Fixed Income Flashcards
1
Q
Give two interpretations for the following forward rate:* The two-year forward rate one year from now is 2%.*
A
- 2% is the rate that will make an investor indifferent between buying a three-year zero-coupon bond or investing in a one-year zero-coupon bond and, when it matures, reinvesting in a zero-coupon bond that matures in two years.
- 2% is the rate that can be locked in today by buying a three-year zero-coupon bond rather than investing in a one-year zero-coupon bond and, when it matures, reinvesting in a zero-coupon bond that matures in two years.
2
Q
How do I interpret this forward rate - F1,2
A
F(When, Where)
2 years rate one year from now
1year from now the 2 year rate
3
Q
If one-period forward rates are decreasing with maturity, the yield curve is most likely
A
**Decreasing **
If one-period forward rates are decreasing with maturity, then the forward curve is downward sloping. This turn implies a downward-sloping yield curve where longer-term spot rates zB–A are less than shorter-term spot rates zA.
4
Q
If interest rates rise, and the future spot rates are below the forward rates, what does it mean?
A
Bonds are undervalued
5
Q
I rates rises, and the future spot prices are above the implied forward curve
A
Bonds are overvalued
6
Q
If rates rises, and the future spot prices are inline with the forward curve
A
Bonds are failry valued
7
Q
Spot rises, but below the forward curve
A
Bonds are undervalued
We should buyer longer bonds than our Investment horizion
8
Q
Spot rises, but above the forward curve
A
Bonds are overvalued
We should follow a maturity matching strategy
9
Q
Swap rate
A
The rate on the fixed leg of a interest rate swap
10
Q
Swap spread
A
The spread between the fixed rate payer of a swap (Swap rate) and the rate of a “on the run” government bond with the same maturity as the swap that pays coupons.
Swap Spread = Swap Rate - Govenment bond (on the run) that pays coupons.
11
Q
Where are forward rates derived from?
A
Forward rates are derived from spot rates/spot curve
12
Q
Where are spot rates derived from?
A
Spor rates are derived from par rates using bootstraping
13
Q
What is the G-Spread
A
Difference between credit risky bond rates - Spot rates
The difference between the yield on Treasury Bonds and the yield on corporate bonds of the same maturity
14
Q
What is the I-Spread
A
The difference between credit-risky bonds and the Swap rate
15
Q
What is the Swap rate
A
The difference between Swap rates and Spot rates
16
Q
Bear Flattener
A
Rates are going up more on the short end than the long end
Bear flattener refers to the convergence of interest rates along the yield curve as short term rates rise faster than long term rates and is seen as a harbinger of an economic contraction.
a situation of rising bond prices which causes the long-end to fall faster than the short-end. Bear steepeners and flatteners are caused by falling bond prices across the curve.
17
Q
Bear Steepener
A
Rates on the short end rise less than on the long end.
Rates on the long end rise more than on the short end.
Causes: Increase in long term inflation expectation with no action of central bank/monetary policy.
18
Q
Bull flattener
A
Rates on the long end of the curve drops more on the long end than the short end.
Causes: QE pushes capital to higher riskier assets. Or a flight to quality.
19
Q
Bull steepener
A
Rates on the short of the curve end decreases more than on the long end.
A bull steepener is a shift in the yield curve caused by falling interest rates—rising bond prices—hence the term “bull.”
The short-end of the yield curve (which is typically driven by the fed funds rate) falls faster than the long-end, steepening the yield curve.
20
Q
How much does Inflation and GDP growth influence interest rates curve for short and intemediary bond.
A
Inflation and GDP 1/3
21
Q
How much does monetary policy influence interest rates curve for short and intemediary rates curve .
A
2/3
22
Q
How much does monetary policy influence interest rates curve for long term rates curve .
A
1/3
23
Q
How much does inflation influence interest rates curve for long term rates curve.
A
2/3
24
Q
The YTM to a bond is the rate that is most likely
A
The weighted average of the spot rates used in the bond valuation
25
What is the Pure Expectation theory?
* Forward rates are unbiased predictors of future spot rates.
* It assumes investors are risk neutral.
* Also known as unbaised expectation theory
* Investors expectation that determines the shapre of the interest rate term strucutre.
* Forward rates are an unbiased predictor o future spot rates and that every maturity strategy has the same expected return over a given instrument horizion.
* Long term interest rates equal the mean of future expected short-term rates.
26
What is the Local Expectation theory?
* Expected returns for all bonds is equal to the risk free rate over a short period of time.
* Preserves the risk-neutrality assumption only for short holding periods.
* Over long periods, risk premium should exist.
27
What is the liquidity preference theory?
* Predicts upward sloping yield curve -> forward rates as an expectation of future spot rates are biased upward by liquidity preference.
* Does not have a supply and demand argument.
* Liquidity: Having to sell a bond at some unertain price.
* Since liquidity premium exist, investors are compensated for interest rate risk when lending long term.
* it increases with maturity.
* Proposes that forward rates reflect investors expectations of future spot rates plus a liquidity premium to compensate investors for exposure to interest rate risk.
* Liquidity premium is positivly related to maturity.
25 year bond should have a larger liquidity premium than a 5 year bond.
28
What is the Segmented Market theory?
Segmented market theory allows for lender and borrower preference to influence the shape of the yield curve. This causes yields to not be a reflection of expected spot rates or liquidity premiums, but solely a function of supply and demand for funds of a particular maturity.
* The shape of the yield curve is determined by the preference of borrowers and lenders, which drives the balance between supply and demand for loans of different maturities.
* Each maturity segment can be thought of as a segmented marketin which yields are determined independently from yields that prevail in other maturity segments.
* Forward rates are not an expectation of future spot rates or liquidity preimiums.
* Market participants are unwilling / unable to invest in anything other than securities of their prefered maturity.
29
What is the preferred habitat theory?
Forward rates represent expected future spot rates plus a premium, but does not support the view that the premium is directly related to maturity.
Preferred habitat theory is similar to the segmented market theory in proposing that many borrowers and lenders have strong preferences for particular maturity.
Borrowers and lenders have a preferrence for particular maturities, buy yields at different maturities are not determined independently.
30
Short term interest rate volatility is mostly linked to ..,
Uncertainty regarding monetary policy.
Monetary policy attributes 2/3 of the volatility
31
If the par curve is flat, then
The spot and the forward curves will also be flat at the same level.
32
Are forward rates determined by supply and demand
NO!!
33
YTM provides the best estimate of expected return when
The Par curve is flat and expected to stay flat until maturity.
With a flat par curve, we get flat spot and forward curve all overlaping at the same rate which will be the YTM.
34
What is a "**Forward Rate**"?
A rate set today for a single payment of security to be issued at a future date
35
What is the **MRR-OIS Spread**?
The difference between the MRR and the overnight index swap rate OIS.
**MRR-OIS Spread** relects risk and liquidity of money market securities.
36
Please name the two different types of **Arbitrage** in binomial tree models
Dominance & Value added
37
What is **Dominance** Arbitrage?
Arbitrage oppertunity that produces a risk-free profit with respect to future pay off.
Only produces risk free profit at payoff.
38
What is "**Value Addiditivity**" Arbitrage?
Produces risk free profit with respect to current prices.
Relies on the sum of two parts not being equal to the sum of the whole. Basically, the two asset prices must equal each other.
39
Interest rate tree is a visual representation of the possible values of interest rates based on
Interest rate model and assumption about volatility.
40
Name the 2 different **equilibrium models** in fixed income binomial models
CIR
(Cox-Ingersoll-Ross)
and
Vasicek models
Singel-Factor Model that uses short term interest rates to describe interest rate dynamics. Primarily focus on **yield levels**.
41
Name the 2 different **Arbitrage Free** models
Ho-Lee
and
Kalotay - William-Fabozzi
42
If off the run bonds price was arrived by using spot rates drived from the benchmark par curve.
If we price the bond on a calibrated interest rate tree, the price recovered will be ...
The same as that arrived by using the spot prices.
43
How do we calculate the number of possible paths in Binomial trees?
2^(n-1)
44
Interest rate tree **i2LL** referes to?
The one year forward rate ar time 2, assuming the lower rates at time 1 and 2.
45
In determining the appropriate level of volatility to use in modeling paths interest rates, we would most likely **NOT** use
Implied volatility based on observed prices of option-free Government bonds.
46
What does the log-normal random walk volatility capture?
The volatility of the one-year rate
47
When are **Callable Bonds** more valueable?
During a **downward sloping** yield curve
Call Option is valuable when** yield curve flattens**
48
When are **Putable Bonds** more valueable?
When the yield curve is **upward sloping**
Put Option is valuable when **yield curve steepens**
49
Formula for Value of **issuer call opion**
Value of stright bond - Value of callable bond
50
Formula for Value **investors Putable bond**
Value of putable bond - Value of stright bond
51
If volatility increases, what will happen to the **value of callable bond**
The new value will be lower than the previous price.
Value of Call = V Stright - V Callable
52
If volatility increases, what will happen to the **value of Putable bond**
The new value will be greater than the previous value
53
Explain the relationship of what will happen to the **value of callable and putable** if volatility increases
Callable bond value decreases
Putable bond value increases
54
If the OAS (Option Adjusted Spread) for a bond is **higher than its peers**, it is considered to be...
**Undervalued**
OAS for a bond is higher than the OAS of its peers, it is considered to be undervalued i.e. attractive
investment meaning it offers a higher compensation for a given level of risk (cheap).
55
If the OAS (Option Adjusted Spread) for a bond is **Lower than its peers**, it is considered to be...
**Overvalued!!**
bonds with
low OAS relative to peers are considered to be overvalued (rich) and should be avoided.
It offers lower compenstation for a given level of risk
56
What is the formula for **Option Cost**
Z-Spread - OAS
57
What is the formula for **Z-Spread**
OAS - Option cost
58
Z-Spread ≥ OAS
Callable bond
59
Z-Spread ≤ OAS
Putable bond
60
**Option cost** for Callable bonds when **Volatility increases**
**Positive Option cost**
Callable Bond = Z-Spread ≥ OAS =
61
**Option cost** for Callable bonds when **Volatility Decreases**
**Negative option cost**
Callable Bond = Z-Spread ≥ OAS
62
**Option cost** for Putable bonds when **Volatility increases**
Negative option cost
Putable Bond = Z-Spread ≤ OAS
63
**Option cost** for Putable bonds when **Volatility Decreases**
Positive option cost
Putable Bond = Z-Spread ≤ OAS
64
What is the most **appropriate duration** to use for bonds with embedded options?
Effective duration
65
How do we interpret **1.97 effective duration**?
for a **100 bsp change in the interest rates**, the bond price will change by 1.97% on average.
66
What is effective duration?
A parallel shift in the yield curve. (benchmark yield curve)
assuming no change in the bond's credit spread, but it is not an accurate
measure of interest rate sensitivity to non-parallel shifts in the yield curve like those described by
'Shaping Risk'. Shaping Risk refers to changes in portfolio value due to changes in the shape of the
benchmark yield curve. However, parallel shifts explain more than 75% of the variation in bond
portfolio returns.
67
Please explain **deep in-the-money** embedded option bonds
When the embedded option (call or put) is deep in the money, **the effective duration of the bond with an embedded option resembles that of the straight bond maturing on the first exercise date**,
reflecting the fact that the bond is highly likely to be called or put on that date.
68
Please explain the relationshop of **out-of -the-money** embedded option bonds
Effective Duration Callable ≤ Effective Duration Straight
Effective Duration Putable ≤ Effective Duration Straight
Effective Duration ZCB ≈ Maturity of the Bond
Effective Duration Fixed Rate Coupon < Maturity of the Bond
Effective Duration Floater ≈ Time in Years to Next Reset
69
Please explain the relationshop of **At -the-money** embedded option bonds
**The effective duration of the callable bond shortens when interest rate falls**, which is when the call
option moves into the money, limiting the price appreciation of the callable bond.
**The effectiveduration of the putable bond shortens when interest rates rise,** which is when the put option moves into the money, limiting the price depreciation of the putable bond.
While effective duration of straight bonds is relatively unaffected by changes in interest rates.
70
What kind of relationship does call option value have with interest rates?
**Inverse relationship**
Effective convexity of the callable bond turns negative when the call option is near the money
which indicates that the upside for a callable bond is much smaller than the downside. When rates are high, callable bonds are unlikely to be called and will exhibit positive convexity.
71
What kind of relationship does Put option value have with interest rates?
**Direct relationship**
Putable bonds always have positive convexity.
When the option is near the money, the upside for a putable bond is much larger than the downside
because the price of a putable bond is floored by the price of the put option, if it is near the exercise
date.
72
Which type of bonds can experience negative convexity?
Callable bonds.
73
Convertible Bonds: **Conversion Value**
Share price x Conversion Ratio
74
Convertible Bonds: **Conversion Ratio**
Bond Price / Conversion Price
75
Convertible Bonds: **Conversion Price**
Par or issue price / Conversion ratio
76
Convertible Bonds: **Market Conversion premium per share**
( PV bond / Conversion Ratio ) - share price
77
Convertible Bonds: **Market Conversion premium per share RATIO**
[ ( PV bond / Conversion Ratio ) / Share price ] -1
78
one-sided durations
Effective durations when interest rates go up or down, which are better at capturing the interest rate sensitivity of bonds with embedded options that do not react symmetrically to positive and negative changes in interest rates of the same magnitude.
79
Effective Duration indicated the sensitivty of the bonds full price to a 100 bsp shift in the government
Par Curve
80
**Downward** sloping yeild curve -> **Upward** sloping yield curve
**Put option**: Increases
**Call option**: Decreases
81
**Upward** sloping yeild curve -> **Downward** sloping yield curve
**Put option**: Decreases
**Call option**: Increases
82
What will happen to **OAS** when **volatility increases**
OAS decreases
83
What will happen to **OAS** when **Volatility Decreases**
OAS increases
84
On-sided duration for **Callable bonds**
On-sided **up** duration **>** on-sided **down** duration
85
On-sided duration for **Putable bonds**
On-sided **Down** duration **>** on-sided **up** duration
86
Default risk
Likelihood of default event
87
Default risk preimium
Reflects uncertainty in timing of default
88
Credit Risk
Given Default, how much is likely to be lost?
L.G.D - Loss Given Default
LGD Formula = Expected Exposure * Loss sensitivity
89
Expected Exposure
The amount of money that could be lost in default without consdidering recovery
**Example**: 1 year 4% bond at par - EE = 104
90
Recovery Rate
% of recovered in default
91
Loss sensitivty
1 - RR
92
Formula for Probability of Default (POD) at time n
(**Probability of survival at n-1**) **x** (**Probability of default**)
93
Formula for Expected loss
LGD x PODn
[EE(1-RR)] x [Pos n-1 x POD]
94
Formula for present value of expected loss
LGD x PODn / (1+rfr) ^n
[EE(1-RR)] x [Pos n-1 x POD] / (1+rfr)^n
95
Credit analysis of securitized debt: **Homogenity**
**THINK OF SIMILARITY**
Degree to which the underlying debt characteristics are similar across individual obligations.
**Homogenity**: General concluion from the class.
**Hetrogenity**: Security on a loan by loan basis
96
Credit analysis of securitized debt: **Granularity**
Actual number of obligations in the structural security
**Many**: Conclusion based on summary statistics
**Few**: Analysis of each individual secuirty.
97
Credit analysis of securitized debt: **Organation and Secuicing**
Exposure to operational counterparty risk over the life of the securitized asset.
98
Credit analysis of securitized debt:
**Structure of the secured debt transaction**
SPV + Any strucutural enhancement
99
What is **Credit Scores**?
Retail lending market
Ranks a borrowers credit riskiness from highest to lowest.
Does not provide estimate of a borrowers default probability.
It is called an ordinal ranking because it only orders borrowers riskiness from highest to lowest.
Does not depend on economic conditions
100
What is **Credit rating**?
Wholesale lending market. Ranks credit risk of a company, government, or ABS.
101
Risk Neutral Probability
FV = [ND(1-P) + DxP] / 1+rfr
**Best way to conceieve Risk neutral probabilities of default** : The historical probability of default + premium for the uncertainty of the timing of default.
102
How to calculate expected return from credit migration
Expected rate of return due to credit migration
-ModDur x (New Credit spread - Old Credit Spread)
103
Probability of default for year n
POS ^(n-1) x POD
104
What is the relationship between credit spreads and benchmark spread in regards to each other and the business cycle.
**Negative and Counter cyclical.**
A stronger economic climate is generally associated with higher benchmark yields but lower credit spreads reflecting lower POD.
Credit spreads have a negative relastionship with benchmark rates - Contracting as rates ris and expanding as rates drop.
And Countercyclical with the business cycle - narrowing as the economy expands and widening as the economy contracts.
105
(In regards to CDS) Short position of underlying
Deteriorating credit quality - **Buyer of CDS**
106
(In regards to CDS) Long position of underlying
Improving Credit quality - **Short CDS**
107
**Seller** of CDS
Improving credit quality - **Long underlying**
108
**Buyer** of CDS
Worsening credit quality - **Short underlying**
109
CDS Buyer
Short Position of underlying credit quality
110
CDS Seller
Long Position
111
What does the **credit protection buyer** do in CDS?
**Premium leg of the CDS**
Makes a series of payments (premiums) in exchange.
112
What does the **Credit protection seller** do in CDS
**Protection leg of CDS**
Makes payment in the event of credit event
113
Singel name CDS
A CDS on a specific borrower (Reference entity)
114
Name the 3 different types of CDS
1. Single name
2. Index
3. Tranche
115
What is Physical Settlement of a CDS?
Holder of the bond sells to CDS seller at par
116
What is Cash Settlement of a CDS?
Seller pays holder for losses
Swap seller -> Swap buyer
Par - Market value
Payout amount = Payout ratio x Notional amount
117
CDS leg: **Protection Leg**
**Seller pays buyer**
Protection seller pays protection buyer if credit event occurs
118
CDS leg: **Premium Leg**
Buyer pays seller
Protection buyer makes periodic payment to seller of protection
119
What is the formula for **upfront payment**
PV Protection leg - PV of Premium leg
120
PV Protection leg **>** PV of Premium leg
> 0
**Protection Buyer pays seller**
121
PV Protection leg **<** PV of Premium leg
**Protection seller pays Buye**r
122
Full formula for uprfont payment
PV Protection - PV premimum
(Spread - rate) x Duration
(Credit Spread - Fixed Coupon) x Duration
123
Formula for Credit Spread
(Upfront payment / Duration) + Fixed Coupon rate
124
Formula for Profit for CDS Buyer
Change in Basis points x Duration x Notional amount
125
% Change in CDS price
(Formula for Profit for CDS Buyer)
Change in basis points x Duration
126
How is the payoff determine for CDS?
The cheapest to delivery
Regardless of TTM, always chose the bond with the lowest % value trading at par
127
When credit quality of the reference rate improves, what will happen to the protection leg of a CDS
Protection leg gains value, since the credit spread will be less than the premium rate
128
When credit quality of the reference rate deteriorates, what will happen
Premium leg gails value, the credit spread will be greater than the premium rate
129
What is stripping?
The ability to seperate the bonds individual cash flows and trade them as zero coupon securities
130
What is OAS (Option Adjusted Spread)
Option Adjusted Spread (OAS) is the constant spread, when added to all one-period forward rates on the interest rate tree which makes the arbitrage-free value of the bond (calculated value) equal to its market price.
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 then adjusted to take into account an embedded option. Typically, an analyst uses Treasury yields for the risk-free rate. The spread is added to the fixed-income security price to make the risk-free bond price the same as the bond.
131
Which combination will lead to lower **put option value**
* Lower Volatility
* Lower put price (strike)
* Higher cupon
132
Which combination will lead to lower **Call option value**
* Lower Volatility
* Higher call price (strike)
* Low cupon price
133
Rates for **investment-grade** company CDS rates
1%
134
Rates for **High-yield** company CDS rates
5%
135
What is Credit spread?
Credit spread is the difference between the yield (return) of two different debt instruments with the same maturity but different credit ratings.
136
Name the 3 types of credit event
1. Bankrupcy
2. Failure to pay
3. Restrucutring (voluntary restructuring is not a credit event)
137
in CDS
Who will pay if
Credit Spread < Standard Rate
Seller (premium leg) pays Buyer (Protection Leg)
138
in CDS
Who will pay if
Credit Spread > Standard Rate
Buyer (Protection Leg) pays Seller (premium leg)
