Problem 14.1. HFrom Book HullL aL
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95 % standard deviation of normal distribution is - 1.65, N H- 1.65L = 0.05
stdpf :=
Sqrt@H100 000 ´ 0.01L ^ 2 + H100 000 ´ 0.01L ^ 2 + 2 ´ 0.3 ´ 100 000 ´ 0.01 ´ 100 000 ´ 0.01D
stdpf
1612.45
The biggest loss in 5 days at 95 % probability level is :
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varloss := Sqrt@5D 1.65 stdpf
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varloss
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5949.16
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The minimum value of the portfolio at 95 % probability in 5 days HVaRL is then :
VaR := 200 000 - varloss
VaR
194 051.
bL
Correlation is 0.
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stdpf1 := Sqrt@H100 000 ´ 0.01L ^ 2 + H100 000 ´ 0.01L ^ 2D
stdpf1
1414.21
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varloss1 := Sqrt@5D 1.65 stdpf1
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varloss1
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5217.76
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VaR1 := 200 000 - varloss1
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VaR1
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194 782.
cL Correlation is 1.
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stdpf2 := Sqrt@H100 000 ´ 0.01L ^ 2 + H100 000 ´ 0.01L ^ 2 + 2 ´ 1 ´ 100 000 ´ 0.01 ´ 100 000 ´ 0.01D
stdpf2
2000.
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varloss2 := Sqrt@5D 1.65 stdpf2
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varloss2
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7379.02
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VaR2 := 200 000 - varloss2
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VaR2
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192 621.
dL 200 000 dollars in asset A
2
invjarahdemo72011.nb
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stdpf3 := Sqrt@H200 000 ´ 0.01L ^ 2D
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stdpf3
2000.
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varloss3 := Sqrt@5D 1.65 stdpf3
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varloss3
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7379.02
Thus the same as in case cL.
Problem 14.15.
The daily standard deviation is :
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stdday :=
[email protected] ´ 300 000L ^ 2 + H0.012 ´ 500 000L ^ 2 + 2 ´ 0.6 ´ 0.018 ´ 300 000 ´ 0.0012 ´ 500 000D
stdday
8309.51
N H0.975L has value 1.96; thus 97.5 % z value is - 1.96
The maximum loss in 10 days at 97.5 % probability is :
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Varlosses := Sqrt@10D stdday 1.96
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Varlosses
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51 502.9
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VaR3 := 800 000 - Varlosses
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VaR3
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748 497.