Slides Gestao Estrategica de Carreiras

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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Risco e Retorno
Prof. Dr. Rafael Paschoarelli Veiga
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Dominância e Aversão ao Risco 1
O Ativo A domina o B se:
A possui mesmo risco de B e retorno esperado maior ou
A possui mesmo retorno esperado e risco menor ou
A possui retorno esperado maior e risco menor
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Risco
Salário Esperado
Dominância e Aversão ao Risco 1
Emprego A: Salário de $50,000.
Emprego B: 
chance de 50% de salário de $40,000.
chance de 50% de salário de $60,000.
					Qual emprego você escolheria ?
$50,000.
A
B
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Risco
Salário Esperado
Dominância e Aversão ao Risco 2
Emprego A: Salário de $50,000.
Emprego B: 
chance de 30% de salário de $40,000.
chance de 70% de salário de $60,000.
					Qual emprego você escolheria ?
$50,000.
A
B
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Risco
Retorno Esperado
Relação Risco x Retorno
Y
X
Conceito de Dominância
B
W
H
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Determinar o retorno diário esperado para para uma carteira composto por 40% de Vale, 30% de Gerdau e 30% de Cosan utilizando dois métodos:
A partir dos retornos históricos diários da carteira
A partir da fórmula da esperança matemática dos retornos individuais
Exercício
a)
Veja resolução do Professor
b)
Resposta: 0,4*0,7032 + 0,3*0,6348 - 0,3*0,0532=0,4558%
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Rafael Paschoarelli Veiga Pg.
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Um dos conceitos de risco é o desvio padrão dos retornos do ativo.
	
Risco Total
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Determinar o risco para cada um dos ativos considerados no slide 6:
Exercício
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Determinar o risco para para uma carteira composta por 40% de Vale, 30% de Gerdau e 30% de Cosan.
Exercício
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Observe o seguinte:
Efeito das ___________ (1)
Rafael Paschoarelli Veiga Pg.
Plan1
		Período		PETR4		GGBR4		Vale3		BBDC4		Natu3		Itau4		GOLL4		CSAN3		NETC4		SBSP3		IBOV
				(R$)		(R$)		(R$)		(R$)		(R$)		(R$)		(R$)		(R$)		(R$)		(R$)		Pontos
		2/16/07		44.33		38.82		75.3		83.61		27.73		76.8		65.8		40.7		26.8		300.05		45,849.03
		2/15/07		44.24		39.1		75.65		84.75		27.7		77.6		67.41		41.37		27.21		299		45,955.07
		2/14/07		44.75		38.6		75.1		86.64		28		78.15		66.42		42.95		27		301.75		45,995.60
		2/13/07		45.06		38.19		73.1		84.17		27.5		76.4		66.32		41.9		27		299.5		45,197.45
		2/12/07		44.25		36		69.65		83.09		26.87		76.5		64.27		40.01		26.89		290.96		43,934.75
		2/9/07		44.8		36.2		70		85.5		26.5		77.35		63.82		39.39		26.56		289.7		44,284.40
		2/8/07		45.6		37		71.18		87.6		26.64		79.25		64.57		37.59		27.3		293		44,891.94
		2/7/07		44.91		36.81		70.8		87.56		26.2		78.71		63.6		37.2		27.8		293		44,587.96
		2/6/07		46.26		38.25		72.6		86.45		27.49		78.75		63.91		39.7		27.15		296.5		45,351.80
		2/5/07		47		36.8		70.85		86.53		27.87		79.24		63.52		41.15		27.09		297.8		45,286.17
																												Carteira
		2/16/07		0.2034%		-0.7161%		-0.4627%		-1.3451%		0.1083%		-1.0309%		-2.3884%		-1.6195%		-1.5068%		0.3512%		-0.2307%				-0.8858%
		2/15/07		-1.1397%		1.2953%		0.7324%		-2.1814%		-1.0714%		-0.7038%		1.4905%		-3.6787%		0.7778%		-0.9114%		-0.0881%				-0.4221%
		2/14/07		-0.6880%		1.0736%		2.7360%		2.9345%		1.8182%		2.2906%		0.1508%		2.5060%		0.0000%		0.7513%		1.7659%				2.1683%
		2/13/07		1.8305%		6.0833%		4.9533%		1.2998%		2.3446%		-0.1307%		3.1897%		4.7238%		0.4091%		2.9351%		2.8740%				5.2235%
		2/12/07		-1.2277%		-0.5525%		-0.5000%		-2.8187%		1.3962%		-1.0989%		0.7051%		1.5740%		1.2425%		0.4349%		-0.7896%				0.1065%
		2/9/07		-1.7544%		-2.1622%		-1.6578%		-2.3973%		-0.5255%		-2.3975%		-1.1615%		4.7885%		-2.7106%		-1.1263%		-1.3533%				0.1248%
		2/8/07		1.5364%		0.5162%		0.5367%		0.0457%		1.6794%		0.6861%		1.5252%		1.0484%		-1.7986%		0.0000%		0.6818%				0.6841%
		2/7/07		-2.9183%		-3.7647%		-2.4793%		1.2840%		-4.6926%		-0.0508%		-0.4851%		-6.2972%		2.3941%		-1.1804%		-1.6843%				-4.0103%
		2/6/07		-1.5745%		3.9402%		2.4700%		-0.0925%		-1.3635%		-0.6184%		0.6140%		-3.5237%		0.2215%		-0.4365%		0.1449%				1.1130%
				PETR4		GGBR4		Vale3		BBDC4		Natu3		Itau4		GOLL4		CSAN3		NETC4		SBSP3		IBOV
		Retorno Esperado		-0.6369%		0.6348%		0.7032%		-0.3634%		-0.0340%		-0.3394%		0.4045%		-0.0532%		-0.1079%		0.0909%		0.1467%
		Risco		1.4702%		2.8219%		2.2075%		1.8569%		2.0784%		1.2291%		1.5433%		3.7014%		1.5219%		1.2065%		1.3753%				2.3308%
Plan3
		
Carteira 1
				Dia 1		Dia 2		Dia 3		Dia 4		Dia 5		Dia 6		Risco
		Retorno A		3.00%		4.00%		3.00%		4.00%		3.00%		4.00%		0.5000%
		Retorno B		2.00%		3.00%		2.00%		3.00%		2.00%		3.00%		0.5000%
		
		Carteira 50%/50%		2.50%		3.50%		2.50%		3.50%		2.50%		3.50%		0.5000%
Carteira 1
		
Retorno A
Retorno B
Carteira 2
				Dias 0		Dias 1		Dias 2		Dias 3		Dias 4		Dias 5		Risco
		Retorno C		3.00%		4.00%		3.00%		4.00%		3.00%		4.00%		0.5000%
		Retorno D		3.00%		2.00%		3.00%		2.00%		3.00%		2.00%		0.5000%
		
		Carteira 50%/50%		3.00%		3.00%		3.00%		3.00%		3.00%		3.00%		0.0000%
Carteira 2
		
Retorno C
Retorno D
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Efeito das ___________ (2)
Observe o seguinte:
Rafael Paschoarelli Veiga Pg.
Plan1
		Período		PETR4		GGBR4		Vale3		BBDC4		Natu3		Itau4		GOLL4		CSAN3		NETC4		SBSP3		IBOV
				(R$)		(R$)		(R$)		(R$)		(R$)		(R$)		(R$)		(R$)		(R$)		(R$)		Pontos
		2/16/07		44.33		38.82		75.3		83.61		27.73		76.8		65.8		40.7		26.8		300.05		45,849.03
		2/15/07		44.24		39.1		75.65		84.75		27.7		77.6		67.41		41.37		27.21		299		45,955.07
		2/14/07		44.75		38.6		75.1		86.64		28		78.15		66.42		42.95		27		301.75		45,995.60
		2/13/07		45.06		38.19		73.1		84.17		27.5		76.4		66.32		41.9		27		299.5		45,197.45
		2/12/07		44.25		36		69.65		83.09		26.87		76.5		64.27		40.01		26.89		290.96		43,934.75
		2/9/07		44.8		36.2		70		85.5		26.5		77.35		63.82		39.39		26.56		289.7		44,284.40
		2/8/07		45.6		37		71.18		87.6		26.64		79.25		64.57		37.59		27.3		293		44,891.94
		2/7/07		44.91		36.81		70.8		87.56		26.2		78.71		63.6		37.2		27.8		293		44,587.96
		2/6/07		46.26		38.25		72.6		86.45		27.49		78.75		63.91		39.7		27.15		296.5		45,351.80
		2/5/07		47		36.8		70.85		86.53		27.87		79.24		63.52		41.15		27.09		297.8		45,286.17
																												Carteira
		2/16/07		0.2034%		-0.7161%		-0.4627%		-1.3451%		0.1083%		-1.0309%		-2.3884%		-1.6195%		-1.5068%		0.3512%		-0.2307%				-0.8858%
		2/15/07		-1.1397%		1.2953%		0.7324%		-2.1814%		-1.0714%		-0.7038%		1.4905%		-3.6787%		0.7778%		-0.9114%		-0.0881%				-0.4221%
		2/14/07		-0.6880%		1.0736%		2.7360%		2.9345%		1.8182%		2.2906%		0.1508%		2.5060%		0.0000%		0.7513%		1.7659%				2.1683%
		2/13/07		1.8305%		6.0833%		4.9533%		1.2998%		2.3446%		-0.1307%		3.1897%		4.7238%		0.4091%		2.9351%		2.8740%				5.2235%
		2/12/07		-1.2277%		-0.5525%		-0.5000%		-2.8187%		1.3962%		-1.0989%		0.7051%		1.5740%		1.2425%		0.4349%		-0.7896%				0.1065%
		2/9/07		-1.7544%
-2.1622%		-1.6578%		-2.3973%		-0.5255%		-2.3975%		-1.1615%		4.7885%		-2.7106%		-1.1263%		-1.3533%				0.1248%
		2/8/07		1.5364%		0.5162%		0.5367%		0.0457%		1.6794%		0.6861%		1.5252%		1.0484%		-1.7986%		0.0000%		0.6818%				0.6841%
		2/7/07		-2.9183%		-3.7647%		-2.4793%		1.2840%		-4.6926%		-0.0508%		-0.4851%		-6.2972%		2.3941%		-1.1804%		-1.6843%				-4.0103%
		2/6/07		-1.5745%		3.9402%		2.4700%		-0.0925%		-1.3635%		-0.6184%		0.6140%		-3.5237%		0.2215%		-0.4365%		0.1449%				1.1130%
				PETR4		GGBR4		Vale3		BBDC4		Natu3		Itau4		GOLL4		CSAN3		NETC4		SBSP3		IBOV
		Retorno Esperado		-0.6369%		0.6348%		0.7032%		-0.3634%		-0.0340%		-0.3394%		0.4045%		-0.0532%		-0.1079%		0.0909%		0.1467%
		Risco		1.4702%		2.8219%		2.2075%		1.8569%		2.0784%		1.2291%		1.5433%		3.7014%		1.5219%		1.2065%		1.3753%				2.3308%
Plan3
		
Carteira 1
				Dias 0		Dias 1		Dias 2		Dias 3		Dias 4		Dias 5		Risco
		Retorno A		3.00%		4.00%		3.00%		4.00%		3.00%		4.00%		0.5000%
		Retorno B		2.00%		3.00%		2.00%		3.00%		2.00%		3.00%		0.5000%
		
		Carteira 50%/50%		2.50%		3.50%		2.50%		3.50%		2.50%		3.50%		0.5000%
Carteira 1
		
Retorno A
Retorno B
Carteira 2
				Dia 1		Dia 2		Dia 3		Dia 4		Dia 5		Dia 6		Risco
		Retorno C		3.00%		4.00%		3.00%		4.00%		3.00%		4.00%		0.5000%
		Retorno D		3.00%		2.00%		3.00%		2.00%		3.00%		2.00%		0.5000%
		
		Carteira 50%/50%		3.00%		3.00%		3.00%		3.00%		3.00%		3.00%		0.0000%
Carteira 2
		
Retorno C
Retorno D
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Rafael Paschoarelli Veiga Pg.
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Risco de uma carteira composta por 2 ativos
q       
Utilizando os retornos históricos, calcule o risco de uma carteira com 30% de Vale e o restante de Gerdau.
Compare o resultado obtido empregando a fórmula acima.
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Gráfico Risco x Retorno: 2 ativos
Retorno
Risco
Retorno
Risco
Retorno
Risco
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Retorno
Risco
Gráfico Risco x Retorno: 2 ativos
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Retorno
Risco
Gráfico Risco x Retorno: 2 ativos
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Retorno
Risco
Gráfico Risco x Retorno: 2 ativos
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Retorno
Risco
Gráfico Risco x Retorno: 2 ativos
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Retorno
Risco
Gráfico Risco x Retorno: 2 ativos
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Retorno
Risco
Gráfico Risco x Retorno: 2 ativos
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Risco para n Ativos
Fórmula do Risco de uma carteira para 3 Ativos:
Fórmula do Risco de uma carteira para n Ativos:
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Rafael Paschoarelli Veiga Pg.
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Considerando os dados da tabela abaixo, calcule o risco e o retorno para uma carteira composta por 70% do ativo A, 30% do ativo B e (0%) do ativo C. 
Correlação entre ativos A e B = +0,3
Correlação entre ativos A e C = +0,1
Correlação entre ativos B e C = -0,2
Exercício
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Rafael Paschoarelli Veiga Pg.
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Considerando os dados da tabela abaixo, calcule o risco e o retorno para uma carteira composta por 50% do ativo A, 30% do ativo B e (20%) do ativo C. 
Correlação entre ativos A e B = +0,3
Correlação entre ativos A e C = +0,1
Correlação entre ativos B e C = -0,2
Exercício
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Gráfico Risco x Retorno para n Ativos
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Variância da Carteira
Número de Ativos
Carteira de N ativos, todos com mesmo peso na carteira, todos os ativos possuem mesmo risco s e a covariância entre todos é igual a cov. 
Observações Pertinentes
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Observações Pertinentes
 Mesmo que se tenha uma carteira com todos os ativos do mercado, esta carteira terá risco.
 Em outras palavras, existe uma componente de risco que não pode ser eliminada.
 Sob o aspecto prático, são necessários ______ ativos para se ter uma carteira suficientemente diversificada.
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O CAPM
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Rafael Paschoarelli Veiga Pg.
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 O CAPM é um modelo de fator único significando que o retorno do ativo pode ser explicado pelo retorno da Carteira de Mercado; 
 A Carteira de Mercado é uma combinação de todos os ativos com risco existentes, em proporções correspondentes aos seus valores de mercado.
CAPM
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Rafael Paschoarelli Veiga Pg.
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Comparando um Ativo com a Carteira de Mercado
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Comparando um Ativo com a Carteira de Mercado (cont)
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Rafael Paschoarelli Veiga Pg.
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Comparando um Ativo com a Carteira de Mercado (cont)
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Obtendo o Beta
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Obtendo o Beta
Perceba que a inclinação da Linha Característica do Título é o Beta. Quanto mais inclinada for a Linha, mais sensível (arriscado) será o título em questão face às oscilações do Mercado.
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O Beta (cont)
Você se recorda que Risco Total de um Título Individual = Risco Sistemático (Não Diversificável ou Risco Conjuntural) + Risco Não Sistemático (Diversificável).
Pois bem, o Beta é uma medida do risco Sistemático do Ativo em questão. Perceba que a influência do risco sistemático sobre a ação é o coeficiente Beta. Em outras palavras, o coeficiente Beta nos diz a sensibilidade do retorno da ação a um risco sistemático. (Ross 242) 
Note que o Risco Sistemático (Ross 242) é qualquer risco que afeta um grande número de ativos, cada um com maior ou menor intensidade;
O Risco Não Sistemático (Ross 242) é um risco que afeta especificamente um único ativo ou um pequeno número de ativos.
Na avaliação do risco de uma carteira, o beta da carteira é a média ponderada de cada ativo contido na carteira.
Segundo Ross (pg 228), as evidências empíricas mostram que praticamente não existem ações com betas negativos.
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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O CAPM
 O retorno requerido para um título deriva do seu risco de mercado. 
 O risco diversificável não afeta
o retorno esperado de um título; 
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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A Linha de Mercado de Títulos - SML
RM
Rlivre
Security Market Line ou Linha do Mercado de Títulos
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
*
Rafael Paschoarelli Veiga Pg.
*
Linha do Mercado de Capitais
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
*
Rafael Paschoarelli Veiga Pg.
*
A Empresa de Investimentos DeadChicken, com sede em Yolanda-PR, tem um capital total de R$ 500MM em 4 ações:
 A: R$ 200MM;	B: R$ 150 MM	C: R$ 50MM	D: R$ 100MM
Beta = 1		Beta = 2		Beta = 1,5		Beta = 0,7
A taxa livre de risco é de 9% ao ano enquanto os retornos esperados do mercado possui a seguinte distribuição de probabilidade:
Probabilidade	Retorno anual esperado para o mercado
10%		10%
35%		15%
25%		20%
20%		25%
10%		30%		
Exercício
Esboce a SML.
Qual é a equação da SML?
Qual é a taxa de retorno exigida pelo fundo para o próximo ano?
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Exercício
D
A
B
C
Considerando as ações A, B, C e D, quais estão caras e quais estão baratas comparativamente aos seus respectivos preços justos?
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Exercício
 Ação	σ			β		
X		0,2			0,9
Y		0,3			0,8
Z		0,25			1,5
Seu objetivo é minimizar o risco do investimento.
Então, você deve escolher o ativo:
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
*
Rafael Paschoarelli Veiga Pg.
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Exercício
A Cano Certo SA, empresa com sede em Carapicuíba, acaba de fazer IPO levantando recursos para investimento. 
O último dividendo pago foi de R$ R$ 0,80 por ação, o beta da empresa é de 1,4, ifree de 10%, prêmio de mercado 3%.
Determine o preço teórico da ação supondo que os dividendos fiquem estáveis.
Supondo crescimento nos dividendos de 10% ao ano, determine o preço teórico da ação.
Supondo crescimento nos dividendos de 30% ao ano nos próximos 3 anos e de 10% ao ano nos anos subsequentes, determine o preço teórico da ação.
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Observações Pertinentes
Surgem os conceitos de:
 Risco não Diversificável ou Risco de Mercado ou Risco Sistemático (Sistêmico);
 Risco Diversificável ou Risco Não Sistemático (Não sistêmico): Note que este tipo de risco pode ser eliminado numa carteira convenientemente diversificada.
 Risco Total de um Ativo s2 = Risco não Diversificável + Risco Diversificável;
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Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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O Índice de Sharpe
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Índice de Sharpe IS
 O IS evidencia o prêmio pago pelo risco assumido e o risco do investimento.
O IS revela prêmio oferecido por um ativo para cada percentual de risco assumido.
 Quanto maior o IS, melhor. (cuidado com IS negativo)
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Índice de Sharpe IS (cont)
 Exemplo 1: IS = 0,7: O ativo promete oferecer mais 0,7% de retorno para cada 1% adicional de risco incorrido; 
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Índice de Sharpe IS (cont)
 Exemplo 2: Calcular IS de carteira composta por ativo sem risco com retorno esperado de 6% (peso 30%) e ativo com risco com retorno esperado de 14% e risco igual a 10% (desvio padrão).
Fonte: Alexandre Assaf Neto. Mercado Financeiro. Editora Atlas. Pg. 311
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Tracking Error
 No caso dos fundos passivos, a principal preocupação dos investidores é se o fundo está acompanhando bem o benchmark ou índice que ele se propõe a reproduzir. Um indicador de desempenho de fundos de investimentos passivos que mede como o fundo acompanha o índice é o Tracking Error. 
Fonte: Gyorgy Varga pg 16 Índice de Sharpe e outros Indicadores de Desempenho Aplicados a Fundos de Ações Brasileiros
Observe que TE nada mais é que o desvio padrão dos retornos excedentes do ativo (fundo) em relação à referência.
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
*
Rafael Paschoarelli Veiga Pg.
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EQM – Erro Quadrático Médio
 Note que quanto menor o EQM, maior a similaridade entre o retorno do ativo e de seu benchmark.
 Naturalmente, quanto menor, melhor.
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Exercício
Calcule o EQM e o TE dos fundos A e B. Discuta os resultados.
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
*
Rafael Paschoarelli Veiga Pg.
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Calcule o EQM e o TE dos fundos A e B. Discuta os resultados.
Exercício
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Valor em Risco (VaR)
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
*
Rafael Paschoarelli Veiga Pg.
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Value at Risk - VaR
O VaR fornece como resposta uma estimativa da pior perda possível dentro de um intervalo de tempo e dado um intervalo de confiança, estando o mercado nas suas condições normais.
JORION (1997: xiii),
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Value at Risk - VaR
Exemplo 1: Um banco que afirme que o VaR de um dia de sua carteira de investimentos é de R$ 4.000.000,00 para um nível de confiança de 99% quer dizer que, sob condições normais de mercado, existe uma chance em 100 de incorrer uma perda superior a R$ 4.000.000,00 no prazo de um dia. 
JORION (1997: xiii),
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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VaR Paramétrico
 Exemplo 2: Um gerente administra uma carteira de investimentos composta por um ativo. O retorno deste ativo possui distribuição normal, a média dos retornos é igual a 10% ao ano e o desvio padrão dos retornos anuais é 30%. O valor do portfólio hoje é de $100 MM 
Adaptado de BENNINGA & WIENER (1998: 1) 
qual é a distribuição do valor do portfólio dentro de um ano?
qual a probabilidade de se perder $30 MM ou mais dentro de um ano, isto é, qual é a probabilidade do valor final do portfólio ser igual ou inferior a $80 MM?
com 99% de probabilidade, qual é a máxima perda dentro de um ano? Isto é, qual é o VaR a 99% considerando que o horizonte de tempo seja igual a um ano ? 
Rafael Paschoarelli Veiga Pg.
Rafael Paschoarelli Veiga Pg.
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Rafael Paschoarelli Veiga Pg.
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Exemplo 2: 
 i) Dentro de um ano o valor esperado para o portfólio é de $ 110 MM com um desvio padrão de $ 30 MM. Estes dados conduzem à seguinte distribuição normal:
VaR Paramétrico
Adaptado de BENNINGA & WIENER (1998: 1) 
Rafael Paschoarelli Veiga Pg.
Gráf1
		0.0001477283
		0.0001552809
		0.0001631743
		0.0001714214
		0.0001800352
		0.0001890294
		0.0001984177
		0.0002082146
		0.0002184344
		0.0002290922
		0.0002402033
		0.0002517834
		0.0002638484
		0.0002764147
		0.0002894992
		0.0003031188
		0.0003172909
		0.0003320335
		0.0003473645
		0.0003633025
		0.0003798662
		0.0003970748
0.0004149477
		0.0004335046
		0.0004527656
		0.0004727511
		0.0004934817
		0.0005149782
		0.0005372619
		0.0005603542
		0.0005842767
		0.0006090513
		0.0006347
		0.0006612451
		0.0006887092
		0.0007171147
		0.0007464843
		0.000776841
		0.0008082077
		0.0008406073
		0.000874063
		0.0009085977
		0.0009442346
		0.0009809967
		0.001018907
		0.0010579884
		0.0010982637
		0.0011397555
		0.0011824864
		0.0012264786
		0.0012717541
		0.0013183347
		0.0013662419
		0.0014154967
		0.0014661199
		0.0015181318
		0.0015715522
		0.0016264006
		0.0016826958
		0.001740456
		0.0017996989
		0.0018604415
		0.0019227001
		0.0019864902
		0.0020518267
		0.0021187236
		0.0021871938
		0.0022572497
		0.0023289025
		0.0024021625
		0.0024770388
		0.0025535396
		0.0026316719
		0.0027114417
		0.0027928534
		0.0028759106
		0.0029606154
		0.0030469684
		0.0031349692
		0.0032246158
		0.0033159046
		0.0034088308
		0.0035033879
		0.0035995679
		0.0036973612
		0.0037967565
		0.003897741
		0.0040003
		0.0041044174
		0.0042100751
		0.0043172532
		0.0044259302
		0.0045360827
		0.0046476855
		0.0047607115
		0.0048751318
		0.0049909155
		0.00510803
		0.0052264406
		0.0053461109
		0.0054670025
		0.0055890751
		0.0057122864
		0.0058365924
		0.0059619472
		0.0060883028
		0.0062156096
		0.006343816
		0.0064728685
		0.006602712
		0.0067332895
		0.0068645423
		0.0069964099
		0.0071288301
		0.0072617392
		0.0073950718
		0.0075287609
		0.007662738
		0.0077969332
		0.007931275
		0.0080656908
		0.0082001065
		0.0083344468
		0.0084686352
		0.0086025942
		0.0087362451
		0.0088695083
		0.0090023034
		0.0091345489
		0.0092661629
		0.0093970625
		0.0095271645
		0.0096563851
		0.00978464
		0.0099118447
		0.0100379144
		0.0101627642
		0.0102863092
		0.0104084644
		0.0105291452
		0.0106482669
		0.0107657453
		0.0108814968
		0.0109954382
		0.0111074868
		0.0112175608
		0.0113255791
		0.0114314618
		0.0115351298
		0.011636505
		0.0117355109
		0.011832072
		0.0119261143
		0.0120175654
		0.0121063544
		0.0121924122
		0.0122756713
		0.0123560663
		0.0124335336
		0.0125080116
		0.0125794409
		0.0126477644
		0.0127129272
		0.0127748766
		0.0128335625
		0.0128889372
		0.0129409557
		0.0129895754
		0.0130347565
		0.0130764618
		0.0131146572
		0.013149311
		0.0131803947
		0.0132078825
		0.0132317516
		0.0132519822
		0.0132685575
		0.0132814638
		0.0132906902
		0.0132962292
		0.013298076
		0.0132962292
		0.0132906902
		0.0132814638
		0.0132685575
		0.0132519822
		0.0132317516
		0.0132078825
		0.0131803947
		0.013149311
		0.0131146572
		0.0130764618
		0.0130347565
		0.0129895754
		0.0129409557
		0.0128889372
		0.0128335625
		0.0127748766
		0.0127129272
		0.0126477644
		0.0125794409
		0.0125080116
		0.0124335336
		0.0123560663
		0.0122756713
		0.0121924122
		0.0121063544
		0.0120175654
		0.0119261143
		0.011832072
		0.0117355109
		0.011636505
		0.0115351298
		0.0114314618
		0.0113255791
		0.0112175608
		0.0111074868
		0.0109954382
		0.0108814968
		0.0107657453
		0.0106482669
		0.0105291452
		0.0104084644
		0.0102863092
		0.0101627642
		0.0100379144
		0.0099118447
		0.00978464
		0.0096563851
		0.0095271645
		0.0093970625
		0.0092661629
		0.0091345489
		0.0090023034
		0.0088695083
		0.0087362451
		0.0086025942
		0.0084686352
		0.0083344468
		0.0082001065
		0.0080656908
		0.007931275
		0.0077969332
		0.007662738
		0.0075287609
		0.0073950718
		0.0072617392
		0.0071288301
		0.0069964099
		0.0068645423
		0.0067332895
		0.006602712
		0.0064728685
		0.006343816
		0.0062156096
		0.0060883028
		0.0059619472
		0.0058365924
		0.0057122864
		0.0055890751
		0.0054670025
		0.0053461109
		0.0052264406
		0.00510803
		0.0049909155
		0.0048751318
		0.0047607115
		0.0046476855
		0.0045360827
		0.0044259302
		0.0043172532
		0.0042100751
		0.0041044174
		0.0040003
		0.003897741
		0.0037967565
		0.0036973612
		0.0035995679
		0.0035033879
		0.0034088308
		0.0033159046
		0.0032246158
		0.0031349692
		0.0030469684
		0.0029606154
		0.0028759106
		0.0027928534
		0.0027114417
		0.0026316719
		0.0025535396
		0.0024770388
		0.0024021625
		0.0023289025
		0.0022572497
		0.0021871938
		0.0021187236
		0.0020518267
		0.0019864902
		0.0019227001
		0.0018604415
		0.0017996989
		0.001740456
		0.0016826958
		0.0016264006
		0.0015715522
		0.0015181318
		0.0014661199
		0.0014154967
		0.0013662419
		0.0013183347
		0.0012717541
		0.0012264786
		0.0011824864
		0.0011397555
		0.0010982637
		0.0010579884
		0.001018907
		0.0009809967
		0.0009442346
		0.0009085977
		0.000874063
		0.0008406073
		0.0008082077
		0.000776841
		0.0007464843
		0.0007171147
		0.0006887092
		0.0006612451
		0.0006347
		0.0006090513
		0.0005842767
		0.0005603542
		0.0005372619
		0.0005149782
		0.0004934817
		0.0004727511
		0.0004527656
		0.0004335046
		0.0004149477
		0.0003970748
		0.0003798662
		0.0003633025
		0.0003473645
		0.0003320335
		0.0003172909
		0.0003031188
		0.0002894992
		0.0002764147
		0.0002638484
		0.0002517834
		0.0002402033
		0.0002290922
		0.0002184344
		0.0002082146
		0.0001984177
		0.0001890294
		0.0001800352
		0.0001714214
		0.0001631743
		0.0001552809
		0.0001477283
		0.000140504
		0.0001335958
		0.0001269921
		0.0001206812
		0.0001146521
		0.000108894
		0.0001033963
		0.0000981489
		0.0000931419
		0.0000883659
		0.0000838114
		0.0000794696
		0.0000753318
		0.0000713896
		0.0000676349
		0.0000640599
		0.000060657
		0.000057419
		0.0000543386
		0.0000514093
		0.0000486244
		0.0000459775
		0.0000434627
		0.000041074
		0.0000388058
		0.0000366527
		0.0000346094
		0.0000326709
		0.0000308325
		0.0000290894
		0.0000274373
		0.0000258718
		0.0000243888
		0.0000229845
		0.000021655
		0.0000203967
		0.0000192063
		0.0000180802
		0.0000170155
		0.000016009
Valor em $MM
Distribuição Normal : média $110 MM; desvio $30 MM
Normal
		0.0001477283		20				0.135%		0.939%						-2.35
		0.0001552809		20.5				0.143%
		0.0001631743		21				0.151%
		0.0001714214		21.5				0.159%
		0.0001800352		22				0.168%
		0.0001890294		22.5				0.177%
		0.0001984177		23				0.187%
		0.0002082146		23.5				0.197%
		0.0002184344		24				0.207%
		0.0002290922		24.5				0.219%
		0.0002402033		25				0.230%
		0.0002517834		25.5				0.243%
		0.0002638484		26				0.256%
		0.0002764147		26.5				0.269%
		0.0002894992		27				0.283%
		0.0003031188		27.5				0.298%
		0.0003172909		28				0.313%
		0.0003320335		28.5				0.330%
		0.0003473645		29				0.347%
		0.0003633025		29.5				0.364%
		0.0003798662		30				0.383%
		0.0003970748		30.5				0.402%
		0.0004149477		31				0.423%
		0.0004335046		31.5				0.444%
		0.0004527656		32				0.466%
		0.0004727511		32.5				0.489%
		0.0004934817		33				0.513%
		0.0005149782		33.5				0.539%
		0.0005372619		34				0.565%
		0.0005603542		34.5				0.592%
		0.0005842767		35				0.621%
		0.0006090513		35.5				0.651%
		0.0006347		36				0.682%
		0.0006612451		36.5				0.714%
		0.0006887092		37				0.748%
		0.0007171147		37.5
0.783%
		0.0007464843		38				0.820%
		0.000776841		38.5				0.858%
		0.0008082077		39				0.897%
		0.0008406073		39.5				0.939%
		0.000874063		40				0.982%
		0.0009085977		40.5				1.026%
		0.0009442346		41
		0.0009809967		41.5
		0.001018907		42
		0.0010579884		42.5
		0.0010982637		43
		0.0011397555		43.5
		0.0011824864		44
		0.0012264786		44.5
		0.0012717541		45
		0.0013183347		45.5
		0.0013662419		46
		0.0014154967		46.5
		0.0014661199		47
		0.0015181318		47.5
		0.0015715522		48
		0.0016264006		48.5
		0.0016826958		49
		0.001740456		49.5
		0.0017996989		50
		0.0018604415		50.5
		0.0019227001		51
		0.0019864902		51.5
		0.0020518267		52
		0.0021187236		52.5
		0.0021871938		53
		0.0022572497		53.5
		0.0023289025		54
		0.0024021625		54.5
		0.0024770388		55
		0.0025535396		55.5
		0.0026316719		56
		0.0027114417		56.5
		0.0027928534		57
		0.0028759106		57.5
		0.0029606154		58
		0.0030469684		58.5
		0.0031349692		59
		0.0032246158		59.5
		0.0033159046		60
		0.0034088308		60.5
		0.0035033879		61
		0.0035995679		61.5
		0.0036973612		62
		0.0037967565		62.5
		0.003897741		63
		0.0040003		63.5
		0.0041044174		64
		0.0042100751		64.5
		0.0043172532		65
		0.0044259302		65.5
		0.0045360827		66
		0.0046476855		66.5
		0.0047607115		67
		0.0048751318		67.5
		0.0049909155		68
		0.00510803		68.5
		0.0052264406		69
		0.0053461109		69.5
		0.0054670025		70
		0.0055890751		70.5
		0.0057122864		71
		0.0058365924		71.5
		0.0059619472		72
		0.0060883028		72.5
		0.0062156096		73
		0.006343816		73.5
		0.0064728685		74
		0.006602712		74.5
		0.0067332895		75
		0.0068645423		75.5
		0.0069964099		76
		0.0071288301		76.5
		0.0072617392		77
		0.0073950718		77.5
		0.0075287609		78
		0.007662738		78.5
		0.0077969332		79
		0.007931275		79.5
		0.0080656908		80
		0.0082001065		80.5
		0.0083344468		81
		0.0084686352		81.5
		0.0086025942		82
		0.0087362451		82.5
		0.0088695083		83
		0.0090023034		83.5
		0.0091345489		84
		0.0092661629		84.5
		0.0093970625		85
		0.0095271645		85.5
		0.0096563851		86
		0.00978464		86.5
		0.0099118447		87
		0.0100379144		87.5
		0.0101627642		88
		0.0102863092		88.5
		0.0104084644		89
		0.0105291452		89.5
		0.0106482669		90
		0.0107657453		90.5
		0.0108814968		91
		0.0109954382		91.5
		0.0111074868		92
		0.0112175608		92.5
		0.0113255791		93
		0.0114314618		93.5
		0.0115351298		94
		0.011636505		94.5
		0.0117355109		95
		0.011832072		95.5
		0.0119261143		96
		0.0120175654		96.5
		0.0121063544		97
		0.0121924122		97.5
		0.0122756713		98
		0.0123560663		98.5
		0.0124335336		99
		0.0125080116		99.5
		0.0125794409		100
		0.0126477644		100.5
		0.0127129272		101
		0.0127748766		101.5
		0.0128335625		102
		0.0128889372		102.5
		0.0129409557		103
		0.0129895754		103.5
		0.0130347565		104
		0.0130764618		104.5
		0.0131146572		105
		0.013149311		105.5
		0.0131803947		106
		0.0132078825		106.5
		0.0132317516		107
		0.0132519822		107.5
		0.0132685575		108
		0.0132814638		108.5
		0.0132906902		109
		0.0132962292		109.5
		0.013298076		110
		0.0132962292		110.5
		0.0132906902		111
		0.0132814638		111.5
		0.0132685575		112
		0.0132519822		112.5
		0.0132317516		113
		0.0132078825		113.5
		0.0131803947		114
		0.013149311		114.5
		0.0131146572		115
		0.0130764618		115.5
		0.0130347565		116
		0.0129895754		116.5
		0.0129409557		117
		0.0128889372		117.5
		0.0128335625		118
		0.0127748766		118.5
		0.0127129272		119
		0.0126477644		119.5
		0.0125794409		120
		0.0125080116		120.5
		0.0124335336		121
		0.0123560663		121.5
		0.0122756713		122
		0.0121924122		122.5
		0.0121063544		123
		0.0120175654		123.5
		0.0119261143		124
		0.011832072		124.5
		0.0117355109		125
		0.011636505		125.5
		0.0115351298		126
		0.0114314618		126.5
		0.0113255791		127
		0.0112175608		127.5
		0.0111074868		128
		0.0109954382		128.5
		0.0108814968		129
		0.0107657453		129.5
		0.0106482669		130
		0.0105291452		130.5
		0.0104084644		131
		0.0102863092		131.5
		0.0101627642		132
		0.0100379144		132.5
		0.0099118447		133
		0.00978464		133.5
		0.0096563851		134
		0.0095271645		134.5
		0.0093970625		135
		0.0092661629		135.5
		0.0091345489		136
		0.0090023034		136.5
		0.0088695083		137
		0.0087362451		137.5
		0.0086025942		138
		0.0084686352		138.5
		0.0083344468		139
		0.0082001065		139.5
		0.0080656908		140
		0.007931275		140.5
		0.0077969332		141
		0.007662738		141.5
		0.0075287609		142
		0.0073950718		142.5
		0.0072617392		143
		0.0071288301		143.5
		0.0069964099		144
		0.0068645423		144.5
		0.0067332895		145
		0.006602712		145.5
		0.0064728685		146
		0.006343816		146.5
		0.0062156096		147
		0.0060883028		147.5
		0.0059619472		148
		0.0058365924		148.5
		0.0057122864		149
		0.0055890751		149.5
		0.0054670025		150
		0.0053461109		150.5
		0.0052264406		151
		0.00510803		151.5
		0.0049909155		152
		0.0048751318		152.5
		0.0047607115		153
		0.0046476855		153.5
		0.0045360827		154
		0.0044259302		154.5
		0.0043172532		155
		0.0042100751		155.5
		0.0041044174		156
		0.0040003		156.5
		0.003897741		157
		0.0037967565		157.5
		0.0036973612		158
		0.0035995679		158.5
		0.0035033879		159
		0.0034088308		159.5
		0.0033159046		160
		0.0032246158		160.5
		0.0031349692		161
		0.0030469684		161.5
		0.0029606154		162
		0.0028759106		162.5
		0.0027928534		163
		0.0027114417		163.5
		0.0026316719		164
		0.0025535396		164.5
		0.0024770388		165
		0.0024021625		165.5
		0.0023289025		166
		0.0022572497		166.5
		0.0021871938		167
		0.0021187236		167.5
		0.0020518267		168
		0.0019864902		168.5
		0.0019227001		169
		0.0018604415		169.5
		0.0017996989		170
		0.001740456		170.5
		0.0016826958		171
		0.0016264006		171.5
		0.0015715522		172
		0.0015181318		172.5
		0.0014661199		173
		0.0014154967		173.5
		0.0013662419		174
		0.0013183347		174.5
		0.0012717541		175
		0.0012264786		175.5
		0.0011824864		176
		0.0011397555		176.5
		0.0010982637		177
		0.0010579884		177.5
		0.001018907		178
		0.0009809967		178.5
		0.0009442346		179
		0.0009085977		179.5
		0.000874063		180
		0.0008406073		180.5
		0.0008082077		181
		0.000776841		181.5
		0.0007464843		182
		0.0007171147		182.5
		0.0006887092		183
		0.0006612451		183.5
		0.0006347		184
		0.0006090513		184.5
		0.0005842767		185
		0.0005603542		185.5
		0.0005372619		186
		0.0005149782		186.5
		0.0004934817		187
		0.0004727511		187.5
		0.0004527656		188
		0.0004335046		188.5
		0.0004149477		189
		0.0003970748		189.5
		0.0003798662		190
		0.0003633025		190.5
		0.0003473645		191
		0.0003320335		191.5
		0.0003172909		192
		0.0003031188		192.5
		0.0002894992		193
		0.0002764147		193.5
		0.0002638484		194
		0.0002517834		194.5
		0.0002402033		195
		0.0002290922		195.5
		0.0002184344		196
		0.0002082146		196.5
		0.0001984177		197
		0.0001890294		197.5
		0.0001800352		198
		0.0001714214		198.5
		0.0001631743		199
		0.0001552809		199.5
		0.0001477283		200
		0.000140504		200.5
		0.0001335958		201
		0.0001269921		201.5
		0.0001206812		202
		0.0001146521		202.5
		0.000108894		203
		0.0001033963		203.5
		0.0000981489		204
		0.0000931419		204.5
		0.0000883659		205
		0.0000838114		205.5
		0.0000794696		206
		0.0000753318		206.5
		0.0000713896		207
		0.0000676349
207.5
		0.0000640599		208
		0.000060657		208.5
		0.000057419		209
		0.0000543386		209.5
		0.0000514093		210
		0.0000486244		210.5
		0.0000459775		211
		0.0000434627		211.5
		0.000041074		212
		0.0000388058		212.5
		0.0000366527		213
		0.0000346094		213.5
		0.0000326709		214
		0.0000308325		214.5
		0.0000290894		215
		0.0000274373		215.5
		0.0000258718		216
		0.0000243888		216.5
		0.0000229845		217
		0.000021655		217.5
		0.0000203967		218
		0.0000192063		218.5
		0.0000180802		219
		0.0000170155		219.5
		0.000016009		220
Normal
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		0
Valor em $MM
Distribuição Normal : média $110MM; desvio $30 MM
ORTN
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		0
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		0
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Valor em $MM
Distribuição Normal : média $110 MM; desvio $30 MM
Tail
		0
		0
		0
		0
		0
		0
		0
		0
		0
		0
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		0
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		0
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		0
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		0
		0
		0
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0
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		0
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		0
Distribuição Normal do Valor Futuro Esperado
Tail na cox
		Data		Valor da ORTN		Juros
		15/12/79		468.71		3.12
		15/01/80		487.83		3.25
		15/02/80		508.33		3.39
		15/03/80		527.14		3.51
		15/04/80		546.64		3.64
		15/05/80		566.86		3.78
		
		Total				20.70
TSF1
		qsi				0.1		0.5
		mi				4%		4%
		sigma				10%		10%
		
		
		x				H para qsi = 0,1		H para qsi = 0,5		normal
		0				4.50027251		4.770733182		3.682701403
		0.0005				4.4652548747		4.7245861102		3.6900280505
		0.001				4.4307073388		4.6793084945		3.6972768411
		0.0015				4.3966219741		4.6348786718		3.7044472591
		0.002				4.3629910118		4.5912756404		3.7115387936
		0.0025				4.3298068382		4.5484790366		3.7185509387
		0.003				4.2970619915		4.5064691117		3.7254831935
		0.0035				4.2647491582		4.4652267103		3.7323350621
		0.004				4.2328611698		4.4247332495		3.7391060537
		0.0045				4.2013909994		4.3849706986		3.7457956829
		0.005				4.1703317587		4.3459215599		3.7524034692
		0.0055				4.1396766943		4.3075688503		3.7589289376
		0.006				4.1094191856		4.2698960833		3.7653716183
		0.0065				4.0795527408		4.2328872523		3.7717310472
		0.007				4.0500709947		4.1965268136		3.7780067653
		0.0075				4.0209677057		4.1607996713		3.7841983193
		0.008				3.9922367528		4.1256911617		3.7903052615
		0.0085				3.9638721334		4.0911870388		3.7963271497
		0.009				3.93586796		4.0572734606		3.8022635475
		0.0095				3.9082184583		4.0239369752		3.8081140241
		0.01				3.8809179643		3.9911645081		3.8138781546
		0.0105				3.8539609222		3.9589433497		3.8195555199
		0.011				3.8273418817		3.9272611433		3.8251457066
		0.0115				3.8010554957		3.8961058736		3.8306483076
		0.012				3.7750965183		3.8654658555		3.8360629215
		0.0125				3.7494598026		3.8353297233		3.8413891531
		0.013				3.7241402983		3.8056864209		3.846626613
		0.0135				3.6991330496		3.7765251912		3.8517749182
		0.014				3.6744331935		3.747835567		3.8568336919
		0.0145				3.6500359576		3.7196073617		3.8618025633
		0.015				3.6259366579		3.6918306605		3.866681168
		0.0155				3.6021306974		3.6644958115		3.8714691479
		0.016				3.5786135639		3.6375934178		3.8761661513
		0.0165				3.5553808285		3.6111143297		3.8807718326
		0.017				3.5324281432		3.5850496365		3.8852858532
		0.0175				3.50975124		3.5593906596		3.8897078804
		0.018				3.4873459287		3.5341289451		3.8940375883
		0.0185				3.4652080953		3.509256257		3.8982746577
		0.019				3.4433337005		3.4847645706		3.9024187757
		0.0195				3.4217187784		3.4606460662		3.9064696362
		0.02				3.4003594343		3.4368931225		3.9104269398
		0.0205				3.3792518438		3.4134983113		3.9142903936
		0.021				3.3583922512		3.390454391		3.9180597118
		0.0215				3.3377769678		3.3677543015		3.9217346151
		0.022				3.3174023709		3.345391159		3.9253148312
		0.0225				3.2972649022		3.3233582502		3.9288000945
		0.023				3.2773610667		3.3016490277		3.9321901463
		0.0235				3.2576874311		3.2802571052		3.935484735
		0.024				3.2382406227		3.2591762524		3.9386836157
		0.0245				3.2190173282		3.2384003912		3.9417865507
		0.025				3.2000142924		3.2179235905		3.9447933091
		0.0255				3.1812283171		3.1977400624		3.9477036672
		0.026				3.1626562599		3.1778441583		3.9505174083
		0.0265				3.1442950332		3.1582303645		3.9532343229
		0.027				3.1261416027		3.1388932986		3.9558542084
		0.0275				3.1081929869		3.1198277057		3.9583768694
		0.028				3.0904462556		3.1010284552		3.9608021179
		0.0285				3.0728985291		3.0824905366		3.9631297729
		0.029				3.0555469771		3.0642090568		3.9653596605
		0.0295				3.0383888177		3.0461792366		3.9674916142
		0.03				3.0214213166		3.0283964076		3.9695254748
		0.0305				3.004641786		3.0108560089		3.9714610902
		0.031				2.9880475836		2.9935535847		3.9732983158
		0.0315				2.971636112		2.9764847809		3.9750370141
		0.032				2.9554048176		2.9596453425		3.9766770551
		0.0325				2.9393511897		2.9430311113		3.9782183161
		0.033				2.9234727599		2.9266380226		3.9796606816
		0.0335				2.9077671011		2.9104621032		3.9810040438
		0.034				2.8922318267		2.894499469		3.982248302
		0.0345				2.8768645897		2.8787463221		3.9833933629
		0.035				2.8616630825		2.8631989492		3.9844391409
		0.0355				2.8466250353		2.8478537189		3.9853855576
		0.036				2.831748216		2.8327070796		3.986232542
		0.0365				2.8170304293		2.8177555576		3.9869800307
		0.037				2.8024695158		2.8029957551		3.9876279676
		0.0375				2.7880633517		2.7884243479		3.9881763042
		0.038				2.7738098477		2.7740380837		3.9886249992
		0.0385				2.7597069488		2.7598337805		3.9889740192
		0.039				2.7457526333		2.7458083244		3.9892233379
		0.0395				2.7319449121		2.7319586679		3.9893729365
		0.04				2.7182818285		2.7182818285		3.989422804
		0.0405				2.7047614572		2.7047748868		3.9893729365
		0.041				2.6913819041		2.6914349851		3.9892233379
		0.0415				2.6781413053		2.6782593257		3.9889740192
		0.042				2.6650378266		2.6652451694		3.9886249992
		0.0425				2.6520696634		2.652389834		3.9881763042
		0.043				2.6392350396		2.6396906933		3.9876279676
		0.0435				2.6265322072		2.6271451749		3.9869800307
		0.044				2.6139594462		2.6147507598		3.986232542
		0.0445				2.6015150635		2.6025049805		3.9853855576
		0.045				2.5891973927		2.5904054198		3.9844391409
		0.0455				2.5770047936		2.5784497098		3.9833933629
		0.046				2.5649356518		2.5666355305		3.982248302
		0.0465				2.552988378		2.5549606088		3.9810040438
		0.047				2.5411614077		2.5434227171		3.9796606816
		0.0475				2.5294532007		2.5320196728		3.9782183161
		0.048				2.5178622407		2.5207493364		3.9766770551
		0.0485				2.506387035		2.509609611		3.9750370141
		0.049				2.4950261136		2.4985984414		3.9732983158
		0.0495				2.4837780293		2.4877138128		3.9714610902
		0.05				2.4726413573		2.4769537498		3.9695254748
		0.0505				2.4616146943		2.4663163158		3.9674916142
		0.051				2.4506966585		2.4557996119		3.9653596605
		0.0515				2.4398858892		2.4454017761		3.9631297729
		0.052				2.4291810464		2.4351209823		3.9608021179
		0.0525				2.4185808104		2.4249554396		3.9583768694
		0.053				2.4080838813		2.4149033915		3.9558542084
		0.0535				2.3976889788		2.404963115		3.9532343229
		0.054				2.3873948422		2.39513292		3.9505174083
		0.0545				2.3772002292		2.3854111484		3.9477036672
		0.055				2.3671039164		2.3757961734		3.9447933091
		0.0555				2.3571046986		2.366286399		3.9417865507
		0.056				2.3472013886		2.3568802588		3.9386836157
		0.0565				2.3373928166		2.3475762161		3.935484735
		0.057				2.3276778303		2.3383727624		3.9321901463
		0.0575				2.3180552944		2.3292684175		3.9288000945
		0.058				2.3085240904		2.3202617284		3.9253148312
0.0585				2.299083116		2.3113512687		3.9217346151
		0.059				2.2897312853		2.3025356386		3.9180597118
		0.0595				2.2804675281		2.2938134634		3.9142903936
		0.06				2.2712907901		2.2851833938		3.9104269398
		0.0605				2.2622000319		2.2766441047		3.9064696362
		0.061				2.2531942297		2.2681942952		3.9024187757
		0.0615				2.244272374		2.2598326877		3.8982746577
		0.062				2.2354334702		2.2515580275		3.8940375883
		0.0625				2.2266765381		2.2433690824		3.8897078804
		0.063				2.2180006113		2.2352646422		3.8852858532
		0.0635				2.2094047375		2.227243518		3.8807718326
		0.064				2.2008879778		2.2193045423		3.8761661513
		0.0645				2.192449407		2.2114465677		3.8714691479
		0.065				2.1840881127		2.2036684673		3.866681168
		0.0655				2.1758031958		2.1959691339		3.8618025633
		0.066				2.1675937696		2.1883474794		3.8568336919
		0.0665				2.1594589603		2.1808024349		3.8517749182
		0.067				2.151397906		2.1733329497		3.846626613
		0.0675				2.1434097572		2.1659379916		3.8413891531
		0.068				2.1354936763		2.1586165459		3.8360629215
		0.0685				2.1276488373		2.1513676152		3.8306483076
		0.069				2.1198744258		2.1441902195		3.8251457066
		0.0695				2.1121696388		2.1370833952		3.8195555199
		0.07				2.1045336842		2.130046195		3.8138781546
		0.0705				2.0969657812		2.1230776879		3.8081140241
		0.071				2.0894651595		2.1161769584		3.8022635475
		0.0715				2.0820310597		2.1093431063		3.7963271497
		0.072				2.0746627326		2.1025752465		3.7903052615
		0.0725				2.0673594395		2.0958725089		3.7841983193
		0.073				2.0601204517		2.0892340376		3.7780067653
		0.0735				2.0529450503		2.0826589909		3.7717310472
		0.074				2.0458325264		2.0761465411		3.7653716183
		0.0745				2.0387821808		2.0696958741		3.7589289376
		0.075				2.0317933236		2.063306189		3.7524034692
		0.0755				2.0248652742		2.0569766982		3.7457956829
		0.076				2.0179973615		2.0507066268		3.7391060537
		0.0765				2.0111889229		2.0444952125		3.7323350621
		0.077				2.0044393053		2.0383417055		3.7254831935
		0.0775				1.997747864		2.0322453677		3.7185509387
		0.078				1.9911139629		2.0262054732		3.7115387936
		0.0785				1.9845369745		2.0202213078		3.7044472591
		0.079				1.9780162796		2.0142921683		3.6972768411
		0.0795				1.9715512674		2.0084173631		3.6900280505
		0.08				1.9651413348		2.0025962114		3.682701403
		0.0805				1.958785887		1.9968280431		3.6752974192
		0.081				1.9524843369		1.9911121988		3.6678166244
		0.0815				1.9462361052		1.9854480294		3.6602595485
		0.082				1.9400406202		1.979834896		3.6526267262
		0.0825				1.9338973176		1.9742721696		3.6449186967
		0.083				1.9278056404		1.968759231		3.6371360037
		0.0835				1.9217650391		1.9632954707		3.6292791954
		0.084				1.9157749712		1.9578802885		3.6213488241
		0.0845				1.9098349012		1.9525130937		3.6133454469
		0.085				1.9039443006		1.9471933042		3.6052696246
		0.0855				1.8981026476		1.9419203474		3.5971219227
		0.086				1.8923094274		1.9366936589		3.5889029103
		0.0865				1.8865641315		1.9315126833		3.5806131611
		0.087				1.8808662582		1.9263768735		3.5722532523
		0.0875				1.8752153118		1.9212856905		3.5638237652
		0.088				1.8696108035		1.9162386036		3.5553252851
		0.0885				1.8640522502		1.9112350902		3.5467584008
		0.089				1.8585391753		1.9062746352		3.538123705
		0.0895				1.853071108		1.9013567315		3.529421794
		0.09				1.8476475836		1.8964808793		3.5206532676
		0.0905				1.8422681433		1.8916465865		3.5118187293
		0.091				1.8369323338		1.886853368		3.5029187859
		0.0915				1.8316397079		1.8821007461		3.4939540475
		0.092				1.8263898236		1.87738825		3.4849251276
		0.0925				1.8211822447		1.8727154158		3.4758326429
		0.093				1.8160165404		1.8680817864		3.4666772134
		0.0935				1.8108922852		1.8634869114		3.4574594619
		0.094				1.8058090589		1.8589303469		3.4481800144
		0.0945				1.8007664466		1.8544116555		3.4388394999
		0.095				1.7957640382		1.849930406		3.4294385502
		0.0955				1.7908014292		1.8454861735		3.4199777999
		0.096				1.7858782197		1.8410785392		3.4104578863
		0.0965				1.7809940147		1.8367070903		3.4008794495
		0.097				1.7761484242		1.8323714198		3.391243132
		0.0975				1.7713410629		1.8280711267		3.3815495791
		0.098				1.7665715502		1.8238058154		3.3717994382
		0.0985				1.7618395102		1.8195750962		3.3619933594
		0.099				1.7571445715		1.8153785847		3.3521319949
		0.0995				1.7524863671		1.811215902		3.3422159992
		0.1				1.7478645347		1.8070866743		3.3322460289
		0.1005				1.7432787161		1.8029905334		3.3222227429
		0.101				1.7387285577		1.798927116		3.3121468019
		0.1015				1.7342137098		1.7948960639		3.3020188686
		0.102				1.7297338272		1.7908970237		3.2918396077
		0.1025				1.7252885686		1.7869296473		3.2816096855
		0.103				1.720877597		1.7829935909		3.2713297702
		0.1035				1.7165005792		1.7790885158		3.2610005315
		0.104				1.7121571861		1.7752140877		3.2506226408
		0.1045				1.7078470924		1.7713699771		3.2401967711
		0.105				1.7035699768		1.7675558589		3.2297235967
		0.1055				1.6993255216		1.7637714122		3.2192037932
		0.106				1.6951134131		1.7600163207		3.2086380377
		0.1065				1.6909333409		1.7562902724		3.1980270084
		0.107				1.6867849987		1.7525929593		3.1873713848
		0.1075				1.6826680834		1.7489240777		3.1766718472
		0.108				1.6785822956		1.7452833278		3.1659290771
		0.1085				1.6745273395		1.7416704141		3.1551437571
		0.109				1.6705029226		1.7380850448		3.1443165703
		0.1095				1.6665087557		1.734526932		3.1334482009
		0.11				1.6625445532		1.7309957916		3.1225393337
		0.1105				1.6586100327		1.7274913434		3.1115906541
		0.111				1.654704915		1.7240133107		3.1006028483
		0.1115				1.650828924		1.7205614206		3.0895766028
		0.112				1.6469817871		1.7171354037		3.0785126047
		0.1125				1.6431632346		1.7137349941		3.0674115413
		0.113				1.6393729998		1.7103599294		3.0562741003
		0.1135				1.6356108194		1.7070099506		3.0451009697
		0.114				1.6318764326		1.7036848021		3.0338928376
		0.1145				1.628169582		1.7003842314		3.0226503921
		0.115				1.6244900129		1.6971079896		3.0113743215
		0.1155				1.6208374735		1.6938558308		3.0000653141
		0.116				1.6172117149		1.6906275121		2.9887240578
		0.1165				1.613612491		1.687422794		2.9773512405
		0.117				1.6100395585		1.68424144		2.9659475499
		0.1175				1.6064926766		1.6810832164		2.9545136734
		0.118				1.6029716075		1.6779478926		2.9430502979
		0.1185				1.5994761159		1.6748352409		2.9315581098
		0.119				1.5960059691		1.6717450367		2.9200377953
		0.1195				1.5925609372		1.6686770577		2.9084900396
		0.12				1.5891407925		1.665631085		2.8969155276
		0.1205				1.5857453101		1.6626069019		2.8853149433
		0.121				1.5823742676		1.6596042948		2.8736889699
		0.1215				1.5790274448		1.6566230525		2.86203829
		0.122				1.5757046242		1.6536629667		2.8503635849
		0.1225				1.5724055905		1.6507238313		2.8386655352
		0.123				1.5691301309		1.6478054431		2.8269448205
		0.1235				1.5658780348		1.6449076012		2.8152021192
		0.124				1.5626490941		1.6420301072		2.8034381084
		0.1245				1.5594431027		1.6391727652		2.7916534642
		0.125				1.556259857		1.6363353817		2.7798488613
		0.1255				1.5530991554		1.6335177655		2.7680249731
		0.126				1.5499607986		1.6307197276		2.7561824715
		0.1265				1.5468445895		1.6279410816		2.7443220271
		0.127				1.5437503329		1.6251816431		2.7324443087
		0.1275				1.5406778361		1.62244123		2.7205499838
		0.128				1.537626908		1.6197196625		2.708639718
		0.1285				1.5345973599		1.6170167627		2.6967141753
		0.129				1.5315890049		1.6143323552		2.684774018
		0.1295				1.5286016584		1.6116662663		2.6728199064
		0.13				1.5256351374		1.6090183247		2.660852499
		0.1305				1.5226892611		1.6063883609		2.6488724524
		0.131				1.5197638505		1.6037762076		2.6368804211
0.1315				1.5168587285		1.6011816993		2.6248770577
		0.132				1.51397372		1.5986046725		2.6128630125
		0.1325				1.5111086516		1.5960449657		2.6008389337
		0.133				1.5082633517		1.5935024194		2.5888054673
		0.1335				1.5054376508		1.5909768756		2.576763257
		0.134				1.5026313808		1.5884681784		2.5647129443
		0.1345				1.4998443756		1.5859761739		2.552655168
		0.135				1.4970764707		1.5835007095		2.5405905647
		0.1355				1.4943275034		1.5810416348		2.5285197685
		0.136				1.4915973127		1.5785988009		2.516443411
		0.1365				1.4888857393		1.5761720608		2.504362121
		0.137				1.4861926253		1.573761269		2.4922765248
		0.1375				1.4835178149		1.5713662818		2.4801872461
		0.138				1.4808611535		1.568986957		2.4680949057
		0.1385				1.4782224882		1.5666231543		2.4560001216
		0.139				1.4756016679		1.5642747348		2.4439035091
		0.1395				1.4729985426		1.5619415611		2.4318056805
		0.14				1.4704129643		1.5596234976		2.4197072452
		0.1405				1.4678447862		1.55732041		2.4076088097
		0.141				1.4652938632		1.5550321657		2.3955109773
		0.1415				1.4627600516		1.5527586334		2.3834143484
		0.142				1.4602432091		1.5504996834		2.3713195202
		0.1425				1.4577431949		1.5482551876		2.3592270868
		0.143				1.4552598696		1.546025019		2.347137639
		0.1435				1.4527930954		1.5438090522		2.3350517644
		0.144				1.4503427355		1.5416071633		2.3229700474
		0.1445				1.4479086549		1.5394192295		2.310893069
		0.145				1.4454907196		1.5372451297		2.2988214068
		0.1455				1.4430887972		1.5350847438		2.2867556351
		0.146				1.4407027566		1.5329379532		2.2746963246
		0.1465				1.4383324679		1.5308046407		2.2626440426
		0.147				1.4359778024		1.5286846901		2.2505993529
		0.1475				1.433638633		1.5265779868		2.2385628156
		0.148				1.4313148337		1.5244844172		2.2265349875
		0.1485				1.4290062796		1.522403869		2.2145164215
		0.149				1.4267128473		1.5203362313		2.2025076668
		0.1495				1.4244344144		1.518281394		2.1905092692
		0.15				1.4221708599		1.5162392487		2.1785217703
		0.1505				1.4199220638		1.5142096878		2.1665457084
		0.151				1.4176879074		1.5121926049		2.1545816177
		0.1515				1.4154682732		1.5101878949		2.1426300286
		0.152				1.4132630448		1.5081954538		2.1306914678
		0.1525				1.4110721069		1.5062151785		2.1187664578
		0.153				1.4088953453		1.5042469673		2.1068555174
		0.1535				1.406732647		1.5022907193		2.0949591613
		0.154				1.4045839		1.500346335		2.0830779005
		0.1545				1.4024489937		1.4984137155		2.0712122415
		0.155				1.400327818		1.4964927634		2.0593626872
		0.1555				1.3982202644		1.4945833821		2.0475297361
		0.156				1.3961262252		1.4926854761		2.0357138829
		0.1565				1.3940455937		1.4907989507		2.0239156179
		0.157				1.3919782644		1.4889237124		2.0121354274
		0.1575				1.3899241326		1.4870596687		2.0003737934
		0.158				1.3878830948		1.485206728		1.9886311939
		0.1585				1.3858550484		1.4833647995		1.9769081025
		0.159				1.3838398917		1.4815337937		1.9652049886
		0.1595				1.3818375242		1.4797136216		1.9535223175
		0.16				1.379847846		1.4779041954		1.9418605498
		0.1605				1.3778707586		1.4761054282		1.9302201423
		0.161				1.375906164		1.4743172339		1.9186015471
		0.1615				1.3739539654		1.4725395273		1.9070052122
		0.162				1.3720140668		1.4707722241		1.8954315809
		0.1625				1.3700863731		1.4690152408		1.8838810925
		0.163				1.3681707903		1.4672684949		1.8723541817
		0.1635				1.3662672249		1.4655319046		1.8608512788
		0.164				1.3643755846		1.463805389		1.8493728096
		0.1645				1.3624957779		1.4620888679		1.8379191957
		0.165				1.360627714		1.4603822622		1.8264908539
		0.1655				1.3587713031		1.4586854932		1.8150881968
		0.166				1.3569264561		1.4569984833		1.8037116323
		0.1665				1.355093085		1.4553211555		1.7923615639
		0.167				1.3532711024		1.4536534337		1.7810383907
		0.1675				1.3514604216		1.4519952426		1.7697425071
		0.168				1.3496609569		1.4503465074		1.758474303
		0.1685				1.3478726234		1.4487071543		1.7472341637
		0.169				1.3460953369		1.4470771102		1.7360224702
		0.1695				1.344329014		1.4454563025		1.7248395985
		0.17				1.342573572		1.4438446596		1.7136859205
		0.1705				1.340828929		1.4422421104		1.7025618031
		0.171				1.339095004		1.4406485848		1.691467609
		0.1715				1.3373717164		1.4390640129		1.680403696
		0.172				1.3356589867		1.437488326		1.6693704174
		0.1725				1.3339567359		1.4359214557		1.658368122
		0.173				1.3322648858		1.4343633345		1.6473971537
		0.1735				1.3305833589		1.4328138954		1.6364578522
		0.174				1.3289120783		1.4312730722		1.6255505523
		0.1745				1.327250968		1.4297407992		1.6146755841
		0.175				1.3255999525		1.4282170114		1.6038332734
		0.1755				1.323958957		1.4267016444		1.5930239412
		0.176				1.3223279075		1.4251946345		1.5822479037
		0.1765				1.3207067306		1.4236959186		1.5715054728
		0.177				1.3190953535		1.4222054341		1.5607969556
		0.1775				1.3174937041		1.4207231191		1.5501226546
		0.178				1.3159017109		1.4192489123		1.5394828676
		0.1785				1.3143193031		1.4177827528		1.528877888
		0.179				1.3127464105		1.4163245806		1.5183080043
		0.1795				1.3111829636		1.4148743361		1.5077735006
		0.18				1.3096288933		1.4134319601		1.4972746564
		0.1805				1.3080841314		1.4119973943		1.4868117463
		0.181				1.30654861		1.4105705807		1.4763850406
		0.1815				1.3050222621		1.4091514619		1.465994805
		0.182				1.3035050211		1.4077399812		1.4556413004
		0.1825				1.3019968209		1.4063360821		1.4453247832
		0.183				1.3004975964		1.404939709		1.4350455054
		0.1835				1.2990072825		1.4035508065		1.4248037142
		0.184				1.2975258151		1.40216932		1.4145996522
		0.1845				1.2960531304		1.4007951952		1.4044335578
		0.185				1.2945891654		1.3994283784		1.3943056645
		0.1855				1.2931338575		1.3980688165		1.3842162013
		0.186				1.2916871445		1.3967164565		1.3741653928
		0.1865				1.2902489651		1.3953712464		1.3641534591
		0.187				1.2888192582		1.3940331343		1.3541806157
		0.1875				1.2873979634		1.3927020691		1.3442470737
		0.188				1.2859850208		1.3913779998		1.3343530395
		0.1885				1.2845803709		1.3900608761		1.3244987153
		0.189				1.2831839549		1.3887506482		1.3146842987
		0.1895				1.2817957144		1.3874472666		1.3049099829
		0.19				1.2804155915		1.3861506823		1.2951759567
		0.1905				1.2790435288		1.3848608469		1.2854824043
		0.191				1.2776794695		1.3835777121		1.2758295057
		0.1915				1.276323357		1.3823012305		1.2662174365
		0.192				1.2749751354		1.3810313547		1.2566463679
		0.1925				1.2736347494		1.379768038		1.2471164666
		0.193				1.2723021439		1.3785112339		1.2376278952
		0.1935				1.2709772643		1.3772608966		1.2281808118
		0.194				1.2696600567		1.3760169805		1.2187753703
		0.1945				1.2683504674		1.3747794404		1.2094117203
		0.195				1.2670484432		1.3735482316		1.200090007
		0.1955				1.2657539315		1.3723233099		1.1908103715
		0.196				1.2644668801		1.3711046311		1.1815729506
		0.1965				1.263187237		1.3698921519		1.1723778769
		0.197				1.2619149508		1.3686858291		1.1632252789
		0.1975				1.2606499708		1.3674856198		1.1541152808
		0.198				1.2593922462		1.3662914816		1.1450480026
		0.1985				1.258141727		1.3651033726		1.1360235603
		0.199				1.2568983635		1.3639212511		1.1270420658
		0.1995				1.2556621064		1.3627450759		1.1181036267
		0.2				1.2544329069		1.3615748058		1.1092083468
		0.2005				1.2532107164		1.3604104005		1.1003563257
		0.201				1.251995487		1.3592518197		1.091547659
		0.2015				1.2507871709		1.3580990235		1.0827824382
		0.202				1.2495857209		1.3569519724		1.0740607511
		0.2025				1.2483910901		1.3558106273		1.0653826813
		0.203				1.2472032319		1.3546749493		1.0567483085
		0.2035				1.2460221004		1.3535448999		1.0481577085
		0.204				1.2448476497		1.3524204409		1.0396109533
		0.2045
1.2436798344		1.3513015346		1.0311081109
		0.205				1.2425186096		1.3501881434		1.0226492456
		0.2055				1.2413639307		1.3490802301		1.0142344179
		0.206				1.2402157533		1.3479777579		1.0058636843
		0.2065				1.2390740336		1.3468806902		0.9975370977
		0.207				1.2379387281		1.3457889907		0.9892547074
		0.2075				1.2368097935		1.3447026236		0.9810165586
		0.208				1.235687187		1.3436215532		0.9728226933
		0.2085				1.2345708661		1.3425457443		0.9646731495
		0.209				1.2334607887		1.3414751617		0.9565679616
		0.2095				1.2323569129		1.3404097707		0.9485071606
		0.21				1.2312591972		1.339349537		0.9404907738
		0.2105				1.2301676006		1.3382944264		0.9325188248
		0.211				1.2290820821		1.337244405		0.924591334
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		0.213				1.2247999854		1.3330945446		0.8933262349
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		0.214				1.2226943688		1.3310492903		0.8779607061
		0.2145				1.221650282		1.3300339693		0.8703446989
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		0.2155				1.21957936		1.328017781		0.8552461641
		0.216				1.2185524492		1.3270168513		0.8477636131
		0.2165				1.2175311885		1.3260206566		0.8403255185
		0.217				1.2165155409		1.3250291663		0.8329318606
		0.2175				1.2155054696		1.32404235		0.8255826164
		0.218				1.214500938		1.3230601777		0.8182777599
		0.2185				1.21350191		1.3220826194		0.811017262
		0.219				1.2125083496		1.3211096455		0.8038010906
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		0.22				1.2105374892		1.3191773337		0.789501583
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		0.221				1.208588075		1.31726301		0.7753789199
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		0.222				1.2066598294		1.3153664459		0.761432737
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		0.227				1.1973267125		1.306142278		0.6943331154
		0.2275				1.1964208656		1.3052429316		0.6878627583
		0.228				1.1955198851		1.3043476755		0.681435661
		0.2285				1.1946237399		1.3034564842		0.6750517393
		0.229				1.1937323994		1.3025693326		0.6687109064
		0.2295				1.1928458328		1.3016861956		0.6624130731
		0.23				1.1919640101		1.3008070485		0.6561581477
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		0.231				1.1902144755		1.2990606253		0.6437766433
		0.2315				1.1893467043		1.2981933007		0.6376498695
		0.232				1.1884835579		1.2973298685		0.6315656144
		0.2325				1.187625007		1.2964703049		0.625523775
		0.233				1.1867710227		1.2956145863		0.6195242463
		0.2335				1.1859215762		1.2947626892		0.6135669209
		0.234				1.1850766391		1.2939145902		0.6076516895
		0.2345				1.1842361829		1.2930702663		0.6017784406
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		0.2355				1.1825686013		1.2913928518		0.5901574341
		0.236				1.1817414203		1.290559716		0.5844094433
		0.2365				1.1809186092		1.2897302645		0.5787029688
		0.237				1.1801001405		1.288904475		0.5730378892
		0.2375				1.1792859873		1.2880823255		0.567414081
		0.238				1.1784761227		1.287263794		0.561831419
		0.2385				1.17767052		1.2864488589		0.5562897762
		0.239				1.1768691528		1.2856374986		0.5507890237
		0.2395				1.1760719947		1.2848296916		0.5453290308
		0.24				1.1752790196		1.2840254167		0.5399096651
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		0.241				1.1737055153		1.282427379		0.5291922772
		0.2415				1.1729249347		1.2816335746		0.5238939817
		0.242				1.1721484348		1.2808432189		0.5186357668
		0.2425				1.1713759904		1.2800562914		0.513417492
		0.243				1.1706075765		1.2792727719		0.5082390149
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		0.244				1.1690827412		1.2777158765		0.4980008774
		0.2445				1.1683262709		1.2769424606		0.4929409248
		0.245				1.167573733		1.2761723731		0.4879201858
		0.2455				1.1668251035		1.2754055943		0.4829385108
		0.246				1.1660803586		1.2746421049		0.4779957488
		0.2465				1.1653394744		1.2738818855		0.4730917474
		0.247				1.1646024275		1.2731249172		0.4682263528
		0.2475				1.1638691945		1.2723711808		0.46339941
		0.248				1.1631397522		1.2716206576		0.4586107627
		0.2485				1.1624140776		1.2708733289		0.4538602534
		0.249				1.1616921477		1.2701291762		0.4491477233
		0.2495				1.1609739399		1.2693881809		0.4444730125
		0.25				1.1602594316		1.2686503249		0.4398359598
		0.2505				1.1595486004		1.2679155899		0.4352364031
		0.251				1.1588414242		1.2671839581		0.4306741789
		0.2515				1.1581378809		1.2664554114		0.4261491229
		0.252				1.1574379485		1.2657299322		0.4216610696
		0.2525				1.1567416053		1.2650075028		0.4172098526
		0.253				1.1560488297		1.2642881058		0.4127953043
		0.2535				1.1553596003		1.2635717237		0.4084172563
		0.254				1.1546738958		1.2628583394		0.4040755392
		0.2545				1.153991695		1.2621479357		0.3997699828
		0.255				1.153312977		1.2614404957		0.3955004159
		0.2555				1.152637721		1.2607360024		0.3912666664
		0.256				1.1519659062		1.2600344392		0.3870685615
		0.2565				1.151297512		1.2593357893		0.3829059274
		0.257				1.1506325182		1.2586400364		0.3787785899
		0.2575				1.1499709044		1.2579471641		0.3746863735
		0.258				1.1493126506		1.257257156		0.3706291025
		0.2585				1.1486577367		1.256569996		0.3666066001
		0.259				1.1480061429		1.2558856681		0.362618689
		0.2595				1.1473578496		1.2552041564		0.3586651914
		0.26				1.1467128371		1.254525445		0.3547459285
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		0.261				1.1454325773		1.2531763608		0.3470093895
		0.2615				1.1447972915		1.2525059568		0.3431917534
		0.262				1.1441652098		1.2518382912		0.3394076318
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		0.264				1.1416685473		1.2491947079		0.3246026564
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		0.265				1.1404389555		1.2478889545		0.3173965184
		0.2655				1.1398287805		1.2472400357		0.3138418946
		0.266				1.1392216621		1.2465937362		0.3103193222
		0.2665				1.1386175824		1.2459500416		0.3068286163
		0.267				1.1380165237		1.2453089374		0.3033695923
		0.2675				1.1374184683		1.2446704096		0.2999420648
		0.268				1.1368233988		1.244034444		0.2965458485
		0.2685				1.1362312978		1.2434010266		0.2931807576
		0.269				1.1356421481		1.2427701435		0.2898466062
		0.2695				1.1350559325		1.2421417809		0.2865432082
		0.27				1.1344726339		1.2415159249		0.2832703774
		0.2705				1.1338922355		1.2408925621		0.2800279274
		0.271				1.1333147205		1.2402716789		0.2768156715
		0.2715				1.1327400722		1.2396532618		0.2736334231
		0.272				1.1321682741		1.2390372975		0.2704809955
		0.2725				1.1315993096		1.2384237727		0.2673582017
		0.273				1.1310331625		1.2378126743		0.264264855
		0.2735				1.1304698166		1.2372039891		0.2612007683
		0.274				1.1299092556		1.2365977043		0.2581657547
		0.2745				1.1293514636		1.2359938069		0.2551596273
		0.275				1.1287964248		1.2353922841		0.2521821992
		0.2755				1.1282441232		1.2347931232		0.2492332833
		0.276				1.1276945433		1.2341963115		0.2463126931
		0.2765				1.1271476694		1.2336018365		0.2434202416
		0.277				1.126603486		1.2330096857		0.2405557421
		0.2775				1.1260619779