Long-Term Asset Allocation

122 Pages·2014·0.9 MB·English

Long-Term Asset Allocation
DISSERTATION
zur Erlangung des Grades eines
Doktors der Wirtschaftswissenschaft (Dr. rer. pol.)
eingereicht bei der
Wirtschaftswissenschaftlichen Fakulta¨t
der Universita¨t Regensburg
von
Dipl.-Math. Oec. Tim Koniarski
Berichterstatter
Prof. Dr. Steffen Sebastian
Prof. Dr. Rolf Tschernig
Tag der Disputation
6. Februar 2014
Contents
1 Introduction 1
2 Inflation-Protecting Asset Allocation: A Downside Risk Analysis 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Modeling Asset Return Dynamics . . . . . . . . . . . . . . . . 10
2.2.2 The Concept of Lower Partial Moments . . . . . . . . . . . . . 12
2.2.3 The Portfolio Choice Problem . . . . . . . . . . . . . . . . . . 13
2.3 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.2 VAR Estimation Results . . . . . . . . . . . . . . . . . . . . . 18
2.3.3 Inflation Protection of Individual Assets . . . . . . . . . . . . 21
2.3.4 Inflation-Protecting Asset Allocation . . . . . . . . . . . . . . 24
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3 Modeling Asset Price Dynamics under a Multivariate Cointegra-
tion Framework 31
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.1 VAR Specification . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.2 VEC Specification . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.3 Horizon-Dependent Variance-Covariance . . . . . . . . . . . . 37
3.2.4 Portfolio Choice Problem . . . . . . . . . . . . . . . . . . . . . 39
3.3 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 Data and Time Series Properties . . . . . . . . . . . . . . . . 41
I
Contents
3.3.2 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.3 Long Horizon Effects . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.4 Asset Allocation Decisions . . . . . . . . . . . . . . . . . . . . 63
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.A Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.A.1 Bootstrap Method . . . . . . . . . . . . . . . . . . . . . . . . 70
3.A.2 Model Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4 Do Stock Prices and Cash Flows Drift Apart? The Influence of
Macroeconomic Proxies 72
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2.1 The Econometric Model . . . . . . . . . . . . . . . . . . . . . 76
4.2.2 Hypotheses Testing . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2.3 Long-Run Analyses . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2.4 Returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.3 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3.1 Data and Time Series Properties . . . . . . . . . . . . . . . . 81
4.3.2 Cointegration Rank Analysis . . . . . . . . . . . . . . . . . . . 87
4.3.3 Restriction Tests . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.3.4 Testing the Financial Ratios . . . . . . . . . . . . . . . . . . . 93
4.3.5 Level Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.3.6 Horizon-Dependent Analysis . . . . . . . . . . . . . . . . . . . 97
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.A Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.A.1 Model Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.A.2 Univariate Stationarity of the Financial Ratios . . . . . . . . . 104
4.A.3 Stability of the Long-Run Matrices across the Models . . . . . 105
4.A.4 Bootstrap Method . . . . . . . . . . . . . . . . . . . . . . . . 107
Bibliography 108
II
List of Figures
2.1 Correlations between Asset Returns and Inflation . . . . . . . . . . . 22
4.1 Level Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.2 Differenced Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3 Impulse Response Functions . . . . . . . . . . . . . . . . . . . . . . . 98
4.4 Impulse Response Functions of Returns . . . . . . . . . . . . . . . . . 100
III
List of Tables
2.1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 VAR Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Lower Partial Moments of the Asset Returns . . . . . . . . . . . . . . 23
2.4 Minimum Semivariance Portfolios with Real Return Target of 0% . . 25
2.5 Minimum Semivariance Portfolios with Positive Real Return Targets . 27
3.1 Abbreviationsg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Simultaneous and Lagged Correlations . . . . . . . . . . . . . . . . . 44
3.4 Unit Root and Cointegration Rank Test . . . . . . . . . . . . . . . . 45
3.5 VAR Parameter Estimatesg . . . . . . . . . . . . . . . . . . . . . . . 47
3.6 VEC Parameter Estimatesg . . . . . . . . . . . . . . . . . . . . . . . 50
3.7 Term Structure of Risk and Correlationsg. . . . . . . . . . . . . . . . 55
3.8 Variance Decomposition for Treasury Bills . . . . . . . . . . . . . . . 57
3.9 Variance Decomposition for Stock Returns . . . . . . . . . . . . . . . 58
3.10 Variance Decomposition for Bond Returns . . . . . . . . . . . . . . . 61
3.11 Global Minimum Variance Portfoliosg . . . . . . . . . . . . . . . . . . 64
3.12 Optimal Portfolio Holdings for γ = 20 . . . . . . . . . . . . . . . . . . 66
3.13 Lag Length Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.1 Univariate Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.3 Cointegration Rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.4 β Restriction Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.5 α Restriction Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
IV
Tables
4.6 Financial Ratio Stationarity Tests . . . . . . . . . . . . . . . . . . . . 94
4.7 Π Matrix of Model M and r = 4 . . . . . . . . . . . . . . . . . . . 96
r 6
4.8 Lag Length Selection and Cointegration Rank Stability . . . . . . . . 103
4.9 Univariate Stationarity of Financial Ratios . . . . . . . . . . . . . . . 104
4.10 Stability Analysis of the Long-Run Matrices . . . . . . . . . . . . . . 106
V
Chapter 1
Introduction
Individual as well as institutional investors face the decision of how to allocate assets
in their portfolios. In general, it is distinguished between strategic and tactical
asset allocation. While strategic asset allocation concentrates on the allocation and
diversification of a portfolio among major asset classes such as cash, bonds, stocks
and real estate, tactical asset allocation is a dynamic adjustment of the strategic
asset allocation weights with the intent to add value due to a changing fundamental
marketenvironment. Thisthesisfocusesonstrategicassetallocationanddetermines
optimal portfolios for investors with specific objectives (inflation-hedging) and/or
with a focus on long-term investments.
The era of modern portfolio theory starts with the seminal work of Markowitz
(1952), which introduces the famous mean-variance optimization framework, an ap-
proach that determines optimal portfolios which exhibit minimum risk measured by
the variance for a given required return. Although Markowitz optimization is still
widely used in academia and in practice, it has the limitation that it is static, i.e.
onlyaone-periodinvestmenthorizonisconsidered, whichisunrealisticforlong-term
investors. Due to the fact that the assets’ term structure of risk and asset corre-
lations vary substantially over the investment horizon, optimal horizon-dependent
asset allocations are also time-varying (Campbell and Viceira, 2005). To take into
account this time variation in the term structure of risk, the asset allocation litera-
ture is currently focusing on more sophisticated portfolio approaches. The complex
dynamics of expected returns and risk are usually captured by stationary vector
1
Introduction
autoregressive (VAR) models, which typically contain the returns of the assets an-
alyzed and some so-called state variables, which are used to predict these returns.
Such VAR models are also used in the following three self-contained chapters/essays
of this thesis, but several contributions to the asset allocation literature are made
as well.
In the essay ’Inflation-Protecting Asset Allocation: A Downside Risk Analysis’
(Chapter 2), written in cooperation with Steffen Sebastian, we are the first to ap-
ply the VAR approach to bootstrap multi-period asset returns, which maintains the
asymmetric asset return distributions. Additionally, we determine the inflation-
protecting abilities of cash, bonds, stocks and real estate and optimal horizon-
dependent inflation-protecting asset allocations within a downside risk framework.
This downside risk analysis was inspired by two facts. First, previous studies only
analyze correlation statistics between asset returns and the inflation rate to inves-
tigate the inflation-hedging qualities of the assets mentioned. However, correlation
only measures the linear relation between the return and inflation. Thus, a posi-
tive correlation does not necessarily imply that the asset is a good inflation hedge,
because the asset return could always be lower than the inflation rate despite the
positive correlation. This issue has not been addressed in earlier studies and hence,
we compare these correlations to lower partial moments (LPM) which measure the
risk of the asset to fall below the inflation rate. Second, we argue that the most
widely used risk measure in the asset allocation context, the variance, does not
adequately represent the risk perception of investors and downside risk measures
are more suitable to investors’ risk understanding and in the presence of asymmet-
ric return distributions. Markowitz (1959) already pointed out the advantages of
downside risk measures compared to the variance, but it was not possible to handle
those risk measures at that time due to their computational complexity.
In the essay ’Modeling Asset Price Dynamics under a Multivariate Cointegration
Framework’ (Chapter 3), written in cooperation with Benedikt Fleischmann, we
argue that the traditional VAR approach to modeling long-run asset price dynamics
ignores common long-run relations between the assets and the state variables. In the
presenceofso-calledcointegrationrelations, deviationsinthelong-termcomovement
of the variables cause forecastable backward movements. To take into account such
2
Introduction
cointegration relations among the assets and state variables, we capture the asset
pricedynamicsusingavectorerrorcorrection(VEC)model, whichisanextensionof
the stationary VAR model. We, then, make several comparisons between the VEC
and the stationary VAR approach, where both models include T-bills, stocks and
bonds and the same set of state variables that have been shown to predict returns
(dividend-price ratio, term spread and inflation). These comparisons include the
modeled short and long-run behavior, the term structure of risk and the resulting
optimal portfolio choice.
In the essay ’Do Stock Prices and Cash Flows Drift Apart? The Influence of
Macroeconomic Proxies’ (Chapter 4), written in cooperation with Benedikt Fleisch-
mann, we examine the validity of cointegration between stock prices and cash flows
and analyze the additional influence of macroeconomic proxies within a cointegrated
VAR framework. This paper is motivated by the fact that the often used state vari-
ables in the traditional VAR approach such as the dividend-price or the earnings-
price ratio are assumed to be stationary. Since these one-for-one cointegration rela-
tions are empirically doubtful and non-stationarity would lead to invalid conclusions
about the return forecastability, we investigate possible macroeconomic influences
(inflation, short-term interest rates, government and corporate bond yields) which
can cause the breakdown of these relations. Thus, although we do not determine
optimal asset allocations, this paper is still relevant for the asset allocation literature
as return predictions are of significant importance for portfolio choices.
3
Introduction
Research Questions
This section gives a short overview of the research questions examined in each essay
of this thesis:
Chapter 2: Inflation-Protecting Asset Allocation: A Downside Risk
Analysis
• DocorrelationsandLPMsprovidethesameresultswithrespecttotheinflation-
protecting abilities of cash, bonds, stocks and real estate?
• Whatareoptimalhorizon-dependentinflation-protectingassetallocationswith-
in the downside risk framework?
• How do optimal allocations differ for investors that require a positive real
return?
Chapter 3: Modeling Asset Price Dynamics under a Multivariate Coin-
tegration Framework
• Are there differences of the VEC compared to the VAR model with respect to
the predictability of cash, stocks and bonds?
• What are the differences in the term structure of risk modeled by the two
approaches and what are the sources of these differences?
• How do the optimal portfolio choices suggested by the two models differ?
Chapter 4: Do Stock Prices and Cash Flows Drift Apart? The Influ-
ence of Macroeconomic Proxies
• Is the assumption of stationarity of the dividend-price ratio and the earnings-
price ratio valid in the multivariate cointegration framework?
• Is the assumption of stationarity of other financial ratios, which are addition-
ally used in the predictability literature, valid in the multivariate cointegration
framework?
• How do the macroeconomic variables influence stock prices and cash flows and
what are the resulting consequences on total stock returns?
4