It is a double transaction all agreed at an initial moment. The original seller becomes the buyer of the security at a
later time and the initial buyer becomes the seller.
•The sale price, repurchase price and term of the transaction are fixed.
•The main difference between a repo and a simultaneous operation is that a simultaneous operation transfers the
availability of the security and a repo does not.
•In the case of payment of coupons during the term of the repurchase agreement transaction, the purchaser of the
simultaneous operation agreement will have the right to collect the coupons. Not so in the repo, where the right to
collect the coupons will be of the seller of the security.
Transaction with Repurchase Agreement. REPOs.
•They are framed as two purchase and sale transactions of opposite sign carried out at two different moments in
time, where the seller undertakes to repurchase the securities within a certain period of time and for a fixed
price fixed to the first buyer.
•It is a double transaction all agreed at an initial moment. The original seller becomes the buyer of the security at a
later time and the initial buyer becomes the seller.
•The sale price, repurchase price and term of the transaction are fixed.
•The main difference between a repo and a simultaneous operation is that a simultaneous operation transfers the
availability of the security and a repo does not.
•In the case of payment of coupons during the term of the repurchase agreement transaction, the purchaser of the
simultaneous operation agreement will have the right to collect the coupons. Not so in the repo, where the right to
collect the coupons will be of the seller of the security.
Transaction with Repurchase Agreement. REPOs.
65 ©Qaracter,2024todoslosderechosreservados
•The operating process of a REPO is as follows:
✓An asset with nominal value "N" and maturity in "n" days is purchased at the origin of the transaction, ensuring
a return "i". This is the same as saying what amount is paid for the purchase (E1).
✓On the other hand, at the same time of the purchase, it is agreed that after “” days the seller will buy this
financial asset and the profitability applied is the same, which means that the buyer sells it in “” days for the
price E2. The operation profitability matches with the agreed interest rate.
✓The Bank of Spain establishes a 360-day base for public debt. In the case of repos over commercial paper,
365 days can be used, as the Financial Intermediaries Association (AIAF) does.
•The operating process of a REPO is as follows:
✓An asset with nominal value "N" and maturity in "n" days is purchased at the origin of the transaction, ensuring
a return "i". This is the same as saying what amount is paid for the purchase (E1).
✓On the other hand, at the same time of the purchase, it is agreed that after “” days the seller will buy this
financial asset and the profitability applied is the same, which means that the buyer sells it in “” days for the
price E2. The operation profitability matches with the agreed interest rate.
✓The Bank of Spain establishes a 360-day base for public debt. In the case of repos over commercial paper,
365 days can be used, as the Financial Intermediaries Association (AIAF) does.
66 ©Qaracter,2024todoslosderechosreservados
Practical example: An investor purchases an autonomic promissory note
through a repurchase agreement transaction. The characteristics of the
purchase are:
•Calculate
✓Price paid by investor on the first sale and purchase.
✓Price of the second sale and purchase after 90 days.
✓Return on investment.
•The price paid by the investor in the first sale and purchase is (E1).
✓364 days to maturity.
✓Nominal value 1000 €.
✓Corresponding yield 2.14%.
✓Investment duration 90 days.
Practical example: An investor purchases an autonomic promissory note
through a repurchase agreement transaction. The characteristics of the
purchase are:
•Calculate
✓Price paid by investor on the first sale and purchase.
✓Price of the second sale and purchase after 90 days.
✓Return on investment.
•The price paid by the investor in the first sale and purchase is (E1).
✓364 days to maturity.
✓Nominal value 1000 €.
✓Corresponding yield 2.14%.
✓Investment duration 90 days.
67 ©Qaracter,2024todoslosderechosreservados
•The price paid by investor in the second sale and purchase is (E2).
•The financial capitals 978.82 and 984.06 must be financially equivalent, then the following equation must be fulfilled:
•The price paid by investor in the second sale and purchase is (E2).
•The financial capitals 978.82 and 984.06 must be financially equivalent, then the following equation must be fulfilled:
Index
68©Qaracter,2024todoslosderechosreservados
68©Qaracter,2024todoslosderechosreservados
69 ©Qaracter,2024todoslosderechosreservados
•Securitizationis a process whereby an illiquid financial asset (such as a house) is transformed into a more liquid
fixed-income security, where the bank transfers the credit risk (inherent in its credit portfolio) to another
counterparty. The most transformed financial assets are mortgage loans, as they include a clause allowing such
transformation.
•To understand the concept of securitization, let us present the balance sheet of a bank:
•Assets:
✓This is made up of a small liquid part, which is the cash office or treasury, while the rest is very illiquid,
including the following assets: credit portfolio (long-term assets), collection rights (loans or credits), trade
discounts, etc.
✓The bank's assets represent the money it owes to citizens and companies and which we will pay back over
time.
•Liabilities:
✓This is made up of the money that citizens and companies lend to the bank through current or savings
accounts, time deposits, marketable securities (bonds, shares), promissory notes, etc.
✓All these items are very liquid, short term.
•Securitizationis a process whereby an illiquid financial asset (such as a house) is transformed into a more liquid
fixed-income security, where the bank transfers the credit risk (inherent in its credit portfolio) to another
counterparty. The most transformed financial assets are mortgage loans, as they include a clause allowing such
transformation.
•To understand the concept of securitization, let us present the balance sheet of a bank:
•Assets:
✓This is made up of a small liquid part, which is the cash office or treasury, while the rest is very illiquid,
including the following assets: credit portfolio (long-term assets), collection rights (loans or credits), trade
discounts, etc.
✓The bank's assets represent the money it owes to citizens and companies and which we will pay back over
time.
•Liabilities:
✓This is made up of the money that citizens and companies lend to the bank through current or savings
accounts, time deposits, marketable securities (bonds, shares), promissory notes, etc.
✓All these items are very liquid, short term.
70 ©Qaracter,2024todoslosderechosreservados
•Comparing Assets and Liabilities, we observe that long-term assets are financed with short-term liabilities. This
represents a mismatch, a temporary mismatch, known in banking jargon as mismatching.
•As explained above, from the bank's loan portfolio (on the asset side of the balance sheet) a set of assets will be
selected that have the characteristics to be transformed and that share a similar nature, for example, mortgage
loans. These securities are grouped together in a portfolio that is sold to a fund (Mortgage SecuritisationFund)
created especially for this operation and managed by the corresponding Securitization Fund Management Company.
In this way the Bank removes illiquid assets (with higher risk) from its balance sheet.
•The portfolio becomes the asset side of the balance sheet of the Mortgage Securitization Fund, which issues bonds
from this portfolio and offers them to investors. These bonds are known as Residential mortgage-backed
securities, which offer the holder interest.
•Comparing Assets and Liabilities, we observe that long-term assets are financed with short-term liabilities. This
represents a mismatch, a temporary mismatch, known in banking jargon as mismatching.
•As explained above, from the bank's loan portfolio (on the asset side of the balance sheet) a set of assets will be
selected that have the characteristics to be transformed and that share a similar nature, for example, mortgage
loans. These securities are grouped together in a portfolio that is sold to a fund (Mortgage SecuritisationFund)
created especially for this operation and managed by the corresponding Securitization Fund Management Company.
In this way the Bank removes illiquid assets (with higher risk) from its balance sheet.
•The portfolio becomes the asset side of the balance sheet of the Mortgage Securitization Fund, which issues bonds
from this portfolio and offers them to investors. These bonds are known as Residential mortgage-backed
securities, which offer the holder interest.
71 ©Qaracter,2024todoslosderechosreservados
•There are different types of bonds depending on the asset securitized:
✓Collateralized bond obligations (CBO): bonds.
✓Collateralized loan obligations (CLOs): loans.
✓Residential mortgage-backed securities (RMBS): residential mortgages.
✓Commercial mortgage-backed securities (CBMS): commercial mortgages.
✓Asset-backed securities (ABS): include different assets (example; credit cards).
•The money that investors pay to buy asset-backed securities goes to the treasury or cash of the bank that initiated
the securitisationprocess, thereby adding liquidity to the assets side of the bank's balance sheet.
•The bank receives money from the loans taken out by the families who took out the mortgage with that bank, who
make their payments (capital amortisationand interest payments). This money does not actually belong to the Bank,
as these loans were sold to the Mortgage Securitization Fund, to which it transfers the money (minus the
corresponding commissions).
•There are different types of bonds depending on the asset securitized:
✓Collateralized bond obligations (CBO): bonds.
✓Collateralized loan obligations (CLOs): loans.
✓Residential mortgage-backed securities (RMBS): residential mortgages.
✓Commercial mortgage-backed securities (CBMS): commercial mortgages.
✓Asset-backed securities (ABS): include different assets (example; credit cards).
•The money that investors pay to buy asset-backed securities goes to the treasury or cash of the bank that initiated
the securitisationprocess, thereby adding liquidity to the assets side of the bank's balance sheet.
•The bank receives money from the loans taken out by the families who took out the mortgage with that bank, who
make their payments (capital amortisationand interest payments). This money does not actually belong to the Bank,
as these loans were sold to the Mortgage Securitization Fund, to which it transfers the money (minus the
corresponding commissions).
72 ©Qaracter,2024todoslosderechosreservados
•Looking at what securitization consists, it does not seem to be a negative process; asset rotation has a positive
effect on the asset profitability. The problem arises when the relevant risk analyses are not carried out or the rating
agencies do not rate these securities in the correct way, as the securitisedasset portfolios are made up of loans of
different risk levels.
•Securitization process diagram:
Interest
+
Principal
1.Borrower(those who borrow from
the bank and pay their instalments).
Loan
Sell
Purchase
Loans
Bank Liabilities
Securitization Fund
Bonds
AAA
AA
A
1.Borrowers borrow money from the bank and pay it back (principal + interest). This cash
flow will remunerate investors, net of fees and commissions.
2.The bank releases liquid assets from its balance sheet in exchange for marketable
securities in organisedmarkets, obtaining liquidity, freeing up its own resources and
transferring the default risk.
3.The SecuritisationFund issues bonds with different ratings, which will offer a return
depending on their credit quality (order of priority in the event of losses).
Cash
Bonds
Investors
•Looking at what securitization consists, it does not seem to be a negative process; asset rotation has a positive
effect on the asset profitability. The problem arises when the relevant risk analyses are not carried out or the rating
agencies do not rate these securities in the correct way, as the securitisedasset portfolios are made up of loans of
different risk levels.
•Securitization process diagram:
Interest
+
Principal
1.Borrower(those who borrow from
the bank and pay their instalments).
Loan
Sell
Purchase
Loans
Bank Liabilities
Securitization Fund
Bonds
AAA
AA
A
1.Borrowers borrow money from the bank and pay it back (principal + interest). This cash
flow will remunerate investors, net of fees and commissions.
2.The bank releases liquid assets from its balance sheet in exchange for marketable
securities in organisedmarkets, obtaining liquidity, freeing up its own resources and
transferring the default risk.
3.The SecuritisationFund issues bonds with different ratings, which will offer a return
depending on their credit quality (order of priority in the event of losses).
Cash
Bonds
Investors
©Qaracter,2022todoslosderechosreservados 73
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