Dario Castagna, CFA, Investment Consultant, Morningstar ...media.morningstar.com/it/eventi/newsletter/AA/... · Prof. Giorgio Di Giorgio, Dean, Economics and Finance, LUISS University,

Prof. Giorgio Di Giorgio, Dean, Economics and Finance, LUISS University, Rome

Consigliere indipendente di Eurizon Capital SGR

© 2012 Morningstar Associates, LLC. All rights reserved. Morningstar Associates is a

registered investment advisor and wholly owned subsidiary of Morningstar, Inc. The

Morningstar name and logo are registered marks of Morningstar, Inc. This presentation

includes proprietary material of Morningstar Associates. Reproduction, transcription or other

use, by any means, in whole or in part, without the prior written consent of Morningstar

Associates is prohibited.

For Internal Use Only. Not For Public Distribution.

Prof. Giorgio Di Giorgio, Dean, Economics and Finance, LUISS University, Rome

Consigliere indipendente di Eurizon Capital SGR

Paul Kaplan, Ph. D., CFA, Quantitative Research Director,

Morningstar Europe, Ltd.

Dario Castagna, CFA, Investment Consultant,

Morningstar Investment Management, LLC.

Hal Ratner, Chief Investment Officer Europe,


Next Generation

Fund of Funds Optimization

Dario Castagna, CFA

© 2012 Morningstar Associates, LLC. All rights reserved. Morningstar Associates is a

registered investment advisor and wholly owned subsidiary of Morningstar, Inc. The

Morningstar name and logo are registered marks of Morningstar, Inc. This presentation

includes proprietary material of Morningstar Associates. Reproduction, transcription or other

use, by any means, in whole or in part, without the prior written consent of Morningstar

Associates is prohibited.

For Internal Use Only. Not For Public Distribution.

Investment Consultant

Morningstar Investment Management

Portfolio ConstructionAlpha-Tracking Error Optimization – Version 1.0

Strategic Asset Allocation Policy

Asset Classes or Risk Factors

?

Fund Specific Portfolio

Mutual Funds, ETFs, Hedge Funds

3 For Internal Use Only. Not For Public Distribution.

?

Portfolio Construction

Alpha-Tracking Error Optimization – Version 1.0



?


Mutual Funds, ETFs, Hedge FundsAlpha-Track Error

Optimizer


?




?



Optimizer


?

Markowitz

2.0

Fund of Funds

Optimization

2.0

2.0


The Alpha (or Product) Decision


Fund of Funds Optimization – Version 1.0

Ex

pecte

d R

etu

rn

Strategic Asset AllocationSet Strategic Asset Allocation Policy

AggressiveRisk Range

10

90

ModerateRisk Range

60 40

Conservative

20

80

% Stocks

Emerging Markets

Non-US Developed

US Bonds

Private Equity

Commodities

US Small Cap

US Large Cap


0Ex

pecte

d R

etu

rn

This is a graphical representation; plot points are not necessarily meaningful.

Risk

ConservativeRisk Range

% Bonds US Bonds

TIPS

Cash

Liability

(Short TIPS-like characteristics)

Ex

pecte

d R

etu

rn

Alp

ha

Tracking Error

Portfolio ConstructionAlpha-Tracking Error Optimization


0Ex

pecte

d R

etu

rn

Risk


Ex

pecte

d R

etu

rn

Alp

ha

Tracking Error


Combinations of asset classes

Combinations of funds


0Ex

pecte

d R

etu

rn

Risk


Combinations of asset classes

Ex

pecte

d R

etu

rn

Alp

ha

Tracking Error

Portfolio ConstructionAlpha-Tracking Error Optimization Better funds

lead to better

implementation

frontiers


0Ex

pecte

d R

etu

rn

Risk


Ex

pecte

d R

etu

rn

Portfolio ConstructionAn Alpha-Tracking Error Optimization occurs for Each Strategic Asset Allocation

% Stocks


0Ex

pecte

d R

etu

rn


Risk

% Bonds

Portfolio ConstructionAlpha Tracking-Error Optimization – Version 1.0

Max UA = Alpha – Penalty for Tracking Error


Alpha

ReturnAsset Class Misfit Risk

Manager

Specific Risk

Aversion to

Misfit Risk

Aversion to

Misfit Risk


MaxA U = Alpha – Penalty for Tracking Error


-0.5

0.0

0.5S

kew

ness

Non-U.S Bonds.

U.S. REITsU.S. TIPS

Non-U.S. REITsCash

Non-U.S. Dev

Emerging Equities

Commodity

Large Value

U.S. BondsSmall Growth

Large Growth

Strategic Asset AllocationNon-Normal Asset Class Returns – Skewness and Kurtosis (1990.2 – 2010.5)


-2.0

-1.5

-1.0

0 4 8 12

Kurtosis

Skew

ness

Global High Yield

U.S. TIPSSmall Value

Large Value

Source: “The Impact of Skewness and Fat Tails On the Asset Allocation Decision” by James Xiong and Thomas Idzorek (2011).

Portfolio ConstructionFund Returns can Depart Significantly from the Normal Distribution

Mutual

Funds

Hedge

Funds

Skewness (5th) -1.9 -2.0

Worst 5th Percentile Fund


Skewness (5th) -1.9 -2.0

Kurtosis (5th) 9.6 15.7

CVaR (5th) - Monthly -17.9 -21.6

Portfolio ConstructionFund Returns can Depart Significantly from the Normal Distribution

Mutual

Funds

Hedge

Funds

Skewness (1st) -2.2 -3.6

Worst 1st Percentile Fund


Skewness (1st) -2.2 -3.6

Kurtosis (1st) 17.0 31.5

CVaR (1st) - Monthly -23.0 -32.0


MaxA U = Alpha – Penalty for Tracking Error



The Alpha (or Product) Decision


Fund of Funds Optimization – Version 2.0





?



Optimizer


?

Markowitz

2.0

Fund of Funds

Optimization

2.0

2.0


Max Ut = Total Return – Penalty for CVar – Penalty for Misfit Risk

Total Portfolio Return


Total Portfolio Return(Benchmark Return + Active Beta Return + Manager Alpha Return)

Penalty for CVaR Penalty for Misfit Risk


Max Ut = Total Return – Penalty for CVar – Penalty for Misfit Risk



Max Ut = Total Return – Penalty for CVar

Constraint: Max Misfit



Out of Sample Test: 1997 – 2011

Each Month: Rank

Funds by Standard

Deviation

Fund of Funds Optimizer – Version 1.0


400 Equity

Funds

Create 25

Opportunity Sets

Each with 16 Funds

Fund of Funds Optimizer – Version 2.0

2.0



8%

12%

16%

Retu

rn

Version 2

Version 1

Equal Weights


0%

4%

8%

10% 14% 18% 22% 26%Standard Deviation

Retu

rn

30%

Equal Weights

The last 15 years:

Two Moments

Not well suited for alternatives

The Near Future:

Four Moments

Well suited for alternatives

Fund of Funds Optimizer – Version 1.0 Fund of Funds Optimizer – Version 2.0




2.0



Social Security

Percezione del problema pensionistico negli USA



Social Security




Social Security


Il Social Security System sta affrontando seri problemi


Il Social Security System sta affrontando seri problemi

finanziari, sono necessarie azioni immediate affinche’ i

giovani di oggi siano pronti per la pensione


Social Security




Social Security


Se non agiamo immediatamente per sostenere il Social

Security, in soli 11 anni pagheremo piu’ soldi di quanto

collezioneremo in tasse. Senza cambiamenti, entro il


collezioneremo in tasse. Senza cambiamenti, entro il

2040, il Social Security Trust Fund sara’ esaurito.





ALLEGATI

Version 1.0 Inputs

►Asset Class Expected Total Returns

►Asset Class Correlations

►Asset Class Standard Deviations

► ----

► Asset Class Correlations

► Asset Class Standard Deviations

►Manager Expected Alphas

Mean-Variance Optimization Fund of Funds Optimization


► Standard Deviation of Alphas

► Correlations of Alphas

►Manager Asset Class Exposures


Alpha

ReturnAsset Class Misfit Risk

Manager

Specific Risk


Return Specific Risk

Aversion to

Misfit Risk

Aversion to

Misfit Risk

Alpha – Penalty for Tracking Error

Portfolio Alpha( )

mTmP αh=α

=mh Manager Holdings or Weights (M x 1 column vector)

Pα

Portfolio ConstructionPortfolio Alpha


=mα Manager Alphas (M x 1 column vector)

Tracking Error ( )

( ) ( ) mmTm

Tb

Tmk

TTb

TmP hVhhXhVhXh +−−=Ψ

=mh Manager Holdings (m x 1 column vector) Manager Specific Risk

Asset Allocation Misfit Risk

Ψ

Portfolio ConstructionTracking Error


=X Manager Asset Class / Style Exposures (m x k matrix, where k is the number of asset classes and m is

the number of managers)

=bh Benchmark Holdings (k x 1 column vector)

=kV Asset Class Covariance Matrix (k x k matrix)

=mV Manager Specific Risk Covariance Matrix (k x k matrix)

Version 2.0 Inputs

►Asset Class Expected Total Returns

►Asset Class Correlations

►Asset Class Standard Deviations

►Asset Class Skewness

► ----

► Asset Class Correlations

► Asset Class Standard Deviations

►Manager Expected Alphas

Mean-CVaR Optimization Fund of Funds Optimization


►Asset Class Kurtosis ► Standard Deviation of Alphas

► Correlations of Alphas

►Manager Asset Class Exposures

►Manager Expected Total Returns

►Manager Standard Deviations

►Manager Skewness

►Manager Kurtosis


Total Portfolio Return(Benchmark Return + Active Beta Return + Manager Alpha Return)


Penalty for CVaR

Subject to: Asset Class Constraints or Asset Class Misfit Risk



8%

12%

16%

Retu

rn

Version 2

Version 1

Equal Weights


0%

4%

8%

10% 14% 18% 22% 26%Standard Deviation

Retu

rn

30%

Equal Weights


Social Security




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Dario Castagna, CFA, Investment Consultant, Morningstar ...media.morningstar.com/it/eventi/newsletter/AA/... · Prof. Giorgio Di Giorgio, Dean, Economics and Finance, LUISS University,