Fixed Income #32 (All) Flashcards
Describe relationship among Spot Rates, Forward Rates, Yield to Maturity, expected and realized return on bonds
(LOS32.a)
- Spot Rate for a particular maturity is equal to geometric average of one-period spot rate and series of one-period forward rates
- When the spot curve is flat, forward rates will equal spot rates and yields.
- When the spot curve is upward sloping, forward rate curves will be above spot curve and yield for a maturity of T will be less than the spot rate
- When the spot curve is downward sloping, forward rate will be below spot curve and yield for a maturity of T will be more than the spot rate
What is Spot Rate?
Spot Rate is the interest rate today
- what is the rate you will be using to get the discount factor
- Imagine you have a zero discount bond…
> The discount factor is today’s price of $1 par, P(T)
> Spot rate is the yield to maturity of this payment
What is Forward Rates?
Forward Rates (for that period) is the annualized interest rate on loan to be initiated at a future period.
Describe how zero coupon rate (spot rate) may be obtained from par curve by bootstrapping
(LOS32.c)
By using process called bootstrapping, spot rates (zero coupon rates) can be derived from par curve iteratively —– one spot rate at a time.
Describe the assumptions concerning the evolution of spot rates in relation to forward rates implicit in active bond portfolio management.
(LOS32.d)
If spot rate evolve as predicted by forward rates bonds of all maturities will realize a 1-period return equal to one-period spot rate AND forward price will remain unchanged.
What is active bond portfolio management?
(LOS 32.d)
Active bond portfolio management is build on the presumption that the current forward curve may not accurately predict future spot curves. Managers attempt to outperform the market by making predictions about how spot rates will change relative to the rates suggested by forward rate curves.
What will happen if future spot rates is lower than corresponding forward rates?
(LOS 32.d) If an investor believes that future spot rates is lower than corresponding forward rates, then investor will purchase bond (at a presumably attractive price) because market appears to be discounting future cash flows at “too high” of a discount rate.
Describe the strategy of riding the yield curve.
(LOS 32.e)
When the yield curve is upward sloping, bond managers may use the strategy of “riding the yield curve” to chase above-market returns.
By holding long-maturity rather than short-maturity bonds, the manager earns an excess return as the bond “rolls down the yield curve” (i.e. approaches maturity and increases in price)
=> Bond is valued in lower yield, since it has shorter maturity now after passing years, therefore it is valued with higher prices.
As long as the yield curve remains upward sloping, this strategy will add to the return of bond portfolio.
Explain the swap rate curve and why and how market participants use it in valuation.
(LOS 32.f)
The swap rate curve provides a benchmark measure of interest rates. It is similar to yield curve except that the rates used represent the interest rates of fixed rate leg in an interest rate swap.
Calculate and interpret the swap spread for a given maturity.
(LOS 32.g)
We define swap spread as additional interest rate paid by fixed rate payer of an interest rate swap over rate of the “on-the-run”government bond of the same maturity.
Describe the Z-spread.
(LOS 32.h)
The Z-spread is the spread that when added to each spot rate on the default-free spot rate curve (yield curve) makes the present value of a bond’s cash flow equal to the bond’s market price.
Describe TED spreads.
(LOS 32.i)
TED Spread is the amount by which the interest rate on loans between banks (LIBOR) exceeds interest rate on Short-Term US government debt (3-month T Bills).
Describe LIBOR-OIS Spread.
(LOS 32.i)
LIBOR-OIS Spread is the amount by which LIBOR rate (which includes credit risk) exceeds overnight indexed swap (*OIS) rate (which includes only minimal credit risk).
*OIS roughly reflects the federal funds rate and includes minimal counterparty risk.
Explain traditional theories of the term structure of interest rates and describe the implications of each theory for forward rates and the shape of the yield curve.
(LOS 32.j)
There are several traditional theories that attempt to explain the term structure of interest rates:
1. Unbiased expectations theory- Forward rates are an unbiased predictor of future spot rates. Also known as pure expectation theory.
2. Local expectations theory- Bond maturity does not influence returns for short holding periods.
[Assumption: Risk Neutrality only preserves for short holding periods] => Over longer periods, risk premiums should exist.
> The Local Expectation theory is shown not to hold
- Since the short-holding period return of long maturity bonds is HIGHER than short-holding period return of short maturity bonds due to liquidity premiums and hedging concerns
3. Liquidity Preference Theory- Investors demand a liquidity premium that is positively related to a bond’s maturity
4. Segmented Markets Theory- The shape of yield curve is the result of the interactions of supply and demand for funds in different market (i.e maturity) segments.
5. Preferred Habitat Theory- Similar to the segmented markets theory, but recognizes that market participants will deviate from their preferred maturity habitat if compensated adequately.
What is Risk Neutrality?
Investors don’t demand a risk premium for maturity strategies that differ from their investment horizon.
Describe modern term structure models and how they are used.
(LOS 32. k)
Equilibrium term structure models- attempt to model the term structure using fundamental economic variables that are thought to determine interest rates.
Arbitrage Free Models- Begins with observed market prices and assumption that securities are correctly priced.
(Advantage: Ability to calibrate arbitrage free models to match current market prices is one advantage of arbitrage-free model)
Explain how a bond’s exposure to each of the factors driving the yield curve can be measured?
(LOS 32.l)
We can measure a bond’s exposures to the factors driving the yield curve in a number of ways:
1. Effective Duration- Measures sensitivity of bond’s price to parallel shifts in the benchmark yield curve
2. Key Rate Duration- Measures bond price sensitivity to a change in a specific spot rate keeping everything else constant
(3) Sensitivity to parallel, steepness and curvature moments- Measures sensitivity to three distinct categories of changes in shape of the benchmark yield curve
What is Yield Curve Risk?
(LOS 32.l) (P.22)
Yield Curve Risk refers to risk to value of a bond portfolio due to unexpected changes in the yield curve.
What is Effective Duration?
(LOS 32.l)
Effective Duration measures the sensitivity of bond’s price to parallel shifts in the benchmark yield curve.
What is Key Rate Duration?
(LOS 32.l)
Key Rate Duration- Measures bond price sensitivity to a change in a specific spot rate keeping everything else constant
- It is superior for measuring the impact of nonparallel yield curve shifts
Explain the maturity structure of yield volatilities and their effect on price volatility
(LOS32.m)
The maturity structure of yield volatilities indicates that the level of yield volatilities at different maturities. This term structure provides an indication of yield curve risk. The volatility term structure usually indicates short term rates (which are linked to uncertainty over monetary policy) are more volatile than long-term rates (which are driven by uncertainty related to real economy and inflation).
- Fixed Income instruments with embedded options can be especially sensitive to interest rate volatility
