Fixed Income Flashcards
What are the three common dimensions that are often used to categorize fixed income securities?
Issuer type, time to maturity and credit quality.
What is a callable bond?
A callable bond is a bond that can be redeemed by the issuer before its maturity date.
What is a puttable bond?
A puttable bond is a bond that can be put back into the market by the bondholder before its maturity date.
What is ‘spread’?
Spread refers to the difference between the yield on a bond and the yield on a benchmark bond, typically a government bond.
True or False: Zero-coupon bonds do not have an implied rate of return?
False. A zero-coupon bond’s implied rate of return is the discount to par it trades at in the primary market.
What is ‘duration’?
Duration is a measure of the sensitivity of a bond’s price to changes in interest rates.
What does ‘credit risk’ refer to in fixed income investing?
Credit risk refers to the risk that a bond issuer will default on its payment obligations.
What is the purpose of a bond indenture?
A bond indenture is a legal contract that outlines the terms of the bond, including covenants and the rights of the bondholders.
What is an affirmative bond covenant?
Affirmative covenants require the bond issuer to perform certain actions or meet specific benchmarks.
What is a negative bond covenant?
Negative covenants restrict the bond issuer from performing certain actions.
What is the typical lifetime of a mortgage-backed security?
Typically greater than 10 years, since the underlying mortgages are likely to be of similar maturities.
What is the lowest possible rating for an investment grade bond?
BBB (for S&P) or Baa (for Moody’s)
What is the difference between primary and secondary bond markets?
Primary markets are where the issuer of a new bond sells it to raise capital. Secondary markets are where investors trade bonds with each other.
What is the difference between a financial intermediary agreeing to underwrite an initial bond issuance and agreeing to act as a broker on a best effort basis, and when would you expect them to do either one?
Underwriting means the intermediary guarantees the sale of the bonds at an agreed price, and will purchase any of the bonds left outstanding. They typically do this with strong companies that have bonds they expect will all be sold. They do this because they charge a fee for underwriting the bonds, not because they want to by the bonds.
Best-effort is when they do not guarantee sale, and will not take on any unsold bonds. This typically happens with lower rated bonds that they do not expect to sell.
What is the definition of liquidity?
Liquidity is the ability to trade both quickly and at prices close to the security’s fair market value.
In repurchase agreements (repos) what is the ‘initial margin’?
The initial margin is the percentage by which the market value of the collateral exceeds the purchase price of the securities. So if the borrower puts up a £50,000,000 Gilt Bond as collateral but the lender only gives them £48,543,689, then the initial margin will be 103%.
£50,000,000 / 1.03 = £48,543,689
In repurchase agreements (repos) what is a ‘haircut’?
The difference between the amount borrowed and the value of the collateral the borrower puts up.
In repurchase agreements (repos) when would either party request for the other to pay the ‘variation margin’?
The value of the collateral can change over the course of the repo agreement. In this case either the cash lender or the borrower can request the other to pay the difference. This difference is called the variation margin.
If the collateral loses value:
The lender becomes overexposed and can ask the borrower for extra money (or securities) to cover the loss.
If the collateral gains value:
The borrower becomes overexposed can ask the buyer to return some money (or securities) since the collateral is now worth more.
What is meant by the ‘yield to maturity’ of a bond?
The interest rate that will make the present value of the bond’s cash flows equal to its market price.
What is the nominal rate (also know as the benchmark rate), and how do you calculate it?
The nominal rate is the stated interest rate on a financial instrument before accounting for inflation or compounding frequency. It can be approximated by the sum of the expected real interest rate and the expected inflation rate.
What are the three assumptions in yield to maturity calculations, and which of the three is typically impossible to achieve?
Bonds are held to maturity, all coupons and principle payments are made on time, and all coupons are reinvested at the yield to maturity stated at time zero.
The third assumption is typically impossible to achieve, as yields come down when duration comes down, so reinvesting the coupon payments at the same yield as the initial investment is not typically possible.
What risk factors make up spread?
Credit risk, liquidity risk, tax risk, and option risk (on callable bonds).
How do you find the settlement price of a coupon-paying bond if you buy it between two coupon payments?
Calculate the price of the bond as though you bought it on the most recent coupon date using the TVM function of the BAII. Take that price and multiply it by 1+YTM raised to the power of the number of days that have passed since the most recent coupon payment divided by the numer of days in the coupon payment cycle.
For example, if you used the TVM and found that the PV of a bond with YTM of 5% was £500, but it has been 90 days since the last coupon payment and payments are made every 183 days, then you would use this calculation:
500*(1 + 0.05)^(90/183) = £512.14
If the coupon rate exceeds the yield of a bond, would you expect it to trade at a premium or a discount to par value?
A premium
What assumption can you make of a bond where the coupon rate is equal to the yield to maturity?
It will trade at par value
What bonds are subject to the most price volatility due to interest rate changes?
Longer-dated bonds, lower-yield bonds, and lower-coupon bonds
For a bond, would you expect the price increase per percent decrease in yield to be equal to the price decrease per percent increase in yield?
No.
The relationship between the bond’s price and its yield is convex, not linear. Bond prices go up quicker than they come down.
What are the nominal rate and the effective rate for bonds, and why are they different? Also what function would you use on the BAII to calculate this?
The nominal rate, also known as the coupon rate, is the stated interest rate that the bond issuer agrees to pay annually, expressed as a percentage of the bond’s face value.
The effective rate is a more accurate measure of return that an investor is likely to get, as it takes the effect of compounding into consideration. It is calculated as ((1 + r/n)^n) - 1), where r is the stated coupon rate, and n is the number of periods you expect to receive that rate.
You can calculate this using the ICONV function on the BAII.
Note: If a 5-year bond has a stated coupon of 5%, but pays out semi-annually, then you use r=2.5% and n=10. Make sure you adjust the rate to match the number of periods in calculations, and vice versa.
What BAII function are you likely to have to use if the question discusses nominal rates and effective rates?
ICONV
Using the BAII, how would you calculate the new nominal rate of a bond if you were to change it from semi-annual compounding to quarterly compounding?
Open the ICONV function on the BAII and enter the nominal rate of the bond, set the number of times it compounds in a year (C/Y) to 2, then compute the effective rate.
Once you have the effective rate, set the number of times it compounds in a year to 4, and compute the nominal rate.
What is the difference between the flat yield and the simple yield?
The flat yield only takes into account the return from interest payments. It is calculated by dividing the annual coupon payment by the PMV of the bond.
The simple yield takes into account both the coupon payments and any capital gain or loss from holding the bond until maturity. So the simple yield for a 5-yr bond with a 10% coupon paid annually priced at £90 (par £100) would be the annual coupon (£5) plus the annualised gain or loss on price (£10 gain over 5 years, so £2) divided by the current price of the bond (£90). (£5 + £2) / £90 = 0.0777 OR 7.77%.
How should you go about answering a question in the exam that asks you to find the static spread/ z-spread over the spot rate for a bond? The spot rates for each year, the coupon rate, and the present value of the bond are all known.
Since the exam is multiple choice, take the middle of the three answers and add it to each of the spot rates, then go through the formula to find the present value, discounting the cashflows in each year by the spot rate PLUS the static spread (remember to raise it to the correct power), add the values together and if the number you get is equal to the value given in the question, then you have your answer. If it is too high, then you have not discounted enough, and should choose the higher static spread. If it is too low, then you have discounted too much, and should choose the lower static spread.
PV = SUM[ Cash flow / ( 1 + Spot rate + Static spread)^N ]
When is the option adjusted spread important?
When the bond has embedded options
What sort of bonds have a negative option risk for investors?
Puttable bonds. The option risk is with the issuers.
What is captured in the Z-spread?
Credit risk, liquidity risk, and option risk.
For what type of instrument is the option adjusted spread smaller than the Z-spread, and why?
Callable bonds.
The OAS is Z-Spread with the option risk taken out. Since an investor takes on option risk when buying a callable bond, and this is factored into the Z-spread, removing it will result in a smaller risk.
What is the difference between the discount rate and the add-on rate?
The discount rate calculates yield by dividing the annual coupon payments by par, whereas the the add-on rate calculates yield by dividing the annual coupon payments by the price you pay (present value).
What is the bond equivalent yield of a money market security?
The BEY is the add-on rate over 365 days.
BEY = (( Par - Security Price) / Security price ) * ( 365 / Days to maturity )
What are the following notations, and what do they mean?
- 2y1y
- 1y1y
- 3y2y
They are forward rates / expected future interest rates
- The one year rate starting in two years time
- The one year rate starting in one years time
- The two year rate starting in three years time
What is the relationship between the 1y1y rate, the 1-year spot rate, and the 2-year spot rate?
The 1y1y rate is the 1-year spot rate starting in one years time. The 1-year spot rate is the rate of interest you could get for one year starting now, and the 2-year spot rate is the average annual rate of interest you could get each year for two years starting now.
The 1y1y rate will be the rate at which the interest of the 1-year rate and the 1y1y rate are equal to the interest of the 2-year rate.
(1 + 1y1y) + (1 + 1-year rate) = (1 + 2-year rate)^2
What is the relationship between forward rates, spot rates, and yield to maturity, and how would you expect them to act in rising interest rate environments compared to falling rate environments?
Spot rates are a geometric average of forward rates, and yield to maturity is a weighted average of spot rates.
Spot rates will move in the same direction as interest rates, but because spot rates are affected by the starting value of the forward rates, it bit move as quickly. In a rising interest rate environment, the forward rate starts low and gets larger, and the spot rate get larger as well, but is dragged down by the initial low spot rate. The same relationship occurs between YTMs and spot rates.
In a falling rate environment, the inverse is true. Spot rates are not dragged down as much as forward rates, and YTMs are not dragged down as much as spot rates.
Interest rate risk for a bond refers to the fact that the value of the bond decreases when interest rates do what?
Rise
A bond’s value is inversely related to movements in interest rates. Should rates increase, other investors would be able to take advantage and buy new bonds at the higher rate, making older bonds issued at the lower rate less valuable.
What is the formula for Macaulay duration?
…………. Σ (n) * (PV of cash flows)
MacD = ____________________________
k * Bond price
Where
n = no. of periods
k = coupon payments per year
Answer is always given in years
What is ‘modified duration’, and how is it calculated?
Modified duration is a measure of a bond’s price’s sensitivity to interest rate changes with respect to its own yield to maturity.
In essence it is the amount you would expect a bond’s price to move per 1% change in interest rates expressed as a percentage.
ModD = Macaulay duration / (1 + Yield)
*yield should be for one period, so for a semi-annual bond this is yield per 6-months
What is ‘effective duration’, how do you calculate it, and when would you use this?
Effective duration is the measure of a bond’s sensitivity to a 1% change in its benchmark’s yield.
Effective duration = (PV1 - PV2) / 2 * PV0 * Change in benchmark yield
You would use this when looking at bond’s with embedded options, since the price when the yield falls (PV1) cannot go above the call price, and the price when the yield rises (PV2) cannot fall below the put price.
What is the ‘duration gap’, how do you calculate it, and how do you interpret it?
The duration gap is the difference between Macaulay duration (the average life of the bond) and your investment horizon (how long you hold the bond for). It is a way to tell where the greatest risk is when you sell a bond, either with coupon reinvestment or with the sale price.
Duration gap = Macaulay duration - Investment horizon
If the gap is zero, both risks are offset by each other.
If the gap is negative, coupon reinvestment risk is greater than the sale price risk, and you should sell the bond.
If the gap is positive, sale price risk is greater than the coupon reinvestment risk, and you should continue holding the bond.
How do you calculate ‘money duration’?
And how do you then use this to work out the ‘price value of a basis point’, and what does this measure?
Money duration = -Modified duration * Bond price
PVBP = Money duration * 0.0001
PVBP measure the dollar price change per basis point of change in the yield.
How do you calculate ‘duration effect’?
Duration effect = -Duration * Change in yield
How do you calculate ‘approximate modified convexity’?
AMC = (PV1 + PV2 - (2 * PV0)) / PV0 * (Change in yield)^2
How do you calculate ‘convexity effect’?
Convexity effect = (1/2 * Convexity) * (Change in yield)^2
If interest rates are low, the convexity of a callable bond will be _________
Negative
What is ‘effective convexity’, and how do you calculate it?
It is secondary effect on the bond with respect to a move in the yield of the benchmark.
Effective convexity = (PV1 + PV2 - (2 * PV0)) / PV0 * (Change in yield)^2
This measure of convexity is best used for bonds with embedded options.
What are the eight ‘Cs’ analysts use to assess creditworthiness?
Top down:
Country - Location/ legal structure of the country
Conditions - Economic/ competitive/ environment
Currency - Issued currency
Bottom up (quantitative):
Capacity - Ability to make payments on time
Capital - Company’s resources/ reliance on debt
Bottom up (qualitative):
Character - Trustworthiness of the business
Covenants - Inbuilt caveats to the bond
Collateral - Quality and value of the assets supporting the bond
When measuring the credit risk of an issuer, how long is the probability of default typically measured over?
Twelve months
What is meant by ‘credit migration risk’?
The risk of one of the major rating agencies lowering a bond’s rating.
This is a risk as if you buy a bond and its rating goes down, the price will fall, and you will therefore be getting a lower yield on it relative to the price you paid and what it is now worth.
