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Fixed Income > The Term Structure and Interest Rate Dynamics > Flashcards

The Term Structure and Interest Rate Dynamics Flashcards

1
Q

Give two interpretations for the following forward rate:The two-year forward rate one year from now is 2%.

A
  • 2% is the rate that will make an investor indifferent between buying a three-year zero-coupon bond or investing in a one-year zero-coupon bond and, when it matures, reinvesting in a zero-coupon bond that matures in two years.
  • 2% is the rate that can be locked in today by buying a three-year zero-coupon bond rather than investing in a one-year zero-coupon bond and, when it matures, reinvesting in a zero-coupon bond that matures in two years.
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2
Q

How do I interpret this forward rate - F1,2

A

F(When, Where)
2 years rate one year from now
1year from now the 2 year rate

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3
Q

If one-period forward rates are decreasing with maturity, the yield curve is most likely

A

Decreasing

If one-period forward rates are decreasing with maturity, then the forward curve is downward sloping. This turn implies a downward-sloping yield curve where longer-term spot rates zB–A are less than shorter-term spot rates zA.

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4
Q

If interest rates rise, and the future spot rates are below the forward rates, what does it mean?

A

Bonds are undervalued

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5
Q

Elaborate Zakarias explenation for where demoninator and rot should go for f(2,3) when calculating forward rates

A

For f(2,3)

The denominator is to the power of 2

and the rooth is the 3rd root.

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6
Q

I rates rises, and the future spot prices are above the implied forward curve

A

Bonds are overvalued

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7
Q

Spot rises, but below the forward curve

A

Bonds are undervalued
We should buyer longer bonds than our Investment horizion

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8
Q

Spot rises, but above the forward curve

A

Bonds are overvalued
We should follow a maturity matching strategy

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9
Q

Swap rate

A

The rate on the fixed leg of a interest rate swap

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10
Q

Swap spread

A

The spread between the fixed rate payer of a swap (Swap rate) and the rate of a “on the run” government bond with the same maturity as the swap that pays coupons.

Swap Spread = Swap Rate - Govenment bond (on the run) that pays coupons.

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11
Q

Where are forward rates derived from?

A

Forward rates are derived from spot rates/spot curve of zero coupon bonds

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12
Q

Where are spot rates derived from?

A

Spor rates are derived from par rates using bootstraping

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13
Q

What is the G-Spread

A

Difference between credit risky bond rates - Spot rates

The difference between the yield on Treasury Bonds and the yield on corporate bonds of the same maturity

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14
Q

What is the I-Spread

A

The difference between credit-risky bonds and the Swap rate

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15
Q

Bear Flattener

A

Rates are going up more on the short end than the long end

Bear flattener refers to the convergence of interest rates along the yield curve as short term rates rise faster than long term rates and is seen as a harbinger of an economic contraction.

a situation of rising bond prices which causes the long-end to fall faster than the short-end. Bear steepeners and flatteners are caused by falling bond prices across the curve.

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16
Q

Bear Steepener

A

Rates on the short end rise less than on the long end.

Long term rates rise more than short term rates.

Rates on the long end rise more than on the short end.

Causes: Increase in long term inflation expectation with no action of central bank/monetary policy.

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17
Q

Bull flattener

A

Rates on the long end of the curve drops more on the long end than the short end.

Causes: QE pushes capital to higher riskier assets. Or a flight to quality.

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18
Q

Bull steepener

A

Rates on the short of the curve end decreases more than on the long end.

A bull steepener is a shift in the yield curve caused by falling interest rates—rising bond prices—hence the term “bull.”

The short-end of the yield curve (which is typically driven by the fed funds rate) falls faster than the long-end, steepening the yield curve.

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19
Q

How much does Inflation and GDP growth influence interest rates curve for short and intemediary bond.

A

Inflation and GDP 1/3

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20
Q

How much does monetary policy influence interest rates curve for short and intemediary rates curve .

A

2/3

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21
Q

How much does monetary policy influence interest rates curve for long term rates curve .

A

1/3

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22
Q

How much does inflation influence interest rates curve for long term rates curve.

A

2/3

23
Q

The YTM to a bond is the rate that is most likely

A

The weighted average of the spot rates used in the bond valuation

24
Q

What is the Pure Expectation theory?

A
  • Forward rates are unbiased predictors of future spot rates.
  • It assumes investors are risk neutral.
  • Also known as unbaised expectation theory
  • Investors expectation that determines the shape of the interest rate term strucutre.
  • Forward rates are an unbiased predictor o future spot rates and that every maturity strategy has the same expected return over a given instrument horizion.
  • Long term interest rates equal the mean of future expected short-term rates.
25
Q

What is the Local Expectation theory?

A
  • Expected returns for all bonds is equal to the risk free rate over a short period of time.
  • Preserves the risk-neutrality assumption only for short holding periods.
  • Over long periods, risk premium should exis
26
Q

What is the liquidity preference theory?

A

Think: For longer time horizion, we demand more liquidity premium.
We demand a higher compensation for investing for long term.

  • Predicts upward sloping yield curve -> forward rates as an expectation of future spot rates are biased upward by liquidity preference.
  • Does not have a supply and demand argument.
  • Liquidity: Having to sell a bond at some unertain price.
  • Since liquidity premium exist, investors are compensated for interest rate risk when lending long term.
  • it increases with maturity.
  • Proposes that forward rates reflect investors expectations of future spot rates plus a liquidity premium to compensate investors for exposure to interest rate risk.
  • Liquidity premium is positivly related to maturity.
  • 25 year bond should have a larger liquidity premium than a 5 year bond.
27
Q

What is the Segmented Market theory?

A

Segmented market theory allows for lender and borrower preference to influence the shape of the yield curve. This causes yields to not be a reflection of expected spot rates or liquidity premiums, but solely a function of supply and demand for funds of a particular maturity.

  • The shape of the yield curve is determined by the preference of borrowers and lenders, which drives the balance between supply and demand for loans of different maturities.
  • Each maturity segment can be thought of as a segmented marketin which yields are determined independently from yields that prevail in other maturity segments.
  • Forward rates are not an expectation of future spot rates or liquidity preimiums.
  • Market participants are unwilling / unable to invest in anything other than securities of their prefered maturity.
28
Q

What is the preferred habitat theory?

A

Forward rates represent expected future spot rates plus a premium, but does not support the view that the premium is directly related to maturity.

Preferred habitat theory is similar to the segmented market theory in proposing that many borrowers and lenders have strong preferences for particular maturity.

Borrowers and lenders have a preferrence for particular maturities, buy yields at different maturities are not determined independently.

29
Q

Short term interest rate volatility is mostly linked to ..

A

Uncertainty regarding monetary policy.

Monetary policy attributes 2/3 of the volatility

30
Q

If the par curve is flat, then

A

The spot and the forward curves will also be flat at the same level.

31
Q

Are forward rates determined by supply and demand

A

NO!!

32
Q

YTM provides the best estimate of expected return when

A

The Par curve is flat and expected to stay flat until maturity.

With a flat par curve, we get flat spot and forward curve all overlaping at the same rate which will be the YTM.

33
Q

What is a “Forward Rate”?

A

A rate set today for a single payment of security to be issued at a future date

34
Q

What is the MRR-OIS Spread?

A

The difference between the MRR and the overnight index swap rate OIS.

MRR-OIS Spread relects risk and liquidity of money market securities.

35
Q

Please name the two different types of Arbitrage in binomial tree models

A

Dominance & Value added

36
Q

What is Dominance Arbitrage?

A

Arbitrage oppertunity that produces a risk-free profit with respect to future pay off.

Only produces risk free profit at payoff.

Future risk free profit

37
Q

What is “Value Addiditivity” Arbitrage?

A

Produces risk free profit with respect to current prices.

Relies on the sum of two parts not being equal to the sum of the whole. Basically, the two asset prices must equal each other.

38
Q

Interest rate tree is a visual representation of the possible values of interest rates based on

A

Interest rate model and assumption about volatility.

39
Q

Name the 2 different equilibrium models in fixed income binomial models

A

CIR
(Cox-Ingersoll-Ross)

and

Vasicek models

Singel-Factor Model that uses short term interest rates to describe interest rate dynamics. Primarily focus on yield levels.

40
Q

Name the 2 different Arbitrage Free models

A

Ho-Lee

and

Kalotay - William-Fabozzi

41
Q

If off the run bonds price was arrived by using spot rates drived from the benchmark par curve.

If we price the bond on a calibrated interest rate tree, the price recovered will be

A

The same as that arrived by using the spot prices.

42
Q

What is stripping?

A

The ability to seperate the bonds individual cash flows and trade them as zero coupon securities

43
Q

Explain Yield Curve: Level

A

Measures general level of interest rate in an economy

44
Q

Explain Yield Curve: Slope

A

Difference between YTM of long term bond vs YTM of short term bonds

45
Q

Explain Yield Curve: Curve

A

Relationship/Curve between Short, intermediate and long term

46
Q

Elaborate Zakarias explenation for how we solve present value of F(2,3) when calculating forward rates

A

F(2,3)
* We take the fifth year spot rate (2+3) = 5
* We inverse it ( 1.04)^-5
* We then multiply the 2 year spot rate.
* Ignore the 3.

47
Q

Forward rate notation for - The forward rate for a two-year loan beginning in one year

A

f1,2

The denominator = The beginning from today
Rot = The loan/rate

48
Q

A one-year zero-coupon bond yields 4.0%. The two- and three-year zero-coupon bonds yield 5.0% and 6.0%, respectively.

The five-year spot rate is not provided here; however, the forward price for a two-year zero-coupon bond beginning in three years is known to be 0.8479. The price today of a five-year zero-coupon bond is closest to:

A

0.7119

convert spot rates to spot prices to find DF3 = 1 / (1.06)^3
= 0.8396.

The forward pricing model can be used to find the price of the five-year zero as DFB = DFA ×FA,B–A,

so

DF5 = DF3F3,2 = 0.8396 × 0.8479 = 0.7119.

49
Q

How do we find the spot price of a zero-coupon bond ?

A

By inverting the spot rate

50
Q

Formula for The forward pricing model is

A

DFB = DFA ×FA,B–A,

DF2 = DF1 x F1,1

spot price for year 2 = DF2
Spot Price year 1 = DF1
forward price of a rate beginning in one year = f11

51
Q

What is the TED spread?

A

The TED spread is the difference between the three-month MRR and the three-month Treasury bill rate

MRR - 3M Tbill

52
Q

During economic expansions, monetary authorities raise benchmark rates to help control inflation. This action is most often consistent with

A

Bearish flattening

This action is most often consistent with bearish flattening, or short-term bond yields rising more than long-term bond yields resulting in a flatter yield curve

53
Q

A flight to quality is most often associated with

A

Bullish flattening.

A flight to quality is most often associated with bullish flattening, in which the yield curve flattens as long term rates fall by more than short-term rates

54
Q

What does Bootstrapping entail?

A

Bootstrapping entails forward substitution, however, using par yields to solve for zero-coupon rates one by one, in order from earliest to latest maturities.

Fixed Income (6 decks)

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