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FM Flashcards

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1
Q

Prospective Method

A

forward-looking based on future cash flow

time-t outstanding loan balance

=

PV(remaining loan payments with i)

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2
Q

Liquidity Preferance Theory / Opportunity Cost Theory

A

To persuade lenders to lend for a longer time, borrowers will have to pay higher interest rate as an incentive.

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3
Q

weighted average of individual asset’s duration

A

Duration of Portfolio

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4
Q

Annuity-Immediate Present Value

A

A angle n, with i. ( 1 - v^(n) ) / i

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5
Q

Accumulation function for Constant Force of Interest

A

a(t) = e ^(delta * time)

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6
Q

Duration of Portfolio

A

weighted average of individual asset’s duration

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7
Q

Payer

A

party who agrees to pay the fixed rate and receive the variable rates

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8
Q

a(t) = e ^(delta * time)

A

Accumulation function for Constant Force of Interest

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9
Q

Terminology Bond Amortization:

Write-down (Premium Bonds)

Write-Up (Discount Bonds)

A

Loan Amortization: Principal Repaid

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10
Q

Expectation theory

A

Interest rate for a long term investment provides future expectation for interest on short term investments

for example; consider 2 year loan with higher interest rate then a 1 year loan. Then one year from now the interest rate on the 1 year loan is expected to be higher than the current interest of the 1 year loan.

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11
Q

Settlement dates

A

specified dates during the swap tenor when the interest payments are exchanged

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12
Q

A(t) = A(0) * ( 1 - (d/m) )^(-mt)

A

Amount Function Nominal Discount Rate

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13
Q

Loan Amoritization:

Pt = R * ( vn-t+1 )

A

Principal Repaid when R is level

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14
Q
A
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15
Q

A(t)

=

A(0)*(1 + i)t

A

Amount Function Effective Interest Rate

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16
Q

S angle n, with i. ( ( 1 + i )^(n) - 1 ) / i

A

Annuity-Immediate Accumulated Value

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17
Q

Loan Amortization

A

repaying a loan with payments at regular intervals

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18
Q

Coupons

A

Periodic interest payments which form an annuity

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19
Q

Loan consist of what two components

A

1.) Interest Due

2.) Principal Repaid

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20
Q

Write-Up for bond

A

Absolute value of write-down

Pt = | (Fr - C*(i)) * (vn-t+1) |

Discount Bonds

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21
Q

First Order Modified Approx.

A

P(in)

=

P(io)*[1 - (in - io)(ModD)]

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22
Q

S double dot angle n, with i. ( ( 1 + i )^(n) - 1 ) / d

A

Annuity-Due Accumulated Value

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23
Q

A(t) = A(0)*(1 + i(t))

A

Amount Function Simple Interest

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24
Q

Accumulation Function For Variable Force of Interest

A

a(t) = e^( integration from 0 to t) of delta

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25
Q

To find R (swap rate)

A

PV(Variable) = PV(Fixed)

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26
Q

a(t) = e^( integration from 0 to t) of delta

A

Accumulation Function For Variable Force of Interest

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27
Q

Annuity-Immediate PV to AV relation

(A angle n) =

A

(S angle n) * ( vn )

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28
Q

Annuity-Due AV to PV relation

(S double-dot angle n) =

A

(A double-dot angle n) * ( ( 1 + i )n )

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29
Q

delta = force of interest constant

A

ln (1 + i)

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30
Q

Discount Bond Formula

A

(Redemption - Price)

or

( C*(i) - Fr ) * (a angle n)

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31
Q

Loan: Outstanding Balance at time t

is equal to

A

Present value at time t of it’s remaining cash flow using the loan’s interest rate

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32
Q

Notional amount

A

is the amount used to determine interest payments and swap payments;

to obtain interest payment or swap payment multiply the notional amount by the respective interest rate

USUALLY THE LOAN AMOUNT

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33
Q

(A(t) - A(t-1)) / A(t-1)

A

Effective Interest Rate

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34
Q

unit decreasing annuity

A

(Da) angle n

=

[n - (a angle n)]

/

i

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35
Q

Market Segmentation Theory

A

Borrowers and Lenders have different preferances on how long they want to borrow or lend for, thus causing different interest rates for different terms

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36
Q

A angle n, with i. ( 1 - v^(n) ) / i

A

Annuity-Immediate Present Value

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37
Q

Discounting Factor with (d)

A

( 1 - d )

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38
Q

( 1 - d )

A

Discounting Factor with (d)

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39
Q

Yield to Maturity

A

Level annual effective rate of interest which equates cash inflows to cash outflows

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40
Q

Amount Function Nominal Discount Rate

A

A(t) = A(0) * ( 1 - (d/m) )^(-mt)

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41
Q

Annuity-Due Present Value

A

A double dot angle n, with i. ( 1 - v^(n) ) / d

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42
Q

Internal Rate of Return (IRR)

A

also called yield rate

it’s the rate that

produces a NPV of 0

also known as breakeven

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43
Q

floating rate

A

also known as the variable rate

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44
Q

[1 - ( (1 + k) / ( 1 +i ) )n]

/

( i - k)

i = interest

k = number of payments in progression/percentage

n = number of total payments

A

Annuity-Immediate geometric progression

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45
Q

Implied Forward Rate

A

(1 + sn)n

=

(1 + sn-1)n-1 * (1 + f[n-1, n])

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46
Q

(A(t) - A(t-1)) / A(t)

A

Effective Discount Rate

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47
Q

Terminology Bonds Amortization: Book value

A

Loan Amortization: Outstanding balance

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48
Q

(1 + i)^(-1) discount factor

A

(1 - d)

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49
Q

Effective Discount Rate defined as

A

(A(t) - A(t-1)) / A(t)

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50
Q

What is opportunity cost of capital?

A

Rate of return

on an equally-risky asset

an investor could have earned

if he or she had NOT invested in the project.

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51
Q

Given a price

A

lowest yield rate calculated is the minimum yield that an investor would earn

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52
Q

swap rate

A

known as the fixed rate

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53
Q

Calculating Interest Due

A

It (Interest Due)

=

(i) * Bt-1 (outstanding balance of previous period)

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54
Q

Effective Interest Rate defined as

A

(A(t) - A(t-1)) / A(t-1)

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55
Q

Annuity-Immediate AV to PV relation

(S angle n)=

A

(A angle n) * ( ( 1 + i )n )

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56
Q

Bonds

A bond’s BOOK VALUE at time t

is equal to

A

Present value at time t of its remaining cash flows using the bond’s initial yield rate

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57
Q

Interest Rate Swap

A

agreement between two parties in which both parties agree to exchange a series of cash flow based on interest rates

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58
Q

Accreting Swap

A

if notional amount increases over time

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59
Q

Solving for bonds

A

Step 1: Identify Cash Flows

Step 2: Calculate the bond price as the PV of future cash flow at time 0

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60
Q

Spot Rates

A

Annual Effective Yield rates on a zero-coupon bond

Measures the yield from the beginning of the investment to the end of the single cash flow

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61
Q

Annuity-Immediate geometric progression

A

[1 - ( (1 + k) / ( 1 +i ) )n]

/

( i - k)

i = interest

k = number of payments in progression/percentage

n = number of total payments

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62
Q

Given a yield rate

A

the lowest price calculated is the maximum price that an investor would pay

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63
Q

Terminology Bond Amortization: Coupon payment

A

Loan Amortization: Loan Payment

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64
Q

Retrospective Formula

A

Bt

=

L(1+i)t - R(s angle t)

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65
Q

Write-Down for bond

same as principal repaid for loans

A

(Coupon Payment - Interest Earned)

Pt = | (Fr - C*(i)) * (vn-t+1) |

Premium bonds

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66
Q

Calculating Outstanding Balance end of period

A

Bt (Outstanding loan balance time t)

=

Bt-1 (Outstanding loan balance time t-1) - Pt (Principal repaid time t)

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67
Q

Redemption Value

A

One large payment at the end of the bond term

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68
Q

Bonds: Basic Formula

A

P(Price of bond)

=

Fr(a angle n) [Pv at time 0 of coupon payments over n periods]

+

C(vn) [Pv at 0 of the redemption value]

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69
Q

Callable Bonds

A

Can be terminated before the redemption dates labeled as call dates

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70
Q

Settlement period

A

is the time between settlement dates

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71
Q

Block Payment Annuity

A

Method 1: Start with payments furthest from the comparison date

2: Make adjustments when moving towards the comparison date

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72
Q

Swap Term / Swap Tenor

A

specified period of the swap

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73
Q

Bond’s Yield Rate

A

Rate of Return from investor’s point of view

constant rate discounting future cash flow

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74
Q

P and Q formula for annuity increasing Arithmetic Progression

A

PV = P*(a angle n)

+

[(Q)*((a angle n) - n( vn )] / i

P = first term

Q = constant amount of increase for each payment

n = number of payments one period before the first payment date

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75
Q

Interest earned on a Bond calculation

A

(BOOK VALUE of PREVIOUS PERIOD) * (YIELD RATE)

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76
Q

a(t) = (1 + i(t))

A

Accumulation Function Simple Interest

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77
Q

Finding additional payment

(Annuity Immediate AV)

A

[ (pmt) * (annuity-immediate(AV)) ]

+

[ (fv) - (PV)(AV factor) ]

=

0

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78
Q

Face amount / par value

A

not a cash flow

used to determine coupon amount

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79
Q

Amount Function Effective Discount Rate

A

A(t) = A(0) * ( 1 - d )-t

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80
Q

Bank Reserve Requirement

A

A central bank requires every bank to deposit and maintain a specific amount of money with it

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81
Q

e(delta) * (t)

=

( 1 + i )t

A

Relationship between Constant Force Of Interest and Constant effective interest rate

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82
Q

(1 - d)^(-1) accumulation factor

A

(1 + i)

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83
Q

What interest rate should be used to discount the cash flow for NPV?

A

interest rate used =

cost of capital

or

opportunity cost of capital

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84
Q

Premium Bond Formula

A

(Price - Redemption)

or

(Fr - C*(i)) * (a angle n)

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85
Q

Finding additional payment

(Annuity Immediate PV )

A

[ (pmt) * ( annuity - immediate( PV ) ) ]

+

[ (fv)(discounted factor) - ( PV ) ]

=

0

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86
Q

Default Risk

A

Is the risk of loan defaulting, the borrower is unable to make a promised payment at the contracted time and for the contracted amount.

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87
Q

Amount Function Simple Interest

A

A(t) = A(0)*(1 + i(t))

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88
Q

A(t)

=

A(0) * ( 1 + (i/m) )(mt)

A

Amount Function Nominal Interest Rate

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89
Q

Loan Amortization

It = R * (1−vn−t+1)

A

Interest Due when R is Level

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90
Q

Bonds: Premium/Discount Formula

A

P(Price of bond)

=

C(Redemption value)

+

(Fr - C * i)(a angle n)

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91
Q

Prospective Method Formula

A

Bt

=

R(a angle (n-t))

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92
Q

Bank’s Reserve

A

The actual amount of deposit with the central bank

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93
Q

Accumulation Function Simple Interest

A

a(t) = (1 + i(t))

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94
Q

Annuity-Immediate Accumulated Value

A

S angle n, with i. ( ( 1 + i )^(n) - 1 ) / i

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95
Q

Force Of Interest

A

a’(t) / a(t)

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96
Q

Amount Function Effective Interest Rate

A

A(t) = A(0)*(1 + i)^t

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97
Q

Receiver

A

counter party who receives the fix rate

and

pays the variable rate

98
Q

Amortizing Swap

A

if the notional amount decreases over time

99
Q

Amount Function Nominal Interest Rate

A

A(t) = A(0) * ( 1 + (i/m) )^(mt)

100
Q

Final Amortization Value for Bond

A

The book value at the end of the bond term which is the redemption value C

101
Q

Calculating Principal Repaid

A

Pt (Principal Repaid)

=

Rt (loan repayment) - It (interest due)

102
Q

Continous Varying Annuities PV

A

PV = [integration from 0 to n]

of

[f(t) * e - (integration from o to t) of ( delta )]

103
Q

Annuity-Due Accumulated Value

A

S double dot angle n, with i. ( ( 1 + i )^(n) - 1 ) / d

104
Q

Loan Amoritization:

Pt+k

/

(1 + i)k

A

Principal Repaid when R is Level

105
Q

Net Present Value (NPV)

A

NPV = Σ CFt * (vt)

summation from (t = 0) to n

NPV = sum of the present value of all cash flow over ( n ) years

106
Q

Preferred Habit Theory

A

Borrowers and Lenders if given enough incentive will be willing to go out of their boundaries.

For example, a lender who only wants to lend for a certain time may be willing to lend for a longer time if given enough incentives.

107
Q

Retrospective Method

A

backward-looking; based on previous cash flows;

time t outstanding loan balance

=

AV(Orginal loan with i) - AV(loan payments)

108
Q

Discounting Factor with (i)

A

v = ( 1 / ( 1 + i )^(n))

109
Q

Call Price

A

additional cash flow the investor receives if the bond terminates on a call date

110
Q

v = ( 1 / ( 1 + i )^(n))

A

Discounting Factor with (i)

111
Q

Perpetuity-Immediate increasing

A

(Ia) angle infinity

=

( ( P / i ) + ( Q / ( i2 ) )

112
Q

A(t) = A(0)*(1-d)^(-t)

A

Amount Function Effective Discount Rate

113
Q
A
114
Q

Relationship between Constant Force Of Interest and Constant effective interest rate

A

e^(delta) = ( 1 + i )

115
Q

Unit Increasing Annuity
[(Ia) angle n]

A

P = Q

[(Ia) angle n]

=
(P) * [( a double dot angle n ) - n( vn )]

/

i

116
Q

Annuity-Due PV to AV relation

(A double-dot angle n) =

A

(S double-dot angle n) * ( vn )

117
Q

Σ t * vt+1 * CFt

/

Σ vt * CFt

A

Modified Duration Formula

118
Q

a’(t) / a(t)

A

Force Of Interest

119
Q

Pt ( principal repaid for bonds at time t )

A

Pt ( principal repaid for bonds at time t )

=

| ( Fr - C(i) )*( vn-t+1 ) |

120
Q

A double dot angle n, with i. ( 1 - v^(n) ) / d

A

Annuity-Due Present Value

121
Q

Default Risk Premium

A

compensates investors for the possibility that a borrower will default

122
Q

Reversed Cards

forward-looking based on future cash flow

time-t outstanding loan balance

=

PV(remaining loan payments with i)

A

Prospective Method

123
Q

Reversed Cards

To persuade lenders to lend for a longer time, borrowers will have to pay higher interest rate as an incentive.

A

Liquidity Preferance Theory / Opportunity Cost Theory

124
Q

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Duration of Portfolio

A

weighted average of individual asset’s duration

125
Q

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A angle n, with i. ( 1 - v^(n) ) / i

A

Annuity-Immediate Present Value

126
Q

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a(t) = e ^(delta * time)

A

Accumulation function for Constant Force of Interest

127
Q

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weighted average of individual asset’s duration

A

Duration of Portfolio

128
Q

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party who agrees to pay the fixed rate and receive the variable rates

A

Payer

129
Q

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Accumulation function for Constant Force of Interest

A

a(t) = e ^(delta * time)

130
Q

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Loan Amortization: Principal Repaid

A

Terminology Bond Amortization:

Write-down (Premium Bonds)

Write-Up (Discount Bonds)

131
Q

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Interest rate for a long term investment provides future expectation for interest on short term investments

for example; consider 2 year loan with higher interest rate then a 1 year loan. Then one year from now the interest rate on the 1 year loan is expected to be higher than the current interest of the 1 year loan.

A

Expectation theory

132
Q

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specified dates during the swap tenor when the interest payments are exchanged

A

Settlement dates

133
Q

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Amount Function Nominal Discount Rate

A

A(t) = A(0) * ( 1 - (d/m) )^(-mt)

134
Q

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Principal Repaid when R is level

A

Loan Amoritization:

Pt = R * ( vn-t+1 )

135
Q
A
136
Q

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Amount Function Effective Interest Rate

A

A(t)

=

A(0)*(1 + i)t

137
Q

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Annuity-Immediate Accumulated Value

A

S angle n, with i. ( ( 1 + i )^(n) - 1 ) / i

138
Q

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repaying a loan with payments at regular intervals

A

Loan Amortization

139
Q

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Periodic interest payments which form an annuity

A

Coupons

140
Q

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1.) Interest Due

2.) Principal Repaid

A

Loan consist of what two components

141
Q

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Absolute value of write-down

Pt = | (Fr - C*(i)) * (vn-t+1) |

Discount Bonds

A

Write-Up for bond

142
Q

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P(in)

=

P(io)*[1 - (in - io)(ModD)]

A

First Order Modified Approx.

143
Q

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Annuity-Due Accumulated Value

A

S double dot angle n, with i. ( ( 1 + i )^(n) - 1 ) / d

144
Q

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Amount Function Simple Interest

A

A(t) = A(0)*(1 + i(t))

145
Q

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a(t) = e^( integration from 0 to t) of delta

A

Accumulation Function For Variable Force of Interest

146
Q

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PV(Variable) = PV(Fixed)

A

To find R (swap rate)

147
Q

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Accumulation Function For Variable Force of Interest

A

a(t) = e^( integration from 0 to t) of delta

148
Q

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(S angle n) * ( vn )

A

Annuity-Immediate PV to AV relation

(A angle n) =

149
Q

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(A double-dot angle n) * ( ( 1 + i )n )

A

Annuity-Due AV to PV relation

(S double-dot angle n) =

150
Q

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ln (1 + i)

A

delta = force of interest constant

151
Q

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(Redemption - Price)

or

( C*(i) - Fr ) * (a angle n)

A

Discount Bond Formula

152
Q

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Present value at time t of it’s remaining cash flow using the loan’s interest rate

A

Loan: Outstanding Balance at time t

is equal to

153
Q

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is the amount used to determine interest payments and swap payments;

to obtain interest payment or swap payment multiply the notional amount by the respective interest rate

USUALLY THE LOAN AMOUNT

A

Notional amount

154
Q

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Effective Interest Rate

A

(A(t) - A(t-1)) / A(t-1)

155
Q

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(Da) angle n

=

[n - (a angle n)]

/

i

A

unit decreasing annuity

156
Q

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Borrowers and Lenders have different preferances on how long they want to borrow or lend for, thus causing different interest rates for different terms

A

Market Segmentation Theory

157
Q

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Annuity-Immediate Present Value

A

A angle n, with i. ( 1 - v^(n) ) / i

158
Q

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( 1 - d )

A

Discounting Factor with (d)

159
Q

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Discounting Factor with (d)

A

( 1 - d )

160
Q

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Level annual effective rate of interest which equates cash inflows to cash outflows

A

Yield to Maturity

161
Q

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A(t) = A(0) * ( 1 - (d/m) )^(-mt)

A

Amount Function Nominal Discount Rate

162
Q

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A double dot angle n, with i. ( 1 - v^(n) ) / d

A

Annuity-Due Present Value

163
Q

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also called yield rate

it’s the rate that

produces a NPV of 0

also known as breakeven

A

Internal Rate of Return (IRR)

164
Q

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also known as the variable rate

A

floating rate

165
Q

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Annuity-Immediate geometric progression

A

[1 - ( (1 + k) / ( 1 +i ) )n]

/

( i - k)

i = interest

k = number of payments in progression/percentage

n = number of total payments

166
Q

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(1 + sn)n

=

(1 + sn-1)n-1 * (1 + f[n-1, n])

A

Implied Forward Rate

167
Q

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Effective Discount Rate

A

(A(t) - A(t-1)) / A(t)

168
Q

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Loan Amortization: Outstanding balance

A

Terminology Bonds Amortization: Book value

169
Q

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(1 - d)

A

(1 + i)^(-1) discount factor

170
Q

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(A(t) - A(t-1)) / A(t)

A

Effective Discount Rate defined as

171
Q

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Rate of return

on an equally-risky asset

an investor could have earned

if he or she had NOT invested in the project.

A

What is opportunity cost of capital?

172
Q

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lowest yield rate calculated is the minimum yield that an investor would earn

A

Given a price

173
Q

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known as the fixed rate

A

swap rate

174
Q

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It (Interest Due)

=

(i) * Bt-1 (outstanding balance of previous period)

A

Calculating Interest Due

175
Q

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(A(t) - A(t-1)) / A(t-1)

A

Effective Interest Rate defined as

176
Q

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(A angle n) * ( ( 1 + i )n )

A

Annuity-Immediate AV to PV relation

(S angle n)=

177
Q

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Present value at time t of its remaining cash flows using the bond’s initial yield rate

A

A bond’s BOOK VALUE at time t

is equal to

178
Q

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agreement between two parties in which both parties agree to exchange a series of cash flow based on interest rates

A

Interest Rate Swap

179
Q

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if notional amount increases over time

A

Accreting Swap

180
Q

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Step 1: Identify Cash Flows

Step 2: Calculate the bond price as the PV of future cash flow at time 0

A

Solving for bonds

181
Q

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Annual Effective Yield rates on a zero-coupon bond

Measures the yield from the beginning of the investment to the end of the single cash flow

A

Spot Rates

182
Q

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[1 - ( (1 + k) / ( 1 +i ) )n]

/

( i - k)

i = interest

k = number of payments in progression/percentage

n = number of total payments

A

Annuity-Immediate geometric progression

183
Q

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the lowest price calculated is the maximum price that an investor would pay

A

Given a yield rate

184
Q

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Loan Amortization: Loan Payment

A

Terminology Bond Amortization: Coupon payment

185
Q

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Bt

=

L(1+i)t - R(s angle t)

A

Retrospective Formula

186
Q

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(Coupon Payment - Interest Earned)

Pt = | (Fr - C*(i)) * (vn-t+1) |

Premium bonds

A

Write-Down for bond

same as principal repaid for loans

187
Q

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Bt (Outstanding loan balance time t)

=

Bt-1 (Outstanding loan balance time t-1) - Pt (Principal repaid time t)

A

Calculating Outstanding Balance end of period

188
Q

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One large payment at the end of the bond term

A

Redemption Value

189
Q

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P(Price of bond)

=

Fr(a angle n) [Pv at time 0 of coupon payments over n periods]

+

C(vn) [Pv at 0 of the redemption value]

A

Bonds: Basic Formula

190
Q

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Can be terminated before the redemption dates labeled as call dates

A

Callable Bonds

191
Q

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is the time between settlement dates

A

Settlement period

192
Q

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Method 1: Start with payments furthest from the comparison date

2: Make adjustments when moving towards the comparison date

A

Block Payment Annuity

193
Q

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specified period of the swap

A

Swap Term / Swap Tenor

194
Q

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Rate of Return from investor’s point of view

constant rate discounting future cash flow

A

Bond’s Yield Rate

195
Q

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PV = P*(a angle n)

+

[(Q)*((a angle n) - n( vn )] / i

P = first term

Q = constant amount of increase for each payment

n = number of payments one period before the first payment date

A

P and Q formula for annuity increasing Arithmetic Progression

196
Q

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(BOOK VALUE of PREVIOUS PERIOD) * (YIELD RATE)

A

Interest earned on a Bond calculation

197
Q

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Accumulation Function Simple Interest

A

a(t) = (1 + i(t))

198
Q

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[ (pmt) * (annuity-immediate(AV)) ]

+

[ (fv) - (PV)(AV factor) ]

=

0

A

Finding additional payment

(Annuity Immediate AV)

199
Q

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not a cash flow

used to determine coupon amount

A

Face amount / par value

200
Q

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A(t) = A(0) * ( 1 - d )-t

A

Amount Function Effective Discount Rate

201
Q

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A central bank requires every bank to deposit and maintain a specific amount of money with it

A

Bank Reserve Requirement

202
Q

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Relationship between Constant Force Of Interest and Constant effective interest rate

A

e(delta) * (t)

=

( 1 + i )t

203
Q

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(1 + i)

A

(1 - d)^(-1) accumulation factor

204
Q

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interest rate used =

cost of capital

or

opportunity cost of capital

A

What interest rate should be used to discount the cash flow for NPV?

205
Q

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(Price - Redemption)

or

(Fr - C*(i)) * (a angle n)

A

Premium Bond Formula

206
Q

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[ (pmt) * ( annuity - immediate( PV ) ) ]

+

[ (fv)(discounted factor) - ( PV ) ]

=

0

A

Finding additional payment

(Annuity Immediate PV )

207
Q

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Is the risk of loan defaulting, the borrower is unable to make a promised payment at the contracted time and for the contracted amount.

A

Default Risk

208
Q

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A(t) = A(0)*(1 + i(t))

A

Amount Function Simple Interest

209
Q

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Amount Function Nominal Interest Rate

A

A(t)

=

A(0) * ( 1 + (i/m) )(mt)

210
Q

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Interest Due when R is Level

A

Loan Amortization

It = R * (1−vn−t+1)

211
Q

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P(Price of bond)

=

C(Redemption value)

+

(Fr - C * i)(a angle n)

A

Bonds: Premium/Discount Formula

212
Q

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Bt

=

R(a angle (n-t))

A

Prospective Method Formula

213
Q

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The actual amount of deposit with the central bank

A

Bank’s Reserve

214
Q

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a(t) = (1 + i(t))

A

Accumulation Function Simple Interest

215
Q

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S angle n, with i. ( ( 1 + i )^(n) - 1 ) / i

A

Annuity-Immediate Accumulated Value

216
Q

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a’(t) / a(t)

A

Force Of Interest

217
Q

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A(t) = A(0)*(1 + i)^t

A

Amount Function Effective Interest Rate

218
Q

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counter party who receives the fix rate

and

pays the variable rate

A

Receiver

219
Q

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if the notional amount decreases over time

A

Amortizing Swap

220
Q

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A(t) = A(0) * ( 1 + (i/m) )^(mt)

A

Amount Function Nominal Interest Rate

221
Q

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The book value at the end of the bond term which is the redemption value C

A

Final Amortization Value for Bond

222
Q

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Pt (Principal Repaid)

=

Rt (loan repayment) - It (interest due)

A

Calculating Principal Repaid

223
Q

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PV = [integration from 0 to n]

of

[f(t) * e - (integration from o to t) of ( delta )]

A

Continous Varying Annuities PV

224
Q

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S double dot angle n, with i. ( ( 1 + i )^(n) - 1 ) / d

A

Annuity-Due Accumulated Value

225
Q

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Principal Repaid when R is Level

A

Loan Amoritization:

Pt+k

/

(1 + i)k

226
Q

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NPV = Σ CFt * (vt)

summation from (t = 0) to n

NPV = sum of the present value of all cash flow over ( n ) years

A

Net Present Value (NPV)

227
Q

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Borrowers and Lenders if given enough incentive will be willing to go out of their boundaries.

For example, a lender who only wants to lend for a certain time may be willing to lend for a longer time if given enough incentives.

A

Preferred Habit Theory

228
Q

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backward-looking; based on previous cash flows;

time t outstanding loan balance

=

AV(Orginal loan with i) - AV(loan payments)

A

Retrospective Method

229
Q

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v = ( 1 / ( 1 + i )^(n))

A

Discounting Factor with (i)

230
Q

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additional cash flow the investor receives if the bond terminates on a call date

A

Call Price

231
Q

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Discounting Factor with (i)

A

v = ( 1 / ( 1 + i )^(n))

232
Q

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(Ia) angle infinity

=

( ( P / i ) + ( Q / ( i2 ) )

A

Perpetuity-Immediate increasing

233
Q

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Amount Function Effective Discount Rate

A

A(t) = A(0)*(1-d)^(-t)

234
Q
A
235
Q

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e^(delta) = ( 1 + i )

A

Relationship between Constant Force Of Interest and Constant effective interest rate

236
Q

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P = Q

[(Ia) angle n]

=
(P) * [( a double dot angle n ) - n( vn )]

/

i

A

Unit Increasing Annuity
[(Ia) angle n]

237
Q

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(S double-dot angle n) * ( vn )

A

Annuity-Due PV to AV relation

(A double-dot angle n) =

238
Q

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Modified Duration Formula

A

Σ t * vt+1 * CFt

/

Σ vt * CFt

239
Q

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Force Of Interest

A

a’(t) / a(t)

240
Q

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Pt ( principal repaid for bonds at time t )

=

| ( Fr - C(i) )*( vn-t+1 ) |

A

Pt ( principal repaid for bonds at time t )

241
Q

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Annuity-Due Present Value

A

A double dot angle n, with i. ( 1 - v^(n) ) / d

242
Q

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compensates investors for the possibility that a borrower will default

A

Default Risk Premium

SOA/CFA (6 decks)

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