Fixed Income Flashcards
1
Q
Spot rates / zero-coupon rates
A
Effective annual rates which pay no interim interest. Geometric averages of forward rates. Not fully observable but required to fully disocunt the cashflows of any bond.
2
Q
Spot curve
A
Annualized return on a risk-free zero coupon bond with a single payment of principal at maturity
3
Q
YTM
A
Annual return an investor would achieve by investing in a particular coupon-paying bond to maturity and reinvesting all cash flows at the yield itself. Weighted average of spot rates.
4
Q
YTM will only be expected return if:
A
- Bond is held to maturity 2. Cash flows are made in full and on time 3. All cash flows are reinvested at the original YTM
5
Q
Forward rates
A
Spot rates starting in the future. They can be derived from Spot rates.
6
Q
Price of a bond is
A
PV of all cash flows discounted at each cash flow’s zero coupon rate aka spot rate
7
Q
Bootstrapping a yield curve
A
In reality we cannot observe zero rates directly. We need to extract them from bond yields = bootstrapping. We generally look at par yield curves where there is no tax distortion.
8
Q
On-the-run bonds
A
Most recently issued! Similar to par yield curves (Y=C // P=Par).
9
Q
Par Yield Curve
A
A par yield curve is a graphical representation of the yields of hypothetical Treasury securities with prices at par. On the par yield curve, the coupon rate will equal the yield to maturity (YTM) of the security, which is why the Treasury bond will trade at par.
10
Q
Valuing a bond / discounting the cash flows with YTM when
A
Coupon = YTM (par) yield
11
Q
Valuing a bond / discounting the cash flows with Spot rates and forward rates when
A
If coupon doesn’t equal YTM (par) yield
Forwards haben keine Potenzen
12
Q
Maturity / Tenor
A
refers to the length of time remaining before a financial contract expires
13
Q
Riding the Yield Curve
A
Purchase long-term bonds with a maturity date longer than their investment time horizon. Sell at the end of their time horizon, profiting from the declining yield that occurs over the life of the bond (profits from the higher six-month yield altough he is only holding 3 months)
Works best in a stable interest rate environment where interest rates are not increasing. Additionally, the strategy only produces excess gains when longer-term interest rates are higher than shorter-term rates (upward sloping yield curve)
14
Q
Swap
A
Derivative contract through which two parties exchange the cash flows or liabilities from two different financial instruments
Like all derivatives the value of an interest rate swap at inception is zero
15
Q
Swap curve
A
Is the yield curve of swap rates
Why use a swap curve as a benchmark?
- Liquidity – if the swap market is more liquid than the government bond market
- It contains more maturities than the government spot curve
- If a bank or client of a bank uses swaps to hedge interest rate risk then it makessense (for hedging purposes) to value their assets and liabilities using the swap curve
16
Q
Par yield
A
The yield on a bond priced at par
17
Q
(Par) Swap Rate
A
18
Q
Swap spread
A
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
It It represents the extra return above the equivalent equivalentrisk -free return which compensates the investor for additional time value, credit and liquidity risk. It is conceptually equivalent to a Z-spread.
19
Q
The Z-spread, ZSPRD
A
Spread over the default-free spot curve
The static spread required to be added to each implied government spot rate such that the present value of cash flows equals the bond price. Reflects compensation for credit, liquidity and option risk. Reflects compensation for credit, liquidity and option risk.
20
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.
Indicator of perceived credit risk in the general economy. A widening of the TED spread indicates higher concerns about the wider wider economy (T-Bills Flight to safety > Prices up > Yields go down = ED Yields go up as people sell)
21
Q
Credit (G) spread
A
A credit spread is the difference in yield between a U.S. Treasury bond and another debt security of the same maturity but different credit quality
G-spread (also called nominal spread) is the difference between yield on Treasury Bonds and yield on corporate bonds of same maturity
- Compensation to the investor for bearing the default risk of the issuer ( investors wants more RETURN)
- Considers the possibility that the issuer fails to make a scheduled payment in full on the due date // losses incurred in the event of default
22
Q
LIBOR-OIS Spread
A
The spread between LIBOR for a given maturity (typically three months) and the
Overnight Indexed Swap (OIS) rate for the equivalent maturity.
A widening of the spread indicates higher concerns about banking default risk
and/or liquidity concerns in the money markets.
OIS in GBP: SONIA; OIS in EUR: EONIA; OIS in USD: FFER
23
Q
Option adjusted spread (OAS)
[Option removed spread]
A
constant interest rate spread that must be added to all of the one period forward rates in a binomial tree so that the theoretical value of the callable bond is the same as the market price. The spread you would receive if the bond had no embedded option. Best thought of as ‘option removed spread
Reflects compensation for credit and liquidity risk (but not option risk)
decline in interest rate volatility corresponds with a higher OAS
24
Q
Flight to safety
A
Investors buy bonds (safer investments) when they sell stocks (higher-risk investments) in order to reduce the losses that investors suffer in crises periods
Demand for T-Bills goes up, Prices go up, Yields go down
25
Pure expectations theory
**Forwards perfectly reflect future zero rates**
Assumes that the term structure of an interest contract only depends on the shorter term segments for determining the pricing and interest rate of longer maturities. Yields at higher maturities (such as that of 5,10, or 30 year bonds), correspond exactly to future realized rates, and are compounded from the yields on shorter maturities. In other words, buying a ten year bond is equal to buying two five year bonds in succession; you’re as safe in a ten-year as in a five-year bond
26
**Local Expectations Theory**
Suggests that the returns of bonds with different maturities should be the same over the short-term investment horizon
27
**Liquidity Preference Theory**
**Higher duration bonds require a highe premium.**
Suggests that an investor should demand a higher interest rate or premium on securities with long-term maturities that carry greater risk because, all other factors being equal, investors prefer cash or other highly liquid holdings
28
Market segmentation theory
Expectations theory predicts future short-term interest rates based on current long-term interest rates. The theory suggests that an investor earns the same amount of interest by investing in two consecutive one-year bond investments versus investing in one two-year bond today
MST: Yield curve is driven entirely by investor preferences (Demand up, Prices up, Yield down). States there is no relationship between the markets for bonds with different maturity lengths and that interest rates affect the supply and demand of bonds
29
The preferred habitat theory
Suggesting that different bond **investors prefer one maturity length over another** and are _only_ willing to buy bonds outside of their maturity preference if a risk premium (**term premium**) for the maturity range is available (other than MST). The theory also suggests that when all else is equal, investors prefer to hold short-term bonds in place of long-term bonds and that the yields on longer-term bonds should be higher than shorter-term bonds.
30
Equilibrium Term Structure Models
**Stochastic interest rate models** used to estimate the correct theoretical term structure. Estimate the stochastic process that describes the dynamics of the yield curve (term structure).
Cox-Ingersoll-Ross Model (CIR) & Vasicek Model in CFA L2. Both model **short term interest rates.**
31
Cox-Ingersoll-Ross model (CIR)
Assumes current consumption and investment (delayed consumption) decisions are made subject to a capital constraint, i.e. individuals need to consider the trade-off between consuming now versus in the future. The short short-term interest rate rewards the individual for the risk of investing
**Two key parts** : **Drift term** incorporates a **mean-reverting element** towards the long-term rate; stochastic term incorporates the **volatility of the interest rate process** (vs. Vasicek with volatility constant)
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32
**Vasicek model**
* Very similar to CIR model in that it includes the same drift element to incorporate the mean reverting property of the short short-term interest rate
* The stochastic term is simplified compared with the CIR model since it **holds volatility constant**
33
Ho-Lee Model (Arbitrage-Free Models)
**Starts with observed market prices** (unlike Cox/ Vasicek)
We use market prices to calibrate the model, i.e. given an assumed **drift term** and
**assumed volatility** we can generate a yield curve such that we can then derive the
observed prices. The underlying model usually uses a binomial approach and an assumption of risk risk-neutral probabilities
34
Factors for return for a bond holder
1. **Changes in the level of interest rates**, i.e. parallel shifts in yield curve (Most significant factor, almost 77%; measured by duration)
2. Changes in the **slope of yield curve** (steeper/ flater?; measured by key rate duration, 17%)
3. Changes in **curvature** (Umgedrehtes U? very little effect, about 3%)
% are commonly referred to as R R2 (coefficient of multiple determination)
35
Interest rate volatility
Short-term volatility is predominantly driven by uncertainty regarding central bank policy whereas longer term volatility is mostly driven by macroeconomic uncertainty such as economic growth and inflation (never constant!)
USUALLY: **ST Vola \> LT Vola**
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36
The Arbitrage Free Valuation Framework
The fundamental assumption is that prices are set such that no (riskless) arbitrage opportunities exist
A central conclusion of this approach is that all assets of the same risk, have the same return: **Law of One Price**
To find the arbitrage free value we need to discount each cash flow using the relevant spot rate and then sum (if yield = coupon tarding at par you can use YTM to discount).
_Arbitrage Opportunities:_
**1. Value additivity:** the sum of the part should equal the whole. A bond can be considered as a portfolio of zero coupon bonds. The sum of the present values of each zero, discounted using an appropriate spot rate should equal the value of the bond.
**2. Dominace**: We can view an asset as being dominant to another asset when for the same risk we are receiving a higher
return.
37
**Formula** for calculating upper forward rate (Binominal interest rate tree).
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Alternatively apply only one SD to the average forward rate (xfxM) (one + and one -)
**For year two**: 2 SD from middle (4SD from higher to lower)
38
Pathwise Valuation
Calculating **PV of all paths cashflows** (8 paths possible in a 3 year tree) and add up all PVs you get s_ame value as the backward induction_ binomial approach
39
Monte-Carlo Model
Primarily used for **interest rate path dependent cash flows** such as Mortgage-backed securities (MBS)
Use a **computer driven Monte Carlo simulation** to generate **thousands of random interest rate paths**, i.e. monthly forward Treasury rates.
No detail in CFA2 on MBS
40
**Callable** bonds
Straight bond that includes a call option _held by the issuer_. **Issuer has right to buy (redeem early) the bond at a given price** (often par), which may be at par or a premium to par.
Main motivation behind exercising the call, is to **refinance** the loan , i.e. buy back a high coupon bond and replace with a lower coupon bond. This normally **happens when interest rates fall**.
Most callables include a **lock out period** (hard protection; can't be called in in first 2 years).
**Price of Callable Bond will be lower** =\> higher yield: YSB+YOption= YCallable (compensation)
**Make whole provisions** generally make it uneconomic for the issuer to refinance the loan (ie higher spreads). Not a call provision!!
Tax exempt municipal bonds (Muni’s) are typically callable at 100% (par),
American style but with a 10 year lock out period.
41
**Putable** Bonds
Straight bond that includes a **put option held by the investor.** Investor has **right to sell** (redeem early) the bond at a given price, which is **normally at par**. This normally happens when interest rates rise.
Investor pays more for the option + bond =\> higher price =\> lower yield: YSB-YOption= YPutable
As with callables , there may be **lock out periods** and **different exercise styles** for the option. Very similar to an extendible bond.
42
Bond indenture
**Details** regarding the **option** are explained in the bond’s indenture (embedded option)
43
**Option styles**: European, American, Bermudan
1. **European** style (option can only be excercised at expiration)
2. **American** style (excercise any time from purchase until expiration)
3. **Bermudan** style (denotes specific days before expiration on which the trader can exercise his option. The specified exercise dates are usually near the time of the option's expiration date.).
44
Embedded Complex Options:
- Estate put
- Sinking bond fund
Bond can be both callable and putable
The option may be contingent upon some future, specific event. For example, an **estate put** (aka survivor’s option) will only **be exercised when the holder dies**. The holder’s estate can put the bond back to the issuer at par if the holder dies before the bond matures.
**Sinking bond fund** requires the issuer to **set aside funds** (usually yearly) to retire the bond and in doing so, reducing risk of default for the investor. Such bonds may be callable, usually at a premium to par and may include other features such as an **acceleration provision** = _buying back prinicpal_ at pat (ie 10% each year)
45
Valuing Bonds With Embedded Options: Effect of Volatility
The higher the assumed volatility the **greater the value of the embedded option**
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46
**Ceiling** / **Floor** **price** for bond with embedded options
With **callable** bonds we need to consider the **call price as a maximum price** (ceiling price = value of a callable bond can increase to only approximately the call value)
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With **putable** bonds we need to consider the put price as a minimum price (**floor price**)
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47
Effect of Change in Level of Interest Rates on the Option
_If yields increase_: Net effect is **call options decrease** in value and **put options increase** in value.
Rates go up \> Prices go down \> Call option gets less attractive / Put option more attrative (people are selling to refinance at higher rate
48
Effect of **Change in Shape of the Yield Curve** on the Option
??? Downward/inverted curve (or flattener) will lead to an increase in the value of the call option. Why?
Remember if the yield curve is downward sloping the forward curve must be lower and therefore the chance of the option being exercised increases
The opposite applies for put options
49
Formula: **Forward rates 1f1H**
## Footnote
**Interest tree**
1f 1H = 1 f 1L x e ^(2x σ)
σ = volatility
50
**OAS vs. Z-spread**
**For _call_ options**:
* **Z**Call = Credit + Liq. Risk + Option Risk
* **OAS**Call = Credit + Liq. Risk + N/A
=\> ZCall \> OASCall
**For _put_ options:**
* **Z**Put = Credit + Liq. Risk - Option Risk
* **OAS**Put = Credit + Liq. Risk + N/A
=\> ZPut \< OASPut
If interest rate volatility rises the OAS must decrease for a given callable bond
(and given price); the OAS must increase for a given putable bond.
If we hold the price constant, yield constant and then the **Z spread will be constant**. If volatility changes then the only aspect directly effected is the option value which in turn **effects the OAS part** (must compensate for option value going up / down): Credit + Liq. Risk.
51
**Determining the OAS** (Option Adjusted Spread)
OAS is **massively dependant** on our assumption of **volatility.** The **higher the vol** the lower the OAS (part) for a callable bond (?must compensate for price going down) = **can eben be negative shortly**
Add constant OAS spread to rates in binominal tree
52
**(Effective) Duration**
**Duration** is a measure of the sensitivity of the price of a bond or other debt instrument to a change in interest rates
CFA L2: **Effective duration** measures the average change in price when yields rise and fall by a given amount. This measure of duration takes into account the fact that expected cash flows will fluctuate as interest rates change and is, therefore, a measure of risk
Duration is a linear concept. The change in price up is the _same_
as the change in price down for a given change in yield
* *Effective (Portfolio) Duration** used if small _parallel shifts_ in yield curve
* *Key rate Duration** used for _non-parallel shifts_ (change of yield in specific maturity)
Duration is stated in % (1% in interest rate change is X% price change) ![]()
53
**One Sided Duration**
```
This is not **appropriate for bonds with embedded options** since they may have a
price ceiling ( callables ) or a price floor putables
```
1. If a callable bond is trading at 100 (assume callable at par) then if yields decrease the price will still be 100. Therefore we should _only consider_ the impact from an increase in yields.
2. Similarly if a putable bond is trading at par then we should _only consider_ the
impact from a decrease in yields.
54
**Key rate Duration**
Looks at the bond’s price sensitivity to a change in yield at o**nly one specific maturity**, whilst holding all other yields constant (**non-parallel shifts**)
55
Duration effect
**Duration effect** = Duration \* Change (delta) of rate (r) \* Price
56
Embedded Option is **_out_ of the money** / **option is _in_ the money**
* When the option is **out of the money** then a callable/ putable will resemble a **straight bond**.
* When the **option is in the money**, it is **likely to be exercised** and therefore the bond r**edeemed early**. This shortens the maturity of the bond and thus **reduces its duration**.
= \> Callables and putables cannot have higher duration than an equivalent straight bond but can have lower durations. **The more in the money** the option becomes, **the lower the duration**.
Normally, the longer the maturity, the higher the duration
57
Convertible Bond
CB is a hybrid security; part bond; part equity: Bond on one side, O**ption to buy shares on the other**
**At any stage** the CB holder can choose to ‘turn the paper over’: If I now prefer equity: Convert my bond into a set number of shares
The cost to the investor of this option is in the form of a **lower coupon**.
(This is the benefit to the
**Conversion Rate**: Exchange this CB for 25 new shares in the company
58
Formulas / Ratios : **Convertible Bond**
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* 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
60
Performance of Convertible Bonds
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1. **Busted area (1)**: The CB is ‘**out of the money**’. The conversion is unlikely because the stock price is too low. The value of the call option is negligible and the CB behaves like a straight bond with no equity sensitivity (not impacted .
2. **Hybrid area (2)**: The CB is ‘**at the money**’. The option to convert gains value. This area offers both fixed income and equity sensitivities as well as the features of the option. _**If Share Price go up** 10 \> Conv. Bond Underperforms (e.g. go up 5 only) Equity. **If Price go down** \> Conv. Bond Outperform Equity._
3. **Equity proxy area (3):** The CB is ‘**in the money**’. Conversion is likely and solely conversion value matters. **The CB equity sensitivity is high** and fixed income sensitivity is low. Shares go up by 10 \> CB goes up by 10
61
Capped / Floored Floater
A **capped floater** will automatically _limit_ the coupon if interest rates rise above a
certain level. In doing so, this protects the issuer (and hurts the investor)
*Value of a capped floater = Value of a straight bond - Value of embedded cap*
A **floored** floater provides a _minimum_ coupon and protects the investor if rates fall
*Value of a floored floater = Value of a straight bond + Value of embedded floor*
Capped floater: In interest tree - if interest rates rise you still only get MAX coupon
62
**Default vs. Credit risk**
Generally the terms get used interchangeably. For CFA2:
1. **Default risk** - Narrower - Addresses the likelihood of an event of default
2. **Credit risk** - Broader - Considers both the default probability & loss given default
63
Credit Valuation Adjustment **CVA**
Reduction in price today for the fact that you take on the credit risk of the company (pay less Price \> Yield must go up - then we can caluclate credit spread)
64
Probability of Default (POD);
Probability of Survival (POS)
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65
**Calculating Credit Spread** with CVA
1. **Recovery Rate**
2. **Loss Severity**
3. Initial POD (**Hazard Rate**)
4. (Expected) **Exposures** at each date
5. (Expected) **Recovery**
6. Loss given default (**LGD**)
7. **Expected Loss** for each date
8. PV of expected Loss
9. Credit Valuation Adjustment (CVA)
10. Fair Value of Corporate Bond
11. **Credit Spread** (expressed in basis points ie 62 if 4.62% and Gov 4%)
1. Percentage of the loss recovered from a bond in default
2. [1 - Recovery Rate]
3. Probability of default in the first year
4. PV of nominal values in each year (Discount 1year with ^2 for 3 year bond)
5. Recovery Rate x Exposure at each date
6. Exposure at each date - Expected Recovery
7. LGD x POD
8. Expected Loss x Discount Rate (DR: 1/1.043 im 3. Jahr)
9. Sum of all PVs of each expected loss
10. FV of Zero Bond - CVA
11. YTM on the corporate bond – YTM on the government bond (YTM mit Calc ausrechnen wenn man FV hat
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66
**Credit Scores**
* Used primarily in the retail lending market for small businesses and individuals
* Credit scoring agencies are generally national in scope because of differences in legal systems and privacy concerns across countries
Fair Isaac Corporation **(FICO)** Score: Used by about 90% of lenders in the US, using data from consumer credit files collected by Experian, Equifax and TransUnion - **Five primary factors** are included in the proprietary algorithm used to compute the credit score:
1. Payment History 35%:Information surrounding bankruptcy, court etc
2. Debt Burden 30%: number of accounts with positive balances etc
3. Credit History 15%
4. Types of Credit Used 10%
5. Recent Searches for Credit 10%: **Hard** inquiry (requesting loan) **Soft** inquiries (employer verifircation; self checking)
67
**Credit Rating**
* Used primarily to **measure credit risk** in corporate & sovereign bond markets
* Three major credit rating agencies: **Fitch Ratings**, **Moody’s** and **Standard and Poor’s** who provide quality ratings for issuers
* Ratings agencies consider the expected loss given default by a process of ‘**notching**’, this represents an adjustment to the issuer rating to reflect the priority of claim for the _specific debt issue_ e.g. B+ down to B or B-
* Outlook for issuer is also given alongside the rating e.g. positive, stable or negative and when the issuer is under ‘watch’
68
Credit rating transitions
The credit transition matrix and the credit spreads from the previous slide can be used to estimate the one-year rate of return on a bond given the possibility of credit migration but still no default
Credit spread migration ty**pically reduces the expected return** for two reasons:
1. Probabilities for change are not symmetrical around the current rating. They are **skewed towards a downgrade**
2. **Increase in credit spread is much larger for downgrades** than the decrease in spread for upgrades.
69
**Structural** credit and **reduced-form** credit models
70
Higher Credit Spread infers...
1. Lower Recovery Rate
2. Higher Hazard Rate: Higher Probability of Default \> Higher CVA \>
71
Analyzing the credit risk of a _fixed coupon_ bond using a **binomial valuation approach**
1. **Build the binomial interest rate tree** (Bootstrapping to get Spot rates \> determine Forward Rates?; We then apply an interest volatility assumption around the forward curve [FM xeSD*Vol]
2. Confirm the binomial tree is arbitrage-free by pricing a government bond using the **backward induction process** [equates to $100 which is indeed the price of the 2-year government bond (Coupon = 2 year YTM)]
3. Now consider a 2-year, annual payment **corporate bond** (higher coupon) and calculate its value assuming no default (VND)
4. Now calculate the credit valuation adjustment (CVA) on the Corp. Bond.
5. Use the CVA to **work out the fair value** of the bond and the credit spread [The fair value of the bond is the VND less the CVA \> solve for YTM given new price \> calculate Credit spread: YTM**CB** - YTM**GovB**
6. **Discoutn margin** (calc?) \> Quoted margin credit situation has worsenend
72
Analyzing the credit risk of a _floating rate note_ bond using a binomial valuation approach
1. **Build the binomial interest rate tree** (Bootstrapping to get Spot rates \> determine Forward Rates?; We then apply an interest volatility assumption around the forward curve [FM xeSD\*Vol]
2. Confirm the binomial tree is arbitrage-free by pricing a government bond using the **backward induction process** [equates to $100 which is indeed the price of the 2-year government bond (Coupon = 2 year YTM)]
3. Now consider a 2-year, annual payment floating rate note and calculate its value assuming no default (VND) [Coupon rate = 1-year Benchmark rate + 60 basis points (*Quoted margin*)] \> **Coupon: 60bps + forward rates im tree**
4. Now calculate the credit valuation adjustment (CVA)
73
Components of a corporate bond yield
1. **Spread over Benchmark**
* Liquidity
* Taxation
* Expected Loss from Default
* Risk Aversion (compensation for above factors)
1. **Benchmark Yield** (Macro factors)
* Expected Inflation Rate
* Expected Real Rate of Return
* Risk Aversion (Compensation regarding the uncertainty of the inflation)
74
**Credit curve**
* The credit risk for a name is unlikely to be constant for all maturities. The plot of credit risk (as measured by credit spread or more commonly CDS) vs. maturity is called a credit curve
* The credit curve is the graphical representation of the relationship between the return offered by a security and the time to maturity of the security
* Shows the yield spread over a benchmark security with increasing maturity
* It measures the **investors’ sentiments about risk** and can affect the return on investments. The difference between the first maturity on the curve (the short end) and the last maturity of the curve (on the long end) determines the **steepness of the curve**
1. The steepness of the curve is usually greater (upward sloping) for companies in cyclical industries such as retail. It is because the probability that such companies will default over time is greater
2. Some companies show a flat curve; it is a sign that the probability of default is uniform over the different points of maturity.
3. A downward sloping or inverted curve shows that the company is likely to default in the near future but far less likely to default in the long term.
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**Key Drivers** of the term structure of credit spreads
1. **Credit quality**
* For investment grade bonds with highest credit ratings and very low spreads, _credit migration is only possible in one direction_. Therefore the credit term structure tends to be _flat or slightly upward_ sloping
* Bonds with lower credit quality have _greater sensitivity to the credit cycle_. The greater chance of default results in a _steeper_ credit curve
1. **Financial conditions**
* Stronger economic climate is associated with higher benchmark yields but lower credit spreads as default probabilities are lower (stronger cash flows and increased profits).
1. **Market supply and demand dynamics**
* The liquidity of corporate bonds varies widely. Credit spread is _wider with less liquidity_ in the bond.
* Most recently issued bonds represent the biggest proportion of trading volume and therefore are responsible for the observed volatility in credit spreads
1. **Microeconomic factors**
* _Company and industry-specific analysis_ should be considered
* Anything that increases implied _default probability_ e.g. greater equity volatility, will result in a higher credit spread
76
**Considerations** when analyzing the term structure of credit spreads
1. **Choosing an appropriate risk-free or benchmark rate**
* A logical choice is a _liquid government security_ with the _nearest maturity_ to the corporate bond, this will have the lowest default risk
* The reality is that the _duration and maturity rarely match_ so _interpolation_ between two government bond yields may be _required_
* The _benchmark swap curve_ based on inter-bank rates is _often used_ because of the _high liquidit_
1. **All-in spread:** The term structure analysis should include only bonds with similar credit characteristics
* Typically senior unsecured general obligations of the issuer
* Therefore exclude bonds that may include embedded options, first or second lien provisions
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**Interpreting Credit Curve**
1. Flat credit spread curve
2. Upward sloping credit spread curve
3. Downward sloping (inverted) credit spread curve
4. Impending default scenarios
| (term structure of credit spreads)
1. **Flat credit spread curve:** Implies a stable expectation of default over time.
2. **Upward sloping credit spread curve:**
* ****Implies investors need greater compensation for assuming issuer default over longer time periods
* High quality issuer with a strong competitive position in a stable industry (low leverage, strong cash flows and high profit margin) will drive down short-term credit spreads. Rising with increasing maturity as macroeconomic uncertainty is factored into the spread along with potential technological changes and shifts in the competitive environment
* Typically investment-grade bond portfolios exhibit upward sloping term structure of credit spreads
* It is because when investors stay invested in a certain security for an extended period of time, they will be rewarded for their commitment
* When the credit spread becomes wider, it results in a **steeper** credit curve. It is also a sign that there will be economic growth or inflation in the economy
1. **Downward sloping (inverted) credit spread curve:** Issuers in cyclical industries such as oil and gas exploration are at the bottom of the economic cycle with investor expectation of a recovery in the industry and hence improving credit spreads over time
2. **Impending default scenarios:** The debt essentially trades at a price equal to the recovery rate, therefore the observed credit spread reflects this default scenario. • The credit spread observed represents an ‘optical’ phenomenon rather than a reflection of the view on the risk-reward profile for short-term vs. long-term bonds from a single issuer.
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**Credit Analysis for Securitized Debt**
- Homogeneity
- Granularity
1. **Homogeneity:** Refers to the degree to which underlying debt characteristics within the structured finance instrument are similar across individual obligations
2. **Granularity**: Refers to the actual number of obligations that comprise the overall structured finance instrument (Highly granular may comprise of hundred’s of underlying creditors)
Approach to credit analysis for a given instrument type:
* **Short-term, granular, homogenous** assets \>\> evaluate using statistical approach to existing book of loans
* **Medium-term, granular, homogenous** assets \>\> switch to portfolio-based approach given the portfolio is not static
* **Non-granular, heterogeneous** assets \>\> a loan-by-loan approach is appropriate
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**Credit Analysis for Securitized Debt**
- Originator/servicer
- Credit enhancements
1. **Originator/servicer** – roles and responsibilities
* Enforcing loan eligibility criteria
* Secure and maintain documentation and records
* Ensure timely repayment & contract enforceability ie loan delinquency
* Investors are exposed to operational and counterparty risk
* A c**areful analysis of the originator/servicer should be carried out**
1. **Analysis of credit enhancements**
* Should be considered alongside the bankruptcy remoteness of the special purpose entity
* Investors should consider the presence of the following when conducting their analysis:
* **Early repayment triggers** – protecting investors in adverse credit events
* **Excess spread**s – enhanced return in the event of declining quality of the assets pool e.g. often present in credit card ABS
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**Covered Bonds**
* One of the oldest forms of secured debt
* It is a senior debt obligation of a financial institution, gives recourse to
* **To the issuer/originator**
* **AND A predetermined underlying collateral pool** e.g. residential or commercial mortgages, or public sector asset exposures
* Ratings agencies often assign a rating to covered bonds that are s**everal notches above** the issuing financial institution
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**Credit default swaps** (CDS)
A credit default swap (CDS) = credit riks insurance
is a financial derivative or contract that allows an investor to "swap" or offset his or her credit risk with that of another investor
**Long CDS / Protection buyer**: Buys a CDS from investor who agrees to reimburse the lender in case borrower defaults with notional amount \>\> Pay premium/ spread \>\> **SHORT CREDIT RISK**
**Short CDS / Protection seller**: Contingent payment if reference entity experiences a credit event \>\> **LONG CREDIT RISK**
*Credit risk is not completely eliminated since there is credit exposure with CDS counterparty.*
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Single name CDS
Tranche CDS
CDS Index tranche
**Single name CDS:** Reference entity is individual corporation or government. Any obligation that ranks equally to the reference obligation can be delivered. The reference obligation is normally a senior unsecured obligation
**Tranche CDS**: Each tranche covers a combination of names but exposure is limited to pre-specified levels
**CDS Index tranche**: Index includes a range of names - three most liquid CDS Indexes, with the two investment grade indexes being the most liquid:
1. CDX IG (125 Name, Investment Grade in North America)
2. iTraxx Europe (125 Name, Investment Grade in Europe)
3. CDX HY (100 Name, High Yield in North America)
4. iTraxx Crossover (50 Name, High Yield in Europe)
5. Index is updated periodically (c6 months) to create a new on-the-run series
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CDS: **ISDA agreements**
* ISDA is the International Swaps & Derivatives Association.
* ISDA agreements: **a master agreeme**nt that parties to derivatives transactions can use to identify, monitor and manage the risks associated with **OTC derivative transactions**
* Removes the risk and expense of individual contracts and provides **standardized documentation** that **enables multiple transactions** to be undertaken with reduced credit, legal, contract and liquidity risk
* **Each region now has a standard agreement**, e.g. Standard North American Contract (SNAC)
* !! CDS premiums are now standardized. The main two standard premiums are **100bp for investment grade** and **500bps for high-yield names**!!
* _If the fair value of the CDS is not the same_ as the standard premium then an **upfront payment** (also called upfront premium) **may be paid or received**
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**CDS**: Credit events
1. **Bankruptcy** is deemed to occur if the reference entity becomes insolvent or unable to pay its debts.
2. **Failure to pay** – the reference entity fails to make payments when due on one or more of its obligations; subject to any applicable grace periods; a minimum threshold payment amount is specified
3. ***Restructuring*** (CD in US don't account for this) - Changing the terms of the debt in such a way as to disadvantage the holder of the debt, e.g. extending the maturity of a loan. Not a credit event if this change is voluntary.
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CDS: **Settlement upon credit event**
Once a credit event has been deemed to have occurred by the determinations committee, an **auction** is carried out to determine the final price of the credit (this gives us the loss or recovery at default)
_CDS holders may either settle by:_
1. **Cash**: Protection buyer **receives par value less auction value** (more common)
2. **Physical**: Protection buyer **receives par value** and **delivers bond** to protection seller
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**Value variables of a CDS**
The value of a CDS is a function of three important variables:
1. Loss given a default (This will be 100 - Recovery rate)
2. Probability of a default (POD)
3. Timing of these two above, i.e. the present value
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CDS Basic Pricing Concepts
**Cumulative probability of default (CPD):** Chance of the Reference Entity defaulting within a set number of periods
**Cumulative Probability of Survival (CPS):** Chance of the Reference Entity not defaulting with a set number of periods [CPS = 1 - CPD]
**Hazard Rate/(λ) aka Marginal Probability of Default:** Chance of a default within a given period, given that the Reference Entity has survived up until this point
**Probability of Default (PD)** for a given time period. Chance of surviving a set number of periods and then defaulting in the next one. Chance of defaulting within any given period. E.g. PD4 = CPS3 x λ4 = CPD4 - CPD3
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CDS Basic Pricing Concepts **Examples**
Survive for the full three years?
**CPS3** = 0.95 x 0.94 x 0.93 = 83.05%
Default within three years?
**CPD3** = (1 - CPS3 )
Default within two years?
**CPD2** = (1 - CPS2)
Default within year 3?
* *PD3** = CPS2 x λ3
* *PD3** = CPD3 - CPD2
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**CDS premium**
* CDS premium is **only paid when** a default event occurs
* This simplified formula assumes that default can occur only on premium payment dates, i.e. we use discrete default probabilities
* For CDS standard contracts with a set premium then rather than solving for CDS we can insert the standard amount. In this case any difference between the two legs will be the upfront payment
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CDS: **Upfront payment** Formula
**(Credit spread - Fixed coupon) x Duration (Macaulay)**
rearrange this to derive the approximate value of the credit spread:
**(Upfront payment / Duration) + Fixed coupon**
Change in the upfront payment and can be approximated to:
**Change in credit spread in bps x Duration x Notional**
as fixed coupon is fixed so cannot change and the duration will only change slowly
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**Factors moving Credit Curve**
* If hazard rates are flat then the curve will be flat
* Rising hazard rates over time will produce an up sloping curve (normal)
* Falling hazard rates will produce a downward sloping curve (less common)
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**Curve Trades**
For example we might think a company will go through a short term period of pain/high credit risk but in the long run is a sound company. The trade would be to **buy short-term CDS** and **sell long-term CDS**
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**Basis Trading**
Yield on a bond includes an amount for credit risk. In this theory this amount should be the same as the spread for a CDS. The difference between these two is referred to as CDS Basis.
**CDS Basis** = CDS premium - Credit spread over LIBOR (Credit Risk)
**EXAMPLE**:
* The yield on a bond is 6%; the CDS has a fair value of 320bps and funding costs are 240bps (LIBOR). Is there a trade here?
* Yes – Credit spread is 600 - 240 = 360bps but CDS is only 320bps
* This means basis is 320 - 360 = -40. We should go long CDS (which is same as being short bond) and long bond
* Either the CDS is too cheap and should be 360, so if we are long we will make money on the yield and therefore the credit spread is too high. If the yield and credit spread falls and we are long the bond then we will make money.
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**CDS vs. Equity Trade**
Particularly relevant for high yield names, there should be a relationship (inverse) between the CDS and the stock price.
**EXAMPLE**
E.g. You believe a company is about to launch a takeover of a competitor using debt finance. If it is successful then the **stock price will rise**. However the higher levels of debt may (at least in the short term before any synergies can be realized) cause the **probability of default to rise**. Going **long CDS** and also **long equity** will provide useful trade. If synergies/efficiencies can be realized quickly then the stock will rise; if not and default probabilities rise then the CDS will rise.
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Conversion Value of Convertible Bond
Conversion value = Marketprice of common stock \* Conversion Ratio
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Convertibles: Market conversion price
Conversion price = Price of convertible bond / Conversion ratio
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Convertible: Market conversion premium per share
Premium per share = market conversion price - market price of common stock
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Convertibles: Market conversion premium ratio
Ratio: Market conversion premium per share / market price common stock
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Convertibles: Premium over straight value
Market price of convertible bond / straight value - 1
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yield curve flattens \> effect on option bonds
All else being equal, as the yield curve flattens, the value of the call option embedded in Bond A increases. Thus, although the value of Bond A increases, the increase is partially offset by the increase in the value of the call option. Therefore, Bond A does not increase as much as the straight bond. As the yield curve flattens, the value of the put option embedded in Bond B declines because opportunities for the investor to put the bond decline. Bond B will increase as the yield curve declines but not as much as the straight bond.
