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Derivative Markets > Fixed Income Securities and Interest Rates > Flashcards

Fixed Income Securities and Interest Rates Flashcards

1
Q

What is a fixed income security?

A

Financial claims with promised cashflows of a fixed amount of money paid at fixed dates (also known as long term debt instruments)

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2
Q

What is collateral?

A

What the issuer of an indenture must put up to secure the debt

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3
Q

What happens to the collateral if the issuer defaults?

A

They may seize the collateral to recoup the principal

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4
Q

Define yield

A

Market required rate of return on a fixed income investment

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5
Q

Is the stock market more or less efficient than the bond market and why?

A

More efficient because there is more disclosure

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6
Q

What is a spot rate?

A

current interest rate

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7
Q

What is a forward rate?

A

Interest rate at a future period

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8
Q

Define interest rate

A

amount of money the borrower is obligated to pay the lender

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9
Q

What does size of interest rate depend on?

A

Chance that the borrower will default on their promise to repay the principal and fixed rate agreed within the lender agreement (CREDIT RISK)

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10
Q

What is a common assumption about the government in terms of defaulting?

A

They are less likely to default, but that is a bad assumption

Because of this assumption, treasury rates are much lower than any other and are referred to as risk free rates

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11
Q

Would bonds with longer time to maturity have higher or lower yield?

A

Higher yield, which is associated with higher risk since we are uncertain what will happen in the distant future

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12
Q

Describe a risk free assets return

A

It doesn’t fluctuate a lot over the life of the bond

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13
Q

What does LIBOR stand for and what is it?

A

London Interbank Offered Rate, and it is the interest rate at which banks are prepared to make large wholesale deposits with other banks

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14
Q

What does LIBID stand for and what is it?

A

London Interbank Bid Rate, and it is the rate at which banks will accept deposits from other banks

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15
Q

How big is the difference between LIBOR and LIBID, and which is higher?

A

Small spread, LIBOR is higher

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16
Q

What is equity?

A

Stocks and shares

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17
Q

Give the formula for rate of return and define all terms

A

r1 = (Mi + IP - M0) / M0

mi = time period i=1,...,n
M0 = initial investment
IP = intermittent payments
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18
Q

In the formula for rate of return, what would be the capital gains part?

A

(mi-m0) / m0

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19
Q

How much is one basis point?

A

One-hundreth of a percent

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20
Q

If an interest rate of 10% increases by 50 basis points, what is the new interest rate?

A

10.5%

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21
Q

Give the holding rate of return of an investment for two periods

A

r_0,2 = (m2 - m0) / m0

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22
Q

Give the formula for the average annualised rate of return

A

(1 + r_0,i) = (1 + ri)^i

where ri is the annualised rate of return

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23
Q

What happens to a bonds cashflow if interest rates rise?

A

The PV of the remaining cashflow decreases - vice versa is also true

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24
Q

What is the valuation of a bond affected by?

A
  • inflation fluctuation
  • liquidity of the bond market/bond itself
  • currency and exchange rate fluctuation
  • credit risk
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25
Q

What is a liquid bond market?

A

Lots of buyers and sellers of that bond

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26
Q

What is yield to maturity of a bond, and what is it also known as?

A

Interest rate required in the market on a bond

also known as the bond’s yield

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27
Q

What is the term structure of interest rates?

A

Relationship between yield and maturity of the bond

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28
Q

If YTM = coupon rate, what is the relationship between the price of the bond and the principal payment?

A

Price of bond (B0) = principal payment

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29
Q

If YTM > coupon rate, what is the relationship between the price of the bond and the principal payment?

A

price of bond < principal payment

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30
Q

If YTM < coupon rate, what is the relationship between the price of the bond and the principal payment?

A

price of bond > principal payment

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31
Q

Are nominal interest adjusted for inflation?

A

No

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32
Q

Are real interest rates adjusted for inflation?

A

Yes

33
Q

What is TSoIR in terms of nominal interest rates?

A

Relationship between nominal interest rates on default free, pure discount securities and time to maturity

34
Q

Explain each part of “pure discount securities”

A

pure - means no coupon payments (zero-coupon bond)

discount - discounting future cashflows

35
Q

What is a pure discount security?

A

Have lower price compared to other bonds, normally price = £1

36
Q

What is spot interest rate rt?

A

rt is annualised interest for maturity date t

  • rt is for payments on period t
  • rt is rate of interest from now and period t
  • rt different for each differrent period t
37
Q

How is TSoIR derived?

A

Set of different spot rates for different maturity rates, i.e plotting spot rates as a function of maturities

38
Q

Draw upwards and downwards term structures

A

DRAW

39
Q

What do central banks use TSoIR for?

A

Informing monetary policy decisions

40
Q

Describe a discount bond

A
  • maturity date t, only pays £1 at time t
  • referred to as STRIPs in US
  • provide info about spot interest rates, hence TSoIR can be referred to as zero-coupon yield curve
41
Q

Give the formula relating current price of a zero-coupon bond (Bt) and spot interest rates (rt)

A

Bt = 1 / (1 + rt)^t

42
Q

What is yield to maturity?

A

market interest rate required to find the current market value of a bond

43
Q

Formula to find PV or current market price (and define terms)

A

PV = sum(t=1 to T) Ct / (1+y)^t + P / (1+y)^T

Ct is coupon payment at time t
P is principal
y = YTM
t is counter of periods, T maturity

44
Q

Give formula for approximate YTM

A

Approx YTM = [coupon + { (principal - current price of bond) / number of periods to maturity } ] / [ (principal + current price) /2 ]

45
Q

When do yield curves change?

A
  1. monetary policy - tightening MP slows economy and flattens/inverts yield curve (tightening means increased interest rates)
  2. investor expectations
46
Q

How do investor expectations change yield curves?

A
  • expectation of future short-term interest rates are related to future real demand for credit and to future inflation
  • increase in short-term interest rates are related to future slowdown in economic activity and demand for credit, therefore downwards pressure of future real interest rates
  • expected declines in short term rates would tend to reduce current long term rates and flatten yield curve
47
Q

what is a forward transaction?

A

borrowing money from the future

48
Q

Outline how a forward transaction works

A
  1. terms of transaction agreed at t0
  2. receive loan at t1
  3. repay loan at t2
49
Q

Give two formulae for forward interest rate

A 
ft = [B(t-1) / Bt] - 1
ft = [(1 + rt)^t / (1 + rt)^(t-1) ] - 1
50
Q

Explain expectations theory

A
  • forward rates predict future spot rates that is ft = E (r1(t))
  • expectations of
    rising short-term interest rates are what create a positive yield curve and visa versa
  • this means the slope of the yeild curve reflects the market’s expectations of future short term interest rates
51
Q

Give a flaw of expectation theory

A

It assumes that bonds of different maturities are perfect substitutes

52
Q

State liquidity preference theory

A
  • investors believe that long-term bonds are far more risky than short-term bonds
  • in other words, investors prefer higher liquidity of short term debt, and therefore any deviance from a positive yield curve will only be temporary
53
Q

What are the implications of liquidity preference theory?

A
  • bonds with longer maturities will always have higher yields
  • forward rates will, on average, over predict future spot rates
  • yield curve will reflect the expectations of future interest rates and risk premiums demanded by investors to hold long term bonds
54
Q

State segmentation theory

A
  • different investors confine themselves to certain maturity segments (different maturity terms)
  • makes the yield curve a reflection of prevailing investment policies
55
Q

Give an assumption of segmentation theory

A

different maturities of debt cannot be substantiated for each other

56
Q

what are the implications of segmentation theory?

A
  • bonds with different maturities are part of separate markets
  • results in separate demand-supply relationships for short-term and long-term debt
57
Q

What is simple maturity?

A

Time left to maturity on a bond

58
Q

What does longer time to maturity mean?

A

The bond is more sensitive to changes in the required rate of return

59
Q

What is a bond’s duration?

A

Weighted average of the maturity of the individual cashflows, t, with the weights being proportional to the PV of these cashflows

60
Q

Give the formula for duration, defining all terms

A

D = sum(t=1 to T) wt * t

where:
wt = [ Ct / (1+y)^t ] / B
Ct cashflow at time t
B is bond price
y is YTM
61
Q

What does duration measure?

A

the average time taken by a bond, on a discounted basis, to pay back the initial investment

62
Q

When are coupons of Treasury notes payed?

A

Semi-annually

63
Q

What must you do to duration if coupon is payed semi-annually?

A

divide it by 2

64
Q

What does modified duration measure?

A
  • volatility (interest rate risk) of a bond

- effectively how small changes in ytm affect the price of the bond

65
Q

Give the formula for modified duration

A

MD = D / (1 + y)

66
Q

What is the difference between maturity and duration?

A
  • maturity considers zero-coupon bonds whereas duration uses coupon paying bonds
67
Q

What is the difference between duration and modified duration?

A

MD measures volatiliy of interest rates etc

68
Q

What is convexity?

A

Shows full relationship between bond price and yield

69
Q

Give the formula for convexity

A

CX = 1/(1+y)^2 * sum(t=1 to T) ( [ {Ct / (1+y)^t} / B] * t * (t+1) )

70
Q

What does convexity correct and what for?

A

Modified duration because it understates true price of the bond

71
Q

Give price change of a bond formula

A

ΔB = (-MD * ΔY) = (0.5 * CX * (ΔY)^2)

72
Q

Is the effect of an increase in YTM symmetric?

A

No

73
Q

What immunisation in fixed income finance?

A

Investors want zero exposure to interest rate risk

74
Q

What is the value of a portfolio?

A

xaBa + xbBb

75
Q

What is the value of the portfolio when interest rates change?

A

xaΔBa + xbΔBb

76
Q

In terms of modified duration, what is the value of a portfolio when interest rates change?

A
  • (xaBaMDa + xbBbMDb) Δy
77
Q

What is the modified duration of a portfolio?

A

[xaBaMDa/(xaBa + xbBb)] + [xbBbMDb/(xaBa + xbBb)]

78
Q

Give the hedge ratio formula for an x-year bond and a y year bond

A

MDx + δMDy = 0

δ is the hedge ratio

Derivative Markets (4 decks)

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