Mercado de Caitales Tema 7. La medida de la erformance Licenciatura en Derecho y Administración n y Dirección n de Emresas Sexto Curso Prof. Dr. Jorge Otero Rodríguez Deartamento de Financiación e Investigación Comercial UNIVERSIDAD AUTÓNOMA DE MADRID Contenidos El conceto de erformance Medidas clásicas: Treynor, Share y Jensen Otras medidas 2 1
SELECCION DE CARTERAS Obetivos de la inversión Política de inversión Selección de carteras Asset allocation. Security selection. Market timing. Revisión de la cartera. Evaluación de la erformance. En el intervalo de evaluación. Comaración a otras carteras de referencia. 3 CARTERA BASE Y BENCHMMARKS Cuantificamos exectativas de rentabilidad y riesgo or categorías de activos en base a rentabilidades generales del mercado, benchmarks asivos. Utilizamos los benchmarks ara valorar la contribución de la gestión activa y su osible comarativa. Problema de la selección del benchmark (deende del estilo de gestión ) Un buen gestor debe cuidar su tracking error: Var ( R ) = β 2 Var(Rm) + var (ε 2 ) Los ε 2 son indeendientes y tienen un valor eserado igual a cero, de tal forma que cuanto mas activos existan en la cartera modelo menor será el imacto del riesgo no sistemático. Var (ε ) = 1/n Var (ε i ) Las conclusiones mas relevantes en los Var (ε ) son : Los ex-ante de grandes carteras tiene un elevada correlación con su valor ex-ost. Así el Var (ε ) mide el nivel de indexación de una cartera de forma ractica y fiable. Para cualquier categoría de activos falta onderar los distintos activos que comonen el benchmark. 4 2
GESTION ACTIVA (I) Esta basado en la anticiación y la selección. Tres niveles: Asset class Tactical asset allocation: se basa en las ineficiencias or valoración y es un roceso de reversión a la media basado en sobrereacciones a corto, convergencias y mercados sin gran momentum. Dinamic hedging: distribución de activos ara generar un erfil rentabilidad/riesgo e idéntico al de una call. Security selection Timing. Renta Variable Países, sectores y valores. Renta Fia Riesgo de crédito, Yield curve, Cash matching, Duration matching Benchmark Hacerlo menos mal que el resto 5 GESTION ACTIVA (II) Estrategias Asset Allocation Security Selection + Market Timing 6 3
VALORACION DE LA GESTION Performance measurement Valoración de la gestión llevada a cabo de un roceso de gestión integrado, estructurado y exlicito Ratio de Share. Ratio de Treynor. Índice de Jensen. Performance attribution Valoración del valor añadido or la gestión activa. Asset allocation. Security selection. Timing. 7 PERFORMANCE MEASUREMENT (I) Ratio Share Muestra la remuneración al riesgo que se obtiene ara cada gestor y fondo en términos de diferencial de rentabilidad sobre la tasa libre de riesgo or cada unto orcentual de desviación tíica del rendimiento de la cartera. S = R f σ Ratio de Treynor Mide la rima de rentabilidad or la exosición al riesgo sistemático. Suone que la beta es un buen indicador del riesgo sistemático de la cartera y en cierta medida asume la verificación del C.A.P.M. R f T = β 8 4
PERFORMANCE MEASUREMENT (II) Índice de Jensen Mide la calidad de la gestión desarrollada or un gestor según al modelo del C.A.P.M. R f = α + β ( R ) Si αi > 0 la gestión es buena y si αi < 0 es no es adecuada. El ratio de Información Muestra la erformance de la cartera en relación a la evolución del índice o índices de referencia (benchmark). I = R f σ cb σ cb : desviación tíica de los diferenciales de rentabilidad entre la cartera y el benchmark durante el eriodo de análisis. m f 9 ESTADISTICAS EQUITY FUND GERMANY 3 AÑOS 5 AÑOS 7 AÑOS 10 AÑOS ALFA -0,58-0,39-0,36-0,36 BETA 0,99 0,98 0,95 0,93 MAX. PERD. -27,57-27,57-27,57-27,57 CORRELACION 0,97 0,98 0,97 0,97 TRACKING ERROR 1,58 1,42 1,37 1,37 VOLATILIDAD ANUAL 24,62 23,23 20,86 18,87 EQUITY FUND SPAIN 3 AÑOS 5 AÑOS 7 AÑOS 10 AÑOS ALFA 0,09 0,11 0,05 0,15 BETA 1,19 1,09 1,08 1,03 MAX. PERD. -35,21-35,21-35,21-35,21 CORRELACION 0,95 0,94 0,94 0,94 TRACKING ERROR 2,64 2,5 2,21 2,06 VOLATILIDAD ANUAL 27,86 26,46 23,43 22,08 10 5
Value Traditional Value The Traditional Value alha ortfolio buys chea stocks and shorts exensive ones. We measure value using rice ratios such as rice to earnings, rice to book, rice to cash flow and rice to sales. We refer to this aroach as traditional value because these ratios have long served as the traditional measures of value. Alha Definitions New York, NY 10010-3629 Relative Value For Relative Value alha we measure value using industry relative rice ratios such as rice to earnings, rice to book, and rice to sales. In this aroach, a stock is considered chea if its ratio is less than the industry average. We also look at same measure across time. We consider a stock chea if the current sread between its ratio and the industry average is less than the historical average sread. We look back five years. Growth Historical Growth The Historical Growth alha ortfolio buys stock with strong records of growth and shorts those with flat or negative growth rates. We measure growth based on earnings growth rates, revenue trends, and changes in cash flows. Exected Growth The Exected Growth alha ortfolio buys stock with high rates of exected earnings growth, and shorts those with low or negative exected growth rates. Profitability Profit Trends Profit Trends alha ortfolio buys stock showing strong bottom line imrovement and short stock showing deteriorating rofits or increasing losses. We measure rofit trends by using following ratios overhead to sales, earnings to sales and sales to assets. We also use trends in following ratios - 1) (Receivables + Inventories)/Sales, 2) Cash Flow to Sales and 3) Overhead to Sales Accelerating Sales The Accelerating Sales alha ortfolio buys stocks with strong records of sales growth and short those with flat or negative sales growth. We measure the rate of increase in sales growth hence the accelerations of sales. Momentum Earnings Momentum We define earnings momentum in terms of earnings estimates, not historical earnings. The Earnings Momentum alha ortfolio buys stock with ositive earnings surrises and uward estimate revisions, and shorts those with negative earnings surrises and downward estimate revisions. Technical Small Size The Small Size alha ortfolio buys the smallest decile stocks in the index and shorts the largest decile in the index. Price Momentum The Price Momentum alha ortfolio buys stock with high returns over the ast 6-12 months, and shorts those with low or negative returns over the last 6-12 months. Price Reversal Price Reversal is the attern whereby short-term winners often suffer downside reversals and short term losers tend to bounce back to the uside. These reversal atterns are evident from horizons of one day to four weeks. 11 Constructing Alha s Measuring Alha Performance Constructing We construct the alha ortfolios from equal-weighted, long-short ortfolios with 10 ercent of universe names on each side. Our aroach is to decile rank the universe on each attribute reresentative of the given alha. We use more than one factor to define each alha. We use Standards and Poors and Russell indexes as our universe. We measure the erformance of each factor by asking the following question: If we ranked the universe on the factor at the beginning of the month and then bought the to 10 ercent while shorting the bottom ten ercent, what would be the resulting long-short ortfolio return? We monitor erformance of the factors on a month-to-date, quarter-to-date, and year-to-date basis. The long-short construction neutralizes the market effect, and essentially eliminates firm-secific influences. The result is a ortfolio whose returns flow almost exclusively from systematic factors such as industry membershi and alha characteristics. Unconstrained Alha We construct our alha ortfolio by taking long ositions in the to ten ercent stocks, and short ositions in the bottom 10 ercent stocks. This rocess maximizes the exosure to a given alha, regardless of sector, or size biases. Sector Neutral Alha To build sector-neutral ortfolios, we first searate the universe into sub universe based on their assigned S&P sector codes. Then we form long-short alha ortfolios for each sector universe. Next, these sector long short ortfolios are combined into a single ortfolio. This rocess ensures same number of long short ositions in each sector in the ortfolio. The erformance of these ortfolios should be immune to any sector movements hence it is a sector neutral. 12 6
Alha Generators S&P 500 Label Index: Sector: Alha Generator S&P 500 All Sectors Outerforming (Max = 10) Unconstrained Sector Returns Benchmarks Sector Neutral Sread EM Earnings Momentum 6 2,73 1,36 1,37 SZ Small Size 6 2,16 1,11 1,05 PR Price Reversal 7 1,21 0,88 0,33 TV Traditional Value 8 1,08 1,62-0,53 RV Relative Value 5 0,56 0,16 0,40 PT Profit Trends 5 0,41 1,00-0,60 AS Accelerating Sales 6 0,26 0,78-0,52 PM Price Momentum 4 0,24-0,37 0,61 HG Historical Growth 5 0,23 0,59-0,36 EG Exected Growth 4-1,62-0,81-0,81 Return on Long-Short Alha Factor s 31/01/07-16/02/07 3,0 2,5 2,0 1,5 1,0 0,5 0,0-0,5-1,0-1,5-2,0 EM SZ PR TV RV PT AS PM HG EG 13 Label Index: Sector: Alha Generators S&P 500 Growth Alha Generator S&P 500 Growth All Sectors Outerforming (Max = 10) Unconstrained Sector Returns Benchmarks Sector Neutral Sread EM Earnings Momentum 5 3,52 1,18 2,33 HG Historical Growth 7 2,58 2,06 0,52 SZ Small Size 5 1,98 1,24 0,74 PR Price Reversal 5 1,45 1,83-0,38 RV Relative Value 4 1,25 0,61 0,65 AS Accelerating Sales 7 0,12 2,02-1,89 PT Profit Trends 4-0,06 0,54-0,60 TV Traditional Value 6-0,35 1,73-2,08 EG Exected Growth 4-0,96-0,71-0,24 PM Price Momentum 3-1,66-0,99-0,68 Return on Long-Short Alha Factor s 4 3 2 1 0-1 31/01/07-16/02/07-2 EM HG SZ PR RV AS PT TV EG PM 14 7
Alha Generators S&P 400 Value Label Index: Sector: Alha Generator S&P 400 Value All Sectors Outerforming (Max = 10) Unconstrained Sector Returns Benchmarks Sector Neutral Sread EM Earnings Momentum 7 3,13 2,68 0,44 AS Accelerating Sales 4 2,92 0,44 2,48 TV Traditional Value 6 1,13 2,02-0,89 PM Price Momentum 5 0,72 1,39-0,67 RV Relative Value 6 0,62 1,04-0,42 EG Exected Growth 6 0,05 0,44-0,39 HG Historical Growth 5 0,00-0,30 0,30 PT Profit Trends 3-0,61-1,05 0,45 SZ Small Size 3-0,91-2,05 1,14 PR Price Reversal 1-1,17-2,76 1,59 Return on Long-Short Alha Factor s 3,5 31/01/07-16/02/07 3,0 2,5 2,0 1,5 1,0 0,5 0,0-0,5-1,0-1,5 EM AS TV PM RV EG HG PT SZ PR 15 PERFORMANCE ATTRIBUTION Ponderaciones Rentabilidades Contribuciones (rent) BM CM BM CM TIR-CM BM CM TIR-CM Cash 30.00% 25.00% 3.00% 2.00% 3.00% 0.90% 0.50% 0.75% RF 40.00% 30.00% 5.00% 5.50% 6.00% 2.00% 1.65% 1.80% RV 30.00% 45.00% 8.00% 8.10% 9.00% 2.40% 3.65% 4.05% Total 100.00% 100.00% 5.30% 5.80% 6.60% Performance Contribuciones (Descom. %) Asset Allocation Security Slection Timming Total BM CM TIR-CM Cash 0.12% -0.25% 0.25% 0.12% 16.98% 8.63% 11.36% RF 0.03% 0.15% 0.15% 0.33% 37.74% 28.47% 27.27% RV 0.41% 0.05% 0.41% 0.86% 45.28% 62.90% 61.36% Total 0.55% -0.06% 0.80% 1.30% 100.00% 100.00% 100.00% AA SS = Timing = ( WCM WBM ) ( R CM CM Global ) ( R CM BM ) WCM = ( TIR CM CM ) WCM R TIR-CM Global BM = m = 1 AA + SS + Timing 8
1,00% PERFORMANCE 0,80% 0,60% Rentabilidad 0,40% 0,20% 0,00% -0,20% Asset Allocation Security Slection Timming Total -0,40% Cash RF RV 17 9