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MindMap Gallery CFA Level 1 fixed income fixed income
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CFA Level 1 fixed income fixed income
Fixed income mind map: including R39 Fixed-Income Securities: Defining Elements, R40 Fixed-Income Markets: Issuance, Trading, andFunding, R40 Fixed-Income Markets: Issuance, Trading, andFunding, etc.
Edited at 2022-05-05 20:15:49
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CFA Level 1 fixed income fixed income
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Fixed income
R39 Fixed-Income Securities: Defining Elements
Basic features of a fixed-income security
1.The issuer of the bond
Supranational organizationsinternational organizations
Sovereign (national) governments
Non-sovereign (local) governments local debt
Quasi-government entities, such as Fannie Mae
Companies (i.e., corporate issuers) corporate bonds
SPE/SPV (special purpose entities/special purpose vehicles) entities with special purposes
2. The maturity date of the bond tenor refers to the remaining maturity date
Money market securities: less than or equal to one year
Capital market securities: greater than 1 year
Perpetual bonds: perpetual debt with no maturity date
3. The par value (principal value to be repaid)
Usually the face value is 1000
4. Coupon rate and frequencyCoupon interest
Plain vanilla bond/conventional bond: A bond that pays fixed interest on the payment date
Zero-coupon bond/pure discount bond: no interest payments until maturity
5. Currency in which payments will be made
Dual-currency bond: makes coupon interest payments in one currency and principal repayment maturity in another currency.
Currency option bond: gives bondholders a choice of which of two currencies they would like to receive their payments in.
Bond Markets & Legal information
Bond Markets
Domestic bonds: The issuer of the bond is the same as the place of issue.
Foreign bonds: The issuer is inconsistent with the place of issue
Eurobonds: Type of bond issued internationally, the currency of issue is inconsistent with the currency of the place of issue
Registered bonds: changes in ownership will be recorded
Bearer bonds (majority of form of Eurobonds): Ownership is not recorded. Attractive to those seeking tax avoidance.
Global bonds: I are issued simultaneously in the European market and at least one domestic market, and there are many situations.
Legal information
Trust deed is also called indenture (trust deed)
general trust deed
Definition: Legal contract that describes the form of the bond, the obligations of the issuer, and the rights of the bondholders.
Description: Market participants frequently call this legal contract the bond indenture, particularly in the United States and Canada.
Written in the name of the issuer: content includes principal, interest rate and coupon rate, date of interest payment, bond maturity date, and contingency provisions.
(Not tested) Other legal and regulatory issue addressed in a trust deed
Legal information
The source of repayment
Collaterals
Credit enhancements
Covenants Terms
Taxation
Legal information about issuing entities
Sovereign bonds
corporate bonds
Securitized bonds
definition: Issued by a separate legal entity created for the purpose of owning specific assets which is called special purpose entities (SPEs) in U.S., and special purpose vehicles (SPVs) in Europe.
Description: Provide bankruptcy isolation (bankruptcy remote). The transfer of assets by the sponsor is considered a legal sale. Once the assets are securitized, the sponsor no longer has ownership. After the sponsor goes bankrupt, no party to the bond will be able to recover assets or income.
Source of repayment proceeds
CollateralCollateral & Credit enhancementsCredit enhancement
Collateral: a way to reduce credit risk.
Unsecured bonds (No collateral): There is no collateral, all depends on credit, and the payment will be made after the contract is signed. represent a claim to the overall assets and cash flows of issuer.
Secured bonds: own the collateral and pay first when maintaining the contract backed by a claim to a specific assets of a corporation.
Type of collateral
Credit enhancements: reduce the credit risk
Internal credit enhancement
Overcollateralization: Overcollateralization, for example, a debt of 1 million yuan is pledged with a collateral of 1.2 million yuan.
Reserve accounts or reserve funds Reserve accounts or reserve funds, when problems arise, pay directly from the reserve account
Subordination/Waterfall structure: Hierarchical/Waterfall structure, create multiple bond categories or layers, and sort claims priority. When liquidating assets, pay back the highest priority creditors first.
External credit enhancement:
Classification
Surety bond: A bond guaranteed by an insurance company. The insurance company will make up for the repayment when the issuer cannot afford it.
Bank guarantee: Bank guarantee, similar to the above, except that the guarantor is a bank
Letter of credit: A letter of credit in which a bank provides a loan commitment to the issuer if the issuer does not have enough cash to pay the secured debt.
limitations
Deterioration of the guarantor's credit will reduce the credit quality of the underlying bonds
Exposed to third-party risk, i.e. the guarantor is unable to perform its obligations
Cash collateral account Cash collateral account can solve the above two problems very well. Because the collateral is cash, even if there is a problem with the guarantor's credit, it will not cause the bond's credit rating to drop.
Covenants Terms & Tax
Covenants
Affirmative covenants are affirmative clauses, which are generally administrative in nature and will not increase costs or affect existing business.
what the issuer will do with the proceeds from the bond issue and the promise of making the contractual payments.
Comply with all laws and regulations
Maintain its current lines of business
Insure and maintain its assets, and pay taxes as they come due
Negative covenants, which increase costs and significantly restrict the issuer's potential business decisions, protect bondholders and are very strong.
Restrictions on debt: Restrictions on the issuance of additional debt
Negative pledges prevent the issuance of bonds with a higher priority than the current bond
Restrictions on prior claims Issuers cannot pledge unencumbered assets to protect bondholders with unencumbered assets
Restrictions on distributions to shareholders Restrictions on distributions of dividends and other payments to shareholders, such as stock buybacks
Restrictions on asset disposals specify the amount of assets that the issuer can dispose of during the life of the bond.
Restrictions on investments restrict the issuer’s investment and cannot make high-risk investments
Restrictions on mergers and acquisitionsThe acquirer needs to submit a supplemental agreement to the trustee clearly stating the terms of the old bonds and old contracts, otherwise mergers and acquisitions will be restricted.
Tax
Interest income: Bond interest paid to the holder, generally taxed at a rate equal to salary
Capital gain or loss: Selling a bond before maturity will incur capital gains tax, which is generally lower than the tax on interest income. Lower tax rates on long-term capital gains
Original issue discount (OID) bonds: Issued at a relatively large discount, the principal is repaid upon maturity, and the difference is taxed according to the interest income tax rate. There is no capital gains tax upon maturity.
Premium bonds: The premium portion can be deducted from the taxable portion of the interest payment
Structure of bond cash flow
Principal repayment structuresPrincipal repayment structures
Plain vanilla bond/bullet bonds: Interest is paid regularly and principal is paid at maturity
Balloon payment: the final payment includes a lump sum in addition to the final period’s interest.
Amortizing loan: regular payment of principal and interest
Fully amortizing, the principal is paid off in full on the last regular payment, similar to the equal principal and interest repayment method of a mortgage)
Partially amortizing: A portion of the principal remains unpaid and will be repaid when it is due in the last period.
Sinking fund provisions: Sinking fund provisions stipulate that the principal will be repaid through a series of payments within a certain issuance period to reduce credit risk.
illustrate
1. Initially a sinking fund is just a cash reserve used to repay principal.
2. At present, it is more common to specify a time point. Before this time point, only interest can be repaid. From this time point, the principal must be repaid in each period thereafter.
3. The bond issuance contains some redemption clauses. The issuer can repurchase the bonds at market price, par value or a specific price.
Advantage
The principal can be redeemed periodically
Disadvantages
1. Reinvestment risks increase, especially when interest rates fall.
2. The issuer has the right to redeem the bond at a price below the market
Coupon payment structuresCoupon payment structures
Floating-rate notesFloating-rate notes
basic information
The reference rate is generally LIBOR or the U.S. Treasury bond rate.
the limit coupon rate has an upper and lower limit for the coupon rate
upper limit (cap)
floor
Have both upper and lower limits (collar)
Variable-rate note: Similar to a floating-rate note, except that the spread is variable rather than constant.
inverse floaters (also called reverse floaters) inverse floating rate bonds, the coupon rate is opposite to the reference rate
When the reference rate increases, the coupon rate decreases and vice versa.
Inverse floaters with a coupon leverage greater than zero but lower than one are called deleveraged inverse floaters (0-1). Inverse floaters with a coupon leverage greater than one are called leveraged inverse floaters (>1).
Deferred coupon bonds Deferred coupon bonds/split coupon bonds: Interest payments are deferred to a specified year. A zero-coupon bond is a deferred bond.
Step-up coupon bonds: Step-up coupon bonds: They can have a fixed interest rate or a floating interest rate, and the coupon increases by a specified amount on a specified date.
New higher coupon rate>market yield of the call price call the bonds---redeem bonds
An increase in bond coupon rates can be viewed as a protection against the increase in market interest rates which is due to the decrease in issuer’s credit rating.
Credit-linked coupon bondscredit-linked coupon bonds
The coupon rate increases by a certain value as the credit rating decreases. The principal remains unchanged, and the coupon is connected to a credit event
Payment-in-kind coupon bonds
Allow the issuer to use other bonds to pay the interest on the bond
Index-linked bonds
Its coupon payments and principal repayments are index-linked.
Inflation-linked bonds: are an example of index-linked bonds.
Zero-coupon-indexed bonds: No interest is paid during normal times, and inflation adjustments are only repaid through principal, such as Sweden
Index-annuity bonds: are fully amortizing bonds, with annuity increases consistent with inflation during the duration, such as Australian local governments
Interest-indexed bonds: A fixed nominal principal is paid on the maturity date of the bond, and an index-linked coupon is paid during the duration, so inflation adjustments only apply to interest payments, such as Australia in the 1980s
Capital-indexed bonds: Pay a fixed coupon rate, and the principal will increase as the index rises during the duration, so both interest and principal are adjusted for inflation.
Treasury Inflation-Protected Securities (TIPS) pay interest semiannually until maturity. If the adjusted book value at maturity is greater than $1,000, the holder will receive the adjusted face value as the maturity payment. If the adjusted book value at maturity is less than $1,000, the holder will receive $1,000 at maturity because this is the minimum repayment amount, regardless of whether the index declines, and the amount it pays at maturity is equal to or exceeds its The original face value is what is called a capital-guaranteed bond.
Bond with contingency provisions
Callable bond and putable bond
callable bonds: beneficial to the issuer
basic information
Callable bonds have higher yields and lower prices than irredeemable bonds because they need to attract investors to buy them.
Deferred call: deferred redemption, which cannot be redeemed before a specific time
Call price: redemption price
First par call date: The date on which the issuer first redeems the par value at face value
Call premium: The call premium is the excess of the call price over the par value
Three styles of exercise for callable bonds
American style: can be called anytime after the first call date.
European style: can only be called on the call date specified.
Bermuda style: can be called on specified dates after the first call date, often on coupon payment dates.
Explanation of special points
Interest rates fall: When interest rates fall, issuers will redeem and then buy new bonds at lower prices, and investors will face reinvestment risk.
Make-whole call provision redeems the bond as a whole: Because it needs to be redeemed early, the issuer must pay off the principal and interest between the redemption time and the maturity date, and compensate investors. This will result in the redemption value being significantly greater than the current market price of the bond. However, issuers rarely do this because bonds with blanket call provisions are very expensive.
Putable bonds: beneficial to the bondholders
Puttable bonds have higher prices and lower yields than non-puttable bonds
If interest rates rise, bondholders will sell the bonds back to the issuer and receive cash, which they then reinvest at higher rates.
Convertible bond convertible bond
Conversion parity
At parity: Conversion value = convertible bond’s price
Above parity: conversion value > convertible bond’s price will be more valuable if converted into stocks and should be converted
Below parity: conversion value < convertible bond’s price It is not cost-effective to convert into stocks and should not be converted
Basic information
beneficial to investors
Conversion price: The price per share that can be converted into shares
Conversion ratio: The number of common shares convertible per bond
Conversion ratio = par value / conversion price
Conversion value: If the bond were now converted into stocks, the convertible bond value would be the current stock price multiplied by the conversion ratio.
Conversion value = market price of stock * conversion ratio
Conversion premium: The difference between the convertible bond price and the conversion value. For example, the price of the convertible bond is 1,000 yuan and the conversion price is 900 yuan, then the conversion premium is 100 yuan.
Warrants
It is an additional option, which is beneficial to investors
The holder has the right to purchase the relevant stocks of the issuing company at a fixed exercise price before the expiration date. Generally, if the stock price rises, and the fixed price is lower, the holder will buy the stock at a lower price.
Contingent convertible bonds (“CoCos”)
Can automatically convert from bonds to common stock if a specific time occurs
Some European banks will issue COCO. For example, the bank must maintain a specific level of equity financing. If it is not reached, the bonds will be automatically converted into ordinary shares. This can reduce the bank's liabilities, increase the bank's equity, and help the bank reach the minimum level. Equity requirements
summary
R40 Fixed-Income Markets: Issuance, Trading, and Funding
Classifications of global fixed income markets
type of issuer who is issuing
By type of issuer
Government and government-related sectors
Supranational (international) organizations
Sovereign (national) governments
Non-sovereign (local) governments
Quasi-government entities
Corporate sector
financial company
Non-financial company
Securitized sector
securitization
By credit quality
investment grade
Baa3 or above by Moody’s Investors Service
BBB- or above by Standard & Poor’s (S&P) and Fitch Ratings
Non-investment grade/high yield
Below investment grade
By original maturity
money market securities
Capital market securities
By coupon structure
Floating-rate bonds
Fixed-rate bonds
By currency
Domestic bonds
Foreign bonds
Eurobonds
Global bonds
By geography
Developed market
Emerging market: higher yield than the old market
By other classification
Indexing
taxable statue
Fixed-income indices Fixed income indices
Barclays Capital Global Aggregate Bond Index
J.P Morgan Emerging Market Bond Index
FTSE Bond Index Series
Investors in Fixed-income SecuritiesWho is investing?
Central banks
Institutional investors
sovereign wealth funds
Retail investors
Primary and secondary market for bonds
Primary market
Public offering
Underwritten offering: with the investment bank or syndicate (syndicate, one cannot do it, multiple banks can help together) purchasing the entire issue and selling the bonds to dealers.
Best efforts offering consignment
Auction: Auction, U.S. Treasury bonds are auctioned
Shelf registration registers a continuous issue
Private placement
sale of an entire issue to a qualified investor or a group of investors, which are typically large institutions
Secondary markets
Exchange market meets exchange regulations
OTC Dealer Market (largest) OTC market is a dealer market, a market maker market. What you earn is the bid-ask spread, which reflects the liquidity of the market. If the bid-ask spread is large, it means that the market liquidity is not good, and vice versa.
Electronic Trading Network (growth) electronic market
Trade settlement:
Corporate bonds: third trading day after trade date (T 3).
Government bonds: the nest trading day after the trade date(T 1).
Money market securities: on the day of trade date.
What types of debt will be issued by different funding entities?
Securities issued by government-related bonds
Sovereign bonds are debt issued by a sovereign government and paid back with taxes.
Debts can be repaid in local currency or foreign currency. The risk of local currency is less than that of foreign currency, because foreign currency needs to be supported by sufficient foreign exchange reserves.
Treasury Strips zero-coupon Treasury bills, zero-coupon notes of various maturities
Coupon Strips, coupon portion, coupon stripped from the original note
Principal Strips: principal part
On-the-Run Issues Newly issued bonds, recently issued, very active, with good liquidity
Off-the-Run Issues are unquoted securities and have been replaced by the latest ones.
Non-sovereign government bonds Local government bonds have slightly higher risks than sovereign bonds, so the returns are slightly higher than sovereign bonds.
eg. Municipal bond (in the U.S.)
ASD
GO (general obligation)/Tax-Backed Debt: Using taxes as the source of repayment
Revenue Bonds: The income from some infrastructure projects is relatively risky and the income is higher.
Agency/quasi-government bondsQuasi-government agencies
There is explicit or implicit government guarantee, so the credit rating will be higher, the risk will be lower, and the price will be higher.
Supranational bonds bonds issued by international organizations
It is endorsed by an international organization, so the credit rating will be high, the risk will be relatively low, and the price will be relatively high.
Types of debt issued by corporations
Bank debt: bilateral loan & syndicated loanBank loan
Bilateral loan: involves only one bank
Syndicated loan: funded by several banks
Commercial paper: short term, unsecured, low rate
Basic Features
Issued with working capital, the term is generally shorter.
short term, unsecured, low rate
Directed issuance is possible, that is, directly placed by selected investors.
It can be traded in the secondary market, but because the term is relatively short, investors generally hold it until maturity, so trading in the secondary market is not active.
Reissued or rolled over when it matures borrow new debt to replace old debt. If the old debt is due to be repaid but the new debt cannot be borrowed, there will be a risk of default.
Rollover risk: the risk arising from borrowing new money to repay old ones
U.S commercial paper Vs. Eurocommercial paper (if the place of issue is not equal to the currency issued, it is called euro bond
Medium-term notes (MTNs) won the ticket and were listed for registration and issuance.
feature
Various maturities(9 months to 100 years);
they can customize the bond issue to their needs and stipulate the amount and characteristics of the securities they want to purchase. They can register for multiple issuances at one time to meet the different needs of investors
corporate bonds
Serial bond issue has a series of maturity dates. For example, I currently issued a bond of 1 million yuan. 100,000 yuan is due in 10 years, 500,000 yuan is due in 20 years, and 400,000 yuan is due in 30 years.
Term maturity structure has only one maturity date
Short-term funding alternatives
Retail DepositsDeposits
Checking accounts
Saving accounts
Money market mutual funds
Short-Term Wholesale Funds Wholesale Business
Negotiable CDs large value certificates of deposit
Reserve Funds reserve account
Interbank funds interbank lending
Repurchase (repo) AgreementRepurchase Agreement
Definition (the borrower is a positive repo, the creditor is a reverse repo)
Repo rate and Repo margin/haircut
Influencing factors
General principle: When the risk is high (good quality is low risk, long time risk is high), the repo rate and margin are relatively high. When the risk is high, both are relatively low.
Repo rate is the return earned by B: mortgage interest rate: (98.5-98)/98
Repo margin/haircut: (100-98)/98
advantage
Repurchase agreements are not regulated by the Federal Reserve
Collateral position of the lender in a repo is better in the event of bankruptcy of the dealer; (liquidity) quality is generally better
Credit risk
Lender: When the price of the collateral has fallen.
Borrower: When the price of the collateral has risen
Structured financial instrumentsStructured products
Capital protected instruments can be treated as a portfolio
feature
1. Buy a 0 coupon bond 2. Buy a call option
tradeoff
There is a lower limit if you lose money, if you lose the option premium, there is no upper limit if you make profit.
Yield enhancement instrumentsyield enhancementi products
The coupon remains unchanged, the principal is connected to a credit event, and the coupon rate is generally high and issued at a discount.
For example: credit linked note (CLN), coupon remains unchanged, principal is connected to a credit event
If credit event dose not occur, the investor receives the par value of the CLN at maturity;
If credit event occurs, the investor receives the par value of the CLN minus the nominal value of the reference asset. (original plan principal minus credit losses)
revenue enhancement methods
offer higher coupons than otherwise similar bonds.
CLNs are usually issued at a discount
Participation instruments participate in changes in market variables, and the benefits obtained are linked to changes in market variables.
For example: floating rate bonds
Leveraged instruments specifically refer to inverse floaters. Coupons move in the opposite direction to market interest rates.
R41 Introduction to Fixed-Income Valuation (qualitative and quantitative exams)
Bond valuation using YTM
Bond Valuation Process
Estimate the cash flows
Determine the appropriate discount rate
Calculate the present value of the estimated cash flows
Relationships between price and yield
The general idea of primary bond valuation is to sum up the discounted cash flows. The discount rate is 1. Use the same discount rate (YTM) 2. Use different discount rates Spot rate
Yield to Maturity (YTM)
Three major assumptions
Hold the bond until maturity;
Full, timely coupon, principal payments (no default);
Coupons are reinvested at original YTM. (The interest rate for coupon reinvestment is YTM) YTM is equivalent to IRR
The assumptions of YTM are very strict and are not often used in practice. When reinvesting, the market rate of return is also used. The rate of return often used in practice will be described in detail in the interest rate risk section.
Calculation 1: Find the bond price given YTM. Use the fifth row of the financial calculator to find the present value (note: the question defaults to discounting twice a year, the face value is 1,000, the interest paid every year is equal, and the principal and the last interest are paid at maturity.
Calculation 2: To find YTM, use the annuity row of the financial computer to find it. Note that our default signs of PV, PMY and FV are opposite (generally PV has a negative sign, PMT and FV have a positive sign). The calculated YTM is for the period and needs to be used To convert to an adult using the simple interest method, simply multiply by 2/4, etc.
Conclusion (generally not directly investigated)
Bond prices and yields have an inverse relationship
Changes in bond prices are convex (convexity). When the yield changes by the same amount, the price will rise more than it will fall (the increase will be greater than the decrease).
A bond will be priced at a discount (premium) to par value if coupon rate is less (more) than its YTM.
Discounted bonds: P<Par, Coupon rate<YTM Parity bond: P=Par, Coupon rate=YTM Premium bonds: P>Par, Coupon rate>YTM
Relationships between price and time
in conclusion
Over time, the value of premium bonds decreases
Over time, the value of discounted bonds continues to increase
Calculation 3 (Generally, it is necessary to keep the interest rate constant and only look at the change in bond value caused by the change of time). Find out how much the bond price changes due to the change of time?
example:
Analysis:
Valuation with spot rates spot rates
Precautions
1. The spot rate of return is the future rate of return at the current point in time.
2. The spot rate of return is the annualized rate of return, for example, S3=7%, which means that if I start investing now, the annual rate of return for three years of investment will be 7%. This principle can also be completely copied for others.
3. The discount rate used to discount a future cash flow to the present can be used as the spot rate of return.
4. The YTM of a zero-coupon bond can be used as the spot yield
Calculation 4. Arbitrage-Free Valuation: Use cash flows at different time points corresponding to spot rates at different time points to perform discount summation. Financial calculators cannot be used to calculate.
Flat price, accumulated interest, and the full price
Accrued InterestAccrued Interest
Clean(flat) Price does not include accrued interest
Full Price (or dirty price): Price that includes accrued interest (clean accrued)
in conclusion
1. The sum of future discounted cash flows is calculated as Full price.
2. When quoting, the clean price is quoted
Calculation 5 (find the full first, then the accrued interest, and use the difference between the two to find the clean price)
Things to note when using a financial calculator to calculate an annuity
1. Wait for time intervals
2. Wait for cash flow
calculation steps
1. If the time intervals are not equal, you can first calculate the full price of the previous interest payment date. 2. Compound interest is rolled over to the delivery date to calculate the full price on the delivery date. 3. Accrued interest is calculated using simple interest 4. Find the clean price by netting
Matrix pricing matrix valuation
Conclusion: Using Matrix Valuation Methods for Inactively Traded Bonds
The valuation method is to find a series of bonds that are closest to the bonds that need to be valued, arrange them in a matrix, and then select the ones with the closest term for valuation.
Linear interpolation linear complement method, which believes that there is a linear relationship between time and rate of return
Calculation 6: Use the idea of relative valuation method: find a benchmark, usually a shorter time, because the risk is lower in a short time. Then add a spread to calculate it. Y=YBbanchmark Yt
Yield Measures
Effective annual rate(EAR)
Street convention yield: Yield regardless of holidays
True yield: consider the holiday rate of return
Current yield (income or interest yield): For example, if I invest in a 3-year bond, the annual interest is 100 yuan, and the principal will be returned at maturity. So what is my rate of return at the end of the first year? CY = revenue/cost
Formula: current yield=annual coupon➗price
Simple yield takes into account the yield of gain and loss. It is the sum of the coupon payments plus the straight-line amortized share of the gain or loss, divided by the flat price.
Yield to call (put) does not hold to maturity, so YTM cannot be used. You can use a financial calculator to solve it.
Yield to Worst: The lowest value between redemption yield and yield to maturity
Option-adjusted yield: Option-adjusted yield, adjusted based on the value of the embedded option sandwiched with the required market discount rate
Yield measures for fixed income valuation
Discount yield:
Discount rate = reference rate required margin (or discount margin): Depends on the discount based on the face value
Annualize simple interest based on 360 days in a year
Add-on yield:
Annualize simple interest based on 360 days in a year
Simple interest years based on 365 days in a year
Bond equivalent yield (investment yield) for money market security: yield stated on a 365-day add-on rate basis.
Difficulty: Put discount rate and BEY together to examine: 90-day bond, discount rate=2%, find BEY, method 1: find the relationship between F and P according to the formula, and then bring it into the formula. Calculation method 2: take the face value to 1000, calculate P, and then do the algebraic calculation
Yield measures for floating-rate notes
basic concept
Coupon rate = reference rate quoted margin
discount rate=L DM/RM
The coupon reset date has 3 points (can only be reset on this day)
CR=CAP/FLOOR
Characteristics of inverse floater
Discount and valuation, calculate discount margin (which is part of the discount rate)
Step 1: Use the financial calculator TVM to find YTM
Step 2: YTM-LIBOR calculates DM
Yield Curve does not involve calculations
Yield curve yield is the structure between time
Spot curve is also called zero curve or strip curve
Yield curve for coupon bonds
YTM curve
Par bond yield curve
Par curve:
Forward yield curve
Use forward rate
Forward rates vs. Spot rates
Forward Rates, interest rates that look at future yields at a certain point in the future.
Expression: 2Y1Y: The first Y represents the starting period, the second Y represents the period, starting from the second year, a 1-year bond
Calculation: If you know the spot, you need to go forward, or if you know the forward, you need to spot. Different paths lead to the same goal.
Calculation: Pricing: The idea is still the sum of discounted future cash flows
Yield spread in the relative valuation method Ycoupon=Ybanchmark spread
Benchmark spread
G-spread: the benchmark is government bond yield (YTM of corporate bonds - YTM of national bonds)
Zero-volatility spread (Z-spread): Corporate bond spot rate-Treasury bond spot rate
Interpolated spread (I-spread): target corporate bond yield-swap rate
Calculate G-spread
The first step is to find the YTM of the two bonds. The second step to make a difference is G-spread
Option-adjusted spread (OAS) spread after excluding rights
Callable bond: ZS > OAS
Putable bond: ZS < OAS
R42 Introduction to Asset-Backed Securities Asset securitization products, different assets, corresponding products are different
Securitization
Introduction to Asset-backed Securities
Asset-backed securities asset-backed securities, fixed income securities that are pooled or mortgaged by assets such as loans or accounts receivable are asset-backed securities.
Securitization is the process of repackaging simple debts and loans into more complex structures and selling them to investors as fixed income products.
Parties in a Securitization Transaction
Main counterparts
The seller of the collateraloriginator or depositor, e.g. Bank (generally refers to the basic financial company or bank
The SPVissuer) bankruptcy-remote vehicle (the issuer of ABS bonds)
Third parties (In practice, there will be many other third parties involved, just take a brief look at them.
Servicer(if different from the seller)
Other parties:
Independent accountants, lawyers/attorneys: Prepare Legal documents
Trustee or trustee agent: safeguard the assets after placed in the trust, hold funds due to the bondholders until they are paid, provides periodic information to the bondholders.
Underwriters, Rating agencies: perform same function as they do in a standard corporate bond offering
Guarantors: guarantees part of the obligations issued by the SPV.
The Securitization Process
Securitization
Benefits of securitization
Lowers or removes the wall between ultimate investors and originating borrowers;
Securitization reduces liquidity risk in the financial system
Securitization enables innovations in investment products
Benefits of SPV in securitization: sell the loan to SPV instead of using it as collateral
bankruptcy-remote vehicle.
Securitization can have lower credit cost than a corporate bond secured by the same collateral.
Funding cost of issuing an asset-backed bond is less than that of issuing a corporate bond
Structures of Securitizations
Credit tranching credit stratification, paying interest and principal according to the level, the risks faced by each level are different senior/subordinated structure
Time tranching. The time at which each level gets interest and principal is different. This is called time tranching.
Generally, both time stratification and credit stratification are included.
Foreclosure recourse
Recourse loan has recourse
For example, if I borrowed 1 million yuan and used my house as a mortgage, but I couldn’t pay back the money, and the house was sold for 600,000 yuan, there was still a shortfall of 400,000 yuan. If you have the right of recourse, you can go after me personally and take it away. The remaining 400,000 yuan was paid back.
Nonrecourse loan has no recourse
For example, if I borrowed 1 million yuan and used my house as collateral, but I couldn’t pay back the money, the house was sold for 600,000 yuan, and I still had a shortfall of 400,000 yuan. You can’t go after me personally without the right of recourse. I can only walk away with 600,000 yuan.
Strategic default means strategic default. For example, during the financial crisis, if house prices fall below the loan limit, then I will not want the house and I will not repay the money.
background information
Mortgage loan: A loan secured by specific collateral that requires the borrower to make a predetermined series of payments to the lender.
Loan-to-value ratio (LTV): the ratio of the amount of the mortgage to the property’s purchase price. Loan-to-value ratio, the ratio of the purchase price of the property to the mortgage amount
The higher the LTV, the lower the borrower’s equity, vice versa.
Lower LTV, the more equity the borrower has, the less likely the borrower will default
Interest rate determination: mortgage rate or contract rate
Fixed rate mortgage interest rate remains unchanged during the mortgage period
Four important features of fixed-rate, level payment, fully amortized mortgage loans
The amount of the principal payment increases as time passes;
The amount of interest decreases as time passes;
The servicing fee also declines as time passes;
The ability of the borrower to prepay results in prepayment risk.
Adjustable or variable rate: Mortgage interest rate resets periodically
Initial period fixed rate mortgage is fixed on a certain initial date and then adjusts
Convertible: A loan can be converted to a fixed rate or an adjustable rate
Amortization scheduleAmortization schedule
Fully amortizing loan: During the mortgage period, all principal is fully amortized and repaid in installments, and the principal is repaid in the final repayment.
Part of the principal of a Partially amortizing loan is not included in the amortization principal and is repaid in one lump sum in the final repayment.
Interest-only mortgage (IO), only interest is paid during the loan period, and the principal is repaid in the last period or periods (balloon risk)
Residential Mortgage-Backed Securities
Weighted average maturity (WAM): the weighted maturities average of all the mortgages in the pool, each weighted by the relative outstanding mortgage balance to the value of the entire pool.
Weighted average coupon (WAC):weight the mortgage rate of each mortgage loan in the pool by the percentage of the mortgage outstanding relative to the outstanding amount of all the mortgages in the pool.
Average life: is the weighted average time until both scheduled principal payments and expected prepayments are received.
Morgage-Backed Securities (MBS) securitizes loans as assets
Residential mortgage loans (RMBS products issued with personal housing loans as assets)
agency MBS three major agencies
basic introduction
Conforming mortgage loans that meet the quality requirements of the three major institutions
Non-conforming mortgage loans that do not meet the quality requirements of the three major institutions
Mortgage pass-through rate: interest paid to investors
Mortgage rate securities: Receive monthly payments from home buyers
Mortgage rate securities-Mortgage pass-through rate=servicing fees
Mortgage assumptions: 1. Equal amounts of PMT 2. All repayments are at fixed interest rates. For example, if the market interest rate drops, then I want to borrow a cheap amount of money to repay the previously more expensive money, which will result in prepayment problem
Prepayment risk
The three major institutions will estimate a prepayment situation. After estimating the average life of an MBS, the actual situation may be different from this expectation. The risk caused by this uncertainty is called prepayment risk.
Prepayment option (early repayment option):
Prepayment penalty mortgage
Prepayment risk
Contraction risk market interest rates will fall, prepayment will rise, and the survival period of MBS will be shortened.
Extension risk market interest rates will rise and prepayment will fall, so the survival period of MBS will be longer than expected.
Prepayment rateThe rate of early repayment
Prepayment rates
Group 1 (annualized)
conditional prepayment rate (CPR) is the prepayment rate summarized by the association and is an annualized rate.
Public Securities Association (PSA) is an association
100PSA Features
200PSA, then the monthly CPR is equal to 0.4%, and the CPR after 30 months is 12%, remaining unchanged
1. The monthly CPR increases by 0.2%, then it will be 6% after 30 months
2. It will remain at 6% and will not change after 30 months.
As long as the second group (monthly) has an impression
Monthly prepayment rate (real CPR every month)
Example for MPS
Classification
Collateralized Mortgage Obligations (CMO)
Different types of CMOs
Sequential-pay CMO illustration
Conclusion: Through stratification, prepayment risk is not eliminated, but it is stratified. Some levels have large contraction, and some levels have large extension.
Planned amortization class (PAC) and Support tranche structure
Definition/Characteristics: It consists of two parts, one is PAC and the other is surport. PAC has stable cash flow, but in practice, due to early repayment, the cash flow cannot be stable, so support must be provided structure to ensure the stability of PAC cash flow. If the cash flow is very large, then PAC will take away the cash flow it should have, and the rest will be absorbed by support. If the cash flow is very small, then PAC will take all or part of it to meet the cash flow needs, and support can absorb none or less. Absorb cash flow.
Prepayment risk (compare PAC and support): The prepayment risk of PAC is much smaller than that of support.
Discuss the Prepayment risk of the PAC structure separately: 1. When the prepayment is within a certain range and reaches the initial collar, the PAC is very stable. 2. When the prepayment rate is greater than the initial, the cash flow is very large, and the support itself is also a bond. It can be offline after paying off all the money. Then the excess will have to be absorbed by the support, and the repayment period will be shortened. , there will be contracting risk. 3. When the prepayment risk is less than the initial, the money is too small, and the PAC money will be less, then the survival period will be longer and there will be extension risk.
Others do not make key requirements
mortgage pass-through securities (MPS)
Non-agency RMBS
Differences between Agency and Non-agency securities
Agency securities: CMOs are created from pools of pass-through securities.
Non-agency securities: CMOs are created from unsecuritized mortgage loans. They are loans that do not meet the requirements of the three major institutions, non-porforming
Non-agency securities have no explicit or implicit government guarantee of payment of interest and principal as agency securities have. Without government endorsement, the risk will be higher and the yield will be higher.
All non-agency securities are credit enhanced: external and internal. Credit enhancement is required
The content is exactly the same as in Chapter 39, so I won’t go into details here. Non-agency RMBS requires one or more credit enhancement.
internal credit enhancement
external credit enhancement
CMBS (Commercial mortgage-backed securities) is a securitization product issued with commercial loans as assets.
feature
Commercial mortgages are non-recourse loans without recourse and the risk will be higher
Basic CMBS Structure – Call Protection
Call protection at the structure level Reduce credit risks faced by investors at the structural level
CMBS are structured to have sequential-pay tranches, by credit rating.
so the AAA rated bonds must be paid off before the AA rated bonds are, and so on. The higher the tier, the higher the rating and the better the quality.
The lower the tier, the worse the rating and the lower the quality.
Call protection at the loan level to reduce prepayment risk from the loan level
Prepayment lockout period, no early repayment in the first five years
Defeasance also has a lock-in period in the first five years. If the loan company wants to repay it in advance in the first five years, it can do so, but the cash flow from the early repayment will not be given to investors. The repaid money can be invested in some treasury bonds with better credit. After that, During the lock-up period, the money repaid in advance will be returned to investors.
Prepayment penalty points: Directly charge penalty interest for early repayment
Yield maintenance charges (make-whole charge): Early repayment is okay, but if you repay the principal early, the remaining principal will be reduced and the interest will be less. As an investor, I need you to repay according to the overall cash flow when you repay in advance, and you can't shortchange me.
Basic CMBS Structure - Balloon Maturity Provision. For example, if there is a 30-year loan, the initial payment is very small, and the last payment is a large amount. This payment is called balloon provision. If it is not paid, , then the duration of CMBS will become longer, resulting in balloon risk, which is a type of extension risk.
Analysis of CMBS securities focuses on the property and not the borrower (a rough understanding is enough)
Debt-to-service coverage ratio is the ratio of the funds that can be used to repay principal and interest in each year to the amount of principal and interest that should be repaid in the current period.
Loan-to-value ratio
Non-mortgage asset backed securities do not use mortgages as underlying assets
1. Auto Loan ABS car loan
1. Contents included in cash flow
Planned repayment of principal and interest
Any prepayment is relatively small, because the term and amount are also very small.
2. Credit enhancement can be done
internal credit enhancement
external credit enhancement
2. Credit Card Receivable ABS Credit Card Accounts Receivable
feature
non-amortizing
cash flow
finance charges collected overdue penalty interest
fees credit card annual fee
principal payment, repay the principal, card account
Lock-up period: The cash flow of the principal part is locked. The principal cash flow generated during the lock-up period will not be paid to investors. It will be paid to investors normally after the lock-up period.
In practice, it is a rollover, because the card account this month may be paid off next month, so there will be a lock-in period, and the locked money is used to replenish the assets in the pool.
Collateralized debt obligations are products issued using junk bonds as assets.
Classification
Collateralized loan obligations (CLOs) assets are junk loans
collateralized bond obligations (CBOs); assets are junk bonds
Will do credit stratification
The garbage recovered may have a fixed interest rate or a floating interest rate, but generally the bonds issued are floating, so a credit swap is required to replace the fixed ones with floating ones.
Covered Bonds non-asset securitization products, guaranteed bonds
Covered bonds: The source of repayment has double guarantee. It can be repaid with the cash flow generated by the operation of the borrowing unit, or with the cash flow generated by the mortgaged bond.
differences against ABS:
dual recourse—that is, to both the issuing financial institution and the
underlying asset pool. It means that the repayment source of covered bond is double guaranteed.
ABS can be layered, but covered bond cannot be layered.
The ABS loan pool is fixed, but the covered bond pool can be dynamically adjusted. It must be ensured that the cash flow generated by the final loan is sufficient to repay the amount owed.
The final duration of ABC is uncertain, while the final repayment period of covered bond is certain.
Redemption regimes
Hard-bullet covered bonds
Soft-bullet covered bonds
Conditional pass-through covered bonds
Advantages: The credit risk will be lower, so the price will be lower.
All contents of R43 Understanding Fixed-Income Risk and Return are possible to examine
Annualized holding period return
Three sources of return:
Coupon and principal payments
Reinvestment of coupon payments
Capital gain or loss if bond is sold before maturity
For calculation questions, just use PAR and subtract the value at the beginning of the period when you purchased it.
If you are taking a qualitative question, you should note that we cannot directly subtract the price at the beginning of the period. What needs to be subtracted is the carrying value (book price), because this value takes depreciation and amortization into account.
You must be able to calculate the annual holding period return. Annualized holding period return and realized return are the same thing (taken in three steps)
Draw a time graph
Step 1: Calculate the price of the bond at time 0. Note that I/Y must be the current interest rate. The financial calculator calculates P0.
Step 2: At the time when I want to sell the bond, calculate how much the current bond is worth from a cash flow perspective. First, take out the coupon separately and calculate the FV. This FV includes both the coupon and the coupon reinvestment income. . Then the par value is calculated using the future cash flow discount method to calculate the price of the bond principal at time t. At this time, the current I/Y is also used in the calculation. The sum of the two is Pt.
Step 3: P0*(1 R)t power=TR, from which r is calculated
Interest rate risk is also called duration
Duration
definition：
Duration: the price sensitivity to interest rate changes. More sensitive, more possible price volatility measures how much the bond price changes when the yield changes by one unit.
Definition:
Interpreting duration
Duration is the approximate percentage change in price of 1% change in yield. A measure of interest rate risk, which is Mod. D
Duration is a weighted average of time (in years) until cash flow will be received. is an average repayment period, which is Mac. D
Duration is the slope of the price-yield curve at the bond’s current YTM. The first derivative of the bond price to the yield curve is the dollar duration. What comes out of the second-order derivative is convexity
The influencing factor of duration is actually the ratio of size
Longer maturity, higher duration; positive correlation maturity effect
As it gradually expires, the duration will show a jagged decreasing curve.
Lower coupon, higher duration; coupon effect
Lower market yield, higher duration;
Bond with embedded option (callable bond & putable bond) has lower duration. Bond with embedded option will make the average repayment period shorter, so the duration will be smaller
negative correlation
Basic explanation (the last thing I want to explore is the impact of changes in interest rates on bond prices)
coupon: itself will not change because it is determined by the coupon rate
coupon reinvestment: It will change with the interest rate (coupon interest risk)
par/sales: Because the current market interest rate is used, it will change (market price risk)
duration in a narrow sense
Duration in a broad sense
Calculations and formulas (Yc=Yt Spread) will definitely be tested
Yield duration (when the spread of the bond itself changes)
Macaulay Duration: When can I get back the money I borrowed? The average repayment period is calculated based on the present value of cash flow.
Step 1: Find the present value at each point in time
Step 2: Calculate the weight by dividing each cash flow by the sum of the present values of all cash flows (in fact, the denominator is the price of the bond)
Step 3: Multiply the weight by the corresponding time, and then sum
Cannot measure equity bonds
summary
MD (Modified duration) measures interest rate risk {MD and interest rate risk do not match up, so MD is introduced}
Cannot measure equity bonds
Approximate modified duration can measure equity bonds
in conclusion
1. Only AMD or Effective duration can be used if the license is included.
2.Formula
Caused by changes in the bond itself
curve duration (benchmark changed)
Effective duration can measure equity bonds
in conclusion
1. Only AMD or Effective duration can be used if the license is included.
2.Formula
Caused by changes in benchmark, usually referring to national debt
Money duration/dollar duration When the yield changes by one unit, how much does the bond price change?
Formula: Money duration=annual MD * full price of bond
Money duration expressed as money duration per 100 of bond par value What is the duration of par value per 100 yuan?
Formula: Money duration per 100 units of par value= annual MD * full price of bond per 100 of par
Price value of a basis point (PVBP): How much does the bond price change if the yield changes by 1bp?
formula:
formula:
Portfolio duration
1. Calculate:
W here refers to the weight of a single asset in the portfolio
2. Limitation: It can only measure the parallel movement of the yield curve. The change in yield at each time point is the same.
If the shape of the yield curve changes, it is called shaping risk/Yield curve risk
Key rate duration/partial duration：加入第五时间点收益率变了1%，其他时间点收益率保持不变，如果KRD5=3，那么整体组合value变动的百分比就是3%
Convexity rises more and falls less
Definition: Convexity is a measure of the curvature of the price-yield curve. Increase more and decrease less
calculate
approximate convexity movement in the bond itself
Effective Convexity is caused by changes in the benchmark
Duration and convexity are combined to see the impact on bond prices
Duration is a straight line, which is not real. There is always a distance between it and convexity, so you need to calculate what this distance is.
formula:
When doing algebra, you need to pay attention to the sign before MD. If the rate of return drops, the sign of Δy should also be -.
Convexity of Rights-containing Bonds
callable
putable
duration gap (when coupon RI risk and market price risk can offset each other) When market interest rates change, interest rates rise, investment income increases, and bond prices fall. The two change in opposite directions.
Formula: Duration gap = Mac. D – investment horizon. During the exam, you should note that the holding period is the investment horizon, and then you need to calculate Mac. D.
analyze
durationgap=0
The two risks offset each other
durationgap<0
Negative gap exposes the investor to reinvestment risk from decreasing interest rates. Reinvestment risk will be greater, investment risk will be greater, interest rates will rise, investment risk will decrease, investment income will increase, which is good for investors, and vice versa. Those who are not good
durationgap>0
MD is relatively large, indicating that the market price risk is high
Positive gap exposes the investor to market price risk from increasing interest rates. It shows that the market price risk is greater. When interest rates fall and prices rise, it is better for investors. When interest rates rise and prices fall, it is bad for investors. Investment may suffer losses
Empirical Duration and Analytical duration
Analytical duration: What is calculated through MD, etc. is the analytical duration (assuming that yield and curve are independent of each other, when one changes, the other does not change)
Empirical duration is the empirical duration based on actual historical data.
summary
For a government bond, because there is only benchmark risk, the analytical and empirical calculation results are very similar at this time.
Corporation bond: When the market is under pressure, the interest rate on government bonds will drop. For high-yield bonds, people generally go back to buy government bonds because of risk aversion. That Treasury bond prices rise and yields fall. Corporate bond yields will rise as more risk compensation is required. At this time, empirical and analytic may not be equal.
Relationships Between Price and Yield
Inverse effect
Coupon effect:
Maturity effect
Convexity effect
R44 Fundamentals of Credit Analysis (the test is qualitative)
Credit risk
Default risk3 default risk needs to consider default probability. If there has been a default in the past, the possibility of default will be higher now.
Loss given default: The 1 million yuan bond defaulted and the assets were sold for 600,000 yuan. This 600,000 yuan is the recovery rate.
Recovery rate: A bond worth 1 million yuan defaulted and the assets were sold for 600,000 yuan. This 600,000 yuan is the recovery rate.
The sum of the two equals 1
Expected loss = Default probability * Loss severity given default (Level 2 will focus on this)
Capital Structure:
Seniority Ranking Claim Order During bankruptcy liquidation, in order to keep the process going, some symbolic repayments will be given to subprime loans, and they are not strictly based on ratings.
1.lien, the one with mortgage is the first to pay back
2. Secured loans are better than unsecured ones
3. Senior is better than junior than subordinate
Pari Passu: Bonds of the same grade are repaid in proportion to the bond
credit rating
investment grade
Moody rating Baa3 and above
S&P and Fitch rated BBB and above
non-investment rating
Moody rating below Baa3
Issuer credit rating gives a company a rating, generally referring to the highest quality debt a company can issue on its own, unsecured.
Issue ratings: The ratings of the debt. Without any credit enhancement, the rating of the debt cannot exceed the company's optimal rating.
Notching: The rating of corporate bonds may be different from the rating of the company. Companies with poor quality are more likely to have notching.
Cross default provisions: Cross default provisions. For example, if A issued two bonds and one of them defaulted when it expired, then the other one can still claim compensation now even if it has not matured.
Structural subordination of a subsidiary company, the credit rating of the subsidiary company will be better than that of the parent company. Because the subsidiary’s repayment source is more clear
Risks in relying on agency ratings (cannot rely too much on credit ratings):
1. Dynamic, ratings may change
2. Credit rating agencies may not be trustworthy
3. Incidental problems are difficult to predict, such as melamine milk powder
4. Credit ratings lag behind market changes. Generally, ratings are adjusted only after they have deteriorated.
The 4Cs of credit analysis
Capacity refers to the ability of the borrower to make its debt payments on time. (content of fundamental analysis)
1.Industry analysis
2. Industry fundamentals
3.Company fundamentals
4. Comments on issuer’s liquidity
Collateral refers to the quality and value of the assets supporting the issuer’s indebtedness. (Refers to the assessment of assets from a company-wide perspective)
Intangible assets
Patents are considered high-quality intangible assets because they can be more easily sold to generate cash flows as compared to other intangibles.
Goodwill is not considered a high-quality intangible asset and is usually written down when the company performance is poor.
Depreciation
High depreciation expense relative to capital expenditures may signal that management is not investing sufficiently in the company.
The quality of the company's assets may be poor, which may lead to reduced operating cash flow and potentially high loss severity.
Equity market capitalization
A stock that trades below book value may indicate that company assets are of low quality.
Human and intellectual capital
These are difficult to value, but a company may have intellectual property that can serve as collateral.
Covenants are the terms and conditions of lending agreements that the issuer must comply with. Affirmative terms and negative terms
Affirmative covenants: obligated to do.
Negative covenants: limited in doing.
Character refers to the quality of management. It depends on whether the company is reliable and whether the management has good character.
Yield and spread, focusing on the influencing factors of yield spread
Yield on corporate bond (for a given maturity) = real interest rate expected inflation rate liquidity premium credit spread tax impact
Credit cycle is equivalent to economic cycle
Economic conditions
Financial performance of the issuer.
If the macro environment improves, whether the credit cycle is good or everyone's interest rates are not good, the spread will be relatively small, and the spread will become larger during the trough.
Broker-dealer capital: If the dealer has a large amount of funds, trading will be active and liquidity will be good, and the spread will become narrower.
General market demand and supply If the demand for corporate bonds is high, the yield will fall and the spread will narrow.
micro perspective
Credit analysis of different bonds was introduced in Chapter 1
high yield bond
sovereign bond
municipal bondmunicipal bond
LIBOR (London Interbank Offered Rate)
1. Published every day, with multiple currencies and different expiry dates
2. There is no single LIBOR, but generally a set of set interest rates, such as 30-day USD LIBOR and 90-day franc LIBOR.
3. Also used as a reference interest rate for other debt instruments, such as mortgage interest rates.
4. The coupon reset date refers to the interest paid on the next coupon date.
5. The new one-year interest rate determines the interest rate at the end of next year
6. LIBOR’s interest rate must match the frequency with which the bond’s coupon rate is reset.