Risk Factors as Building Blocks of Asset Allocation

128 Pages·2013·1.83 MB·English

Risk Factors as Building Blocks of
Asset Allocation
A Conceptual and Empirical Analysis
MASTER’S THESIS
Submitted in Partial Fulfillment of the Requirements for the Degree of
MASTER OF SCIENCE
in Banking and Finance
Assoz.Prof. PD Dr. Jochen LAWRENZ
Department of Banking and Finance
The University of Innsbruck School of Management
Submitted by
Josef ZORN
Innsbruck, June 2013
Contents
List of Tables III
List of Figures IV
List of Symbols V
List of Abbreviations VII
1. Introduction 1
2. Traditional Approaches in Asset Allocation 4
2.1. Modern Portfolio Theory . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2. The Concept of Asset Classes . . . . . . . . . . . . . . . . . . . . . . 9
2.3. Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1. Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2. Characteristics Across Asset Classes . . . . . . . . . . . . . . . 17
2.3.3. Correlation of Asset Classes . . . . . . . . . . . . . . . . . . . 18
2.3.4. Regime Shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.5. Diversification . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3. Risk Factors as Building Blocks of Asset Allocation 25
3.1. The Concept of Risk Factors . . . . . . . . . . . . . . . . . . . . . . . 25
3.2. Determining Risk Factors . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3. Key Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.1. Macroeconomic Factors . . . . . . . . . . . . . . . . . . . . . . 32
3.3.2. Regional Factors . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3.3. Fundamental Factors . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.4. Fixed Income Factors . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.5. Other Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4. Exposure to Risk Factors . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5. Factor Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4. Empirical Analysis - Factor Loadings 49
4.1. Previous Research on Factor Loadings . . . . . . . . . . . . . . . . . 49
4.2. Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.1. Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2.2. Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
I
Contents
4.2.3. Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.4. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3. Descriptive Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.1. Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.2. Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4. Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.5. Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5. Implications for Portfolio Construction 67
5.1. Alternative Categorizations of Assets . . . . . . . . . . . . . . . . . . 68
5.2. Investment Approaches Based on Risk Factors . . . . . . . . . . . . . 73
5.3. Risk Factor Portfolios versus Asset Class Portfolios . . . . . . . . . . 76
5.3.1. Ex Post Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.3.2. Ex Ante Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.4. Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6. Summary and Conclusions 89
Bibliography 92
A. Appendix 103
B. Affidavit 120
II
List of Tables
3.1. Possibilities to Gain Risk Factor Exposure . . . . . . . . . . . . . . . 44
4.1. List of Factor Variables and Data Sources . . . . . . . . . . . . . . . 55
4.2. List of Indices and Data Sources . . . . . . . . . . . . . . . . . . . . . 56
4.3. Correlation Matrix of Factors, Sample 1990-2013 . . . . . . . . . . . . 58
4.4. Regression Results for SPX - Sample 1990-2013 . . . . . . . . . . . . 60
4.5. Main Regression Results for Indices - Sample 1990-2013 . . . . . . . . 62
5.1. Factor Categorization . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2. Fundamental Factor Categorization . . . . . . . . . . . . . . . . . . . 71
5.3. Asset Classes and Sensitivities to Factors . . . . . . . . . . . . . . . . 72
5.4. Out-of-Sample Statistics 1998-2012 . . . . . . . . . . . . . . . . . . . 82
A.1. Correlation of Asset Classes 1978-1995 . . . . . . . . . . . . . . . . . 104
A.2. Correlation of Asset Classes 1991-2008 . . . . . . . . . . . . . . . . . 104
A.3. Correlation in Calm Periods 1987-2009 . . . . . . . . . . . . . . . . . 105
A.4. Correlation in Turbulent Periods 1987-2009 . . . . . . . . . . . . . . . 105
A.5. Risk Factor Correlations for 5, 10 and 15 Years . . . . . . . . . . . . 106
A.6. Correlation of Style and Strategy Factors 1995-2008 . . . . . . . . . . 107
A.7. Asset Class Diversification Potential . . . . . . . . . . . . . . . . . . . 108
A.8. Summary Statistics for Factors . . . . . . . . . . . . . . . . . . . . . 109
A.9. Summary Statistics for Indices . . . . . . . . . . . . . . . . . . . . . . 114
A.10.Correlation of Selected Indices . . . . . . . . . . . . . . . . . . . . . . 116
A.11.Main Regression Results for Indices - Sample 2000-2013 . . . . . . . . 118
A.12.Matlab Code for Portfolio Optimization . . . . . . . . . . . . . . . . . 119
III
List of Figures
2.1. Traditional and Alternative Asset Classes . . . . . . . . . . . . . . . . 11
2.2. Asset Classes in the µ−σ Space 1991 - 2008 . . . . . . . . . . . . . . 12
2.3. Correlations between S&P 500 and EAFE 1970-2009 . . . . . . . . . 20
2.4. Correlation Profile between U.S. and World Ex-U.S. 1979-2009 . . . . 21
3.1. Sampling of Risk Factors and Potential Groupings . . . . . . . . . . . 31
3.2. Factor Exposure across U.S. Stocks and Bonds . . . . . . . . . . . . . 31
4.1. Descriptive Statistics for SPX 1990-2013 . . . . . . . . . . . . . . . . 58
4.2. Factors Loadings Bar Chart - Sample 1990-2013 . . . . . . . . . . . . 63
4.3. Factors Decomposition Chart - Sample 1990-2013 . . . . . . . . . . . 64
5.1. Categorization Based on Macroeconomic Scenarios . . . . . . . . . . 69
5.2. Mean-Variance Optimal Risk Factor Portfolios . . . . . . . . . . . . . 75
5.3. µ−σ Scatterplot and Efficient Frontier for Traditional Portfolio . . . 77
5.4. Comparison of Portfolios with Zero-β-CAPM . . . . . . . . . . . . . . 79
5.5. Rolling Blanket Charts (Out-of-Sample) . . . . . . . . . . . . . . . . 80
5.6. Cumulative Return of Risk Factor, Asset Class and 60/40 Portfolio . 82
A.1. Average Correlations: Risk Factors vs. Asset Classes . . . . . . . . . 107
A.2. Histogram of Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
A.3. Graph for Each Factor Across Time . . . . . . . . . . . . . . . . . . . 111
A.4. Factors Decomposition Chart - Sample 2000-2013 . . . . . . . . . . . 112
A.5. Scatterplot Matrix for all Constructed Factors . . . . . . . . . . . . . 113
A.6. µ−σ Diagram for Index Returns 1990-2013 . . . . . . . . . . . . . . 115
A.7. µ−σ Diagram for Index Returns 2000-2013 . . . . . . . . . . . . . . 115
A.8. Rolling Efficient Frontiers . . . . . . . . . . . . . . . . . . . . . . . . 117
A.9. µ−σ Scatterplot and Efficient Frontier for Factors . . . . . . . . . . 117
IV
List of Symbols and Notations
a Regression intercept
A Risk aversion parameter
b Regression coefficient
B n×k matrix of factor betas (loadings)
β Beta of a portfolio [= Cov(R ,R )/Var(R )]
i i m m
c Constant
C Convexity of a bond
CF Cash flow
def Default risk factor
D Macaulay duration of a bond
DW Durbin-Watson statistic
E Expected value operator
(cid:15) n vector of asset specific returns
f k vector of factor returns
g Economic growth factor
h n vector of ones
HML Value factor (high minus low book-to-market ratio)
i = 1,··· ,N Index for cross sectional observations
iid Identically and independently distributed
m Market portfolio
M Momentum factor
MD Modified duration of a bond
µ Mean return
V
List of Symbols and Notations
N(µ, σ2) Normal distribution with mean µ and variance σ2
PV Cash flow payment
π Inflation factor, where subscript ∆e is the change in expectation and
ue the unexpected inflation
r Vector of random returns on n assets
R2 Coefficient of determination
R Return, where subscript p denotes portfolio return, f the risk free
return, m the market return and z the zero-beta portfolio return,
respectively
ρ Pearson correlation coefficient
S Sharpe ratio
i
σ Standard deviation
σ Covariance between the zero-beta portfolio and the market
1m
σ2 Variance of the portfolio
p
Σ Variance/covariance matrix for all N assets
SMB Size factor (small minus big)
t = 1,··· ,T Index for time series
term Term structure factor
V Present value of all cash payments from an asset
vol Volatility factor
w Portfolio weight
i
w n vector of weights in the market portfolio
m
w0 k vector of weights in the minimum-variance-zero-beta portfolio
1
y Yield or discount rate
z Zero-beta portfolio
VI
List of Abbreviations
AMH Adaptive Markets Hypothesis
APT Arbitrage Pricing Theory
CAL Capital Allocation Line
CAPM Capital Asset Pricing Model
CML Capital Market Line
CPI Consumer Price Index
CVaR Conditional Value at Risk
EMH Efficient Market Hypothesis
ETF Exchange Traded Fund
IP Industrial Production
LIBOR London Interbank Offered Rate
MPT Modern Portfolio Theory
MVO Mean Variance Optimization
OLS Ordinary Least Square
OTC Over The Counter
PCA Principal Component Analysis
REIT Real Estate Investment Trust
TIPS Treasury Inflation-Protected Securities
VaR Value at Risk
VIX Chicago Board Options Exchange Market Volatility Index
VII
1. Introduction
Asset allocation is a crucial step in designing balanced investment strategies. The
mix between different assets in a portfolio is the major key to balance risk and re-
turn. With the possibility of diversification investors can achieve better long term
returns from equal risk portfolios than from individual assets, given less than perfect
correlation. Based on this simple idea a whole theory emerged in the last century,
most influenced by Harry Markowitz (1952). The associated framework, modern
portfolio theory (MPT), can hardly be neglected in financial theory when it comes
to investment decisions. In line with MPT, the traditional method builds upon the
division of asset classes as starting points for portfolio construction. It is assumed
that the correlation between different asset classes is significantly different to the
correlation within each asset class. To some extent this is true. However, critics
point to the weaknesses of traditional asset allocation. This weaknesses, inter alia,
comprise unstable and asymmetric correlation between asset classes and diminished
diversification. Moreover, the classification in asset classes deludes the true risk
inherent in assets. Prominently, after the recent crisis, critics grew even louder on
traditional asset class diversification as portfolios performed worse amid turmoil.
As Lum (2012) argues, traditional asset management may have worked in the 1990s
during the ‘great moderation’, yet, it clearly did not work over the past 15 years.
Given the instability in markets and evolving crises a shift in the industry with
respect to the asset allocation approach seems to take place.
1
1. Introduction
The objective of this thesis is to outline an alternative approach to asset allocation.
Given the weaknesses of traditional approaches in asset allocation, specifically with
regard to the concept of asset classes, it seems worthwhile to investigate different
methods in this discipline. Particularly, this paper attempts to focus on risk factors
as building blocks for portfolio design. Although, the idea of risk-factor approaches
is not new, the recent crises in 2001 and most strikingly the global financial crisis
beginning 2007 envisioned the poor diversification and performance of conventional
portfolios. Therefore, this thesis aims on finding an alternative to asset allocation by
lookingatthemicroscopicdriversofassetreturnsthroughthelensofrisk. Insteadof
looking at the more granular level of asset classes this approach focuses on multiple
underlying systemic influences that drive risk and returns for each asset. It will
be elaborated which of the varying risk factors are relevant and how diversification
can benefit from low correlations between these factors. Furthermore, an empirical
part will shed some light on how exposed (sub-) asset classes are to specific risk
factorsandwhetherseeminglydiverseassetclassessharesomesimilarriskexposures.
Based on this results, it will be analyzed whether risk factor portfolios are superior
to traditional ‘asset class’ portfolios. Also, this thesis tries to outline a different
categorization of asset classes based on risk factors.
The thesis is organized as follows. Section 2 reviews the traditional concepts of
asset allocation starting from Markowitz (1952) and modern portfolio theory to re-
cent developments. Crucially, this chapter highlights the major weaknesses in this
traditional approach stemming from the categorization of asset classes. Section 3
drafts an approach for asset allocation based on risk classes. The importance of risk
factors is described and a categorization of possible factors and their justification is
exemplified. Further, differences in correlation between asset classes and risk classes
are illustrated as well as the potential benefits for diversification of portfolios. An
empirical analysis is conducted in Section 4. The empirical part tries to capture the
risk exposure or factor loadings of (sub-) asset class indices and analyzes them with
statistical tools. Inferences from the empirical part and the theoretical discussion
2