Morningstar Magazine - June/July 2017 - 73

m

m

r˜ it =

it

f˜ + u˜ it

+

m

Bik RAkt

2
i

= Var[˜ui]

Akt

RBMit =

+ u˜ it

k

=1

IRSt =

= Var[˜ui]

PSt - ∆t
P

2
2
2
A = M + S
components of manager returns are not only
independent of∑the asset-class returns, but also of
m
m specific
each
other,k=1
is simply:
∑ q=1 ( risk
M =
k - k ) ( q - q ) k q kq

ISt
PSt - ∆t

Because
we assume
that unsystematic
2
2
2
PSt
A = M + S
=
PRStindependent
-1
components of manager returns are
PSt - ∆t
of the asset-class returns, we can split the
m
ISt
m
square of )active risk ( A) into two components:
∑
q ui]k q kq
IR
Bikq=1
RAkt( k - k ) i2( =q -Var[˜
StSt =
TR
= IR
St + PRSt
P
)
and
specific
risk
(
):
misfit
risk
(
St - ∆t
=1
M
S

S

n
i=1

=

2
i

∑

ISt

k =1

n
= ∑ i=1
xi Bik

IRSt =

2
i

Bik RAkt

k=1

k=1

r˜ it of
= theit return
+ i r˜Mtof+ each
u˜ it fund i:

Bikt

=

ikt kt

m

St
Kaplan,
PRSt =Paul D. 2016b
- 1. "Being a Bayesian." Morningstar,
P
St
∆t
April/May, pp.- 52-54
.

Kaplan, Paul D. 2017. "From Markowitz 1.0 to Markowitz
TRSt = a IR
St + PR
2.0 with
Detour
to StPostmodern Portfolio Theory and Back."
Journal of Investing, Spring, pp. 122-130.
- qT

2
i

(

yst -∆ t (T )

)

PZt-∆ t T; yHarry
= . "Portfolio
1+
st -∆ t (T
Markowitz,
M.) 1952
qSelection." Journal of
Finance, Vol. 7, No. 1, pp.77-91.

∑
What About Alphas?
Markowitz, Harry
. Portfolio
Selection. 2nd
PZtM.T1991
- ∆t;
yst (T - ∆t)
While RBSA provides estimates for the asset-class
ed.
TRZtOxford:
- 1 in 1959.)
(T ) =Basil Blackwell. (1st edition published
PZt -∆ t T ; yst -∆ t (T )
exposures and-the
qT unsystematic risk of each
2
2
y (T )
i
i
2
2
2
Morningstar, Inc. 2016. "Morningstar Global Risk Model
P-∆ t (T ) = 1manager
+ st -∆ t from historical data, it would be unwise
PPR
A = M + S
Zt-∆ t = T; ystSt
-1
q
St
Methodology." Morningstar Research paper. May
PSt - ∆t
to estimate alphas from the difference between
27. https://corporate.morningstar.com/us/documents/PR/
PZt T - ∆t; yst -∆ t (T
)
Measuring Misfit Risk
each manager's performance and that of the
RiskModel-Global-Methodology-v
1.pdf
m
=
IR
-1
P
(T
)
(T
-
∆t)
T
-
∆t;
y
(
-
)
)
∑ q=1 ( k - Misfit
Zt
Zt
q standard
kq
st
q risk
q iskthe
k
RBSA
-custom benchmark because past
deviation
TR of =theIR + PRSt
PZt -∆ t T ; yst -∆ t (T )
TRZtSt (T ) = St
-1
Sharpe,
William
F.
1988
,
"Determining
a
Fund's
may not be indicative of future
difference between the portfolio of asset-classPZt -∆ t T ; ystperformance
-∆ t (T )
Effective Asset Mix," Investment Management Review,
- qT
2
2
performance.
indexes at the target weights and the effective
yst -∆ t (T ) Instead, a future-looking framework,
i
i
December, pp. 59-69.
PZt-∆ t T; yst -∆ t (T ) = 1 +
such asqthe one presented by Waring and
allocation of the portfolio managers. The
Sharpe, William F. 1992. "Asset Allocation: Management
higher the misfit risk, the more that the effective
(2008) should be used. And regardless
PZt T - ∆t; ystRamkumar
-∆ t (T )
Style and Performance Measurement," Journal of Portfolio
=
IR
-
1
(T
)
Zt
asset mix differs from the target. The
PPZt T - ∆t;
- ∆t)alphas are estimated, they should always
yof(Thow
Management,
∑ Winter, pp. 7-19.
Zt -∆ t T ; ystst-∆ t (T )
effective
be net of fees.
m asset allocation is measured
mby
TRZt (T
-1
) =taking
I
St
2
(Ti])
= Bikt Akt + u˜ it averageRof
u˜ it
IRSt =
= assetBik RAkt PZt -∆ t i T=; yVar[˜
st -∆ t u
BMitthe
Waring, M. Barton and
R.q∆tRamkumar. 2008.
a manager-weighted
yst -∆Sunder
PSt - ∆t
t (T )
k=1
k =1
+
"Forecasting
Fund
Manager
Alphas:
=
IR
-The
1 Impossible Just
1
(T
)
Zt
class exposures:
Here, I have given a brief outline of managerq
Takes Longer." Financial Analysts Journal, Vol. 64,
structure
2
2
2 optimization. For a detailed description,
PSt
No. 2 (March/April), pp. 65-79.
M +
S
PZt T - A∆t;=yst -∆
n
t (T )
PRSt =
-1
(2016a)
see
Kaplan
k = ∑ i=1 xi Bik
it
PSt - ∆t
IRZt (T ) =
-1 .
Waring,
PZt -∆ t T ; yst -∆ t (T )
PRZt (T )M.= Barton,
TRZt (TDuane
) - IRZtWhitney,
(T ) John Pirone, and
Charles Castille. 2000. "Optimizing Manager Structure and
m
m
q∆t
where:
Summing Up
M =
k=1 ∑ q=1 ( k - y k ) ( q(T-) q ) k q kq
Budgeting Manager Risk," Journal of Portfolio
TRSt = IRSt + PRSt
+ st -∆ t Over the
=
IR
- 1 course of this three-part
1
(T
)
=
the
effective
allocation
to
asset
series,
Zt
Management, Vol. 26, No. 3 (Spring),cpp. 90-104. y - n(T )
k
q
+
PBt -∆ t c,T
- qT ; y = yBt -∆ t (c,T ) =
class k
I
have
summarized
a
variety
of
factor
models
and
n
2
2
∑
y 1- 1 q
yst -∆ t (T )
i
S =
i=1 i
m
ISt applications,Pespecially
1+
some of their
portfolio
n 2 2= the
number of 2managers
Zt-∆ t T; yst -∆
t (T ) =
2
q
R =+ iB2ik RAkt
IRSt =
˜ it
i = Var[˜ui]
Akt + u
y - n(T )
y f (T )
i = BMit
P
+ 1+
portfolio
weight
on
manager
i
optimization.
Given
how
important
these
xi i M= k =the
1+ q
St
-
∆t
PRZt (T ) = TRZt (T ) - IRZt (T )
1
q
models are in investment practice, I encourage
q∆t
2
2
2
2
= i risk
P find any of these models PZt T - ∆t; yst (T - ∆t)
(T
)
y
ij Misfit
j M is:
=
+
readers
who
A
M
-1
IRZt (TS) = 1 + st -∆ t PRSt -=c1 St - 1 y - n(T )TRZt (T ) =
Bik
PBt c,T - ∆t; yBt ( c,T - ∆t)
+ practice to read thePZtsource
PSt1their
PBt -∆ t c,T ; y = yBt -∆ t q(c,T )relevant
= y to
--∆t 1own
-∆ t T ; yst -∆ t (T )
q
n n
n
TRBt (c,T ) =
-1
2
material that I refer to in these issues of
PBt -∆t c,T; yBt-∆ t (c,T )
wmi wj i m j M2 + wi 2 i 2
P =
- n(T )
f (T )
y TR =U.IRK + PR
M i=
q ) k q y kq
= 1 j = 1 k=1 ∑ q=1 ( k -i = 1k ) ( q - +
1+
1 + Quant
St
St
St
PRZt (T ) q= TRZt (T ) - IRqZt (T )
PZt T - ∆t; yst -∆ t (T )
- qT
n
2
2
IRZt (T )of=research
-1
Paul D. Kaplan, Ph.D., CFA, is director
with
c +
where:
y
(T
)
i
i
S =
st -∆ t
PZt -∆ t board
E [ r˜ it ] = i Ei=1[ r˜ Mt ]
T ; yst -∆ t (T )
+
P
=
Morningstar
Canada.
He
is
a
member
of
the
editorial
T;
y
(T
)
1
q PBt c,T - ∆t; yBt ( c,T -∆t)
Zt-∆
t
t
- n(T )
PBt c,T - ∆t; yBt (cc,Tst--∆∆t)
q
y
=
the
effective
allocation
to
asset
TRBt (c,T ) =
-1
k
PTR
= y 1 -magazine.
1 + q- 1
Bt -∆(c,T
t c,T
) =; y = yBt -∆ t (c,T )of Morningstar
PBt -∆t c,T; yBt-∆ t (c,T )
Bt
class k
PBt -∆t c,T; yBt-∆ t (c,T )
r˜ M ]standard deviation of the return
Cov=[ r˜ i ,the
f (T )
PZt T - ∆t; yst (T - ∆t)
y - n(T ) on y References
k
i =
2
+ 1+
1 + q Davidson,
M asset class k
TRZt (T ) =Lee. 2016. "A New Way to Interpret
- 1 Equity Risk."
q
PBt c,T - ∆t; yBt ( c,T )
Morningstar, October/November,
pp.) 37-40.
PZt -∆ t T ; yst -∆ t (T
= the correlation of the returns of asset
c +
kq
=
IR
-1
(c,T
)
Bt
n
-∆t; yBt ( c,T - ∆t)
q PBt c,T
μP - k and q
PBt -∆t c,T; yBt-∆ t (c,T )
max
classes
Elton, Edwin J. and Martin -J.1Gruber. 1994. "Multi-Index
=
=
TR
≥
s.
t.
w
0
,
w
1
P
(c,T
)
(
c,T
-
∆t)
c,T
-
∆t;
y
Bt i
i
Bt
Bt
w1 , w2 , ..., wn
Using
Simultaneous Estimation of All Parameters." q∆t
P
PBt -∆t Models
c,T; yBt-∆
i =1
t (c,T )
TR
- 1 y (T )
(T )
y
Bt (c,T ) =
Zt T -
A
Practitioner's
to∆t;
Factor
Models,
st -∆
t Zt (T ) Charlottesville,
= 1 + st -∆ t
IR
-1
yBt-∆ t (c,T )PGuide
The standard deviation of the returns on each PBt -∆t c,T;
q∆ t
q
=
IR
-
1
(T )Research Foundation of the Institute of Chartered
VA:ZtThe
yBt-∆ t ( c,T )
P
T
;
y
(T
)
assetn class and the correlations between them can
Zt -∆ t
st -∆ t
IRBt (c,T ) = 1 +
-1
Financial Analysts.
q
P
of the Bt c,T -∆t; yBt ( c,T )
μP be
= estimated
wi μi from the historical returns
IRBt (c,T ) = c
- 1. "Portfolio Theory Evolving: Markowitz
Kaplan,
Paul
D. 2015
i =1
+ PBtc,T;c,T
PRZt (T ) = TRZt (T ) - IRZt (T )
asset-class
indexes.
- ∆t)
-∆t;
yBt)( c,T
PqBt -∆t
yBt-∆
t (c,T
PRBt (c,T ) = TRBt (c,T ) - IRBt (c,T )
2.0."
Morningstar,
December/January,
pp. 54-56.
TRBt (c,T ) =
-1
PBt -∆t c,T; yBt-∆ t (c,T )
Kaplan,
D. 2016a. "Combining Alpha with Beta."
μi Measuring
= i μM Specific Risk
q∆ Paul
t
y - n(T )
c
2
)
yBt-∆ t ( c,T
PBt pp.
c,T ; .y = yBt -∆ t (c,T ) = y∆ P 1≈-- D1m+∆yq + 12 C ( ∆y )
Morningstar,
December/January,
-∆ t 48-54
Because we assume that unsystematic
IRBt (c,T ) = 1 +
-1
P
q
PBt c,T -∆t; yBt ( c,T )
q∆t
y - n(T )
y f (T )
IRBt (c,T ) =
- 1yst -∆ t (T ) + 1 +
1+ q
+
=
IR
-
1
q
1
(T
)
Zt
P
PRBt (c,T ) = TRBtBt-∆t
(c,T )c,T;
- IRyBt-∆
) )
q
t (c,T
global.morningstar.com/Morningstarmagazine
73
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https://corporate.morningstar.com/us/documents/PR/riskmodel-global-methodology-v1.pdf https://corporate.morningstar.com/us/documents/PR/riskmodel-global-methodology-v1.pdf http://global.morningstar.com/Morningstarmagazine

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https://www.nxtbook.com/nxtbooks/morningstar/advisor_20111201
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20101011
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100809_lincoln
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100809
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100607_lincoln
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100607
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100405_lincoln
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100405
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20100203
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20101201
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20091011
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20090809
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20090607
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20090405
https://www.nxtbook.com/nxtbooks/morningstar/advisor_20090203
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https://www.nxtbook.com/nxtbooks/morningstar/advisor_2008winter
https://www.nxtbookmedia.com