Fixed Income Fundamentals Flashcards
What is fixed income?
A broad class of financial products that comprises any investment where the investor earns a set payment on a predetermined schedule.
What are common fixed income investment products?
- Bonds
- Vanilla and exotic derivatives
- Asset-backed securities (ABS)
- Mortgage-backed securities (MBS)
- Preferred securities
What is a bond?
The simplest form of fixed income.
When was the first bond issued?
2400 BC, ancient Mesopotamia.
What is a coupon in bond terminology?
The set interest paid in a predetermined schedule (e.g., annually or semi-annually).
What is principal in the context of bonds?
The amount that the issuer owes to the investor; paid at maturity.
What is par value?
The nominal value of a bond, typically $100 for calculation purposes.
Who typically invests in bonds?
- Central banks / governments
- Insurance companies
- Hedge funds
- Asset managers
- Pension funds
- Corporates / family offices
- Institutional investors
- Retail investors
- Individuals
- Private banks / brokers
What are some reasons for investing in bonds?
- Liquidity
- Different risk profile relative to equities
- Easy for investors to match their liabilities
Who issues bonds?
- National governments
- Corporates
- Regional governments and municipalities
- Supranationals and agencies
What risks are associated with investing in bonds?
- Inflation
- Shifts in the yield curve
- Default risk
- FX and capital control risks
What is the bond market?
One of the largest financial markets in the world.
What was the size of the global bond market in 2018?
$102.8 trillion.
What is the relationship between bond price and par value?
The bond price should equal the par value at issuance and at maturity.
What are the factors affecting bond price fluctuations?
- Inflation
- Market yield
- Issuer and/or sector fundamentals
What is accrued interest?
Accumulated interest that is unpaid.
What are the day count market conventions?
- Actual/Actual
- 30/360
- Actual/365
How is accrued interest calculated under Actual/Actual convention?
Interest accrues based on the actual number of days since the last coupon payment over the actual number of total days between coupon periods.
What is modified duration?
Macaulay duration divided by (1 + YTM).
What is the formula for convexity?
Convexity = 1/1+(y/f))^2+ (t^2+t) PVCFt/ f^2 x PVTCF.
Fill in the blank: A bond is essentially a _______.
loan.
True or False: Corporate bonds typically have a minimum investment of $5,000.
True.
What is the minimum investment for government bonds?
Minimum $100, €100, or £100.
What are the Day Count Conventions?
- Actual/Actual
- 30/360
- Actual/365
- Actual/360
These conventions are used to calculate interest on bonds.
What are the three measures of yield?
- Current yield
- Yield-to-maturity (YTM)
- Yield-to-call (YTC)
These measures help assess the potential return on bonds.
How is Current Yield calculated?
Current yield = Annual dollar coupon / Current price
For example, with a face value of $100, coupon rate of 5%, and current price of $105, the current yield is 4.76%.
What is Yield-to-Maturity (YTM)?
The internal rate of return (IRR) of all cash flows from the bond
YTM is realized only if coupons are reinvested at the same YTM and the bond is held to maturity.
What factors affect Yield-to-Maturity?
- Coupons reinvested at the same YTM
- Bond held to maturity
YTM reflects the total return expected if these conditions are met.
What is Yield-to-Call (YTC)?
The return if the bond is called before maturity
YTC is calculated using cash flows from the bond if called at the earliest opportunity.
What is the difference between Nominal and Effective yields?
- Nominal rate: Stated interest rate without compounding
- Effective rate: Interest earned with compounding
Effective yield accounts for the effects of compounding.
How do you calculate Real yields?
Real yields = Nominal yields - Inflation
This calculation accounts for the purchasing power of money.
What does the yield curve represent?
A graphical representation of yields for a range of maturities
It does not show changes in yields over time.
What does a steep yield curve indicate?
Long-term investments pay a higher return than shorter-term investments
This is often a sign of economic growth expectations.
What can cause credit spreads to widen?
- Deteriorating financials
- Negative news
- Excess supply in secondary markets
- New issuances
Wider spreads indicate higher risk perceptions.
What are the types of credit ratings?
- Investment grade (BBB- or higher)
- High yield or junk (BB+ or lower)
These ratings reflect the credit quality of issuers.
What is the significance of the Economic Cycle on yield curves?
Yield curves move together with the economic cycle
Changes in government bond yields can signal economic growth.
What are the main theories explaining the shape of the yield curve?
- Liquidity preference
- Pure expectations
- Market segmentation
These theories help explain why yield curves take different shapes.
How is the price of a bond determined?
Bond price is the present value of all future cash flows generated by the bond
This includes the present value of coupon payments and principal repayment.
What is the formula for Present Value (PV)?
PV = FV x 1 / (1 + i)^n
Where FV is future value, i is interest rate, and n is the number of periods.
Define Clean Price in the context of bonds.
The price that is quoted without accrued interest.
Define Dirty Price in the context of bonds.
The clean price plus accrued interest.
What happens to bond prices as yields increase?
Prices will fall.
What happens to bond prices as yields decrease?
Prices will rise.
What is Duration in the context of bonds?
Duration measures how long it takes for an investor to receive the bond’s present value based on the expected future cash flows.
How is Duration related to the riskiness of a bond?
A bond with longer duration is riskier than a bond with shorter duration.
What is the relationship between Duration and time to maturity?
Duration is not the same as time to maturity.
What is a zero-coupon bond?
A bond that pays no interest for its life and pays all interest at maturity.
What is Macaulay Duration?
The weighted average time to all cash flows, measured in years.
What is the formula for Macaulay Duration?
D Mac = Σ (t x PVCFt) / PVTCF
What is the significance of a bond trading at a premium?
Cash flows from the coupons are higher than comparable investments.
Fill in the blank: Duration will never be more than the _______.
term to maturity.
What is the relationship between maturity and Macaulay duration?
A longer maturity bond will have a longer Macaulay duration.
What does Modified Duration measure?
The percentage change in price with respect to the change in its yield.
What is the formula for Modified Duration?
Modified Duration = Macaulay Duration / (1 + YTM)
What is Dollar Duration?
The dollar price changes as yield moves.
How do you calculate Dollar Duration?
Dollar Duration = Modified Duration x Dollar price x 0.01
True or False: The Macaulay duration of a coupon bond will always be equal to the maturity of the bond.
False.
What is the coupon payment for a bond with a par value of $100 and a coupon rate of 5%?
$5 per year.
What is the price of a bond with a yield-to-maturity of 5%?
$100.00
What is the price of a bond trading at a discount with a yield-to-maturity of 6%?
$97.33
What is the accrued interest in the context of bond pricing?
The interest that accumulates on a bond since the last coupon payment.
What is the par value of a bond?
$100.
What is dollar duration?
Dollar duration = Modified duration x Dollar price x 0.01
This measures how the dollar price changes as yield moves.
What does a 1% change in yield mean in terms of dollar price change?
$2.8278 change in price for a bond priced at $102.78 with a modified duration of 2.7513
This is calculated using the dollar duration formula.
How is dollar duration calculated for Bond A priced at $100 with a modified duration of 5?
$5
Dollar duration = 100 x 5 x 0.01.
How is dollar duration calculated for Bond B priced at $90 with a modified duration of 5?
$4.5
Dollar duration = 90 x 5 x 0.01.
What does a longer duration indicate about a bond’s price sensitivity?
The price will move significantly
Longer duration means higher sensitivity to yield changes.
What does a shorter duration indicate about a bond’s price sensitivity?
The price will move much less
Shorter duration means lower sensitivity to yield changes.
What is DV01?
Dollar value of a basis point
DV01 = Modified duration x Dollar price x 0.0001.
What is the formula for convexity?
Convexity = 1/σn t² + t PVCFt f² x PVTCF
This formula is used to measure the curvature of a bond’s price/yield relationship.
What does positive convexity indicate?
Gains are larger and losses are smaller than predicted by duration alone
Positive convexity is desirable in bond pricing.
How does a 1% increase in yields affect the price of the U.S. Treasury On-the-Run 10-Year Note?
Price decreases by 9.2044%
This demonstrates the price sensitivity of the bond to yield changes.
What is the relationship between price and yield?
Not linear; prices rise at an increasing rate as yield falls and fall at a decreasing rate as yields increase
This relationship is described by convexity.
What is the effect of a 1% drop in yield on Bond A with modified duration of 4?
4% increase in price
This reflects the bond’s price sensitivity to yield changes.
What is the effect of a 1% drop in yield on Bond B with modified duration of 2?
2% increase in price
This shows different sensitivities based on modified duration.
What does the formula for total change in price include?
Duration effect + Convexity adjustment
This formula helps in accurately predicting price changes given yield changes.
How is the change in price calculated?
Change in price (%) = Duration effect + Convexity adjustment
This accounts for both linear and curvature effects on price.
What are the drivers of convexity?
- Remaining term
- Coupon
- Yield
These factors influence the curvature of the price/yield relationship.
What is the significance of convexity in bond pricing?
It allows for adjustments in price impact calculations due to yield changes
Convexity helps refine sensitivity measures beyond duration.
What happens to estimated price changes as yields rise?
Estimated fall in price will be greater than actual fall in price
This illustrates how convexity affects price expectations.
What happens to estimated price changes as yields decrease?
Estimated rise in price will be less than actual rise in price
This further demonstrates the impact of convexity on pricing.
