05 - Yanet Santillan

Vista previa del material en texto

EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
Finanzas I
CAPM
José Tessada
Escuela de Administración
Octubre 2018
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
Lı́nea Mercado de Capitales
E(Rp)
sp
RF
M
E(RM)
sM
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
Lı́nea Mercado de Valores
RF
E(Rp)
M
E(RM)
1 bi
E(Ri) = RF + βi(E(RM)− RF)
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
Implicancias
Modelo de Precios
Con retornos esperados (exigidos) =⇒ tenemos un modelo de pricing
Capital Asset Pricing Model (CAPM)
Estos valores son los asociados con equilibrio en mercado de activos
¿Dónde entran los precios?
El CAPM nos da las tasas de descuento para flujos de acuerdo a clase de riesgo (β)
Aplicamos estas tasas de descuento para calcular valor presente
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
Figura 1. Retornos de dos activos con β1 = 0,25 y β2 = 1,5, pero con igual varianza idiosincrática
σ2e = 0,03 (equivalente a una desviación estándar de 17,3 %)
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
(a) Retornos activo 1 y retornos de mercado, cada
punto es una observación.
(b) Retornos activo 2 y retornos de mercado, cada
punto es una observación.
Figura 2. Retornos de dos activos con β1 = 0,25 y β2 = 1,5, y con igual varianza de riesgo
idiosincrático σ2e = 0,03. En este caso el riesgo total es σ21 = 0,0325 y σ
2
2 = 0,12, respectivamente.
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
Figura 3. Retornos de dos activos con β1 = 0,25 (azul) y β2 = 1,5 (negro), y con igual
varianza de riesgo idiosincrático σ2e = 0,03. En este caso el riesgo total es σ21 = 0,0325 y
σ22 = 0,12, respectivamente. Ambos están graficados versus retornos de mercado, cada punto es
una observación.
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
Usando CAPM
Betas en Estados Unidos
Sector β Sector β
Advertising 1,79 Canadian Energy 1,14
Air Transport 1,21 Financial Svcs 1,37
Auto Parts 1,78 Food Processing 0,87
Bank 0,75 Newspaper 1,71
Cable TV 1,43 Water utility 0,70
Tabla 1. Datos de http://pages.stern.nyu.edu/∼adamodar/.
http://pages.stern.nyu.edu/~adamodar/.
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
Fig. 3. Survey evidence on the popularity of di!erent methods of calculat the cost of equity capital.
We report the percentage of CFOs who always or almost always use a particular technique. CAPM
represents the capital asset pricing model. The survey is based on the responses of 392 CFOs.
is determined by `what investors tell us they requirea. CEOs with MBAs are
more likely to use the single-factor CAPM or the CAPM with extra risk factors
than are non-MBA CEOs, but the di!erence is only signi"cant for the single-
factor CAPM.
We also "nd that "rms with low leverage or small management ownership are
signi"cantly more likely to use the CAPM. We "nd signi"cant di!erences for
private versus public "rms (public more likely to use the CAPM). This is perhaps
expected given that the beta of the private "rm could only be calculated via
analysis of comparable publicly traded "rms. Finally, we "nd that "rms with
high foreign sales are more likely to use the CAPM.
Given the sharp di!erence between large and small "rms, it is important to
check whether some of these control e!ects just proxy for size. It is, indeed, the
case that foreign sales proxy for size. Table 1 shows that that there is a signi"-
cant correlation between percent of foreign sales and size. When we analyze the
use of the CAPM by foreign sales controlling for size, we "nd no signi"cant
di!erences. However, this is not true for some of the other control variables.
There is a signi"cant di!erence in use of the CAPM across leverage that is
robust to size. The public/private e!ect is also robust to size. Finally, the
di!erence in the use of the CAPM based on management ownership holds for
small "rms but not for large "rms. That is, among small "rms, CAPM use is
inversely related to managerial ownership. There is no signi"cant relation for
larger "rms.
J.R. Graham, C.R. Harvey / Journal of Financial Economics 60 (2001) 187}243 203
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
Evidencia Empı́rica
Calculando β
¿Qué datos tenemos?
Información histórica –retornos observados
No tenemos retornos esperados
CAPM es una teorı́a acerca de estos –relaciones “en promedio”
Calcular covarianzas y varianzas –obtenemos β usando (??)
Alternativa, podemos estimar regresión
Reit =αi + βiR
e
mt + eit (1)
Tenemos T observaciones, Re retorno en exceso sobre Rf
Estimado de regresión lineal
β̂ =
∑Tt=1(R
e
it − R̄ei )(Remt − R̄em)
∑Tt=1(R
e
mt − R̄em)2
lo que nos da exactamente una estimación de β
Se toma como mercado un ı́ndice de mercado que incluya una gran cantidad de
activos
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
Evidencia Empı́rica
CAPM
CAPM nos dice que sólo β importa como medida de riesgo
Derivamos relación entre retorno esperado y β
No debe haber exceso de retorno: αi = 0, ∀i
Pendiente de SML – E(Rm)− Rf
Podemos obtener relación empı́rica entre βi y E(Ri)
Estimar αi –no necesitan ser 0 en la muestra
Testear si son estadı́sticamente 0 –puede ser test conjunto
Pero también sabemos pendiente teórica
Relación entre retornos largo plazo y β
se observa, pero pendiente es menor
evidencia que relación era peor en perı́odos más recientes (Black, “Beta and Return”)
Otros factores también parecen importar: tamaño firma, crecimiento, liquidez, etc.
Crı́tica de Roll: portafolio de mercado es inobservable
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
line, with an intercept equal to the risk-free rate, Rf , and a slope equal to the
expected excess return on the market, E(RM) � Rf. We use the average one-month
Treasury bill rate and the average excess CRSP market return for 1928–2003 to
estimate the predicted line in Figure 2. Confirming earlier evidence, the relation
between beta and average return for the ten portfolios is much flatter than the
Sharpe-Lintner CAPM predicts. The returns on the low beta portfolios are too high,
and the returns on the high beta portfolios are too low. For example, the predicted
return on the portfolio with the lowest beta is 8.3 percent per year; the actual return
is 11.1 percent. The predicted return on the portfolio with the highest beta is
16.8 percent per year; the actual is 13.7 percent.
Although the observed premium per unit of beta is lower than the Sharpe-
Lintner model predicts, the relation between average return and beta in Figure 2
is roughly linear. This is consistent with the Black version of the CAPM, which
predicts only that the beta premium is positive. Even this less restrictive model,
however, eventually succumbs to the data.
Testing Whether Market Betas Explain Expected Returns
The Sharpe-Lintner and Black versions of the CAPM share the prediction that
the market portfolio is mean-variance-efficient. This implies that differences in
expected return across securities and portfolios are entirely explained by differ-
ences in market beta; other variables should add nothing to the explanation of
expected return. This prediction plays a prominent role in tests of the CAPM. In
the early work, the weapon of choice is cross-section regressions.
In the framework of Fama and MacBeth (1973), one simply adds predeter-
mined explanatory variables to the month-by-month cross-section regressions of
Figure 2
Average Annualized Monthly Return versus Beta for Value Weight Portfolios
Formed on Prior Beta, 1928–2003
Average returns
predicted by the
CAPM
0.5
6
8
10
12
14
16
18
0.7 0.9 1.1 1.3 1.5 1.7 1.9
A
ve
ra
ge
 a
n
n
ua
liz
ed
 m
on
th
ly
 r
et
ur
n
 (
%
)
The Capital Asset PricingModel: Theory and Evidence 33
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
market proxies, like the value-weight portfolio of U.S. stocks, that lead to rejections
of the model in empirical tests. The contradictions of the CAPM observed when
such proxies are used in tests of the model show up as bad estimates of expected
returns in applications; for example, estimates of the cost of equity capital that are
too low (relative to historical average returns) for small stocks and for stocks with
high book-to-market equity ratios. In short, if a market proxy does not work in tests
of the CAPM, it does not work in applications.
Conclusions
The version of the CAPM developed by Sharpe (1964) and Lintner (1965) has
never been an empirical success. In the early empirical work, the Black (1972)
version of the model, which can accommodate a flatter tradeoff of average return
for market beta, has some success. But in the late 1970s, research begins to uncover
variables like size, various price ratios and momentum that add to the explanation
of average returns provided by beta. The problems are serious enough to invalidate
most applications of the CAPM.
For example, finance textbooks often recommend using the Sharpe-Lintner
CAPM risk-return relation to estimate the cost of equity capital. The prescription is
to estimate a stock’s market beta and combine it with the risk-free interest rate and
the average market risk premium to produce an estimate of the cost of equity. The
typical market portfolio in these exercises includes just U.S. common stocks. But
empirical work, old and new, tells us that the relation between beta and average
return is flatter than predicted by the Sharpe-Lintner version of the CAPM. As a
Figure 3
Average Annualized Monthly Return versus Beta for Value Weight Portfolios
Formed on B/M, 1963–2003
Average returns
predicted by
the CAPM
0.7
9
10
11
12
13
14
15
16
17
0.8
10 (highest B/M)
9
6
3
2
1 (lowest B/M)
5 4
7
8
0.9 1 1.1 1.2
A
ve
ra
ge
 a
n
n
ua
liz
ed
 m
on
th
ly
 r
et
ur
n
 (
%
)
Eugene F. Fama and Kenneth R. French 43
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
EAA220B
CAPM
J. Tessada
2-2018
Evidencia
Empı́rica del
CAPM
Conclusiones
Conclusiones
CAPM es ampliamente usado – debe tener ventajas. . .
Atractivo de CAPM
Es fácil de implementar
Simple y “razonable”
distinción de riesgos sistemático y no-sistemático
simple modelo de pricing
anclado en teorı́a de portafolio
Pero también tiene problemas
No es claro que se pueda testear directamente
se necesita estimar retornos y β
elemento clave es esencialmente inobservable: portafolio de mercado
Evidencia empı́rica
Modelos alternativos pueden tener mejor performance
CAPM multi-factor
CAPM consumo
APT
EAA220B
CAPM
J. Tessada
2-2018
Extensiones
CAPM Multi-factor
Una potencial motivación
CAPM asume que inversión es en horizonte corto –oportunidades no cambian
Además (algunos) inversionistas si tienen horizontes largos =⇒ están expuestos a
cambios en oportunidades de inversión futuras
Algunos activos pueden proteger contra este riesgo
Este riesgo no es lo mismo que la variación del portafolio de mercado
=⇒ inversionistas aceptan menor retorno en activos que dan “protección” contra
este riesgo
Ejemplo: inversionistas que desean protegerse contra cambios en tasas de interés
reales
Agregar E(r)− Rf como elemento de riesgo
CAPM con dos factores de riesgo: E(RM)− Rf y E(r)− Rf
E(Ri)− Rf =βiM(E(RM)− Rf ) + βir(E(r)− Rf )
Más general: riesgo sistemático estático e intertemporal
Este último son los cambios en las oportunidades de inversión
Usualmente se usan variables macroeconómicas -“factores”
EAA220B
CAPM
J. Tessada
2-2018
Extensiones
CAPM Consumo
Requiere información que no conocemos directamente: consumo y funciones de
utilidad
Reduce muchos factores de riesgo a uno solo: utilidad marginal del consumo
Veamos como funciona
Considere las siguientes oportunidades
1 consumir $1 hoy con utilidad u′(c0)
2 ahorrar y comprar activo i: recibe 1 + ri con beneficio de consumo (1 + ri)u′(c1)
Un agente debe estar indiferente entre ambas: ajusta el portafolio de modo que esto
ocurra
Esto debe cumplirse para todos los activos
u′(c0) =E0
[
(1 + ri)u′(c1)
]
u′(c0) =E0
[
(1 + rf )u
′(c1)
]
EAA220B
CAPM
J. Tessada
2-2018
Extensiones
CAPM Consumo
Por diferencia obtenemos que
E0
[
(ri − rf )u′(c1)
]
=0
que podemos reescribir como
E0(ri)− rf =−
1
E0 [u′(c1)]
Cov
[
u′(c1), ri
]
(2)
	Evidencia Empírica del CAPM
	Conclusiones
	Apéndice
	Extensiones