Fixed Income Flashcards
(105 cards)
1
Q
Convenience yield
A
Benefit of holding the physical commodity (not through a future)
2
Q
Super classes of assets
A
- Capital assets
- Store of value assets
- Consumable or transferable assets (C/T)
3
Q
- Futures contract size
- Tick
A
- Point value
- Smallest change in price
4
Q
- Backwardation
- Contango
A
- Futures prices are lower than the spot price
- Futures prices are higher than the spot price
5
Q
Total return on futures investments
A
= spot return + roll return + collateral return
6
Q
Excess return
A
= spot return + roll return
7
Q
Spot curve
A
Annualized return on a risk-free zero coupon bond with a single payment of principal at maturity
8
Q
Forward price P(T* + T)
A
P(T* + T) = P(T*) F(T*, T)
- T* = number of years before the initiation of the contract
- T = tenor of the contract
9
Q
- When the spot curve is upward sloping
- When the spot curve is downward sloping
A
- f(T*, T) > r(T* + T), r(T* + T) > r(T*)
- f(T*, T) < r(T* + T), r(T* + T) < r(T*)
10
Q
Par curve
A
YTM on a risk-free coupon-paying bond priced at par
11
Q
Fixed-rate leg of an interest swap
A
Swap rate
12
Q
- Discount factor
- Rate associated with the previous discount factor
A
- 0.95/1.00 = 0.95
- [1/0.95] - 1 = 0.05263
13
Q
- s(T)
- P(T)
- r(T)
A
- Swap rate a time T
- Discount factor with maturity T
- Spot rate at time T (YTM)
14
Q
“On-the-run” government security
A
The most recently issued security
15
Q
Gilts
A
UK government bonds
16
Q
The Z-spread, ZSPRD
A
Spread over the default-free spot curve
/
The constant basis point spread that would need to be added to the implied spot yield curve so that the discounted cash flows of a bond are equal to its current market price
17
Q
The Interpolated Spread - I-spread - ISPRD of a bond
A
Difference between its yield to maturity and the linearly interpolated yield for the same maturity on an appropriate reference yield curve
18
Q
The pure expectations or unbiased expectations theory
A
The forward rate is an unbiased predictor of the future spot rate
19
Q
Local expectations theory
A
A form of the pure expectations theory that suggests that the returns on bonds of different maturities will be the same over a short-term investment horizon
20
Q
Liquidity preference theory
A
A premium exist for long-term securities
21
Q
Segmented markets theory
A
The yield curve is influenced by the preferences of lenders and borrowers
22
Q
The preferred habitat theory
A
Agents and institutions will accept additional risk in return for additional expected returns
23
Q
Riding the yield curve
A
Buying bonds with maturities longer than the investment horizon
24
Q
TED spread
A
Difference between the interest rates on interbank loans and on short-term U.S. government debt (“T-bills”). TED is an acronym formed from T-Bill and ED, the ticker symbol for the Eurodollar futures contract.
25
* Spot curve - S
* Par curve (yield curve) - Y
* Forward curve - F
* The spot curve gives a yield that is used to discount a single cash flow at a given maturity
* The par curve is the single discount rate that you would use to discount all of the bond’s cash flows to get today’s market price
* The forward curve is similar to the spot curve (from which it is derived) in that it discounts a single payment. The difference is that it doesn’t discount that payment back to today; instead, it discounts it back one period
26
Arbitrage-free value of a bond
Present value of its cash flows discounted at the spot rate
27
Bootstrapping
Because the T-bills offered by the government are not available for every time period, the bootstrapping method is used to fill in the missing figures in order to derive the yield curve
28
Vanilla bond
Straight option-free bond
29
* European-style callable bond
* American-style callable bond
* Bermudan-style callable bond
* Can be called on a single date after the lock-up period
* Can be called continuously after the lock-up period
* Can be called on a predetermined schedule after the lock-up period
30
Putable bonds
Either European or Bermudan
31
OAS on a zero volatility bond
Equals the Z-spread on an option-free bond
32
Option-adjusted-spread (OAS)
The option-adjusted spread (OAS) is the measurement of the spread of a fixed-income security rate and the risk-free rate of return, which is adjusted to take into account an embedded option
33
Effect of changes in volatility on an option-free bond
An option-free bond is not affected by changes in yield volatility
34
* High OAS
* Low OAS
* Likely underpriced
* Likely overpriced
35
Key rate duration
Sensitivity of a bond's price to changes in specific maturities on the benchmark curve
36
Convexity of callable and putable bonds
* A putable bond always has a positive convexity
* A callable bond's convexity turns negative when the call option is near the money
37
Set in arrears on floaters
The coupon rate is set at the beginning of the coupon period and the coupon is paid at the end
38
Ratchet bonds
At every coupon reset, the rate can only go down - also contain a contingent put allowing the investors to put the bond back to the issuer at par when the coupon is reset
39
Forced conversion
Forces investors to convert their bonds into shares when the underlying share price increases above the conversion price
40
* Conversion value
* Conversion price
* Conversion value = underlying share price x conversion ratio
* Conversion price = par price of the bond / conversion ratio
41
* Market conversion premium per share
* Market conversion price
* Premium over straight value
* Market conversion premium per share = Market conversion price – Underlying share price
* Market conversion price = Convertible bond price / Conversion ratio
* Premium over straight value = (Convertible bond price / Straight value) − 1
42
The five Cs of credit
* Character
* Capacity
* Capital
* Collateral
* Conditions
43
Busted convertible
When the price of the share is below the conversion price
44
* Value of convertible bond
* Value of callable convertible bond
* Value of callable putable convertible bond
* Value of convertible bond = Value of straight bond + Value of call option on the issuer’s stock
* Value of callable convertible bond = Value of straight bond + Value of call option on the issuer’s stock – Value of issuer call option
* Value of callable putable convertible bond = Value of straight bond + Value of call option on the issuer’s stock – Value of issuer call option + Value of investor put option
45
Effective duration for floating rate bonds
Close to their next coupon reset
46
Debt option analogy
Owning a company's debt is equivalent to owning a risk-free bond that pays K dollar at maturity and selling a European put option on the assets of the company with strike price K
47
Reduced form model assumptions
* The company’s zero-coupon bond trades in frictionless markets that are arbitrage free
* The riskless rate of interest, rt, is **stochastic**
* The state of the economy can be described by a vector of stochastic variables Xt that represent the macroeconomic factors influencing the economy at time t
* The company defaults at a random time t, where the probability of default over [t,t + Δ] when the economy is in state Xt is given by λ(Xt)Δ
* Given the vector of macroeconomic state variables Xt, a company’s default represents idiosyncratic risk
* Given default, the percentage loss on the company’s debt is 0 ≤ ι(Xt) ≤ 1
48
Structural model assumptions
* The company’s assets trade in frictionless markets that are arbitrage free
* The riskless rate of interest, r, is **constant over time**
* The time T value of the company’s assets has a lognormal distribution with mean *u*T and variance σ2T
* These three assumptions are identical to those for stock price behavior in the original Black–Scholes option pricing model
49
Implicit estimations for credit models
* Both the structural and the reduced form models
* Only the reduced form model can use historical estimations
50
* f(T\*,T)
* F(T\*,T)
* forward rate
* forward price
51
Forward curve in relation to the spot curve
When the spot curve is upward sloping, the forward curve will lie above the spot curve, and that when the spot curve is downward sloping, the forward curve will lie below the spot curve
52
Positive convexity
Property of some bonds that when market interest rates rise their price depreciates at a rate slower than the rate at which their price appreciates when the interest rates fall
53
Swap spread
Is defined as the spread paid by the fixed-rate payer of an interest rate swap over the rate of the **on-the-run** (most recently issued) government security with the same maturity as the swap
54
Market evidence shows that forward rates are upwardly biased predictors of future spot rates
The existence of a liquidity premium ensures that the forward rate is an upwardly biased estimate of the future spot rate. Market evidence clearly shows that liquidity premiums exist, and this evidence effectively refutes the predictions of the unbiased expectations theory
55
**Arbitrage-free term structure** models versus **equilibirum term structure** models
* Arbitrage-free valuation refers to an approach to security valuation that determines security values that are consistent with the absence of an arbitrage opportunity
* Equilibrium term structure models are models that seek to describe the dynamics of the term structure using fundamental economic variables that are assumed to affect interest rates
56
Shaping risk
Shaping risk is defined as the sensitivity of a bond’s price to the changing shape of the yield curve
57
Yield curve factor model
A yield curve factor model is defined as a model or a description of yield curve movements that can be considered realistic when compared with historical data
58
Principal components analysis
The approach that focuses on identifying the factors that best explain historical variances
59
The most important factor in explaining changes in the yield
The level (the other factors are the steepness and the curvature)
60
Short-term rates volatility versus long-term rates volatility
Short-term rates are more volatile
61
Discounting a bond with the arbitrage-free method
To be arbitrage-free, each cash flow of a bond must be discounted by the spot rate for zero-coupon bonds maturing on the same date as the cash flow. Discounting early coupons by the bond’s yield to maturity gives too much discounting with an upward sloping yield curve and too little discounting for a downward sloping yield curve
62
Holding a scarce commodity
* Y = convenience yield
* U = storage costs
63
Roll return
64
F(T\*, T) =
65
Forward rate model - r(T\* + T)
66
Forward rate model - f(T\*, T)
67
If the spot rates evolve as implied by the current forward curve
68
The value of a swap at origination must satisfy this equation
example p.241
69
r(T) in relation to P(T)
70
P(T) in relation to r(T)
71
P(t,T) - discount factor for a T-period security at time t
72
One-period return when the forward rate are realized (pure expectations theory)
73
One-period return when the forward rate are realized while considering uncertainty (local expectations theory)
74
The term structure of volatilities
75
Lognormal relation between i1,H & i1,L
* σ = assumed volatility of the one-year rate
* i1,L = the lower one-year forward rate one year from now at Time 1
* i1,H = the higher one-year forward rate one year from now at Time 1
76
The relationship between i2,LL and the other two one-year rates
* i2,HH = i2,LL (e4σ)
* i2,HL = i2,LL (e2σ)
77
The relationship between i3,LLL and the other three one-year rates
* i3,HHH = (e6σ) i3,LLL
* i3,HHL = (e4σ) i3,LLL
* i3,LLH = (e2σ) i3,LLL
78
Relation between Ru & Rd - rates including volatility
79
Effective duration - sensitivity of a bond's price to a 100bps parallel shift of the benchmark yield curve
* VariationCurve = magnitude in decimal
* PV- = price when the curve is shifted down
* PV+ = price when the curve is shifted up
80
Finding the spot rates using the par rates
example p.282
81
Effective convexity - formula
82
Black-Scholes option pricing formula
83
Black-Scholes d1, d2
84
Black-Scholes value of debt
85
Cox-Ingersoll-Ross (CIR) model
* a = speed of the adjustment factor
* b = long-run value for the short-term rate
86
Vasicek model
* a = speed of the adjustment factor
* b = long-run value for the short-term rate
87
Yield curve risk based on key rate duration model
* Di = (sum of years to maturity affecting this factor) / (total capital in portfolio x change in basis points)
example p. 265
88
Change in the value of a portfolio using key rate duration
* D1 to Dn are the key rate durations
* Δ in portfolio value → Σ i = 1 to n of **-Di \* (curve shift in bps)**
* Example: D1 = 0.5, D2 = 0.7, D3 = 0.90 → For a parallel shift of -50 bps → Portfolio value = -0.50 (-0.005) - 0.70 (-0.005) - 0.90 (-0.005) = 1.05%
89
Standard deviation of the one-year rate for a lognormal distribution
i0σ
90
Pricing a bond with the binomial model
example p.289
91
Increase in interest rate volatility effect on callable/putable bonds
* Callable bond: higher option value → lower bond value
* Putable bond: higher option value → higher bond value
92
Value of callable and putable bonds
* Value of callable bond = Value of straight bond – Value of issuer call option
* Value of putable bond = Value of straight bond + Value of investor put option
93
Increase in interest rate volatility effect on callable/putable bonds OAS
* Callable bond: lower OAS
* Putable bond: higher OAS
94
OAS for callable/putable bonds
* OAS = Z-spread - option cost (call)
* OAS = Z-spread + option cost (put)
95
Types of bonds and their effective duration
96
* Value of a capped floater
* Value of floored floater
* Value of capped floater = Value of straight bond – Value of embedded cap
* Value of floored floater = Value of straight bond + Value of embedded floor
97
Binomial tree and spot rate curve valuation
Should produce the same value because the binomial three is based on the spot rate curve and a no-arbitrage condition
98
Produce a **benchmark** bond value equal to the **market price** using a **Monte Carlo** simulation
Requires adding a constant on all interest rate paths such that the average present value for each benchmark bond equals its market value
99
Realized return versus YTM
* YTM assumes that coupons are reinvested at the YTM rate
* Realized return assumes that coupons are reinvested at the forward rate
100
Credit ratings relation to the business cycle
* Credit ratings tend to remain stable over the business cycle even though the probability of default changes depending on the state of the economy
* This stability tends to reduce price volatility in the debt market
101
The difference between the **expected loss** and the **present value of the expected loss** for credit models includes
Both a discount for the time value of money and a premium for the risk of credit loss
102
Credit analysis for ABS
Focuses on the probability of loss instead of the probability of default because ABS do not default when an underlying collateral defaults
103
Present value of expected loss on cash flows
= PV (risk-free rate - PV (total yield)
104
Spread Risk Compensation
* Nominal Spread Treasury → Yield Curve Credit, Liquidity, Option
* Z-Spread Treasury → Spot Rate Curve Credit, Liquidity, Option
* OAS Treasury → Spot Rate Curve Credit, Liquidity
105
Swap curve
* Is the yield curve of swap rates
* It contains more maturities than the government spot curve
* Retail bank are more likely to use the government spot curve due to their minimal exposure to swaps
