Fixed Flashcards
What is the spot rate?
Interest rate on ZERO coupon bond
Forward rate, what is that?
An interest rate predicted/calculated for some point in the future
f(i,j) - what does this mean f(1,2)
This is the Future Spot Rate in one year, for two years. e.g. a term deposit rate in one year (2022), for two years
How to calculate forward rates from spot rate?
Spot (T* + t) = [Spot T* ^ T] * [Future T,t}^t
T* is a spot rate for x years, the t is for how many years it lasts.
Where is the forward rate relative to the spot rate on the yield curve.
Pretty much, the Forward rate is always more gnarly than the spot rate - if the spot curve is upward sloping, the forward rate is higher, and vise versa.
Harmonic mean formula
Product of (1+ all values) ^ 1/number of values.
Explain how to find spot rate using harmonic mean
Spot rate 3 = Spot rate 1 * Forward 1,1 * Forward 1,2 ^1/3
What is par rate ?
Par rate is the yield on a bond at par value
How does bootstrapping work
Bootstrapping assumes uses a portfolio of PAR value bonds to create a spot rate curve. Using the par rate, you can determine the spot rate for each period you have information for?
Does the spot rate and par rate at year 1 equal?
Yes
Formula bootstrapping
1 = Par Rate / Spot Rate 1 + Par Rate / Spot Rate 2.
If you are solving for spot rate 2, you use the 2 year par rate. You will have all inputs expect spot rate 2. You then use spot rate 2 as a new input (as well as updated par rate) to solve for spot rate 3
What is an assumption of YTM
Flat curve
Coupons reinvested at YTM
Bond held to maturity
How to solve for YTM? Think Spot Rate, Par rate
Once you have determined all spot rates, you can discount each coupon to get the actual price of the bond (PV of cash flows). Inputing the actual price to your calc can solve for YTM (I/Y)
Is ytm like the weighted average of spot rates
Yes, therefore it sits under the spot rate on the curve.
Explain, rolling down yield curve
This assumes upward sloping curve. As maturity comes closer, the risk factor decreases (because yield decreases) and what happens when yield decreases, yeah, Prices increase.
This is an active trading strategy.
What is the z spread
Adding a nominal premium onto a bond
Ted Spead, what is it
A premium added to bonds, the difference between Libor and 10 Year T Bill USA
Segmented Market Theory and Preferred Habitat - what are these
Interest Rate Theories. Preferred habitat means that investors are willing to go outside their preferred maturity for a premium, segmented market says no
Local expectations theory
Holding any bond for a short time will get you the risk free rate
What is shaping risk
How sensitive a bond’s price is to the yield curve
What are the 3 descriptive factors of the yield curve, and which is the most important
Curve, Level and steepness. Level is the most important
What does an equilibrium model do?
Shape/predict yield curve
What fluctuate more, short or long term rates, and why
Short. Long term rates is a game of averages, so nothing changes too much. Short term rates change more because the averages are on less data points, meaning the % can shift more dramatically
State each type of yield in order of sophistication.
Coupon Current/Running Yield to maturity Yield to Call/Put/Worst Spot Yield Static Yield (Z) Option adjusted
Increased volatility has what effect on the value of a Call option ?
Increase
Difference between YTM and YTC
YTM is measured to maturity, YTC is measured to the next call date
What is the z spread
Z spread is the addition to the spot rate to account for credit and liquidity premiums on risky bonds (not treasury)
What is stripping in bonds?
Treating each coupon as a zero coupon bond and selling it indiviudally?
What is reconstitution in bonds?
The opposite of stripping
Explain the binomial pricing model for pricing bonds?
This is working through right to left to price a bond. It relies on you knowing the coupon of the bond, and discounting is by one period at a time to reach the value today, placing a 50% weighting on each value of the bond derived from the period AFTER
What is the dominance theory in arbitrage?
That risk free rates must always be equal
What is the additivity theory in arbitrage?
That securities should sell for equal amounts (before transaction costs) on seperate exchanges
Does the binomial tree pricing model take embedded options into consideration?
Yes, since it accounts for multiple interest rates. It is able to price these options under multiple scenarios
How to calculate path wise model (as opposed to binomial model)
PMT/Spot1 + PMT/SPOT1SPOT2 + PMT/SPOT1SPOT2*SPOT3 etc.
It acts as an average of all rates present
Does the end value post binomial analysis get effected by volatility?
No it doesn’t. As it is an average of both the upper and lower volatility. The vol doesn’t effect the end answer
What happens to the Price of a bond (fundamentally) if the modified duration is 6, and interest rates increase by 100bp
A 6% DECREASE in the price of the bond.
Does duration explain both large and small IR changes in the price of a bond?
No, duration explains most of the low IR changes, but convexity along with duration explain the large changes in IR
What is effective duration and convexity?
This is what is used to estimate the price change in the bond. Effective duration accounts for options embedded in bonds
Will an increase or decrease in IR effect a bonds price more
Decrease will effect much much more
Formula for price change in bond
-Duration * delta R + Convexity * delta r ^2
In a call option, what happens when IR go DOWN?
Corporations have incentive to call back the bond, so the price of the bond regresses to the call price of the bond.
What is the option value of a bond?
The difference between the call price regressed line on the price yield graph vs. the price of a non option bond. This value accrues to the issuer (corporation)
Price appreciation compression is inherent in which sort of option given a decrease in IR?
Call options
What does interest rate volatility do to the value of a putable bond?
Increases its value, there is more opportunity to be in the money
When interest rates decrease, what will happen to a callable bond and why
It will be called at the call price, and maybe one more coupon. This will happen because the corporation issuing the bond will be able to issue the same bond at a lower coupon with no worries
How do you find the value of a callable bond?
The value of a callable bond is:
Value of normal straight bond - Value of the call option
When determining an option value using the binomial tree, which sort of rates do we use, spot, par or forward?
Forward rates give the best indication of bond value in the future, that is what should be used. Forward rates also help determine if a bond will be called or put.
When determining the value of a bond through the binomial pricing tree (right to left), and a bond can be called at par, what is the process if the bond’s value is higher/lower than par?
We work back right to left to determine the Embedded value of the bond today. Same as a option free bond, BUT if the predicted bond value is MORE than the call price, you assume the bond is called, and thus DECREASES the value of the bond in the present.
What formula do we use on the binomial tree to go left one step
V-1 = PMT + (.5 * v1+v1)
OAS - what does it do to the binomial pricing tree
Shifts the whole thing up (everything is higher)
OAS, if volatility increases, what happens to it?
Decreases
Remember what the bootstrapping formula is? Then how it can be converted to future rates?
Spot 3 = Spot 1 + Future (in 1 year, for 2 years)
Bootstrapping is the par value into the spot rate
Effective duration formula
PV— - PV+ / 2 * delta r + PVo
Convexity formula
PV— + PV+ - 2PVo / delta curve^2 * PVo
Increase in IR does what to a put bonds duration
Decreases. You are closer to receiving the cash.
When a call option gets closer to in the money, what happen to convexity?
Decreases to concavity
Floaters effect the coupon on the ir
Coupon
Is a lower interest rate good for a call
Option and why?
Lower interest rate means there is a better opportunity for the option to be in the money, so the value of the option increases , reducing the value of the overall security
How to calculate the TED spread, and what does it measure
LIBOR - US T Bill. Measures riskier corporate market vs defualt free treasuries.
Why is the swap curve preferred to the spot rate curve?
The swap rate curve takes more maturities into consideration than the Treasury bond market. Also, the swap curve takes more risk (liquidity and credit into consideration)
How to calculate spot rates from just futures rates, and why does this work?
Under the arbitrage free valuation framework, the spot rate for one year, plus the one year rates in 2 and 3 years must equal the 3 year spot rate (For example), so Spot 1 * Future 1,1 * Future 2,1 = Spot 3
If spot rates in the market, under your opinion, are too high, what does that mean?
It means you should be buying securities/ Bonds in the current market are being discounted at a higher price, meaning that the instrinsic value is higher than what is reflected in the market.
Explain 3 factors for riding the yield curve, what do you need for it to work
A bond with a longer maturity than your investment horizon, an upward sloping yield curve, the need for the curve to NOT invert
Swap market, why is it preferred to spot rate to price bonds
Can be used to compare bonds across markets - better for private enterprise valuation
What is the I spread?
The difference between the swap rate, and the yield on a particular corporate bond
What are the 2 type of interest rate models, and examples? And what do these models do?
THese models explain/predict the yield curve. There are equilibrium models, which are single factor, and rely on economics, and there is arbitrage free valuation, which is the binomial tree we will speak about
Explain why we use KEY RATE DURATION, and what is means for a portfolio
Key rate duration is grouping your bonds into short, medium and long term buckets, and discounting each bucket by the anticipated yield at that period.
This is because we cannot always use a parellel shift in the yield curve (Short medium and long term bonds all increase by 100bps in yield)
You must also assume each cashflow as a zero coupon bond
What is the TED spread useful for?
Pricing credit risk
If interest rates rise, what happens to the duration of a callable bond?
Increases
A decrease in IR will do what to an embedded put option’s value
Decrease dramatically
What does a lower OAS mean for the price of a bond?
Higher price
A capped floating bond - does this effect the COUPON or the Interest rate that we use to discount the bond?
The coupon. This really effects the binomial interest rate tree
Pure expectation theory, what is it? AKA unbiased expectations.
This is the theory we use to calculate forward rates from spot rates. The curve represents the markets expectations for futures. There is no risk premium
The bias expectations or liquidity premium theory?
That to take on a longer termed bond, that may be lower in liquidity, that one must be paid a premium to take on that additional risk
Can the price of a callable bond be above the call price?
No way. All prices of a callable bond must be at or below the call price. Because if ir goes down, and therefore the price rises, the bond will be called back
What does an increase in volatility do to the oas of a bond
Decreases
Does a callable bond have more or less duration than a vanilla bond and why?
Less duration. Bonds are more effected by a decrease in IR. Since there is price compression on the upside, the duration is lower (not as sensitive to IR)
What is the duration of a floating bond?
The time til the next tick over date
How do you treat a callable bond during a lockout period?
As if it were a vanilla bond?
Conversion ratio, what is it?
The amount of shares you get for your bond holding. Remember, this is the par value of the bond, divided by the conversion price (pre determined price of bond)
One sided duration, give examples what it means?
It means that for either IR up or down, price diffences are apparent. For example, a decrease in IR would LOWER have a low one sided duration, because the bond will be called faster and there is less price appreciation.
Does a putable bond have positive convexity
Only yes
Explain the convexity of a callable bond
Both positive and negative convexity, negative when IR lessens
Do you treat a capped floater more like a callable of putable bond
Callable
Explain convertible bonds
Convertible bonds can be converted into x shares. The conversion ratio
What is straight value in convertible bonds?
It is just the PV of the coupon cash flows
What is conversion price?
Conversion price is pre-determined price the stock is at when you convert the bond. It is divided against the ISSUE PRICE (PAR PRICE) of the bond to determine the conversion ratio
Conversion ratio, what is it?
The amount of shares you get for your bond holding. Remember, this is the par value of the bond, divided by the conversion price (pre determined price of bond)
Conversion value, what is it, and how do you use it?
Conversion value is the conversion RATIO times the current market value of the stock. It is how much the convertible bond is worth (if exercised)
If the conversion value is lower than the conversion price, how will that effect the risk-return charecteristics of the bond?
Since the conversion price is lower than the stock price currently(so the bond can be converted to a higher amount of common stock) the security will act just like common stock. Think about it, if you can convert par value by a conversion price of 10 (to get $10) or convert it by 20 (to get $5) which would you rather pick.
The credit spread can also be called ?
The G spread
The credit spread represents
The probability of default
What is the credit valuation adjustment
It is the present value of the expected loss arising from default of a bond. You subtract this from the price of the bond using the risk free rate. You can then reverse engineer the YTM
Decrease volatility does what to OAS and bond value
Increase
What is notching?
Changing the rating of a bond based on the priority of payments
WHat is a structural credit model of predicting default?
Predicting when assets are less than liabilities.
Reduced form credit models - what is unique about them?
They predict when a bond will default. It is more company specific
Fair Value of bond - what = Actual value of bond?
Credit valuation adjustment
How to caclulate CVA - in depth.
Find exposure (value of bond discounted, times 1 - recovery rate. This gives loss given default. Then you gotta find the probability of default. That is the prob of default in year 1 times (1 minus prob of default)^n-1. This will give you the current prob of default. Times that by the loss given default and you have an undiscounted CVA. Discount it to present value, and add them all up.
is a spot rate and a swap spread a sufficient measure for yield?
Yes
Which is the best form of credit model?
Reduced form. You can use your own inputs, and is not constrained by some of the assumptions of the structural model
What are the assumptions of the structural credit model?
Constant risk free rate, that your assets trade on the market
What is a structural credit model?
How to price the probability of default by treating that probability as a put option on the company
If a bond is changing rating from AAA to AA, which formula do we use to capture the price change in the bond?
- Mod duration * Change in credit spread + Coupon
How to find the value of credit spread?
Value of risk free bond - Value of risky bond = CVA
YTM of risk free bond - YTM of risky bond = credit spread
Changes in credit spread on the yield curve can be effected by what factors?
Incoming recessions, supply and demand, expectations of default, changes in the recovery rate
How does a credit analyst analyze ABS?
Check the collateral pool (homogeneity and transparency) servicer quality and Credit enhancements
Risk neutral prob or default questions, how is the formula structured?
100 = (expected value at maturity * 1- prob of default + (recovered amount * prob of default) / 1+ r
Risk neural = equal 100
Who pays the premiums in a cds. Buyer or seller
Buyer
Name the 3 types of CDS
Single name
Index
Tranche
Who regulates the cds market
ISDA
What are some examples of a Credit event, that could trigger a CDS payment
Bankruptcy, restructuring, failure to pay
Who decides when a CDs should be paid if there is ambiguity ?
The determinations committee
Cheapest to deliver, what does it mean with CDS?
It means that the seller will deliver the cash value of the bond that is cheapest in the market. Investors will always prefer cash paid if default, unless their exact bond that defaults matches that which was cheapest to deliver
How to find recovery rate in CDS
It is the discount from par of whatever bond.
How to find exposure to a bond using index and single name CDS.
How much you’ve sold - how much you’ve bought . You can work out our hedged against a position you are.
How to find notional value / upfront costs for CDS
It is Spread - Coupon * Duration
What is curve trading for CDS?
Buying and selling based on perceived changes in the yield curve. Buying and selling on the same firm but for different maturities.
Credit risk of CDS = Credit risk of Bond. True False
True
What is basis trading for CDS
Buying a CDS for a bond when the CDS spread is lower than that of the bond. Buying both
When a firm defaults, are they still included in a CDS index?
no
How to find the probability of default in periods beyond the first?
You do the probability of not defaulting in the period prior * the shown probability of default
Naked CDS. What is it?
Taking a position in a CDS when you do NOT have a bond of the opposing side
If conversion value is above market value of a stock, how will it trade?
Like common stock. You are getting more than what it’s worth by converting
If a bond is downgraded in credit rating, how will it effect the value of the bond?
Decrease
Max value of call option on Binomial tree
100, it should be less that 100
