Term
| Investment Strategy 1: Swap Risk Free for Risky Investment |
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Definition
| If you will need X capital in 1 year, invest X/(1+Rf) s.t. you will have X available |
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Term
| Investment Strategy 2: Purchase Put Options |
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Definition
| Continue to invest in risky assets, but purchase put options s.t. at minimum, X capital will be available when needed. |
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Term
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Definition
| 1)Safety Constraint - Simply requires funds to be available to pay claim =loss safety level 2) Investment variance constraint: requires IRR of combined re+invest strategy to be no more volatile than the direct investment in risky assets. |
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Term
| Swap Formula (loss safety) |
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Definition
(1+IRR)*A=(1+rf)*(P+A)-L
A=(s-uL)/(1+y)
=> Riskload R =
=A*(y-rf)/(1+rf) |
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Term
| Safety Constraint for swap |
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Definition
(1+rf)*(P+A) ≥ s
=> A≥ (s-uL)/(1+y) |
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Term
| Variance Constraint for Swap |
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Definition
A≥σL/σY
Then
R = (σL/σY) *
[y-rf]/[1+rf] |
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Term
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Definition
(1+y)*A =
(1+i)*F -uf
Where i is investment return on put protected investment |
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Term
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Definition
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Term
Put Option
Safety Constraint Approach |
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Definition
- Solve for F: (1+rf)*F ≥s
- Solve for A:(1+y)*A=(1+i)*F-uf
- Solve for P: F=(P+A)/(1+r)
- Solve for R: P= R + uL/(1+rf)
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Term
Put Option
Variance Constraint |
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Definition
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Term
Swap Method
Variance Constraint |
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Definition
A=σL/σy
and
R=(y-rf)/(1+rf) *
[σL/σy] |
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Term
| ROL for high excess layer |
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Definition
Probability of loss almost 0, Safety level = whole layer. Use formulas with
s= whole layer
& uL = 0 |
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Term
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Definition
- losses occur at year end
- spot rates for rf depend on time
- may be correlation across years
- assumption that risks were standalone
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