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CFA Level 2 2016 > Fixed Income #43 - The Term Structure and Interest Rate Dynamics > Flashcards

Fixed Income #43 - The Term Structure and Interest Rate Dynamics Flashcards

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1
Q

spot rate

forward rate

yield to maturity

A

LOS 43.a

spot rate - annualized market interest rate for a single payment to be received in the future.

forward rate - annualized market interest rate (agreed to today) for a loan to be initiated in the future

yield to maturity - yield of a zero coupon bond; for a coupon bond, YTM and spot rate are not same unless yield curve is flat

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2
Q

discount factor

A

LOS 43.a

the price today of a $1 par, zero coupon bond

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3
Q

relationship between spot rate and discount factor

A

LOS 43.a

PT = 1 / (1 + ST)T

PT is discount factor

ST is spot rate

T is maturity

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4
Q

spot yield curve

aka spot curve

A

LOS 43.a

spot curve - the grpah of the spot rate ST versus the maturity T; “the term structure of spot rates”

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5
Q

for a given bond, its expected return will equal its YTM only when…

A

LOS 43.a

  1. the bond is held to maturity
  2. all payments (coupon and principal) are made on time and in full (i.e. bond is option-free and there is no default risk)
  3. all coupons are reinvested at the original YTM (can only be true if the yield curve is flat)
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6
Q

forward pricing model

A

LOS 43.b

forward pricing model values forward contracts based on arbitrage-free pricing:

P(j+k) = PjF(j,k)

F(j,k) = P(j+k) / Pj

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7
Q

forward rate model

A

LOS 43.b

forward rate model relates forward and spot rates:

[1 + S(j+k)](j+k) = (1 + Sj)j [1 + f(j,k)]k

[1 + f(j,k)]k = [1 + S(j+k)](j+k) / (1 + Sj)j

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8
Q

relate forward and spot rates to the shape of the yield curve

A

LOS 43.b

If the yield curve is upward sloping, then the forward rate from j to k is greater than the spot rate for maturity j+k; that is:

if Sj+k > Sj ⇒f(j,k) > Sj+k

if Sj+k < Sj ⇒f(j,k) < Sj+k

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9
Q

par rate and par rate curve

A

LOS 43.c

  • par rate - yield to maturity of a bond trading at par
  • par rate curve (aka par curve) - graph of par bond rates of different maturities
  • for a bond with a single cash flow remaining (i.e. last coupon + principal), par rate = spot rate
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10
Q

bootstrapping

A

LOS 43.c

bootstrapping - the process of deriving spot rates (i.e. zero coupon rates) from the par curve by using the output (e.g. S1) of one step as the input for the next step (e.g. solving for S2​)

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11
Q

relationship between spot curve slope and forward rates

A

LOS 43.d

+ slope spot curve: forward rate rises as j increases

  • slope spot curve: forward rate declines as j increases
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12
Q

spot rate and forward rate evolution relationship to long maturity bonds

A

LOS 43.d

The spot rate for a long-maturity, T, security will equal the geometric mean of the one-period spot rate and a series of one-year forward rates:

(1 + ST)T = (1 + S1) [1 + f (1, 1)] [1 + f (2, 1)] …. [1 + f (T-1, 1)]

If after one year spot rates reflect last year’s forward rates, then the 1-year holding period return for a long-maturity bond is always equal to the one-year risk-free rate.

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13
Q

investor actions wrt forward price evolution

A

LOS 43.d

  • when current spot rates reflect last year’s forward rates: forward price remains unchanged, so
    investor return = 1-yr risk-free return
  • current spot rates < implied by last year’s forward curve: forward prices increase, so
    investor return > 1-yr risk-free return, because market is discounting future cash flows at “too high” of a discount rate
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14
Q

“riding the yield curve”

A

LOS 43.e

compared to “maturity matching” (i.e. buy bonds with maturity = investment horizon):

riding the curve - in upward-sloping yield curve environment, purchase bonds with maturities > investment horizon, then as maturity shortens, bond CFs discounted at successively lower yields. If yield curve remains unchanged, investors earns higher return (by taking on interest rate risk)

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15
Q

swap rate curve

A

LOS 43.f

  • (plain vanilla) interest rate swap - one party makes payments based on a fixed rate while counterparty makes payments based on a floating rate
  • swap (fixed) rate - the fixed rate in an interest swap
  • swap rate curve - how rates vary for various maturities
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16
Q

how and why market participants use the swap rate curve

A

LOS 43.f

participants prefer the swap rate curve as a benchmark interest rate curve (rather than government bond yield curve) because:

  • swap rates reflect credit risk of commercial banks (rather than credit risk of goverments)
  • swap market is not regulated by any government, making swap rates in different countries more comparable
  • swap curve typically has yield quotes at many maturities, whereas US bonds yield curve have on-the-run issues trading at only a small number of maturities.

Wholesale banks that manage risk using swaps use swap yield curve

Retail banks tend to use government bond yield curve

17
Q

value the fixed rate swap payments on a swap contract

A

LOS 43.f

given notional $1 principal, swap tenor T, spot rates St and swap fixed rate SFRT :

sum(t=1 to T)[SFRT / (1+St)t] + 1 / (1+ST)T = 1

SFR can be thought of as the coupon rate of a $1 par value bond given the underlying spot rate curve

18
Q

calculate and interpret swap spread for a given maturity

A

LOS 43.g

swap spread - amount by which the swap rate exceeds the yield of a government bond with same maturity

swap spreadt = swap ratet - Treasury yieldt

swap spreads are almost always positive

LIBOR swap curve is most commonly usede; it reflects the default risk of a commercial bank

I-spread aka “interpolated spread” - yield difference between a risky credit bond and swap rate of same maturity

19
Q

interpolated rate

A

LOS 43.g

interpolated rate “ri” having maturity “Ti” where
Tlow < Ti < Thigh

ri = rlow + (Ti - Tlow)(rhigh - rlow) / (Thigh - Tlow)

20
Q

Describe the Z-spread

A

LOS 43.h

Z-spread - a constant incremental spread rate that, when added to each spot rate on the default-free spot curve, makes the PV of a bond’s cash flows equal to the bond’s market price

Z-spread representd a bond’s overall credit and liquidity risk premiums

“Z” stands for “zero volatility” - assumes zero interest rate volatility i.e. a constant offset over time.

Z-spread is not appropriate for use with bonds having embedded options. But, if used this way Z-spread would include the option risk premium (in addition to credit and liquidity risk premiums)

21
Q

TED spread

A

LOS 43.i

  • TED stands for “T-bill - EuroDollars”
  • TED spread is the rate difference between interbank loans and government debt, e.g.:

TED spread = LIBORT - T-BillT

  • TED spread reflects the risk of interbank loans, and does so more accurately than the 10-year swap spread
22
Q

LIBOR-OIS spread

A

LOS 43.i

  • OIS stands for “overnight indexed swap”; OIS rate reflects the Fed funds rate and includes minimal party risk
  • LIBOR-OIS spread is the amount by which LIBOR (includes credit risk) exceeds the OIS rate (min. credit risk)
  • LIBOR-OIS indictes the overall wellbeing of the banking system:
    • low - high market liquidity
    • high - banks unwilling to lend to each other due to creditworthiness
23
Q

list the traditional theories of term structure of interest rates

A

LOS 43.j

Explains why yield curve takes on a particular shape and how forward rates are interpreted

  1. unbiased expectations theory
  2. local expectations theory
  3. liquidity prederence theory
  4. segmented markets theory
  5. preferred habitat theory
24
Q

unbiased expectations theory

A

LOS 43.j

aka “pure expectations” theory

hypothesis: “investors’ expectations determine the shape of the interest rate term structure”

  • foward rates = expected future spot rates
  • long-term interest rates equal the mean of future expected short-term rates

underlying principal: “risk neutrality” - investors do not demand a risk premium for maturity strategies that differ from their investment horizon

yield curve shape implications:

  • If yield curve is upward sloping then short-term rates are expected to rise
  • If yield curve is downward sloping then short-term rates are expected to fall
  • If yield curve is flat then short-term rates are expected to remain constant
25
Q

local expectations theory

A

LOS 43.j

  • similar to unbiased expectations theory, except does not say every maturity strategy should have the same return over a given investment horizon
  • risk premium exists over longer periods
  • risk-neutrality is preserved for short term only
  • shown not to work ⇒ short holding period returns of long-maturity bonds is higher tha short-maturity bonds
26
Q

liquidity preference theory

A

LOS 43.j

  • proposes that forward rates reflect investors’expectations of future spot rates, plus a liquidity pre,ium for interest rate risk
  • interest rate risk: longer dated cash flows more sensitive to rate changes
    • premium is positively related to maturity
    • 25-year bond will have larger premium compared to a 2-year bond
  • forward rates are biased estimates of future rates because of the liquidity premium
  • a positive-sloping yield curve may be due to future expectations or liquidity premium
27
Q

segmented markets theory

A

LOS 43.j

  • yield at each maturity is determined independently of yields at other maturities
  • various market participants only deal in securities of a particular maturity
    • because they are prevented from operating at different maturities
  • yield determined by supply and demand
28
Q

preferred habitat theory

A

LOS 43.j

  • like liquidity preference theory, preferred habitat also proposes that forward rates are expected future spot rates plus a premuim
    • does not state that premium is directly related to maturity
    • investors prefer a particular maturity
    • would be willing to leave preferred maturity habitat to obtain a lower price (hence higher yield)
    • can be used to explain almost any yield curve shape
29
Q

modern theories of the term structure of interest rates

A

LOS 43.j

  • equilibrium term structure models: “single-factor models”
    • Vasicek Model
    • Cox-Ingersoll-Ross Model
  • arbitrage-free models: “binomial tree models”
    • Ho-Lee model
30
Q

Vasiek Model 1977

A

LOS 43.k

31
Q

Cox-Ingersoll-Ross (CIR) Model 1985

A

LOS 43.k

32
Q

Vasicek vs CIR Model

A

LOS 43.k

  • Under Vasicek model:
    • volatility does not increase as the level of interest rates increase
    • interest rates could become negative
  • Under CIR model:
    • volatility is related to the current level of the interest rate (prevents negative interest rates)
33
Q

Ho-Lee Model 1986

A

LOS 43.k

34
Q

yield curve shifts

A

LOS 43.l

35
Q

methods of measuring yield curve sensitivity

A

LOS 43.l

  1. effective duration
  2. key rate inflation
  3. sensitivity to parallel, steepness, and curvature movements
36
Q

effective duration

A

LOS 43.l

effective duration measures price risk for small parallel shifts in yield curve

  • problem: most yield curve shifts have nonparallel characteristics
  • solution: use key rate duration which measures impact of nonparallel shifts
37
Q

key rate duration

A

LOS 43.l

key rate duration is a more sophisticated method used to quantify price sensitivity to nonparallel yield curve shifts

key rate duration is price sensitivity to 1% change in a single par rate, holding other par rates constant

38
Q

sensitivity to level, steepness, and curvature movements

A

LOS 43.l

  • decomposes risk into to these categories of yield of yield movements:
    • level - d(xL) : a parallel increase or decrease of interest rates
    • steepness - d(xS) : long maturity interest rates increase, and short rates decrease
    • curvature - d(xC) : short and long rates increase; middle rates do not change
  • model like this:

d(P)/P ≈ -DLd(xL) - SSd(xS) - DCd(xC)

39
Q

maturity structure of yield curve volatilities

A

LOS 43.m

maturity structure of yield curve volatilities is the graph of yield volatility (annualized standard deviation ofversus maturity

  • short-term interest rates are generally more voltatile than long-term rates (i.e. graph is downward sloping)
  • embedded options are especially sensitive to yield volatility
  • short-term volatility primary component: monetary policy
  • long-term volatility primary components: uncertainty regarding:
    • the real economy
    • inflation

CFA Level 2 2016 (43 decks)

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