Fixed Income

Question 1

Forward Rates and Bracketing - derive fwd rate from spot, and spot from fwd rate

Answer 1

Remember fwds are based on pure expectations

• pure expectations:
  
  • fwds are unbiased predictors of future spots
  • no risk premium across maturities

Question 2

Swap Spreads

Answer 2

• Won’t have to calculate Z or OAS spreads, but may need to choose from a grid

Question 3

Term Structure Theories: Pure Expectations and Liquidity Preference

Answer 3

Question 4

Modern Term Structure Theories - Describe Models (Don’t need to know formulas)

Answer 4

likely will have to describe difference between the top 2, or a “comment” question

Question 5

Yield Curve Shifts

Answer 5

• 90% comes from parallel shifts (level not shape)
• Steepness & Curvature = shaping risk
• ST rates: lower but more volatile
• LT rateS: higher, but less volatile

Question 6

Key Rate Duration and Effective Duration

Answer 6

• 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

Question 7

Arbitrage-Free Valuation

Answer 7

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

Question 8

Methods of Valuation

1) Backward Induction
2) pathwise
3) Monte Carlo

Answer 8

Question 9

Bonds With Embedded Options

Answer 9

• 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
• • Vcallable = Vs - Vcall
• Vputable = Vs + Vput

Question 10

Duration and Convexity - Memorize Relationships

Answer 10

Question 11

Convertible Bond Formulas

Answer 11

Question 12

Credit Analysis and Risk

Answer 12

Question 13

Credit Analysis Models and Attributes

Answer 13

Question 14

Par Rates

Answer 14

• Basically the coupon rate that makes par = 100

Question 15

Level & Shape of Yield Curve - Options

Answer 15

Very testable - won’t have to calculate, but must understand

Question 16

Valuing Bonds with Call Options - Important on Exam

Answer 16

• 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

Question 17

OAS and Volatility (very testable)

Answer 17

• 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

Question 18

One-Sided Durations (Important Intuition)

Answer 18

Question 19

Effective Convexity

Answer 19

Question 20

Convertible Bond Terms

Answer 20

• 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

Question 21

Intuition of Convertible Bonds (equivalents: IMPORTANT)

Answer 21

Question 22

Credit Risk Measures (Loss formulas)

Answer 22

• Expected Loss = Probability of Default x Loss Given Default
• Credit Valuation Adjustment (CVA) = value of comparable risk-free bond - value of risky bond

Question 23

Risk-Neutral Probability of Default

Answer 23

• Not digging in deep but should know - it’s an FC, but DNF

Question 24

Structural Models

Answer 24

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

Question 25

Reduced-form Models

Answer 25

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

Question 26

Term Structure of Credit Spread

Answer 26

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

Question 27

CDS Basics

Answer 27

• 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

Question 28

Two CDS Formulas need to know:

Upfront Premium

Profit for protection buyer

Answer 28

1. Upfront premium = (CDS Spread - CDS Coupon) X Duration
2. Profit for protection buyer = approx change in spread (in bps) X duration X notional principal

Question 29

Traditional Term Structure Theories:

Pure Expectations (Unbiased)

Local Expectations

Liquidity Preference

Segmented Markets

Preferred Habitat

Answer 29

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