Fixed Income Flashcards
Forward Rates and Bracketing - derive fwd rate from spot, and spot from fwd rate
Remember fwds are based on pure expectations
- pure expectations:
- fwds are unbiased predictors of future spots
- no risk premium across maturities
Swap Spreads
- Won’t have to calculate Z or OAS spreads, but may need to choose from a grid
Term Structure Theories: Pure Expectations and Liquidity Preference
Modern Term Structure Theories - Describe Models (Don’t need to know formulas)
likely will have to describe difference between the top 2, or a “comment” question
Yield Curve Shifts
- 90% comes from parallel shifts (level not shape)
- Steepness & Curvature = shaping risk
- ST rates: lower but more volatile
- LT rateS: higher, but less volatile
Key Rate Duration and Effective Duration
- Effective Duration will be on exam (WONT have to calc any of this)
- Key Rate Duration (should know):
- price impact of par rate changes for specific maturities
- applicable for nonparallel shifts in yield curve
- captures shaping risk
- Option-free bond’s maturity-matched rate is the most important -> its key rate duration is highest
- matched = ties to maturity eg 6y rate for a 6y bond
- Callable Bond with option deep out of the money (low coupon rate) will have highest key rate duration corresponding to its maturity - will look like a straight bond
- Putable Bond with option deep out of the money (high coupon rate) will have highest key rate duration corresponding to maturity
- As option moves into the money the time-to-exercise rate becomes important. Key rate duration corresponding to the time-to-exercise will be highest.
- as rates fall towards rate where it will be in the money
Arbitrage-Free Valuation
Just says that the model will give us the rate for on the run treasury securities
note for int rate trees: always 50/50 chance of up or down moves - only changes for stock options in other part of curriculum
Methods of Valuation
1) Backward Induction
2) pathwise
3) Monte Carlo
Bonds With Embedded Options
- Issue is that when interest rates change not just the PV of the cash flows change, but the cash flows themselves can change - because bond can get called away or put to issuer
- Internalize this:
- the callable bond value is equal to the value of a straight bond MINUS the value of the embedded call
- doesn’t help me as bondholder because the issuer has the option
- the callable bond value is equal to the value of a straight bond MINUS the value of the embedded call
- Vcallable = Vs - Vcall
- Vputable = Vs + Vput
Duration and Convexity - Memorize Relationships
Convertible Bond Formulas
Credit Analysis and Risk
Credit Analysis Models and Attributes
Par Rates
- Basically the coupon rate that makes par = 100
Level & Shape of Yield Curve - Options
Very testable - won’t have to calculate, but must understand
Valuing Bonds with Call Options - Important on Exam
- Use the same backward induction process as the tree
- Whenever the option can be exercised:
- CALL: Value at any node is LOWER either A) average PV of the two values from the next part of the tree or B) call price
- PUT: Value at any node is the HIGHER of either A) average PV of the next two values or B) the put price
- You can get the value of the option by just valuing the bond as if it were straight and finding delta:
- Vcall = Vstraight - Vcallable
- Vput = Vputable - Vstraight
OAS and Volatility (very testable)
- Assumed level of volatility in a binomial tree affects the value of the underlying options - values of options are higher
- If option valued higher, Vcallable is lower and Vputable is higher
Callable:
- increase in volatility = call option value is higher = value of bond is lower = OAS is lower
- decrease in volatility = option is lower = value of bond is higher = OAS is higher
Putable:
- increase in volatility = put option is higher = putable bond value higher = OAS is higher
- decrease in volatility = put option value lower = putable bond lower = OAS is lower
One-Sided Durations (Important Intuition)
Effective Convexity
Convertible Bond Terms
- Convertible to fixed # of shares
- Intuition: option on stock held by hondholder
- Important Point: conversion option is NOT affected by interest rates
-
IMPORTANT: KNOW THE TERMINOLOGY:
- Conversion Ratio = # shares / bond
- Conversion Price = issue price / conversion ratio
- Market Conversion Price = Effective price per share when converting
- Conversion Value = market price of stock after conversion X conversion ratio
- Straight value = PV of all CFs if not convertible
- * Minimum Value of a convertible bond = greater of conversion value (AKA stock value) and straight value (AKA bond value)
- Market conversion premium ratio = market conversion premium / market price
- Premium over straight value = (MV of bond / Straight Value) - 1
Intuition of Convertible Bonds (equivalents: IMPORTANT)
Credit Risk Measures (Loss formulas)
- Expected Loss = Probability of Default x Loss Given Default
- Credit Valuation Adjustment (CVA) = value of comparable risk-free bond - value of risky bond
Risk-Neutral Probability of Default
- Not digging in deep but should know - it’s an FC, but DNF
Structural Models
DNF, but this is what you need to know:
- Based on balance sheet and insights from option pricing
- Value of risky debt = value of risk-free debt minus value of a PUT option on the company’s assets
- Value of a put option = CVA
- Explain why default occurs, but company assets are not actually traded and therefore value is not observable
- also doesnt work with complex balance sheets or with off-BS liabilities
Reduced-form Models
DNF, but this is what you need to know: (curriculum doesn’t tell us exactly what a RF model is)
- Does not explain WHY default occurs (as opposed to Structural, which does) - random surprises
- uses default intensity
- allows linkage of default intensity, RfR and recovery rate to the state of the economy
- Strength: does not assume company assets traide, and default intensity is allowed to fluctuate as company fundamentals change and with biz cycle
Term Structure of Credit Spread
Determinants:
- Quality: Higher-rated sectors have flatter term structures
- Financial conditions: they are steeper when expecting recessions
- Equity market volatility: increases in equity mkt volatility increases credit spreads
CDS Basics
- Dont get bogged down in details - it’s basically just buying insurance on credit risk on a bond
- typically 10 year bond - can trade in secondary market typically after 2 years
- Protection buyer is short credit risk and is obligated to make CDS spread payments
- Protection seller is long credit risk and is obligated to make a payment if credit event occurs
- CDS on a single specific borrower is called a single-name CDS
- Payoff on a single-name CDS is based on the cheapest-to-deliver obligation with the same seniority
- CDS on an equally weighted combo of borrowers is an index CDS - credit correlation is important for these
-
IMPORTANT PART:
- Standardization in CDS market makes CDS coupon not equal the CDS spread
- CDS spread = market price of protection, NOT the coupon
- but was standardized after 2008
- Coupon = upfront payment from buyer to seller
- Coupon > spread = upfront payment from seller to buyer
- Hence, an upfront payment is made by one of the counterparties; called an upfront premium
- Standardization in CDS market makes CDS coupon not equal the CDS spread
Two CDS Formulas need to know:
Upfront Premium
Profit for protection buyer
- Upfront premium = (CDS Spread - CDS Coupon) X Duration
- Profit for protection buyer = approx change in spread (in bps) X duration X notional principal
Traditional Term Structure Theories:
Pure Expectations (Unbiased)
Local Expectations
Liquidity Preference
Segmented Markets
Preferred Habitat
Pure Expectations (Unbiased:
- Forwards are unbiased predictors of future spots; NO risk premium across maturities
- Wherever yield curve is going, that’s where rates are going
Local Expectations
- Similar to Pure Expectations –> ONLY SHORT TERM expected returns are risk free
- Risk premiums rexist over longer terms
- Buying 3 one-yr bonds does NOT equal the same as buyin one 3-yr bond because longer maturity = higher rate risk
Liquidity Preference
- Forwards are biased upwards by LIQUIDITY premium
- up-slope is most likely, but can still be going down or lumped –> it’s just a little bit higher than it would be at longer maturities bc LIQUIDITY premium
Segmented Markets
- premium determined by supply and demand in each mkt segment (segments are independent)
- supply and demand for short, medium, and long term bonds drives the shape of the yield curve; eg more demand for medium will cause the middle part of the curve to go up
Preferred Habitat
- Similar to Segmented BUT players defiate from preferred segment if there is enough premium offered in another “habitat” (segment)
- basically, segmented markets says players prefer to be in one spot, but pref habitat says that if demand is high enough, pricing can draw people out of their preferred segment
