I
High average returns that are unrelated to the market
I
Why? Don’t need a fund manager to get market exposure
!
simply invest in
S&P 500 fund
How to quantify this? Compute alpha from
r
p

r
f
=
↵
p
+
β
p
(
r
m

r
f
) +
"
p
For hedge funds, the goal is to produce alpha, returns unrelated to the market
What makes a good manager? Generally speaking a manager that has an
alpha over a couple of percentage points is doing a good job.
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BCSIX  Is
↵
statistically significant?
Using data on monthly total returns Aug 2013  July 2016 with
Morningstar Small Growth TR as the market index:
Russell 200 Growth TR as the market index:
In both cases,
↵
(here, monthly) is not statistically significant...
42 / 77
Today’s lecture
1
Recap: portfolio theory
2
Applying meanvariance analysis
3
CAPM
4
Performance evaluation
5
Testing CAPM
6
APT
43 / 77
Testing CAPM empirically
CAPM predicts a linear ("crosssectional") proportional relation between the
risk premium
RP
k
(longrun average excess return) on an asset (
k
) and its
β
Idea of the test:
I
work with portfolios (Can measure
β
’s more accurately)
I
choose portfolios with wide range of
β
’s
I
do second regression with portfolio risk premia (left hand side) and portfolio
β
’s (right hand side)
Questions:
I
Is the slope significant? (i.e., do
β
’s explain any of the di
ff
erence in risk
premia between portfolios?)
I
Is the intercept zero? (i.e., is the risk premium for assets with a zero beta
actually zero?)
This is the approach taken in early tests, e.g., by Black, Jensen and Scholes
(1972)
44 / 77
Aste
calculate
B
's
of
portfolios
⊥
choose
a
wide
range
of
B
's
CAR
N
:
Rp

rt
=o
+
Bp
MRP
Bi
=
O
㱺
Ri
=
rt
t.sk#2.Sep
a
n
Rp
rt

Atf
Bps
LHS
=

RHS
=
Testing CAPM empirically
45 / 77

r
g
s
J

•
0
#
Testing CAPM empirically
46 / 77
*
of
"
Testing CAPM empirically
47 / 77
Book

to

market
=
Bvequily
Mr
equity
BM
I
low

o
Growth
fi
firm
T
ygo
line
undopotom
relative
to
CAPM
£
outperform
high
→
Value

firm
w
f
⊥
relation
*
O
O
㱺
a
>
o
"
value
Premium

E
l
A
Rp¥Rma

rft
Testing CAPM empirically
Average returns vs market
β
 25 size and BE/ME sorted stock portfolios
48 / 77
sine
:
!
Why doesn’t
β
work?
Wrong theory?
Behavioural biases
No relation between return and marginal risk
Frictionless market assumption in CAPM is invalid
!
Leverage?
Nontradable risks?
Wrong test?
Tests don’t capture the correct market portfolio
If you had the right portfolio, you’d see the risk priced
49 / 77
✓
I
Rolliscrtigne
Does CAPM hold?
How do we create a size or a booktomarket factor?
How do we interpret the return on the factor?