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Fixed Income Securities Valuation
Part A: Credit Analysis
1. Credit Ratings
Credit rating is conducted by a ratings agency. For long-term Debt, credit rating assesses the probability of default and the magnitude of loss.
For short-term Debt, credit rating focuses on the probability of default.
Rating Information:
- Downgrade/Upgrade Watch: reduce/increase current rating by 2 notches
- Negative/Positive Outlook: reduce/increase current rating by 1 notch
- Stable Outlook: remain current rating 2. Traditional Credit Analysis
1) Analysis of a Corporate Bond
4C’s: Capacity to Pay, Collateral, Covenants, Character
- Capacity to Pay Factors: Industry Trends, Regulatory Environment, Operating and Competitive Position, Financial
Position and Source of Liquidity, Company Structure, Parent Company Support Agreements, Special Event Risk
- Ratio Analysis
Focused Aspects Ratios
Profitability ROE, ROA, Profit Margin, Asset Turnover
Short-Term Solvency Current Ratio, Acid-test, Cash Ratio
Capitalization LT Debt/(LT Debt + Equity), Total Debt/(Total Debt + Equity)
Coverage EBIT (or EBITDA) / Interest,
Funds from Operation (or Free Operating Cash Flow) / Debt Cash Flow Funds from Operation / Total Debt, (Free Operating Cash Flow + Interest) / Interest
(Free Operating Cash Flow + Interest) /(Interest + Annual Debt Principal Repayment) [DSR]
Total Debt / Discretionary Cash Flow [Debt Payback Period]
Funds from Operation / Capital Spending Requirement
Funds from Operation (FFO) = NI + Depreciation + Amortization + Deferred Income Taxes + Other Noncash Items
Discretionary Cash Flow=FFO+Decrease in Noncash Liquid Assets+Increase in Non-Debt Liquid Liabilities - Analysis of Collateral: Important to Secured Position
- Analysis of Covenants: Affirmative/Negative Covenants
- Character of Corporation: Governance, Agency Problem, Stakeholders, etc
- Corporate Governance Rating: Ownership structures and external influences, shareholder rights and stakeholder
relations, transparency and audit, board structure and effectiveness
- Special Issues for High-yield: Debt Structure, Corporate Structure, Covenants, Equity Analysis Approach 2) Analysis of an Asset-backed Security & Non-agency Mortgage-backed Security
Factors considered: Credit Quality of Collateral, Quality of Seller/Servicer (in true securitization,
servicer is simply to collect and distribute cash flows), Cash flow Stress and Payment Structure, Legal Structure
3) Analysis of Municipal Bond
Bond-security Areas Considered: limits of basic security, flow-of-funds structure, covenants ( different to corporate
bond, thus additional credit analysis is needed), priority-of-revenue claims, additional-bonds tests, other relevant covenants
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bond, thus additional credit analysis is needed), priority-of-revenue claims, additional-bonds tests, other relevant covenants
4) Analysis of Sovereign Bond
Factor Considered: Political Risk, Income and Economic Structure, Fiscal Flexibility, Public Debt
Stability, Balance of Payments Flexibility, External Debt and Liquidity
Two ratings assigned: local currency rating and foreign currency rating
3. Credit Scoring Models (TA-Total Assets)
Z = 1.2 (working capital/TA) + 1.4 (RE/TA) + 3.3 (EBIT/TA) + 0.6 (MV-E/TA) + 1.0(Sales/TA)
4. Credit Risk Models
Structural Model: based on BSM Option Pricing, probability of default directly links to volatility of asset
Reduced Form Model: directly model probability of default and downgrade
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Part B: Interest Rate Term Structure and Volatility
1. Yield Curve Shape: Positively Sloped, Flat, Negatively Sloped, Humped
Shifting of Yield Curve: Parallel Shift, Steepening and Flattening, Positive/Negative Butterfly
Constructing Theoretical Spot Rate Curve:
- Treasury Coupon Strips: easy to view but drawbacks: limited liquidity, different tax, yield-tax trade-off
- On-the-run Treasury Issues: observed yield but differential tax treatment distorts yield, gap between maturities
- On-the-run and Selected Off-the-run: Linear interpolation and Bootstrapping Methods used - All Coupon Securities and Bills: complex methodologies, adjustments for taxes
Use of Swap Curve:
- Element: Swap is used, Swap Spread = Swap Rate – Government yield on a same-maturity bond
- Reasons: No government regulation, Supply/Demand determined by market, easy comparison
more maturity points available
- Constructing: bootstrapping methodology
2. Expectation Theories
Pure Expectation Theory
- Drawback: Neglecting risks inherent in investing in bonds: uncertainty about price at the end
reinvestment risk (rate at which proceeds will be invested)
- Broadest Interpretation: investors expect the return for any investment horizon to be the same regardless of the
maturity strategy selected. But because of price different, the expected return should be different.
- Local Interpretation: return over a short-term investment horizon will be the same
- Forward Rate: break-even rate, lock-in rate, market consensus
Liquidity Preference Theory: investors will hold long-term maturities if they are compensated by a premium
Preferred Habitat Theory: investors have to be paid a premium to shift out of their preferred sector
3. Measuring Yield Curve Risk Key Rate Duration: sensitivity of portfolio’s value to the change in a particular rate
Most Popular Key Rate duration: 11 key maturities (3-mo, 1,2,3,5,7,10,15,20,25,30 –yr maturities) used
Ladder Portfolio: key rate durations for every maturity is roughly the same
Barbell Portfolio: Some maturities’ duration is significantly greater
Bullet Portfolio: one maturity’s duration is significantly greater
Part C: Bond Valuation 1. Relative Valuation
Note: Nominal Spread is spread measured relative to treasury yield curve, and zero-volatility spread and OAS are
spreads relative to treasury spot-rate curve.
OAS will be affected by different interest rate volatility assumptions.
Benchmarks
Benchmark Spread Measure Risk Treasury Yield Nominal Credit, Option, Liquidity
Spot-Rate Zero-Volatility Credit, Option, Liquidity
Spot-Rate Option Adjusted (OAS) Credit, Liquidity
Sector
(Given Credit Rating)
Yield Nominal Credit, Option, Liquidity
Spot-Rate Zero-Volatility Credit, Option, Liquidity
Spot-Rate Option Adjusted (OAS) Credit, Liquidity
Issuer-Specific Yield Nominal Option, Liquidity
Spot-Rate Zero-Volatility Option, Liquidity
Spot-Rate Option Adjusted (OAS) Liquidity
Relative Value
Benchmark Negative OAS Zero OAS Positive OAS
Treasury Market Overpriced Overpriced If Security OAS < Required OAS, Overpriced
If Security OAS = Required OAS, Fairly Priced
If Security OAS > Required OAS, Underpriced
Sector (Given Credit Rating) Overpriced Overpriced If Security OAS < Required OAS, Overpriced
If Security OAS = Required OAS, Fairly Priced
If Security OAS > Required OAS, UnderpricedIssuer Specific Overpriced Fairly Priced Underpriced
2. Absolute Valuation (Binomial Model, based on No-Arbitrage Theory)
Requirement of Interest Rate Tree:
- Consistent with both interest rate volatility assumption and interest rate model
- Observed market price for securities generated
- When a tree is used to value an on-the-run issue for benchmark, the resulting value should be arbitrage free. Pre-condition of Construction of Interest Rate Movement: Interest Rate Volatility
Pre-condition of Construction of Interest Rate Movement: Interest Rate Volatility
Call Option Value = Value of Option-free Bond – Value of Callable Bond
Option Adjusted Spread: constant spread that when added to all the 1-year rates on binomial interest tree will make
the non-arbitrage value equals to price. If modeled value is higher, add a constant OAS to adjust value downward.
Effective Duration: (V- - V+)/ 2V0 (change in yield)
Effective Convexity: (V- + V+-2 V0)/ 2V0 (change in yield) 2
Calculating Duration and Convexity using Binomial Model:
- Calculate OAS using old tree before adjusting for changes in interest rate
- When new interest rate tree is formulated, then add OAS to each one-year rate. Therefore
interest rate do not contain OAS
- Duration will take into account of changes in cash flow due to embedded option.
Put Option Value: Value of Option-free Bond- Value of Putable Bond
Floating Rate Bond: Price = Par Value
Capped Floater: higher the cap, closer the price to par
Convertible Bond:
- Traditional Analysis
Conversion Value = Market Price of Common Stock * Conversion Ratio (set by covenants) Minimum Price of Convertible Security = MAX [Conversion Value, Value as security without conversion option]
Market Conversion Price = market Price of Convertible Security/Conversion Ratio
Market Conversion Premium per Share = Market Conversion Price – Current market Price
Market Conversion Premium Ratio = Market Conversion Premium/Market Price for Common Stock
Premium Payback Period = Market Conversion Premium per Share / Favorable Income Differential per Share
Favorable Income Differential per Share = [Coupon – (Conversion Ratio * Dividend)] / Conversion Ratio - Option-Based: Value of Convertible = Straight + Call on Stock + Put on Bond – Call on Bond
- Investment Characteristics: Hybrid Security
- Assumption: Straight Value does not change over time
- Risk/Return: limited upside potential, limited downside risk
- Hard puts and soft puts: hard put means issuer must redeem the bond with cash, while soft puts issuers can
select put methods. Part D: Structured Securities Valuation
1. Mortgage-Backed Securities (MBS)
Fixed Rate, Level-Payment, Fully Amortized Mortgage
- Mortgage rate fixed, same amount payment for all period, zero balance of principal after final payment
- Servicing Fee: some basis points, a portion of mortgage rate
- Prepayments: cash flow uncertainty associated with interest rates Mortgage Pass-through Securities
- Cash Flow Characteristics: Monthly Payments of Interest, Scheduled Principal Payments, Prepayments
- Weighted Average Coupon: Weighted Average of Mortgage Rates in Each Mortgage in the Pool
- Weighted Average Coupon: Weighted Average of Mortgage Rates in Each Mortgage in the Pool
- Weighted Average Maturity: Weighted Average of Maturity of Each Mortgage
- Types: Conforming (meeting specified requirements), Non-conforming (fail to meet such standards)
- Prepayment Measurement: Single Monthly Mortality Rate (SMM) = Prepayment t / (Beginning Balancet – Scheduled Principal Payment
Conditional Prepayment Rate (CPR) = 1-(1-SMM) 12
PSA Benchmark: 100%PSA refers to if t<30, CPR = 6% (t/30), otherwise CPR = 6%
If WAM is less than original loans year, and the different is n, CPR and SMM are applicable from month n+1.
SMM = 1 – (1-%PSA * CPR) 1/12
- Factors Affecting Prepayment: prevailing mortgage rate, housing turnover, characteristics of underlying - Prepayment Risk Categorization
Contraction Risk: Falling mortgage rate resulting in lower reinvestment, shortening in term of timing
Extension Risk: Rising mortgage rate resulting lower PV of cash flow, lengthening in term of timing
2. Collateralized Mortgage Obligation: Tool to distribute prepayment unequally among investors
Sequential-Pay Tranches
- Rule of distribution: distribute cash flows to lower tranches after higher ones are fully paid off. - Total Par Value = Par Value of Collateral, Coupon Rate on All Tranches = Coupon Rate on Collateral
- Principal Pay-down Window: time between beginning and ending of principal payment of a tranche
- Average Lives of Tranches: shorter or longer than collateral.
- Protection: Higher tranches are protected against extension; lowers are protected against contraction.
Accrual Tranches (Tranche Z or Z bond)
- Interest payments to Tranche Z are diverted to pay down principal of other higher tranches - Lives of other tranches are therefore shorter.
- Tranche Z does not get any interest payment until all other tranches are paid off.
- Tranche Z does not have effect on prepayment risk.
- Tranche Z eliminates reinvestment risk until all other tranches are paid off.
Floating-rate Tranches (FL) and Inverse Floaters (IFL)
- Floater and Inverse Floater must be created simultaneously
- Cap rate for IFL = IFL Interest when Reference Rate is Zero / Principal for IFL
- Total Principal for FL & IFL = Principal before “Sliced-up”; Total Coupon = Coupon before “Sliced-up
- Cap Rate for FL = Collateral Tranche Interest / Principal for Floater
- Appealing to investors who have floating-rate exposures
Structured Interest-only Tranches (IO)
- Other tranches’ coupon rate is set to be lower than coupon for collateral
- No par amount. Amount shown is the amount upon which interest will be determined. Notional Amount
- Notional Amount for x% IO = Original Tranche’s par value * Excess Interest / x%
Planned Amortization Class Tranches (PAC)
- If prepayment speed is within a specified band over the collateral ’s life, the cash flow pattern is known.
-
Within the specified band, the average life of tranche is stable. - PAC window: length of time over which expected repayment of principal are made. Narrower the window, more
the tranche resembles a corporate bond with bullet payments. PAC buyers appear to prefer tight widows.
- Effective Collar: Lower/Upper PSA that still allow maintenance of scheduled principal payments. Wider Effective
- Effective Collar: Lower/Upper PSA that still allow maintenance of scheduled principal payments. Wider Effective
Collar, more protection gained against prepayments.
- If PAC tranche is attractive, it must have lowest option costs: minimum Z-spread minus OAS.
Support Tranches (S) - Support tranches do not receive any principal until PAC tranches receive their scheduled principal payments.
- Support tranches are created to absorb prepayment risk, offering greater certainty for PACs
- Support tranches receive excess principal prepayments.
- S tranches have greatest level of prepayment risk.
- If S is paid off due to prepayment, the structure is broken and all PACs become sequential-pays.
3. Stripped MBS
Principal-Only Strips (PO)
- PO is purchased at substantial discount from par value.
- Faster prepayments, higher return for PO. Investor ’s return is solely determined by prepayment speed.
- Lower mortgage rate, faster prepayments, higher return and vice versa.
Interest-Only Strips (IO)
- No par value when purchased.
- IO investors want prepayments to be slow.
- Lower mortgage rate, faster prepayments, less interest generated, lower return.
- Higher mortgage rate, slower prepayments, but higher discount rate, lower return (too high rate, net effect)
4. Non-Agency Residential Mortgage Backed Securities
Underlying Mortgage Loans Underwriting Standards:
- Maximum Loan-to-Value, maximum Payment-to-Income, maximum Loan Amount Differences between Non-Agencies and Agencies: Guarantee.
5. Commercial Mortgage-Backed Securities
Credit risk: if defaults, lenders look into the proceeds of sale of property for repayment.
Analysis: lender must view each property on a stand-along basis.
Pay-down structure: highest-rating bond will get paid off first.
Call Protection: - Loan Level: Prepayment Lock-out, Defeasance, Prepayment Penalty Points, Yield Maintenance Charge
- Structural Level: Prepayments and defaults impact principal losses.
Balloon Maturity Provisions: principal payment at the end of maturity
Balloon risk: the risk that the loan will extend beyond the scheduled maturity date.
6. Asset-Backed Securities
1) General Concepts and Need-to-Knows - Parties Involved in Securitization
Party Description
Seller Originate loans and sell loans to SPV
Issuer/Trust SPV, buying loans and issuing securities against loans
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Issuer/Trust SPV, buying loans and issuing securities against loans
Servicer Service the loan
- Reason for creating structures: redistribute cash flows and risks among investors.
- Collateral Classification: Amortizing (Mortgages, Loans, etc), Non-Amortizing (Receivables)
- Securities backed by non-amortizing collateral have change in collateral.
- Projecting default is important to non-amortizing collaterals.
- Credit Enhancement:
External: Insurance Company (wrapped), letter of credit from a bank and guarantee by seller. Downgrade of the
third party can result in downgrade of securities in a structure.
Internal: Cash Reserve Funds, Excess Spread Accounts (points paid to reserve accounts to absorb possible future
loss, often Gross WAC – Service and other fees – Net WAC), Overcollateralization (absorbing losses to a certain
amount without affecting bond classes), senior-subordinate structure (prone to prepayments)
2) Home Equity Loan
Prepayments: PPC (Prospectus Prepayment Curve), issuer-specific Payment Structure:
- Non-Accelerating Senior Tranches: stable average life
3) Manufactured Housing-Backed Securities
Loan may be either mortgage or customer retail installment loan.
Prepayments are stable as the loans are not sensitive to refinancing.
Payment Structure: Same as MBS and Home Equity Loan
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