Fixed income Flashcards
Module 28.1, LOS 28.a
What are the conditions for expected return on a bond being equal to the yield?
1) HTM
2) All payments (coupon and principal) are made on time and in full.
3) All coupons are reinvested at the original YTM (mostly unrealistic due to the curve form)
Module 28.1, LOS 28.a
What is greater given timeline 0-j-k: forward rate for period j-k or spot rate for period 0-k?
Depends on the curve slope:
1) if upwardsloping - then forward rate is greater
2) if downwardsloping - then spot rate is greater
Module 28.1, LOS 28.a
The model that equates buying a long-maturity zero-coupon bond to entering into a forward contract to buy a zero-coupon bond that matures at the same time is known as:
Forward pricing model
Module 28.2, LOS 28.c
If investor expects that future spot rate will be lower than currently implied future spot rate, what should be the strategy?
Purchase bonds (at a presumably attractive price) because the market appears to be discounting future cash flows at “too high” of a discount rate
Module 28.2, LOS 28.d
What is maturity matching strategy?
Purchasing bonds that have a maturity equal to the investor’s investment horizon.
Profit earned - only coupon payments
Module 28.2, LOS 28.d
What is rolling down the yield curve strategy?
Purchase bonds with maturities longer than his investment horizon if yield curve is upword sloping.
Profit earned - difference in price over holding period due to higher future periods yield
Module 28.2, LOS 28.d
What is the risk of rolling down the yield curve strategy?
The risk of such a leveraged strategy is the possibility of an increase in spot rates
Module 28.3, LOS 28.e
Why market participants use swap rate curve?
1) Reflect the credit risk of commercial banks rather than of governments
2) Swap market is not regulated by any government -> swap rates in different countries are more comparable
3) Yield quotes at many maturities, unlike government bond yield curve
Module 28.3, LOS 28.e
Which discount rates would be preffered by:
1) retail banks?
2) wholesale banks?
1) retail banks - government spot curve
2) wholesale banks - swap curve
Module 28.4, LOS 28.f
What is swap spread?
Amount by which the swap rate exceeds the yield of a government bond with the same maturity
Module 28.4, LOS 28.f
What is the usual sign of swap spread and why?
Positive, reflecting the lower credit risk of governments compared to the credit risk of surveyed banks
Module 28.4, LOS 28.g
Which short-term rates spread reflect sredit and liquidity risk of a bond?
I-spread - amount by which the yield on the risky bond exceeds the swap rate for the same maturity
Module 28.4, LOS 28.h
What is zero-volatility spread?
Z-spread - spread that, when added to each spot rate on the default-free spot curve, makes the present value of a bond’s cash flows equal to the bond’s market price
Not appropriate to use to value bonds with embedded options
Module 28.4, LOS 28.h
What is TED spread?
TED spread - amount by which the interest rate on loans between banks (formally, 3M LIBOR) exceeds the interest rate on short-term U.S. government debt (3M T-bills)
Module 28.5, LOS 28.h
What are main yield curve shape theories? Which one explains almost any yield curve shape?
1) unbiased expectations theory
2) local expectations theory (doesn’t hold)
3) liquidity preference theory
4) segmented markets theory
5) preferred habitat theory - explains most shapes
Module 28.5, LOS 28.h
What are the main assumptions of unbiased expectations theory?
1) investors’ expectations determine the shape of the interest rate term structure
2) every maturity strategy has the same expected return over a given investment horizon -> risk neutrality
Module 28.5, LOS 28.h
How assumptions of local expectations theory are different from unbiased expectations theory?
Local expectations theory preserves the risk-neutrality assumption only for short holding periods:
1) over longer periods, risk premiums should exist
2) over short time periods, every bond (even long-maturity risky bonds) should earn the risk-free rate
Module 28.5, LOS 28.h
What are the main assumptions and implications of liquidity preference theory?
Assumption:
forward rates reflect investors’ expectations of future spot rates, plus a liquidity premium to compensate investors for exposure to interest rate risk
Implications:
1) positive-sloping curve - either rates expected to rise or stay flat/fall + liq. premium brining it up
2) negative-sloping curve - fall in rates expected
Module 28.5, LOS 28.h
What are the main assumptions of segmented markets theory?
1) yield at each maturity is determined independently of the yields at other maturities
2) shape of the yield curve is determined by the preferences of borrowers and lenders
3) various market participants only deal in securities of a particular maturity
Module 28.5, LOS 28.h
What are the main assumptions of preferred habitat theory?
1) orward rates represent expected future spot rates plus a premium
2) existence of an imbalance between the supply and demand for funds in a given maturity range will induce lenders and borrowers to shift to other maturities
3) borrowers require cost savings (i.e., lower yields) and lenders require a yield premium (i.e., higher yields) to move out of their preferred habitats
Module 28.6, LOS 28.i
What are the main measures of yield curve risk?
1) Effective duration (measures sensitivity to small parallel changes in yield curve which explains ~75% variation of the price)
2) Key rate duration (separately measures sensitivity to some rate point changes -> if summed together = effective duration)
3) Sensitivity to Parallel (level), Steepness, and Curvature Movements (decomposes sensitivity to parallel shifts, long-term up +short-term down, long and short term up + others unchanged)
Module 28.6, LOS 28.j
What does short and long term yield curve volatility represent?
1) long-maturity end is thought to be associated with uncertainty regarding the real economy and inflation
2) short-maturity end reflects risks regarding monetary policy (expansions -> increase st rates -> bearish flattening, recession -> reduce st rates -> bullish steepening)
Module 28.6, LOS 28.k
Which macro factors impact yield curve changes?
1) Major - Inflation (2/3 variation of short and intermediate-term), GDP (1/6), monetary policy (1/6)
2) Others - fiscal policy (restrictive decreases yields), supply of gov. bonds maturities, investors demand
Module 28.6, LOS 28.k
What is the bond risk premium?
Bond risk premium (term premium or duration premium) is the excess return (over the one-year risk-free rate) earned by investors for investing in long-term government bonds.
Module 29.1, LOS 29.b
What are the two types of arbitrage?
1) value additivity violation - the value of whole differs from the sum of the values of parts
2) dominance - one asset trades at a lower price than another asset with identical characteristics
Module 29.1, LOS 29.c
In a binomial interest rate tree what is the relation between 2 adjasent forward rates in the same period?
Adjacent forward rates (at the same period) are two standard deviations apart - i1,U = i1,L e2σ
Module 29.1, LOS 29.c
What is the binomial interest rate tree?
Lognormal random walk model with two properties: (1) higher volatility at higher rates and (2) non-negative interest rates
Module 29.1, LOS 29.e
What is the backward induction?
Backward induction refers to the process of valuing a bond using a binomial interest rate tree
Module 29.2, LOS 29.d
What are the key assumptions of reconstructing binomial tree interest rates?
1) The interest rate tree should generate arbitrage-free values for the benchmark security
2) adjacent forward rates (for the same period) are two standard deviations apart (calculated as e2σ)
3) middle forward rate in a period is approximately equal to the implied (from the benchmark spot rate curve) one-period forward rate for that period
Module 29.2, LOS 29.f
What is the main difference between valuing bond with zero-coupon rate and binomial tree?
Bonds with embeded options can only be measured with binomial tree (allows for rates flactuations)
Option-free bonds can be valued with both
Module 29.2, LOS 29.g
How pathwise valuation is performed?
1) For a binomial interest rate tree with n periods, there will be 2(n–1) unique paths
2) Pathwise valuation discounts cash flows one year at a time using one-year forward rates.
3) Pathwise valuation goes one path at a time. Then average PV is found
Module 29.2, LOS 29.h
In which situation Monte-Carlo is preferred over binomial tree?
When cash flows are path dependent
Module 29.2, LOS 29.h
What is the drift adjusted model?
Result of calibration process of adding (subtracting) a constant to all rates when the value obtained from the simulated paths is too high (too low) relative to market prices
Module 29.3, LOS 29.i
What are the two main types of term structure models?
1) Equilibrium term structure models - describe changes in the term structure through the use of fundamental economic variables that drive interest rates
2) Arbitrage-Free Models - assumption that bonds trading in the market are correctly priced, and the model is calibrated to value such bonds consistent with their market price
Module 29.3, LOS 29.i
Describe Cox-Ingersoll-Ross (CIR) model
1) (CIR) model is based on the idea that interest rate movements are driven by individuals choosing between consumption today versus investing and consuming at a later time
2) volatility increases with the interest rate
3) interest rates are mean reverting to some long-run value
Module 29.3, LOS 29.i
Describe Vasicek model
1) volatility is constant
2) interest rates are mean reverting to some long-run value
3) model does not force interest rates to be non negative
Module 29.3, LOS 29.i
Describe Ho-Lee model
1) Derived using the relative pricing concepts of the Black-Scholes model
2) calibrated by using market prices to find the time-dependent drift term θt
3) assumes constant volatility and produces a symmetrical (normal) distribution of future rates
Module 29.3, LOS 29.i
Describe Kalotay-Williams-Fabozzi (KWF) model
Same as Ho-Lee model but assumes lognormal distribution of future rates
1) Derived using the relative pricing concepts of the Black-Scholes model
2) calibrated by using market prices to find the time-dependent drift term θt
3) assumes constant volatility and produces a lognormal distribution of future rates