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FM > General cash flow, Portfolio and immunization > Flashcards

General cash flow, Portfolio and immunization Flashcards

1
Q

What is a spot rate?

A
  • It is the annual effective yield rate on zero-coupon bonds.
  • It measures the yield from the beginning of the investment to the end of the single cash flow.
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2
Q

What is the term structure of interest rates?

A

It is the collection of spot rates.

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3
Q

What is the yield curve?

A

It is the curve representing the yield rate for maturity.

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4
Q

What happens if the maturity goes up?

A

The spot rate goes up.

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5
Q

What is the normal yield curve?

A

It is an upward-sloping yield curve.

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6
Q

What are the 5 steps to price a bond?

A

1) Calculate spot rates from zero-coupon prices.
2) Identify CF from coupon and redemption value.
3) Discount each CF using the appropriate spot rate (ex 1yr CF for 1-yr spot rate)
4) Sum the PV of the discounted CF to calculate the bond price.
5) Calculate the YTM by solving for the annual effective yield that equates the PV of the CF to price.

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7
Q

What is bootstrapping?

A

It is an iterative process to determine spot rates.

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8
Q

What is a forward rate?

A

It is an m-year spot rate that comes into effect t-years in the future what will be referred to as the “m-year forward rate, deferred t-years” or as the “m-year forward rate, starting in t-years”. Basically, it is an annualized interest rate that will be earned from time t1 to time t2

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9
Q

What is the Macaulay duration?

A
  • It is the economic balance point of the CF of an investment.
  • It is denoted as MacD and it’s expressed on an annual basis.
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10
Q

What is the modified duration?

A

It happens when we find the price’s derivative with respect to “i”.

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11
Q

What is the first-order modified approximation?

A

It is the equation calculating the point on the line that estimates the point on the price curve.

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12
Q

What is the portfolio duration?

A

It is the weighted average of the individual assets’ durations.

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13
Q

What is convexity?

A
  • It measures a function’s curvature.
  • It is the second derivative of the price function divided by the price.
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14
Q

What are the 2 types of convexity?

A
  • Modified convexity
  • Macaulay convexity
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15
Q

What is Macaulay convexity?

A

It is the second derivative of the price function with respect to 𝝳.

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16
Q

What is portfolio convexity?

A

It is the weighted average of each asset’s convexity.

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17
Q

What is liability cash flow?

A

They are payments that a company is required to make.

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18
Q

What is an asset cash flow?

A

They are payments that a company receives from its investments.

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19
Q

What is a surplus?

A

It is the excess of a company’s PV of assets over its PV of liabilities.

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20
Q

What happens when the interest rates decrease?

A

The increase in the PV of liability CF might be more than the increase in the PV of asset CF.

21
Q

What happens when the interest rates increase?

A

The decrease in the PV of asset CF might be more than the decrease in the PV of asset CF.

22
Q

What are the 3 assumptions to benefit from the Redington immunization?

A

1) Interest rates for all maturities are the same.
2) When interest rates change, they change by the same amount for all maturities. This produces a parallel shift in the yield curve, thus maintaining a flat yield curve.
3) CF doesn’t change when interest rates change.

23
Q

What are the 3 conditions to be immunized from small, parallel interest changes with the Redington immunization?

A

1) PV of assets = PV of liability
2) Duration of asset = Duration of liability
3) Convexity of asset > Convexity of liability

24
Q

What is a full immunization?

A

It immunizes a single liability CF from any rate change.

25
Q

What are the assumptions for full immunization?

A

1) A flat yield curve.
2) A parallel shift in the yield curve.
3) The CF must be fixed.

26
Q

What are the 3 conditions to be immunized from small, parallel interest changes with full immunization?

A

1) PV of assets = PV of liability
2) Duration of asset = Duration of liability
3) There must be at least one asset CF before and after the liability CF.

27
Q

What happens if there are multiple liabilities that fit the immunization criteria?

A

1) You need to immunize each liability separately.
2) After that, you add up the resulting values.

28
Q

What are the reasons for the surplus not being immunized really long?

A

1) CF are added or removed
2) Time changes
3) Interest rate changes

29
Q

What is CF matching (dedication)?

A

It is an alternative solution to the assumptions of the other immunization techniques.

30
Q

What is the only assumption for the dedication (CF matching)?

A

It is that the CF are fixed.

31
Q

What are the steps to match CF?

A

1) Create a table that organizes asset and liability CF.
2) Start with the liability with the longest duration.
3) Buy an asset that exactly matches the liability CF.
4) Move to the next longest liability.
5) Repeat until all liabilities are matched.

32
Q

What is the t-year spot rate?

A
33
Q

What is the forward rate between 2 adjacent times?

A
34
Q

Draw a graph of the spot rate for n-years along with the forward rate for each year.

A
35
Q

What is the MacD formula?

A
36
Q

What is the ModD formula?

A
37
Q

What is the equivalence between the MacD and the ModD?

A
38
Q

What is the formula for a MacD for a geometric increasing perpetuity?

A
39
Q

What is the formula for the MacD of an n-year par bond?

A
40
Q

What is the first-order modified approximation formula?

A
41
Q

What is the first-order Macaulay approximation formula?

A
42
Q

What is the passage of time given that the FC is the same at t1 and t2 for a Macaulay duration?

A
43
Q

What is the passage of time given that the FC is the same at t1 and t2 for a modified duration?

A
44
Q

Explain the duration of a portfolio formula based on this image:

A
45
Q

What is the formula for the MacC?

A
46
Q

What is the formula for the ModC?

A
47
Q

What is the relation between the MacC and the ModC?

A
48
Q

Describe the immunization shortcut.

A

FM (6 decks)

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