Mercado de Capitales

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Licenciatura en Derecho y Administraci

ó

n y Direcci

ó

n de Empresas

Sexto Curso

Prof. Dr. Jorge Otero Rodr

í

guez

Departamento de Financiación e Investigación Comercial

UNIVERSIDAD AUTÓNOMA DE MADRID

Mercado de Capitales

Tema 7. La medida de la

“

performance

”

2

2 Contenidos

Contenidos

El concepto de “performance”

Medidas clásicas: Treynor, Sharpe y Jensen

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3

3 SELECCION DE CARTERAS

SELECCION DE CARTERAS

Objetivos de la inversión

Política de inversión

Selección de carteras

Asset allocation.

Security selection.

Market timing.

Revisión de la cartera.

Evaluación de la performance.

En el intervalo de evaluación.

Comparación a otras carteras de referencia.

CARTERA BASE Y BENCHMMARKS

Cuantificamos expectativas de rentabilidad y riesgo por categorías de activos en base a

rentabilidades generales del mercado, benchmarks pasivos.

Utilizamos los benchmarks para valorar la contribución de la gestión activa y su posible

comparativa.

Problema de la selección del benchmark (depende del estilo de gestión )

Un buen gestor debe cuidar su tracking error: Var ( Rp ) = β

2 _{Var(Rm) + var (ε}

2 )

Los ε

₂

son independientes y tienen un valor esperado igual a cero, de tal forma que cuanto

mas activos existan en la cartera modelo menor será el impacto del riesgo no sistemático.

Var (ε

_p

) = 1/n Var (ε

_i

)

Las conclusiones mas relevantes en los Var (ε

_p

) son :

Los ex-ante de grandes carteras tiene un elevada correlación con su valor ex-post.

Así el Var (ε

_p

) mide el nivel de indexación de una cartera de forma practica y fiable.

Para cualquier categoría de activos falta ponderar los distintos activos que componen el

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5

5 GESTION ACTIVA (I)

GESTION ACTIVA (I)

Esta basado en la anticipación y la selección.

Tres niveles:

Asset class

Tactical asset allocation: se basa en las ineficiencias por valoración y es un

proceso de reversión a la media basado en sobrereacciones a corto,

convergencias y mercados sin gran momentum.

Dinamic hedging: distribución de activos para generar un perfil rentabilidad/riesgo

e idéntico al de una call.

Security selection

Timing.

Renta Variable

Países, sectores y valores.

Renta Fija

Riesgo de crédito, Yield curve, Cash matching, Duration matching

Benchmark

Hacerlo “menos mal” que el resto

6

6 Es

tr

ate

g

ias

As

se

t

A

llo

c

a

tion

Security Selection + Market Timing

GESTION ACTIVA (II)

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7

7 VALORACION DE LA GESTION

VALORACION DE LA GESTION

Performance measurement

Valoración de la gestión llevada a cabo de un proceso de gestión integrado,

estructurado y explicito

Ratio de Sharpe.

Ratio de Treynor.

Índice de Jensen.

Performance attribution

Valoración del valor añadido por la gestión activa.

Asset allocation.

Security selection.

Timing.

PERFORMANCE MEASUREMENT (I)

Ratio Sharpe

Muestra la remuneración al riesgo que se obtiene para cada gestor y fondo en

términos de diferencial de rentabilidad sobre la tasa libre de riesgo por cada

punto porcentual de desviación típica del rendimiento de la cartera.

Ratio de Treynor

Mide la prima de rentabilidad por la exposición al riesgo sistemático.

Supone 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.

p

f

p

R

S

σ

−

=

p

f

p

R

T

β

−

=

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9

9 Índice de Jensen

Mide la calidad de la gestión desarrollada por un gestor según al modelo

del C.A.P.M.

Si αi > 0 la gestión es buena y si αi < 0 es no es adecuada.

El ratio de Información

Muestra la performance de la cartera en relación a la evolución del índice o

índices de referencia (benchmark).

σ

cb

: desviación típica de los diferenciales de rentabilidad entre la cartera y el

benchmark durante el periodo de análisis.

PERFORMANCE MEASUREMENT (II)

(

m

f

)

p

f

p

R

−

=

α

+

β

⋅

−

cb

f

p

R

I

σ

−

=

10

10 EQUITY FUND GERMANY

3 AÑOS

5 AÑOS

7 AÑOS

10 AÑOS

ALFA

-0,58

-0,39

-0,36

BETA

0,99

0,98

0,95

0,93

MAX. PERD.

-27,57

CORRELACION

0,97

0,98

0,97

TRACKING ERROR

1,58

1,42

1,37

VOLATILIDAD ANUAL

24,62

23,23

20,86

18,87

ESTADISTICAS

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

CORRELACION

0,95

0,94

TRACKING ERROR

2,64

2,5

2,21

2,06

VOLATILIDAD ANUAL

27,86

26,46

23,43

22,08

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11

Value Growth Profitability Momentum Technical

Alpha Definitions

Traditional Value

The Traditional Value alpha portfolio buys cheap stocks and shorts expensive

ones. We measure value using price ratios such as price to earnings, price to book, price to cash flow and price to sales. We refer to this approach as traditional value because these ratios have long served as the traditional measures of value.

Relative Value

For Relative Value alpha we measure value using industry relative price ratios such as price to

earnings, price to book, and price to sales. In this approach, a stock is considered cheap if its ratio is less than the industry average. We also look at same measure across time. We consider a stock cheap if the current spread between its ratio and the industry average is less than the historical average spread. We look back five years.

Historical Growth

The Historical Growth alpha portfolio 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.

Expected Growth

The Expected Growth alpha portfolio buys stock with high rates of expected earnings growth,

and shorts those with low or negative expected growth rates.

New York, NY 10010-3629

Profit Trends

Profit Trends alpha portfolio buys stock showing strong bottom line

improvement and short stock showing deteriorating profits or increasing losses. We measure profit 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 alpha portfolio 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.

Price Momentum

The Price Momentum alpha portfolio buys stock with high returns over the past 6-12 months,

and shorts those with low or negative returns over the last 6-12 months.

Earnings Momentum

We define earnings momentum in terms of earnings estimates, not historical

earnings. The Earnings Momentum alpha portfolio buys stock with positive earnings surprises and upward estimate revisions, and shorts those with negative earnings surprises and downward estimate revisions.

Price Reversal

Price Reversal is the pattern whereby short-term winners often suffer downside reversals and

short term losers tend to bounce back to the upside. These reversal patterns are evident from horizons of one day to four weeks.

Small Size

The Small Size alpha portfolio buys the smallest decile stocks in the

index and shorts the largest decile in the index.

Constructing Alpha Portfolios

Measuring Alpha Performance

“Unconstrained” Alpha Portfolio

“Sector Neutral” Alpha Portfolio

To build sector-neutral portfolios, we first separate the universe into sub universe based on their assigned S&P sector codes. Then we form long-short alpha portfolios for each sector universe. Next, these sector long short portfolios are combined into a single portfolio. This process ensures same number of long short positions in each sector in the portfolio. The performance of these portfolios should be immune to any sector movements hence it is a sector neutral.

Constructing Portfolio

We construct the alpha portfolios from equal-weighted, long-short portfolios with 10 percent of universe names on each side. Our approach is to decile rank the universe on each attribute representative of the given alpha. We use more than one factor to define each alpha. We use Standards and Poors and Russell indexes as our universe.

We measure the performance 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 top 10 percent while shorting the bottom ten percent, what would be the resulting long-short portfolio return? We monitor performance 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-specific influences. The result is a portfolio whose returns flow almost exclusively from systematic factors such as industry membership and alpha characteristics.

We construct our alpha portfolio by taking long positions in the top ten percent stocks, and short positions in the bottom 10 percent stocks. This process maximizes the exposure to a given alpha, regardless of sector, or size biases.

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13

Label Alpha Generator

Sectors Outperforming (Max = 10) Return on L-S Unconstrained Portfolio Return on L-S Sector Neutral Portfolio Spread 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 Expected Growth 4 -1,62 -0,81 -0,81

Alpha Generators S&P 500

Return on Long-Short Alpha Factor Portfolios

-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0 2,5 3,0 EM SZ PR TV RV PT AS PM HG EG S&P 500

Index:

Sector Returns

Benchmarks

All

Sector:

31/01/07-16/02/07

14

Sectors Outperforming (Max = 10) Return on L-S Unconstrained Portfolio Return on L-S Sector Neutral Portfolio Spread 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 Expected Growth 4 -0,96 -0,71 -0,24 PM Price Momentum 3 -1,66 -0,99 -0,68

Alpha Generators S&P 500 Growth

Return on Long-Short Alpha Factor Portfolios

-2 -1 0 1 2 3 4 EM HG SZ PR RV AS PT TV EG PM S&P 500 Growth

Index:

Sector Returns

Benchmarks

All

Sector:

31/01/07-16/02/07

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15

Sectors Outperforming (Max = 10) Return on L-S Unconstrained Portfolio Return on L-S Sector Neutral Portfolio Spread 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 Expected 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

Alpha Generators S&P 400 Value

Return on Long-Short Alpha Factor Portfolios

-1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 EM AS TV PM RV EG HG PT SZ PR S&P 400 Value