Medidas de Performance en Fondos de Inversión.

(1)

Medidas de Performance en Fondos

de Inversión.

Profesor: David Moreno Profesor: David Moreno

Esquema de la Presentación



¿Qué son las Medidas de Performance?



¿Qué son las Medidas de Performance?



Utilidad y Relevancia de Medidas de

Performance



Medidas de Performance Clásicas

2



Nuevas Medidas de Performance

(2)

1-¿Qué son las Medidas de Performance?



Medidas de evaluación de resultados de:

 Una cartera de valores.  De la actuación de un gestor

 De uno/varios fondos de inversión

No se debe No se debe olvidar el olvidar el riesgo como riesgo como característi característi ca de una ca de una inversión inversión 3



Permiten unir rentabilidad-riesgo en una

cifra.

Clases de Medidas de Performance



Tienen en cuenta diferentes medidas del

i

riesgo:

 De riesgo total.

 De riesgo sistemático.  Con Var o Donwside Risk.



Diferentes benchmark:

4



Diferentes benchmark:

 Benchmark absoluto (IBEX-35, índice AFI)  Benchmark relativo (Mediana Sharpe)

(3)

3-Utilidad y Relevancia de Medidas de Performance

 Para determinar la actuación de gestores de fondos

d i ió de inversión.

 Para determinar la remuneración de cada gestor de

fondos:

 Dentro de una gestora.

 En el conjunto de FI de esa categoría.

5

j g

 Para estudios de Persistencia

Si hay persistencia Permite adquirir el

mejor fondo de inversión

3-Medidas de Performance Clásicas



Índice de Sharpe.

pp



Information ratio



Índice de Treynor.



Alpha

Alpha--Jensen

Jensen

6



Appraisal ratio.



(4)

1. Índice de Sharpe:

Medidas de Performance Clásicas

 Pendiente de CAL 2. Índice de Treynor: p f p r r S    7 y p f p r r T    3. Alpha’s Jensen

Medidas de Performance Clásicas

A i l i



_f _p( _M _f)



p p r  r  r r  8 4. Appraisal ratio.

 

p p p e A   

(5)

1- INFORMATION RATIO

 This ratio gives us the

active return divided by

B p R

R D

IR   _{active return divided by}

tracking error.

 σ_Dmeasures the deviations

from the benchmark. It is also called tracking error.

Thi i l d B p D D R R D IR    

• Benchmarks could be an index or a set of fund:

 This measure is commonly used

by Hedge Funds. David Moreno 9 • Benchmark (IBEX-35, S&P500…) • Relative Benchmark (Median of competitors, Average funds in the same style investment,..)

2- TRACKING ERROR

 Tracking error measures the

d i ti b t t l

 Two ways to compute

deviation between a mutual fund return of its

Benchmark index.

 In passive or index funds TE

should be close to zero

 The lower the better  TE can deviate from zero

TE: 1 ) ( 1 2 , ,     



 n R R TE R R TE T t t B t p B p because:  Transaction cost  Fund fees  Cash holdings  Sampling bias

• It is more common to compute TE as

the standard deviation of the differences

• Usually we annualized it

(6)

3- APPRAISAL RATIO

 If a portfolio manager is

allocating W in an passive p

AR



 This ratio gives us the

alpha per unit of idiosyncratic risk

allocating WMin an passive

portfolio (M, that is well-diversified) and WAin an active

portfolio (A).

 The Sharpe Ratio is:

h ݄ܵ݌ൌ ݄ܵܯ൅ ߙܣ ߪሺߝܣሻ p p

AR







idiosyncratic risk

 σ(ε_p) measures the specific

risk of the portfolio. It is also called tracking error.

 IR measures the extra-return we

obtain from active management compared to the firm specific risk we incur when we over- or underweight securities relative to the passive index (M)

David Moreno 11

5. Information ratio

Medidas de Performance Clásicas

6. Modigliani-Modigliani D B p D r r D IR      2 12 1 ) 1 (     i B di B i d     f f p B f p p p r r r p r d r d M        ) ( ) 1 ( 2  

(7)

Medida M

2

_{: Modigliani-Modigliani}



Busca corregir sesgo y error de Ratio de

Sh

Sharpe

 M2 si da medida en unidades lógicas

 Diferencia de rentabilidad en puntos básicos, para igual nivel

de riesgo.

 Igual ranking que Ratio de Sharpe

13



Proceso de ajuste por apalancamiento o

desapalancamiento

(8)

4-Nuevas Medidas de Performance

 1-Modigliani-Modigliani ¿?  GH1 y GH2

 Reward-to Semivariability

 Medidas de Donwside Risk.

15

 (Nawrocki, 1999)

 Medidas con más momentos de la distribución

 Prakash y Bear (1986)

 Moreno y Rodriguez (2007, 2008, 2009)

Medidas de Graham

Medidas de Graham--Harvey

Harvey

 GH1: Abnormal return

Riesgo del índice igual al de la cartera. Apalancamiento o inversión en t-bills para

igualar el riesgo.

 Cov(rf,rp)0

16



 GH2: Riesgo de todas las carteras igual al del

benchmark.

) , ( _f _p

(9)

Gráfico de GH1

17

Gráfico de GH2

18

(10)

Medidas de Donwside-Risk



Los rendimientos no siguen una distribución

normal.



Es importante considerar:

Su asimetría

Sus valores en colas

19



De moda en EEUU

 En España… ASEVAL

4- USING DOWNSIDE-RISK MEASURES

 Given that asset’s return distribution is not Gaussian

the variance is not an effective risk measure.

 Mao (1970) demonstrated that investors are only interested in downside riskinvestors are only interested in downside risk as

risk measure.

 Even Markowitz recognizes this in his book on portfolio theory in 1959.  Downside risk measures have its origin in the Roy’s work (1952) where the

S f t fi t i i l d l d Safety first principle was developed.

 Results below the disaster level (or target return).

David Moreno

These distributions have the same mean and variance

(11)

4- USING DOWNSIDE-RISK MEASURES

 Moreno, D., and R. Rodriguez, 2009. "The Value of Coskewness in Mutual Funds

Evaluation ” Journal of Banking and Finance Vol 33 1664–1676 Evaluation, Journal of Banking and Finance, Vol 33, 1664 1676

Table 1

Summary Statistics of Mutual Funds: January 1962 - March 2006.

Mean Return Standard Deviation Kurtosis Max. Losses Max. Returns Test Normality Aggressive Growth 11.038 21.698 4.272 -18.777 17.574 51 Growth/Income 7.610 14.662 4.191 -13.416 10.624 53 Long-term Growth 7.441 17.674 4.215 -15.132 13.749 44 All Funds 8.595 18.206 4.272 -15.854 14.192 48 Number of Funds 36-84 84-120 120-156 156-288 >288 >432 Aggressive Growth 2112 1054 600 244 169 45 18 Growth/Income 1617 751 426 197 167 76 50

Long term Growth 3090 1708 715 366 196 105 61

Around 50% of funds do not show normality

David Moreno

Long-term Growth 3090 1708 715 366 196 105 61

All Funds 6819 3513 1741 807 532 226 129

Table 3

Skewness and Coskewness of Mutual Funds.

All Funds Aggressive

Growth

Growth/ Income

Long-term Growth Panel A: Unconditional Skewness

Mean _-0.355 _-0.299 _-0.455 _-0.340

Median _-0.399 _-0.327 _-0.470 _-0.391

Positive and Sign. at 5% _4.458 _7.955 _1.546 _3.592

Negative and Sign. at 5% _49.890 _42.330 _61.534 _48.964

Around 50% of funds rejects symmetry

Medidas de Downside-Risk

(12)

4- USING DOWNSIDE-RISK MEASURES

 The most popular downside risk measure is the

semivariance semivariance.

 There are two different semivariances depending on

the target established:

A. Below-target SV





_



T T S 1 ( 0 )2 1 ([ ] )2 B. Below-mean SV





_



       t t i t t i i R T R T SV 1 2 , 1 2 , ([ ] ) 1 ) , 0 max( 1 _ _







   T t t i i i E R R T SV 1 2 , )) ] [ ( , 0 max( 1

4.1- SORTINO RATIO

 This measure is also

d

 Given that funds’ return

distribution are not Gaussian or

named as:



 RewardReward--toto--semivariabilitysemivariability 

 RewardReward--toto--downside riskdownside risk

distribution are not Gaussian or normal, using variance makes not sense.

Sortino Rp Rf

Semi

p

 τis the target return (rf,0,mean,…)

 Jarque-Bera Test David Moreno 24 Semi p 1 T ([Rt]  t1 T