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MindMap Gallery Fixed Income CFA Level 2
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Fixed Income CFA Level 2
Mind map for Fixed Income CFA Level 210%-15%, including term structure, risk-free arbitrage pricing, equity bond valuation, credit analysis models, and credit default swaps.
Edited at 2023-09-13 19:56:13
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Fixed Income CFA Level 2
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- Outline
Fixed income 10%-15%
term structure
Yields and Spreads
spot rate spot rate
forward rate forward rate
interest rate curve
The yield curve is upward, and the forward interest rate curve is upward.
The yield curve is downward, and the forward interest rate curve is downward.
discount factor discount factor
rate of return
Hold-to-maturity yield YTM
expected rate of return
Use YTM instead
hold until maturity
Pay coupon and principal in full
The reinvestment rate of return is YTM
bootstrapping method
par curve
par rate: the coupon rate when issuing at par
Find the spot interest rate through the parity interest rate curve
forward pricing model
Forward price: first discount from the final period to the current period, and then discount to the issuance period
swap rate curve
Reflects the credit risk of commercial banks rather than the government
Not subject to government regulation, making comparisons between different countries easier
The market is large and there are corresponding interest rates for different maturities.
spread
swap spread
Swap Rate – Government Bond Rate
Z-spread
Reflect the company's unique credit risk and liquidity risk, as well as rights-related risks
TED spread
Libor - T-bill interest rate for the same term
Reflects overall economic credit risk
Libor-OIS spread
OIS is the overnight swap rate
Reflect money market credit risk and liquidity risk
term structure theory
Tradition
pure expectation theory pure expectation thoery
Idea: Forward rates are unbiased estimates of future spot rates
risk neutral
Conclusion: The yield curve and short-term interest rate expectations move in the same direction
local expectation theorylocal expectation theory
The risk neutrality assumption is established in the short term, and the perfect expectations theory is only established in the short term.
Liquidity preference theory Liquidity preference theory
Forward rate = expected spot rate Liquidity premium
Investors demand a risk premium in the form of a liquidity premium to compensate them for the additional interest rate risk they face when purchasing long-term bonds. The theory also states that liquidity premiums increase with maturity.
based on expectations
market segmentation theory segmented markets theory
Bonds of different maturities are in independent segmented markets, and interest rates are only affected by supply and demand within the segmented market.
preferred habitat theory
The market is not completely segmented, and investors will migrate to other markets according to their own preferences.
And to the market
modern
equilibrium term structure modelequilibrium term structure model
Vasicek model
shortcoming
Interest rates may be negative
Interest rate volatility remains constant over time
formula
Cox-Ingersoll-Ross, CIR model
Choices between today’s consumption and future consumption
Thoughts: interest rate ↑, investment ↑, consumption ↓, currency ↑, interest rate ↓
Drift term
formula
Disturbance term
arbitrary free model
Ho-Lee model
Advantages: consistent with market data
Kalotay-Williams-Fabozzi, KWFmodel
gauss model
Comprehensive short, medium and long-term interest rates
long term interest rate
Mean reversion reflects the trend of macro variables
medium term interest rate
Return to long term interest rates
short term interest rate
Consistent with short-term interest rates controlled by the central bank
Hump-shaped fluctuation curve, the most unstable in the mid-term
factor model
Compared
active bond portfolio managementactive bond management
riding the yield curve riding the yield curve
The yield curve slopes upward and remains unchanged. It is profitable to buy bonds with a maturity period greater than the investment period.
Earn capital gains Coupon income
Risk Management
Yield Curve Volatility
The future cash flow of rights-containing bonds is uncertain, and YTM cannot be accurately determined
index
effective durationeffective duration
Yield curve parallel shift
ΔCurve
The distance of a small parallel shift of the yield curve upward or downward
Embedded call option or put option will result in low effective duration
key rate durationkey rate duration
Non-parallel shifts in the yield curve, measuring small changes in a specific point
Unpacking the Yield Curve Movement
Horizontal Level, parallel movement
Steepness
Curvature
The term structure of volatility
High short-term interest rate volatility High long-term interest rate volatility
Short term: impact of monetary policy
Long term: real economy and inflationary impact
Factors affecting bond prices
Duration
interest rate fluctuations
Economic factors that affect interest rates
Monetary Policy
bearish flattening bearish flattening
A bull market occurs when interest rates fall, when prices rise
During an expansion, short-term interest rates increase more than long-term interest rates.
Bulling steepening
During a recession, short-term interest rates fall more
Fiscal policy
Increased deficit: more borrowing, higher interest rates
Deficit reduction: less borrowing, lower interest rates
flight to quality
In a recessionary market, long-term interest rates fall more than short-term interest rates
In a recession, buy government bonds and high-quality assets
Long-term interest rates fell more than short-term interest rates
Risk-free arbitrage pricing
arbitrage opportunities
Value additivity
stripping
Splitting interest-bearing bonds into zero-coupon bonds
Reconstitution
Zero-coupon bonds are restructured into interest-bearing bonds and then sold
Dominance arbitrage opportunity dominance
Risk-free return assets must have positive prices in the future
Binary tree pricing
in principle
There are two methods commonly used to estimate potential interest rate fluctuations in binomial interest rate trees. The first method estimates based on historical interest rate volatility. The second approach uses observed market prices of interest rate derivatives.
backward induction valuation backward induction valuation
Given coupon rate and investment period
Given a binary tree of interest rates
Discount from back to front
pathwise valuation
step
Variation of spot interest rate valuation method
Given coupon rate and investment period
Given a binary tree of interest rates
Find the value of each path
Find the mean of all paths
Monte Carlo simulation
path dependency
Such as MBS early repayment
Equity Bond Valuation
Bonds with rights
callable bond callable
beneficial to the issuer
When interest rates fall, the issuer redeems the bond
Bond investors sell call options on bonds to the issuer
Putable bonds putable
beneficial to holders
When interest rates rise, bonds are sold back to the bond issuer
Bondholders hold put options
extendablebondextendible
Expiration period
estate put bonds estate put bonds
After the bondholder dies, the heirs elect to sell the bond back to the issuer
sinking fund bonds sinking fund bonds
Before maturity, the issuer redeems part of the bonds in advance
Factors affecting the value of bonds with rights
Impact of interest rate fluctuations
Volatility rises, option values rise
Callable bonds↓
Puttable bonds↑
The impact of yield curve levels
Look at the picture
The impact of yield curve shape
The interest rate curve slopes downward, bond prices ↑, bond call options ↑, callable bonds ↓
The interest rate curve slopes downward, bond prices ↑, bond puts ↓, callable bonds ↓
Valuation
Binary tree model
The spot interest rate is not available, so backward induction can only be used
Determine whether to exercise rights at each node
Callable bonds choose a lower price
Because it is detrimental to the holder
Putable bonds choose higher prices
Because it is beneficial to the holder
Valuation with risk premium
Z-spread
Includes credit risk premium, liquidity risk premium, and option premium
OAS, option adjusted spread
concept
Remove the discount of callable or the premium of putable
Eliminates the impact of options
Value Analysis
Compared with the benchmark bond, a bond has a lower OAS and the bond is overvalued.
Compared with the benchmark bond, a bond has a higher OAS, which means the bond is undervalued.
Impact of interest rate fluctuations
callable bonds, volatility ↑, options ↑, removed premium increase, OAS ↓
putable bonds, volatility ↑, options ↑, the discount removed increases (negative makes positive), OAS↑
floating bonds with rights
capped floater
Interest rates are capped to protect issuers
value of capped floating-rate bond = value of a straight floater - value of the embedded cap
floored floating-rate bond
There is a lower limit on interest rates to protect bondholders
value of floored floating-rate bond = value of a straight floater value of the embedded floor
Determine whether cap and floor are applicable at each node
Interest Rate Risk
effective durationeffective duration
Yield curve parallel shift
summary
ΔCurve
The distance of a small parallel shift of the yield curve upward or downward
Embedded call option or put option will result in low effective duration
interest rate impact
Interest rate ↓ callable bond duration ↓
Interest rate ↑ putable bond duration ↓
key rate durationkey rate duration
Non-parallel shifts in the yield curve, measuring small changes in a specific point
Unilateral duration
one-side up duration one-side up duration
Sensitivity when measuring interest rates
one-side up duration one-side up duration
Sensitivity when measuring interest rates ↓
effective convexity
Measures the sensitivity of duration to interest rates
Convertible bond concept
A call option equivalent to the stock of the issuing company
index
conversion ratioconversion ratio
The number of common shares that the bond can convert into
conversion price= issue price / conversion ratio
Conversion value = market value of common stock × conversion ratio (number of shares)
straight value
value as an ordinary bond
Minimum value = max (conversion value, pure value)
market conversion price=market price of convertible bonds/conversion ratio
The actual price paid when purchasing convertible bonds and converting them into stocks
market conversion premium per share market conversion premium per share
Market conversion price - market price per share
Market conversion premium ratio = market conversion premium per share / market price per share
Valuation
Convertible bond value = bond value Stock call option value
Value of callable convertible bonds = value of bonds Stock call option value – Value of bond call options
Value of putable convertible bonds = value of bond, value of stock call option, value of bond put option
risk
downside riskdownside risk
pure value premium
Convertible bond price/pure price-1
Potential upside, no upper limit
feature
The stock price is lower than the conversion price, showing debt attributes
The stock price is higher than the conversion price, showing stock attributes
Credit analysis model
Credit risk measurement
credit spread credit spread
G-spread
credit valuation adjustments
credit valuation adjustment, CVA
Present value of expected credit losses
concept
exposureexposure
Balance of assets exposed to risk
Probability of default, POD
The probability of default before maturity
hazard rate hazard rate
Default at time t, conditional probability of no default at t-1 and before
probability of survival, POS
The probability that there is no default in the current period and in previous periods
Loss given default, LGD
Loss given default = 100% - recovery rate
calculate
credit scoringcredit scoring
Ordinal ranking of credit, only high and low, no multiple relationship
does not change with the economic environment
Does not reflect the borrower’s position among all borrowers, with the same score
Mainly used for small individuals
credit rating credit rating
Rating
investment grade
speculative grade
advantage
Simple and intuitive
Stable rating results will help reduce bond market price volatility
shortcoming
Stable, but insensitive to changes in default probability
The rating results do not change with the economic cycle, but the probability of default changes with the cycle.
Profitability, principal-agent problem
Rating migration
Expectations for each path
Credit analysis model
structure modelsstructure models
Option Pricing Theory BSM Financial Report
Holding a company's stock is equivalent to holding a European call option on the company's assets.
The subject is company asset A
Exercise price K, face value of the company’s zero-coupon bond
Exercise maturity date T, zero-coupon bond maturity date
hypothesis
No arbitrage, no friction
Asset values follow a lognormal distribution
Risk-free interest rate is constant
Liabilities are only zero-coupon debt
Advantages and Disadvantages
advantage
Understanding corporate bond default probabilities and recovery rates from an options perspective
Estimated through models based on market prices
shortcoming
Assumptions 1 and 4 are not realistic
Without considering the economic cycle, assumption 3 is usually not true
reduced form models
hypothesis
Frictionless and arbitrage-free trading of corporate zero-coupon bonds
Risk-free interest rate stochastic
The economic state is represented by a random vector composed of a set of macro factors
The economic state and recovery rate are random, and the probability of default changes with the economic state.
Default depends on the company's own circumstances
Advantages and Disadvantages
advantage
Input variables are observable and historical data are available
Credit risk changes with economic cycles
No need to make assumptions about the balance sheet
shortcoming
Inaccurate calculation of hazard rate
Securitized Debt & Corporate Debt
The securitized asset pool will not default at the same time, and the probability distribution of losses is used to measure credit risk.
credit default swap
credit derivatives credit derivatives
total return swaps
credit spread optionscredit spread options
credit-linked notes credit-linked notes
credit default swap, CDS
The target is a measure of the borrower's credit quality.
concept
definition
The credit protection buyer pays cash flow (premium) to the credit protection seller, and the seller compensates the buyer in the event of default.
credit curve
Time on the horizontal axis, credit spread on the vertical axis
nominal amount
Insurance protection amount
CDS spread
Premium as a percentage
actual market price
CDS coupon rate
Standardized premium, CDS premium for investment grade bonds is 1%, speculative grade is 5%
upfront payment/premium
The difference between the standard coupon rate and spread
spread is greater than the coupon rate, the risk protection seller pays a prepaid premium to the risk protection buyer
The buyer pays the seller the standard coupon price, and the seller returns the difference between the coupon and the actual market price spread to the buyer.
multiply by year
credit eventscredit events
Bankruptcy
Insufficient repayment of principal and interest
Restructure bond terms
settlement protocol settlement protocol
physical settlement
When a risk event occurs, the credit risk buyer gives the defaulted bond to the credit risk seller, and the seller gives the nominal principal to the buyer.
cash settlement
When a risk event occurs, the seller directly compensates the buyer’s loss value.
single name credit default swapsingle name CDS
Borrower-specific CDS
The specific borrower is called the reference entity
The underlying bonds agreed in the contract
reference obligation
The underlying bonds are senior unsecured obligations.
The contract covers the underlying bonds and higher-grade bonds
In the event of default, the buyer gives the seller the cheapest bond with the same credit rating
cheapest to deliver
index CDS
A group of bond issuers, the higher the correlation between the group, the higher the premium
Pricing
Thought
Given the CDS coupon rate, determine the CDS interest spread or prepaid premium
Prepaid premium paid by the buyer ≈ (CDS spread – coupon rate of CDS) × CDS duration
Influencing factors
The higher the probability of default, the higher the spread
The higher the LGD, the higher the spread
Expected loss = Hazard × loss given default rate loss given default
profit
spread change rate × CDS duration
application
Manage credit risk exposure
Adjust credit risk exposure
naked credit risk swap naked CDS
Long and short trading
Credit spread curve trading
valuation disparity arbitrage
Take advantage of the difference between temporary credit spreads in the bond market and credit spreads in the CDS market
arbitrage trade
Synthetic CDO = Long position in risk-free bonds Sell CDS (credit risk seller)