Tarea 3 (Pauta)

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a) Datos
									Portafolios posibles Corr 0,95													Portafolios posibles Corr 0,5													Portafolios posibles Corr 0													Portafolios posibles Corr -0,5													Portafolios posibles Corr -0,75													Portafolios posibles Corr -0,95
	Activo 1								w activo 1	w activo 2	Ret Esp	Desv Est		Activo 1								w activo 1	w activo 2	Ret Esp	Desv Est		Activo 1								w activo 1	w activo 2	Ret Esp	Desv Est		Activo 1								w activo 1	w activo 2	Ret Esp	Desv Est		Activo 1								w activo 1	w activo 2	Ret Esp	Desv Est		Activo 1								w activo 1	w activo 2	Ret Esp	Desv Est
	Retorno esperado		8.0%						1.50	-0.50	6.50%	9.0554%		Retorno esperado		8.0%						1.50	-0.50	6.50%	15.6205%		Retorno esperado		8.0%						1.50	-0.50	6.50%	20.5913%		Retorno esperado		8.0%						1.50	-0.50	6.50%	24.5764%		Retorno esperado		8.0%						1.50	-0.50	6.50%	26.3439%		Retorno esperado		8.0%						1.50	-0.50	6.50%	27.6767%
	Desviación estándar		12.0%						1.45	-0.45	6.65%	9.2855%		Desviación estándar		12.0%						1.45	-0.45	6.65%	15.0718%		Desviación estándar		12.0%						1.45	-0.45	6.65%	19.5898%		Desviación estándar		12.0%						1.45	-0.45	6.65%	23.2456%		Desviación estándar		12.0%						1.45	-0.45	6.65%	24.8729%		Desviación estándar		12.0%						1.45	-0.45	6.65%	26.1017%
									1.40	-0.40	6.80%	9.5331%										1.40	-0.40	6.80%	14.5547%										1.40	-0.40	6.80%	18.6075%										1.40	-0.40	6.80%	21.9235%										1.40	-0.40	6.80%	23.4060%										1.40	-0.40	6.80%	24.5275%
	Activo 2								1.35	-0.35	6.95%	9.7969%		Activo 2								1.35	-0.35	6.95%	14.0727%		Activo 2								1.35	-0.35	6.95%	17.6477%		Activo 2								1.35	-0.35	6.95%	20.6116%		Activo 2								1.35	-0.35	6.95%	21.9440%		Activo 2								1.35	-0.35	6.95%	22.9543%
	Retorno esperado		11.0%						1.30	-0.30	7.10%	10.0757%		Retorno esperado		11.0%						1.30	-0.30	7.10%	13.6294%		Retorno esperado		11.0%						1.30	-0.30	7.10%	16.7141%		Retorno esperado		11.0%						1.30	-0.30	7.10%	19.3122%		Retorno esperado		11.0%						1.30	-0.30	7.10%	20.4880%		Retorno esperado		11.0%						1.30	-0.30	7.10%	21.3822%
	Desviación estándar		20.0%						1.25	-0.25	7.25%	10.3682%		Desviación estándar		20.0%						1.25	-0.25	7.25%	13.2288%		Desviación estándar		20.0%						1.25	-0.25	7.25%	15.8114%		Desviación estándar		20.0%						1.25	-0.25	7.25%	18.0278%		Desviación estándar		20.0%						1.25	-0.25	7.25%	19.0394%		Desviación estándar		20.0%						1.25	-0.25	7.25%	19.8116%
									1.20	-0.20	7.40%	10.6733%										1.20	-0.20	7.40%	12.8748%										1.20	-0.20	7.40%	14.9452%										1.20	-0.20	7.40%	16.7619%										1.20	-0.20	7.40%	17.6000%										1.20	-0.20	7.40%	18.2428%
	Correlación 1 y 2		0.95						1.15	-0.15	7.55%	10.9900%		Correlación 1 y 2		0.5						1.15	-0.15	7.55%	12.5714%		Correlación 1 y 2		0						1.15	-0.15	7.55%	14.1223%		Correlación 1 y 2		-0.5						1.15	-0.15	7.55%	15.5190%		Correlación 1 y 2		-0.75						1.15	-0.15	7.55%	16.1722%		Correlación 1 y 2		-0.95						1.15	-0.15	7.55%	16.6763%
									1.10	-0.10	7.70%	11.3172%										1.10	-0.10	7.70%	12.3223%										1.10	-0.10	7.70%	13.3507%										1.10	-0.10	7.70%	14.3052%										1.10	-0.10	7.70%	14.7594%										1.10	-0.10	7.70%	15.1129%
									1.05	-0.05	7.85%	11.6542%										1.05	-0.05	7.85%	12.1310%										1.05	-0.05	7.85%	12.6396%										1.05	-0.05	7.85%	13.1286%										1.05	-0.05	7.85%	13.3664%										1.05	-0.05	7.85%	13.5536%
									1.00	0.00	8.00%	12.0000%										1.00	0.00	8.00%	12.0000%										1.00	0.00	8.00%	12.0000%										1.00	0.00	8.00%	12.0000%										1.00	0.00	8.00%	12.0000%										1.00	0.00	8.00%	12.0000%
									0.95	0.05	8.15%	12.3539%										0.95	0.05	8.15%	11.9315%										0.95	0.05	8.15%	11.4438%										0.95	0.05	8.15%	10.9343%										0.95	0.05	8.15%	10.6705%										0.95	0.05	8.15%	10.4547%
		Retornos Esperados			Matriz Varianza Covarianza				0.90	0.10	8.30%	12.7153%			Retornos Esperados			Matriz Varianza Covarianza				0.90	0.10	8.30%	11.9264%			Retornos Esperados			Matriz Varianza Covarianza				0.90	0.10	8.30%	10.9836%			Retornos Esperados			Matriz Varianza Covarianza				0.90	0.10	8.30%	9.9519%			Retornos Esperados			Matriz Varianza Covarianza				0.90	0.10	8.30%	9.3936%			Retornos Esperados			Matriz Varianza Covarianza				0.90	0.10	8.30%	8.9219%
					Activo 1	Activo 2			0.85	0.15	8.45%	13.0836%						Activo 1	Activo 2			0.85	0.15	8.45%	11.9850%						Activo 1	Activo 2			0.85	0.15	8.45%	10.6320%						Activo 1	Activo 2			0.85	0.15	8.45%	9.0796%						Activo 1	Activo 2			0.85	0.15	8.45%	8.1939%						Activo 1	Activo 2			0.85	0.15	8.45%	7.4095%
	Activo 1	0.08		Activo 1	0.0144	0.0228			0.80	0.20	8.60%	13.4581%		Activo 1	0.08		Activo 1	0.0144	0.012			0.80	0.20	8.60%	12.1062%		Activo 1	0.08		Activo 1	0.0144	0			0.80	0.20	8.60%	10.4000%		Activo 1	0.08		Activo 1	0.0144	-0.012			0.80	0.20	8.60%	8.3522%		Activo 1	0.08		Activo 1	0.0144	-0.018			0.80	0.20	8.60%	7.1106%		Activo 1	0.08		Activo 1	0.0144	-0.0228			0.80	0.20	8.60%	5.9330%
	Activo 2	0.11		Activo 2	0.0228	0.04			0.75	0.25	8.75%	13.8384%		Activo 2	0.11		Activo 2	0.012	0.04			0.75	0.25	8.75%	12.2882%		Activo 2	0.11		Activo 2	0	0.04			0.75	0.25	8.75%	10.2956%		Activo 2	0.11		Activo 2	-0.012	0.04			0.75	0.25	8.75%	7.8102%		Activo 2	0.11		Activo 2	-0.018	0.04			0.75	0.25	8.75%	6.2048%		Activo 2	0.11		Activo 2	-0.0228	0.04			0.75	0.25	8.75%	4.5277%
									0.70	0.30	8.90%	14.2239%										0.70	0.30	8.90%	12.5284%										0.70	0.30	8.90%	10.3228%										0.70	0.30	8.90%	7.4940%										0.70	0.30	8.90%	5.5642%										0.70	0.30	8.90%	3.2863%
									0.65	0.35	9.05%	14.6144%										0.65	0.35	9.05%	12.8234%										0.65	0.35	9.05%	10.4805%										0.65	0.35	9.05%	7.4324%										0.65	0.35	9.05%	5.2858%										0.65	0.35	9.05%	2.4698%
									0.60	0.40	9.20%	15.0093%										0.60	0.40	9.20%	13.1697%										0.60	0.40	9.20%	10.7629%										0.60	0.40	9.20%	7.6315%										0.60	0.40	9.20%	5.4259%										0.60	0.40	9.20%	2.5298%
									0.55	0.45	9.35%	15.4084%										0.55	0.45	9.35%	13.5632%										0.55	0.45	9.35%	11.1606%										0.55	0.45	9.35%	8.0722%										0.55	0.45	9.35%	5.9548%										0.55	0.45	9.35%	3.4205%
									0.50	0.50	9.50%	15.8114%										0.50	0.50	9.50%	14.0000%										0.50	0.50	9.50%	11.6619%										0.50	0.50	9.50%	8.7178%										0.50	0.50	9.50%	6.7823%										0.50	0.50	9.50%	4.6904%
	Portafolio minima var Corr 0,95			RESPUESTA: USANDO COMO FUNCIÓN DE UTILIDAD LAS PREFERENCIAS "CUADRATICAS " DEFINIDAS SOBRE LA MEDIA Y LA VARIANZA, LLEGAMOS A QUE LA CANTIDAD DEL ACTIVO A ESTA DADA POR LA FORMULA DEL CUADRO. CON ESTA FORMULA SE CALCULO LA CANTIDAD DE A QUE DEBERÍA TENER CADA PORTAFOLIO (CUADRO CON AMARILLO DE LA IZQUIERDA), LO CUAL HACE SENTIDO AL VER LOS GRÁFICOS.					0.45	0.55	9.65%	16.2179%										0.45	0.55	9.65%	14.4762%										0.45	0.55	9.65%	12.2540%										0.45	0.55	9.65%	9.5268%										0.45	0.55	9.65%	7.8141%										0.45	0.55	9.65%	6.1074%
	w activo 1	w activo 2							0.40	0.60	9.80%	16.6277%										0.40	0.60	9.80%	14.9880%										0.40	0.60	9.80%	12.9244%										0.40	0.60	9.80%	10.4614%										0.40	0.60	9.80%	8.9800%										0.40	0.60	9.80%	7.5895%
	1.9545454545	-0.9545454545							0.35	0.65	9.95%	17.0405%										0.35	0.65	9.95%	15.5319%										0.35	0.65	9.95%	13.6616%										0.35	0.65	9.95%	11.4909%										0.35	0.65	9.95%	10.2343%										0.35	0.65	9.95%	9.1049%
	En este caso el portafolio es 1,5 de w1 y -0,5 de w2, dada la restricción								0.30	0.70	10.10%	17.4562%										0.30	0.70	10.10%	16.1047%										0.30	0.70	10.10%	14.4554%										0.30	0.70	10.10%	12.5921%										0.30	0.70	10.10%	11.5482%										0.30	0.70	10.10%	10.6395%
									0.25	0.75	10.25%	17.8746%										0.25	0.75	10.25%	16.7033%										0.25	0.75	10.25%	15.2971%										0.25	0.75	10.25%	13.7477%										0.25	0.75	10.25%	12.9035%										0.25	0.75	10.25%	12.1861%
									0.20	0.80	10.40%	18.2954%										0.20	0.80	10.40%	17.3251%										0.20	0.80	10.40%	16.1790%										0.20	0.80	10.40%	14.9452%										0.20	0.80	10.40%	14.2885%0.20	0.80	10.40%	13.7405%
	Portafolio minima var Corr 0,5								0.15	0.85	10.55%	18.7184%										0.15	0.85	10.55%	17.9677%										0.15	0.85	10.55%	17.0950%										0.15	0.85	10.55%	16.1753%										0.15	0.85	10.55%	15.6952%										0.15	0.85	10.55%	15.3003%
	w activo 1	w activo 2							0.10	0.90	10.70%	19.1437%										0.10	0.90	10.70%	18.6290%										0.10	0.90	10.70%	18.0400%										0.10	0.90	10.70%	17.4310%										0.10	0.90	10.70%	17.1184%										0.10	0.90	10.70%	16.8642%
	0.9210526316	0.0789473684							0.05	0.95	10.85%	19.5709%										0.05	0.95	10.85%	19.3070%										0.05	0.95	10.85%	19.0095%										0.05	0.95	10.85%	18.7072%										0.05	0.95	10.85%	18.5542%										0.05	0.95	10.85%	18.4310%
									0.00	1.00	11.00%	20.0000%										0.00	1.00	11.00%	20.0000%										0.00	1.00	11.00%	20.0000%										0.00	1.00	11.00%	20.0000%										0.00	1.00	11.00%	20.0000%										0.00	1.00	11.00%	20.0000%
	Portafolio minima var Corr 0								-0.05	1.05	11.15%	20.4309%										-0.05	1.05	11.15%	20.7065%										-0.05	1.05	11.15%	21.0086%										-0.05	1.05	11.15%	21.3063%										-0.05	1.05	11.15%	21.4537%										-0.05	1.05	11.15%	21.5708%
	w activo 1	w activo 2							-0.10	1.10	11.30%	20.8634%										-0.10	1.10	11.30%	21.4252%										-0.10	1.10	11.30%	22.0327%										-0.10	1.10	11.30%	22.6239%										-0.10	1.10	11.30%	22.9138%										-0.10	1.10	11.30%	23.1430%
	0.7352941176	0.2647058824							-0.15	1.15	11.45%	21.2974%										-0.15	1.15	11.45%	22.1549%										-0.15	1.15	11.45%	23.0703%										-0.15	1.15	11.45%	23.9508%										-0.15	1.15	11.45%	24.3791%										-0.15	1.15	11.45%	24.7164%
									-0.20	1.20	11.60%	21.7329%										-0.20	1.20	11.60%	22.8945%										-0.20	1.20	11.60%	24.1197%										-0.20	1.20	11.60%	25.2856%										-0.20	1.20	11.60%	25.8488%										-0.20	1.20	11.60%	26.2907%
	Portafolio minima var Corr -0,5								-0.25	1.25	11.75%	22.1698%										-0.25	1.25	11.75%	23.6432%										-0.25	1.25	11.75%	25.1794%										-0.25	1.25	11.75%	26.6271%										-0.25	1.25	11.75%	27.3222%										-0.25	1.25	11.75%	27.8657%
	w activo 1	w activo 2							-0.30	1.30	11.90%	22.6080%										-0.30	1.30	11.90%	24.4000%										-0.30	1.30	11.90%	26.2480%										-0.30	1.30	11.90%	27.9743%										-0.30	1.30	11.90%	28.7986%										-0.30	1.30	11.90%	29.4415%
	0.6632653061	0.3367346939							-0.35	1.35	12.05%	23.0473%										-0.35	1.35	12.05%	25.1643%										-0.35	1.35	12.05%	27.3247%										-0.35	1.35	12.05%	29.3264%										-0.35	1.35	12.05%	30.2777%										-0.35	1.35	12.05%	31.0177%
									-0.40	1.40	12.20%	23.4879%										-0.40	1.40	12.20%	25.9353%										-0.40	1.40	12.20%	28.4084%										-0.40	1.40	12.20%	30.6829%										-0.40	1.40	12.20%	31.7591%										-0.40	1.40	12.20%	32.5945%
	Portafolio minima var Corr -0,75								-0.45	1.45	12.35%	23.9295%										-0.45	1.45	12.35%	26.7125%										-0.45	1.45	12.35%	29.4985%										-0.45	1.45	12.35%	32.0431%										-0.45	1.45	12.35%	33.2424%										-0.45	1.45	12.35%	34.1716%
	w activo 1	w activo 2							-0.50	1.50	12.50%	24.3721%										-0.50	1.50	12.50%	27.4955%										-0.50	1.50	12.50%	30.5941%										-0.50	1.50	12.50%	33.4066%										-0.50	1.50	12.50%	34.7275%										-0.50	1.50	12.50%	35.7491%
	0.6415929204	0.3584070796
	Portafolio minima var Corr -0,95
	w activo 1	w activo 2
	0.628	0.372
a) Gráficos
Correlaciones mayores o iguales a 0
Portafolios posibles Corr 0,95	9.0553851381374173E-2	9.2854725243252959E-2	9.5331002302503881E-2	9.7969382972436847E-2	0.10075713374247998	0.1036822067666386	0.10673331251301069	0.10989995450408523	0.11317243480636086	0.11654183798104438	0.12	0.12353946737783841	0.12715345060201866	0.13083577492413917	0.13458083073008578	0.13838352503098048	0.14223923509355646	0.14614376483449448	0.15009330431434983	0.15408439246075517	0.15811388300841905	0.16217891354920352	0.1662768775266123	0.17040539897550205	0.17456230979223436	0.17874562931719479	0.18295354601646838	0.18718440105949	0.19143667360252584	0.195	70896760240705	0.2	0.20430859012777708	0.20863365021012312	0.21297417683841391	0.21732924331529802	0.22169799277395366	0.22607963198837711	0.23047342580002586	0.23487869209445117	0.23929479726897537	0.24372115213907886	6.5000000000000002E-2	6.6500000000000004E-2	6.8000000000000005E-2	6.9500000000000006E-2	7.1000000000000008E-2	7.2500000000000009E-2	7.400000000000001E-2	7.5500000000000012E-2	7.6999999999999999E-2	7.85E-2	0.08	8.1500000000000003E-2	8.3000000000000004E-2	8.4500000000000006E-2	8.5999999999999993E-2	8.7499999999999994E-2	8.9000000000000024E-2	9.0500000000000025E-2	9.2000000000000026E-2	9.3500000000000028E-2	9.5000000000000029E-2	9.650000000000003E-2	9.8000000000000032E-2	9.9500000000000033E-2	0.10100000000000001	0.10250000000000001	0.10400000000000001	0.1055	0.10700000000000001	0.1085	0.11	0.1115	0.11299999999999999	0.1145	0.11600000000000001	0.11750000000000001	0.11900000000000002	0.12050000000000002	0.12	2	0.1235	0.125	Portafolios posibles Corr 0,5	0.15620499351813311	0.15071828024496564	0.145547243189282	0.14072668545801825	0.13629380029920657	0.13228756555322954	0.12874781551544864	0.12571396103854177	0.1232233744059949	0.121309521472966	0.12	0.11931470990619723	0.11926441212700459	0.11984990613262908	0.12106196760337244	0.12288205727444508	0.12528367810692667	0.12823416081528363	0.13169662106523469	0.13563185466548786	0.1400000000000001	0.14476187343358066	0.14987995196156167	0.15531902652283153	0.16104657711357917	0.1670	3293088490068	0.17325126262166174	0.17967748885155313	0.18629009635512031	0.19306993551560536	0.2	0.2070652071208488	0.21425218785347327	0.22154909162531	0.22894540834006699	0.23643180835073782	0.24400000000000005	0.25164260370612929	0.25935304123915726	0.26712543869875066	0.27495454169735045	6.5000000000000002E-2	6.6500000000000004E-2	6.8000000000000005E-2	6.9500000000000006E-2	7.1000000000000008E-2	7.2500000000000009E-2	7.400000000000001E-2	7.5500000000000012E-2	7.6999999999999999E-2	7.85E-2	0.08	8.1500000000000003E-2	8.3000000000000004E-2	8.4500000000000006E-2	8.5999999999999993E-2	8.7499999999999994E-2	8.9000000000000024E-2	9.0500000000000025E-2	9.2000000000000026E-2	9.3500000000000028E-2	9.5000000000000029E-2	9.650000000000003E-2	9.8000000000000032E-2	9.9500000000000033E-2	0.10100000000000001	0.10250000000000001	0.10400000000000001	0.1055	0.10700000000000001	0.1085	0.11	0.1115	0.11299999999999999	0.1145	0.11600000000000001	0.11750000000000001	0.11900000000000002	0.12050000000000002	0.122	0.1235	0.125	Portafolios posibles Corr 0	0.20591260281974	0.19589793260777408	0.18607525359380811	0.17647662734764624	0.16714065932620945	0.15811388300841897	0.14945233353815524	0.14122322755127781	0.13350655414622911	0.12639620247459968	0.12	0.11443775600735973	0.10983624174196784	0.1063202708800161	0.104	0.10295630140987	0.10322790320451154	0.10480458005259127	0.10762899237658975	0.11160645142642973	0.11661903789690613	0.12253978945632324	0.12924395537122824	0.13661625086350471	0.14455448799674123	0.15297058540778358	0.16178998732925351	0.17095028517086483	0.18039955654047493	0.19009471323527125	0.2	0.21008569680013919	0.22032702966272658	0.23070327262524909	0.24119701490690137	0.25179356624028343	0.26248047546436676	0.27324714088165686	0.2840844944730353	0.29498474536829866	0.30594117081556715	6.5000000000000002E-2	6.6500000000000004E-2	6.8000000000000005E-2	6.9500000000000006E-2	7.1000000000000008E-2	7.2500000000000009E-2	7.400000000000001E-2	7.5500000000000012E-2	7.6999999999999999E-2	7.85E-2	0.08	8.1500000000000003E-2	8.3000000000000004E-2	8.4500000000000006E-2	8.5999999999999993E-2	8.7499999999999994E-2	8.9000000000000024E-2	9.0500000000000025E-2	9.2000000000000026E-2	9.3500000000000028E-2	9.5000000000000029E-2	9.650000000000003E-2	9.8000000000000032E-2	9.9500000000000033E-2	0.10100000000000001	0.10250000000000001	0.10400000000000001	0.1055	0.10700000000000001	0.1085	0.11	0.1115	0.11299999999999999	0.1145	0.11600000000000001	0.11750000000000001	0.11900000000000002	0.120500000000000020.122	0.1235	0.125	Desviación estandar Portafolio
Rentabilidad Esperada
Correlaciones menores o iguales a 0
Portafolios posibles Corr 0	0.20591260281974	0.19589793260777408	0.18607525359380811	0.17647662734764624	0.16714065932620945	0.15811388300841897	0.14945233353815524	0.14122322755127781	0.13350655414622911	0.12639620247459968	0.12	0.11443775600735973	0.10983624174196784	0.1063202708800161	0.104	0.10295630140987	0.10322790320451154	0.10480458005259127	0.10762899237658975	0.11160645142642973	0.11661903789690613	0.12253978945632324	0.12924395537122824	0.13661625086350471	0.14455448799674123	0.15297058540778358	0.16178998732925351	0.17095028517086483	0.18039	955654047493	0.19009471323527125	0.2	0.21008569680013919	0.22032702966272658	0.23070327262524909	0.24119701490690137	0.25179356624028343	0.26248047546436676	0.27324714088165686	0.2840844944730353	0.29498474536829866	0.30594117081556715	6.5000000000000002E-2	6.6500000000000004E-2	6.8000000000000005E-2	6.9500000000000006E-2	7.1000000000000008E-2	7.2500000000000009E-2	7.400000000000001E-2	7.5500000000000012E-2	7.6999999999999999E-2	7.85E-2	0.08	8.1500000000000003E-2	8.3000000000000004E-2	8.4500000000000006E-2	8.5999999999999993E-2	8.7499999999999994E-2	8.9000000000000024E-2	9.0500000000000025E-2	9.2000000000000026E-2	9.3500000000000028E-2	9.5000000000000029E-2	9.650000000000003E-2	9.8000000000000032E-2	9.9500000000000033E-2	0.10100000000000001	0.10250000000000001	0.10400000000000001	0.1055	0.10700000000000001	0.1085	0.11	0.1115	0.11299999999999999	0.1145	0.1160	0000000000001	0.11750000000000001	0.11900000000000002	0.12050000000000002	0.122	0.1235	0.125	Portafolios posibles Corr -0,5	0.24576411454889016	0.23245644753372618	0.21923503369671551	0.20611647192788843	0.19312172327317298	0.18027756377319945	0.1676186147180557	0.15519020587653073	0.14305243793798134	0.13128594745821048	0.12	0.10934349546269316	9.9518842436997823E-2	9.0796475702529328E-2	8.3522452071284406E-2	7.8102496759066553E-2	7.493997598078074E-2	7.432361670424821E-2	7.6315136113355733E-2	8.0721744282442373E-2	8.7177978870813633E-2	9.52680429	10516604E-2	0.10461357464497636	0.11490865937778603	0.12592060990957757	0.13747727084867523	0.14945233353815526	0.161752897964766	0.17431006855600745	0.1870721785835617	0.2	0.21306337085477647	0.22623881187806835	0.23950782868207043	0.25285569006846575	0.26627053911388698	0.27974273895849378	0.29326438583639852	0.30682894257224169	0.32043095980257591	0.33406586176980135	6.5000000000000002E-2	6.6500000000000004E-2	6.8000000000000005E-2	6.9500000000000006E-2	7.1000000000000008E-2	7.2500000000000009E-2	7.400000000000001E-2	7.5500000000000012E-2	7.6999999999999999E-2	7.85E-2	0.08	8.1500000000000003E-2	8.3000000000000004E-2	8.4500000000000006E-2	8.5999999999999993E-2	8.7499999999999994E-2	8.9000000000000024E-2	9.05000	00000000025E-2	9.2000000000000026E-2	9.3500000000000028E-2	9.5000000000000029E-2	9.650000000000003E-2	9.8000000000000032E-2	9.9500000000000033E-2	0.10100000000000001	0.10250000000000001	0.10400000000000001	0.1055	0.10700000000000001	0.1085	0.11	0.1115	0.11299999999999999	0.1145	0.11600000000000001	0.11750000000000001	0.11900000000000002	0.12050000000000002	0.122	0.1235	0.125	Portafolios posibles Corr -0,75	0.26343879744638982	0.24872876793808951	0.23405982141324466	0.21944019686465835	0.20488045294756649	0.19039432764659769	0.17599999999999999	0.16172198366332263	0.14759403781996078	0.1336637572418192	8	0.12	0.10670520137275406	9.3936148526539032E-2	8.193900170248597E-2	7.1105555338524723E-2	6.2048368229954284E-2	5.5641710972974122E-2	5.2858301145610041E-2	5.425863986500222E-2	5.9548299723837753E-2	6.782329983125289E-2	7.814089838234542E-2	8.9799777282574822E-2	0.10234256201600611	0.11548160026601641	0.1290348790056394	0.14288456879593403	0.15695222202950807	0.17118411141224529	0.18554244797350283	0.2	0.21453671014537351	0.22913751329714652	0.24379089400549811	0.2584879107424562	0.27322152184628501	0.28798611077619701	0.30277714576896325	0.31759093186046733	0.33242442750195117	0.34727510708370679	6.5000000000000002E-2	6.6500000000000004E-2	6.8000000000000005E-2	6.9500000000000006E-2	7.1000000000000008E-2	7.2500000000000009E-2	7.400000000000001E-2	7.5500000000000012E-2	7.6999999999999999E-2	7.85E-2	0.08	8.1500000000000003E-2	8.3000000000000004E-2	8.4500000000000006E-2	8.5999999999999993E-2	8.7499999999999994E-2	8.9000000000000024E-2	9.0500000000000025E-2	9.2000000000000026E-2	9.3500000000000028E-2	9.5000000000000029E-2	9.650000000000003E-2	9.8000000000000032E-2	9.9500000000000033E-2	0.10100000000000001	0.10250000000000001	0.10400000000000001	0.1055	0.10700000000000001	0.1085	0.11	0.1115	0.11299999999999999	0.1145	0.11600000000000001	0.11750000000000001	0.11900000000000002	0.12050000000000002	0.122	0.1235	0.125	Portafolios posibles Corr -0,95	0.27676705006196095	0.26101724080987448	0.24527535546809423	0.22954302428956541	0.21382235617446557	0.1981161275615895	0.18242806801586206	0.16676330531624753	0.15112908389850052	0.13553597308463905	0.12	0.10454664030948099	8.9218832092781863E-2	7.4094534211370799E-2	5.9329587896765318E-2	4.5276925690687087E-2	3.2863353450309739E-2	2.4698178070456874E-2	2.5298221281347167E-2	3.4205262752974364E-2	4.6904157598234596E-2	6.1073725938410164E-2	7.5894663844041407E-2	9.1049437120720625E-2	0.1063954886261631	0.12186057606953943	0.13740451229854136	0.15300326793895613	0.16864163187066239	0.18430952227163958	0.2	0.2157081361469706	0.23143033509028152	0.24716391322359338	0.26290682760247974	0.2786574958618	5551	0.2944146735473625	0.31017736861350803	0.32594478059941384	0.34171625656383403	0.35749125863438957	6.5000000000000002E-2	6.6500000000000004E-2	6.8000000000000005E-2	6.9500000000000006E-2	7.1000000000000008E-2	7.2500000000000009E-2	7.400000000000001E-2	7.5500000000000012E-2	7.6999999999999999E-2	7.85E-2	0.08	8.1500000000000003E-2	8.3000000000000004E-2	8.4500000000000006E-2	8.5999999999999993E-2	8.7499999999999994E-2	8.9000000000000024E-2	9.0500000000000025E-2	9.2000000000000026E-2	9.3500000000000028E-2	9.5000000000000029E-2	9.650000000000003E-2	9.8000000000000032E-2	9.9500000000000033E-2	0.10100000000000001	0.10250000000000001	0.10400000000000001	0.1055	0.10700000000000001	0.1085	0.11	0.1115	0.11299999999999999	0.1145	0.11600000000000001	0.11750000000000001	0.11900000000000002	0.12050000000000002	0.122	0.1235	0.125	Desviación estandar Portafolio
 Rentabilidad Esperada
b)
	Activo C				Portafolio minima var Corr 0
	Retorno esperado		7.0%		w activo A	w activo B	Retorno esp.	Desv. Est.
	Desviación estándar		10.0%		0.7352941176	0.2647058824	0.0879411765	0.1028991511
	Correlación A		-0.6
	Correlación B		0.7		Portafolio equal Weight
					w activo A	w activo B	Retorno esp.	Desv. Est.
					0.5	0.5	0.095	0.1166190379
	Activo A
	Retorno esperado		8.0%
	Desviación estándar		12.0%
	Activo C
	Retorno esperado		11.0%
	Desviación estándar		20.0%
	Correlación A y B		0
	Para calcular el riesgo relativo es necesario escribir la covariaza del activo C con el portafolio, en terminos de A,B y C. Basicamente usaremos la siguiente formula:
	Además sabemos que la Covarianza se puede escribir como la multiplicación de las varianzas por la correlación.
	Riesgo relativo caso portafolio de mínima varianza
	-0.15
	Riesgo relativo caso portafolio equal weight
	0.25
c)
	Activo C				Matriz de covarianzas
	Retorno esperado		7.0%			A	B	C
	Desviación estándar		10.0%		A	0.0144	0	-0.0072
	Correlación A		-0.6		B	0	0.04	0.014
	Correlación B		0.7		C	-0.0072	0.014	0.01
	Activo A				Para calcular el portafolio de mínima varianza utilizaremos la siguiente formula, y luego resolveremos con solver
	Retorno esperado		8.0%
	Desviación estándar		12.0%
	Activo B
	Retorno esperado		11.0%
	Desviación estándar		20.0%
	Correlación 1 y 2		0
						Restricción de retorno
	Portafolio de mínima varianza					0.064667046	>=	5%
	Wa	Wb	Wc
	0.463858849	-0.2492885633	0.7854297143			Restricción ponderadores
						1.00	=	1
	Ra	Rb	Rc
	8.0%	11.0%	7.0%			Desviación Estandar
						0.0320073981
c) Gráficos
	Para graficar, buscaremospuntos con solver. Supondremos que la restricción de ventas cortas solo se utiliza para la letra a)
	Activo C				Matriz de covarianzas
	Retorno esperado		7.0%			A	B	C
	Desviación estándar		10.0%		A	0.0144	0	-0.0072
	Correlación A		-0.6		B	0	0.04	0.014
	Correlación B		0.7		C	-0.0072	0.014	0.01
	Activo A				Para calcular el portafolio de mínima varianza utilizaremos la siguiente formula, y luego resolveremos con solver
	Retorno esperado		8.0%
	Desviación estándar		12.0%
	Activo B
	Retorno esperado		11.0%
	Desviación estándar		20.0%
	Correlación 1 y 2		0
						Restricción de retorno
	Portafolio de mínima varianza					0.0879412643	>=	0.05
	Wa	Wb	Wc
	0.7352948504	0.2647061479	0
						1.00	=	1
	Ra	Rb	Rc
	8.0%	11.0%	7.0%			Desviación Estandar
						0.1028992538
	Portafolio de mínima varianza
	Wa	Wb	Wc	Desviación Estandar	E(Rp)
	0.3972780235	-1.3493195059	1.9520414824	0.1681865458	0.02
	0.4121840897	-1.1030460224	1.6908619327	0.1320843423	0.03
	0.427090091	-0.8567725224	1.4296824312	0.0966369021	0.04
	0.4419960935	-0.6104990272	1.1685029342	0.0629600378	0.05
	0.453920933	-0.4134802341	0.9595593011	0.0403960947	0.058
	0.463858849	-0.2492885633	0.7854297143	0.0320073981	0.064667046
	0.4718081706	-0.1179520433	0.6461438714	0.0375911076	0.07
	0.4792612009	0.0051847271	0.5155540693	0.0498338163	0.075
	0.4941672153	0.2514581428	0.2543746544	0.0816926343	0.085
	0.5016202384	0.3745949135	0.1237848623	0.0989628621	0.09
	0.5090731992	0.4977316811	-0.0068048604	0.1166054195	0.095
	0.5165262218	0.6208684248	-0.1373946316	0.1344738408	0.1
	0.5239792683	0.7440051632	-0.2679844156	0.1524887486	0.105
	0.5299416738	0.8425145536	-0.3724562068	0.166974298	0.109
	Portafolio de mínima varianza con A=0
	Wa	Wb	Wc	Desviación Estandar	E(Rp)
	0	-1.25	2.25	0.1854049622	0.02
	0	-0.625001375	1.625001375	0.1165923531	0.045
	0	-0.375	1.375	0.1004676565	0.055
	0	-0.1249767631	1.1249777631	0.0966634735	0.065
	0	0.0249999785	0.9750000338	0.1010630994	0.071
	0	0.0749999777	0.925000035	0.1035555407	0.073
	0	0.1249999746	0.8750000399	0.1065070418	0.075
	0	0.2499999769	0.7500000364	0.1156503344	0.08
	0	0.3749999816	0.6250000289	0.1268611437	0.085
	0	0.5	0.5	0.1396423996	0.09
	0	0.625	0.375	0.1536025716	0.095
	0	0.7499983734	0.2500025561	0.1684486791	0.1
	0	0.875	0.125	0.1839667089	0.105
	Portafolio de mínima varianza con B=0
	Wa	Wb	Wc	Desviación Estandar	E(Rp)
	-0.7	0	1.7	0.2304170133	0.063
	-0.3	0	1.3	0.1543113735	0.067
	0.4432994124	0	0.5567015876	0.0487366647	0.071
	0.6999930716	0	0.3000079182	0.0702271881	0.077
	0.8999930768	0	0.1000079122	0.2137770631	0.085
	Portafolio de mínima varianza con C=0
	Wa	Wb	Wc	Desviación Estandar	E(Rp)
	1.4	-0.4	0	0.1860752536	0.068
	1.1666666667	-0.1666666667	0	0.1439135543	0.075
	1.0000036425	-0.0000026425	0	0.12	0.08
	0.7352941176	0.2647058824	0	0.1028991511	0.0879412643
	0.4999999378	0.5000000452	0	0.1166190418	0.095
	0.1666665755	0.8333333996	0	0.1678623894	0.105
Frontera de minima varianza
Mínima varianza 3 activos	0.1681865458207088	0.13208434234317137	9.6636902128908117E-2	6.2960037806463892E-2	4.0396094711820971E-2	3.2007398120336129E-2	3.7591107628185669E-2	4.9833816252609256E-2	8.1692634290133251E-2	9.896286208844858E-2	0.11660541952740988	0.13447384080888414	0.15248874857852726	0.16697429799325217	0.02	0.03	0.04	0.05	5.8000000000000003E-2	6.4667045956546293E-2	7.0000000000000007E-2	7.4999999999999997E-2	8.5000000000000006E-2	0.09	9.5000000000000001E-2	0.1	0.105	0.109	A=0	0.18540496217741806	0.11659235314777457	0.10046765648707515	9.6663473475750147E-2	0.10106309936130996	0.10355554070405652	0.10650704184190733	0.11565033441918181	0.12686114374159529	0.13964239956673716	0.15360257159305568	0.16844867905637584	0.18396670894485212	0.02	4.4999999999999998E-2	5.5E-2	6.5000000000000002E-2	7.0999999999999994E-2	7.2999999999999995E-2	7.4999999999999997E-2	0.08	8.5000000000000006E-2	0.09	9.5000000000000001E-2	0.1	0.105	B=	0	0.23041701326018951	0.15431137352739804	4.8736664663029637E-2	7.022718811061332E-2	0.21377706309778	6.3E-2	6.7000000000000004E-2	7.0999999999999994E-2	7.6999999999999999E-2	8.5000000000000006E-2	C=0	0.18607525359366064	0.14391355429947814	0.12	0.102899151	085505	0.11661904181165808	0.1678623893518402	6.8000000000000005E-2	7.4999999999999997E-2	0.08	8.7941264296878013E-2	9.5000000000000001E-2	0.105	Desviación Estándar
E(Rp)
d)
	Activo C				Matriz de covarianzas
	Retorno esperado		7.0%			A	B	C
	Desviación estándar		10.0%		A	0.0144	0	-0.0072
	Correlación A		-0.6		B	0	0.04	0.014
	Correlación B		0.7		C	-0.0072	0.014	0.01
	Activo A				Para calcular el portafolio de mínima varianza utilizaremos la siguiente formula, y luego resolveremos con solver
	Retorno esperado		8.0%
	Desviación estándar		12.0%
	Activo B
	Retorno esperado		11.0%
	Desviación estándar		20.0%
	Correlación 1 y 2		0
						Restricción de retorno
	Portafolio de mínima varianza					0.1100000229	>=	11%
	Wa	Wb	Wc
	0.5314325821	0.8671409738	-0.398572726
						1.00	=	1
	Ra	Rb	Rc
	8.0%	11.0%	7.0%			Desviación Estandar
						0.1706036398
	Usando solver para el caso de a y b, llegamos a las siguientes respuestas:
	Desviación portafolio eficiente con retorno igual al del activo A (8%):					0.0650917884
	Por lo tanto la diferencia seria de:			0.0549082116
	Desviación portafolio eficiente con retorno igual al del activo B (11%):					0.1706036398
	Por lo tanto la diferencia seria de:			0.0293963602
e)
	Activo D				Portafolio minima var Corr 0
	Retorno esperado		5.0%		w activo A	w activo B	Retorno esp.	Desv. Est.
	Desviación estándar		10.0%		0.7352941176	0.2647058824	0.0879411765	0.1028991511
	Correlación A		0.5
	Correlación B		-0.5		Portafolio equal Weight
					w activo A	w activo B	Retorno esp.	Desv. Est.
					0.5	0.5	0.095	0.1166190379
	Activo A
	Retorno esperado		8.0%
	Desviación estándar		12.0%
	Activo C
	Retorno esperado		11.0%
	Desviación estándar		20.0%
	Correlación A y B		0
	Para calcular el riesgo relativo es necesario escribir la covariaza del activo D con el portafolio, en terminos de A,B y D. Basicamente usaremos la siguiente formula:
	Además sabemos que la Covarianza se puede escribir como la multiplicación de las varianzas por la correlación.
	Riesgo relativo caso portafolio de mínima varianza
	0.1666666667
	Riesgo relativo caso portafolio equal weight
	-0.1470588235
f)
	Activo C				Matriz de covarianzas
	Retorno esperado		7.0%			A	B	C	D
	Desviación estándar		10.0%		A	0.0144	0	-0.0072	0.006
	Correlación A		-0.6		B	0	0.04	0.014	-0.01
	Correlación B		0.7		C	-0.0072	0.014	0.01	-0.004
					D	0.006	-0.01	-0.004	0.01
	Activo A				Para calcular el portafolio de mínima varianza utilizaremos la siguiente formula, y luego resolveremos con solver
	Retorno esperado		8.0%
	Desviación estándar		12.0%
	Activo B
	Retorno esperado		11.0%
	Desviación estándar		20.0%
	Correlación A y B		0
						Restricción de retorno
	Activo D					0.0673625351	>=	5%
	Retorno esperado		5.0%
	Desviación estándar		10.0%
	Correlación A		0.5			1.00	=	1
	Correlación B		-0.5
	Correlacion C		-0.4			Desviación Estandar		0.0204788892
	Portafolio de mínima varianza
	Wa	Wb	Wc	Wd
	0.8713886538	-0.5563839902	1.2301957453	-0.545200409
	Ra	Rb	Rc	Rd
	8.0%	11.0%	7.0%	5.0%
f) Gráficos
	Activo C				Matriz de covarianzas
	Retorno esperado		7.0%			A	B	C	D
	Desviación estándar		10.0%		A	0.0144	0	-0.0072	0.006
	Correlación A		-0.6		B	0	0.04	0.014	-0.01
	Correlación B		0.7		C	-0.0072	0.014	0.01	-0.004
					D	0.006	-0.01	-0.004	0.01
	Activo A				Para calcular el portafolio de mínima varianza utilizaremos la siguiente formula, y luego resolveremos con solver
	Retorno esperado		8.0%
	Desviación estándar		12.0%
	Activo B
	Retorno esperado		11.0%
	Desviación estándar		20.0%
	Correlación A y B		0
						Restricción de retorno
	Activo D					0.0199999974	>=	2%
	Retorno esperado		5.0%
	Desviación estándar		10.0%
	Correlación A		0.5			1.00	=	1
	Correlación B		-0.5
	Correlacion C		-0.4			Desviación Estandar		0.1635570402
	Portafolio de mínima varianza
	Wa	Wb	Wc	Wd
	-0.1985558246	-0.7978341195	1.1913359655	0.8050539786
	Ra	Rb	Rc	Rd
	8.0%	11.0%	7.0%5.0%
	Portafolio de mínima varianza A,B,C y D
	Wa	Wb	Wc	Wd	Desviación Estandar	E(Rp)
	-0.1985558246	-0.7978341195	1.1913359655	0.8050539786	0.1635570402	0.02
	0.4791599369	-0.6448967108	1.2159502268	-0.0502134529	0.06291257	0.05
	0.5921125164	-0.6194071211	1.2200525805	-0.1927579759	0.0470465655	0.055
	0.7050652275	-0.5939176287	1.2241550456	-0.3353026444	0.0324912786	0.06
	0.8713886538	-0.5563839902	1.2301957453	-0.545200409	0.0204788892	0.0673625351
	0.9309703556	-0.5429383951	1.2323596841	-0.6203916447	0.0223839075	0.07
	1.0439229192	-0.5174488028	1.2364620299	-0.7629361463	0.0332278717	0.075
	1.1568755041	-0.4919592138	1.2405643855	-0.9054806759	0.0478963436	0.08
	1.2698281494	-0.4664696649	1.2446667787	-1.0480252632	0.063803951	0.085
	1.8345911662	-0.3390217827	1.2651786217	-1.7607480052	0.1475096871	0.11
Frontera de minima varianza
A, B y C	0.1681865458207088	0.13208434234317137	9.6636902128908117E-2	6.2960037806463892E-2	4.0396094711820971E-2	3.2007398120336129E-2	3.7591107628185669E-2	4.9833816252609256E-2	8.1692634290133251E-2	9.896286208844858E-2	0.11660541952740988	0.13447384080888414	0.15248874857852726	0.16697429799325217	0.02	0.03	0.04	0.05	5.8000000000000003E-2	6.4667045956546293E-2	7.0000000000000007E-2	7.4999999999999997E-2	8.5000000000000006E-2	0.09	9.5000000000000001E-2	0.1	0.105	0.109	A y 	B	0.18607525359366064	0.14391355429947814	0.12	0.102899151085505	0.11661904181165808	0.1678623893518402	6.8000000000000005E-2	7.4999999999999997E-2	0.08	8.7941264296878013E-2	9.5000000000000001E-2	0.105	A,B,C y D	0.16355704024660897	6.2912570047510025E-2	4.7046565517502435E-2	3.2491278570195598E-2	2.0478889182363756E-2	2.238390746873177E-2	3.	3227871695035743E-2	4.7896343629151558E-2	6.380395101266402E-2	0.14750968705980796	0.02	0.05	5.5E-2	0.06	6.7362535110912738E-2	7.0000000000000007E-2	7.4999999999999997E-2	0.08	8.5000000000000006E-2	0.11	A=0	0.18540496217741806	0.11659235314777457	0.10046765648707515	9.6663473475750147E-2	0.10106309936130996	0.10355554070405652	0.10650704184190733	0.11565033441918181	0.12686114374159529	0.13964239956673716	0.15360257159305568	0.16844867905637584	0.18396670894485212	0.02	4.4999999999999998E-2	5.5E-2	6.5000000000000002E-2	7.0999999999999994E-2	7.2999999999999995E-2	7.4999999999999997E-2	0.08	8.5000000000000006E-2	0.09	9.5000000000000001E-2	0.1	0.105	B=0	0.23041701326018951	0.15431137352739804	4.8736664663029637E-2	7.022718	811061332E-2	0.21377706309778	6.3E-2	6.7000000000000004E-2	7.0999999999999994E-2	7.6999999999999999E-2	8.5000000000000006E-2	Desviación Estándar
E(Rp)
g) 
	Activo C				Matriz de covarianzas
	Retorno esperado		7.0%			A	B	C	D
	Desviación estándar		10.0%		A	0.0144	0	-0.0072	0.006
	Correlación A		-0.6		B	0	0.04	0.014	-0.01
	Correlación B		0.7		C	-0.0072	0.014	0.01	-0.004
					D	0.006	-0.01	-0.004	0.01
	Activo A				Para calcular el portafolio de mínima varianza utilizaremos la siguiente formula, y luego resolveremos con solver
	Retorno esperado		8.0%
	Desviación estándar		12.0%
	Activo B
	Retorno esperado		11.0%
	Desviación estándar		20.0%
	Correlación A y B		0
						Restricción de retorno
	Activo D					0.110000001	=	11%
	Retorno esperado		5.0%
	Desviación estándar		10.0%
	Correlación A		0.5			1.00	=	1
	Correlación B		-0.5
	Correlacion C		-0.4			Desviación Estandar		0.1475096888
	Portafolio de mínima varianza
	Wa	Wb	Wc	Wd
	1.8345913505	-0.3390219141	1.2651787651	-1.7607482014
	Ra	Rb	Rc	Rd
	8.0%	11.0%	7.0%	5.0%
	Usando solver para el caso de a y b, llegamos a las siguientes respuestas:
	Desviación portafolio eficiente con retorno igual al del activo A (8%):					0.0478963439
	Por lo tanto la diferencia seria de:			0.0721036561
	Desviación portafolio eficiente con retorno igual al del activo B (11%):					0.1475096888
	Por lo tanto la diferencia seria de:			0.0524903112