Dynamic Asset Allocation with Liabilities

Published date01 March 2017
DOIhttp://doi.org/10.1111/eufm.12097
Date01 March 2017
Dynamic Asset Allocation with
Liabilities
Daniel Giamouridis
Quantitative Solutions, Bank of America Merrill Lynch, United Kingdom
E-mail: daniel.giamouridis@baml.com
Athanasios Sakkas
Southampton Business School, University of Southampton, United Kingdom
E-mail: a.sakkas@soton.ac.uk
Nikolaos Tessaromatis
EDHEC Business School and EDHEC Risk Institute, France
E-mail: nikolaos.tessaromatis@edhec.edu
Abstract
We develop an analytical solution to the dynamic multi-period portfolio choice
problem of an investor with risky liabilities and time varying investment
opportunities. We use the model to compare the asset allocation of investors who
take liabilities into account, assuming time varying returns and a multi-period
setting with the asset allocation of myopic ALM investors. In the absence of
regulatory constraints on asset allocation weights, there are signicant gains to
investors who have access to a dynamic asset allocation model with liabilities. The
gains are smaller under the typical funding ratio constraints faced by pension
funds.
The authors are grateful to the Editor, John Doukas and three anonymous referees for their
constructive comments. Furthermore, the paper has benefited from comments by Andrew
Ang, Michael Rockinger, Stephen Zeldes and participants at Fourth Joint BIS-World Bank
Public Investors Conference, Washington, DC 2012, at the DauphineAmundi Chair in
Asset Management 2012 Annual Workshop, Paris 2012 and Nineteenth International
Conference Forecasting Financial Markets, Marseille 2012. The authors are grateful for
financial support from the Dauphine-Amundi Chair in Asset Management. Daniel
Giamouridis also greatly acknowledges financial support from the Athens University of
Economics and Business Research Center (EP-1681-01, EP-1994-01) and notes that the
views expressed in this paper are his own and do not necessarily reflect those of Bank of
America Merrill Lynch. Daniel Giamouridis is also affiliated with LUMS, Cass Business
School, and the EDHEC-Risk Institute. This work was largely completed when Daniel
Giamouridis was an Associate Professor of Finance in the Department of Accounting and
Finance at Athens University of Economics and Business. Any remaining errors are the
responsibility of the authors.
European Financial Management, Vol. 23, No. 2, 2017, 254291
doi: 10.1111/eufm.12097
© 2016 John Wiley & Sons, Ltd.
Keywords: strategic asset allocation, dynamic asset allocation, asset-liability
management, return predictability, myopic investors
JEL classification: G11, G12, G23
1. Introduction
It is known since the work of Samuelson (1969) and Merton (1969; 1971; 1973) that
long-term investors might judge risks very differently from short-term investors and
hence hold different portfolios. Although Merton (1971; 1973) developed an analytical
framework for understanding the portfolio demands of long-term investors, empirical
implementation of his work lagged far behind due to the difculty of solving Mertons
intertemporal model (Campbell and Viceira, 2002). The importance of liabilities in
strategic asset allocation has also been long recognised by both practitioners and
academics with analytical discrete-time solutions available only under static, one-period
horizons. In this paper we develop an analytical solution to the dynamic multi-period
portfolio choice problem of an investor under time-varying investment opportunities.
We then use the model to compare the asset allocation of investors who ignore the time-
varying properties of future asset risks and returns (myopic investors).
A brief taxonomy of multi-period portfolio choice solutions in an asset-only
framework is provided in Jurek and Viceira (2011, JV hereafter). JV identify three types
of approaches to optimal portfolio selection. First, optimal portfolios can be obtained as
exact analytical solutions for special cases of the multi-period portfolio choice problem
in a continuous time setting (Brennan and Xia, 2002; Chacko and Viceira, 2005; Kim and
Omberg, 1996; Liu, 2007; Sorensen, 1999; Wachter, 2002). Second, optimal portfolios
can be determined with numerical methods (Barberis, 2000; Brandt, 1999; Brandt et al.,
2005; Brennan et al., 1997; Dammon et al., 2001; Detemple et al., 2003; Koijen et al.,
2010; Lynch, 2001). Third, optimal portfolios can be computed in closed-form through
approximate analytical methods (Campbell and Viceira, 1999; 2001; 2002, Campbell
et al., 2003). JV also discuss the shortcomings of these approaches and propose an
analytical recursive approach which results in a closed-form solution for the dynamic
multi-period portfolio choice problem.
Multi-period portfolio choice is particularly relevant for investors who invest with the
objective to nance a long-term stream of liabilities. Best known examples of such
investors are pension funds, foundations and endowment funds. It is also relevant to
individual investors who manage their own retirement funds or build portfolios to
nance their childrens education. In this paper we study the portfolio choice problem of
this type of investor, a problem that is generally referred to as Asset Liability
Management (ALM hereafter).
Leibowitz (1987) and Sharpe and Tint (1990) are the rst papers that incorporate
liabilities in a single period context. Since then the literature on portfolio choice in a
multi-period context in the presence of liabilities, parallels developments in the asset-
only portfolio choice literature. In a continuous setting Boulier et al. (1995) formulate a
dynamic programming model of pension fund behaviour. Sundaresan and Zapatero
(1997) formulate and solve a continuous time model for the strategic asset allocation of a
dened benet pension fund taking into account the marginal productivity of the
employee under a constant investment opportunity set. Rudolf and Ziemba (2004)
© 2016 John Wiley & Sons, Ltd.
Dynamic Asset Allocation with Liabilities 255
assume time-varying investment opportunities and develop a four-fund theorem for
intertemporal surplus optimisation.
A second strand of the literature, closer to asset-liability modeling practice,
1
uses
stochastic programming techniques (Cari~
no et al., 1998; Cari~
no and Ziemba, 1998;
Geyer and Ziemba, 2008) to nd optimal asset weights. A third approach is based on
simulation (Binsbergen and Brandt, 2016). These approaches are however subject to the
criticisms expressed in JV in the context of asset-only portfolio choice. Stochastic
programming techniques for example face the cost of tractability; the traditional
numerical methods cannot handle more than a few state variables, magnifying the effects
of estimation risk even further; and the ALM models carried out under a continuous time
context have been mostly studied under a constant investment opportunity set.
Another strand of the ALM literature, closer in spirit to our paper, uses approximate
analytical solutions and extends the asset-only models introduced by Campbell and
Viceira (1999; 2001; 2002) and Campbell et al. (2003) by incorporating liabilities.
Hoevenaars et al. (2008, HMSS hereafter) is a signicant contribution in this literature.
HMSS assume that an investor with risky liabilities chooses the optimal portfolio
weights at the beginning of the investment horizon and rebalances to the initial allocation
at a rebalancing time shorter than the investment horizon. Barberis (2000) describes the
latter strategy as myopic rebalancing; it is myopic because the investor ignores the
information available at the rebalancing time. Myopic investors maintain the initial static
solution, through rebalancing, until the end of the horizon. In contrast, dynamic investors
follow a dynamic investment strategy where the portfolio weights take into account
changes in the investors investment opportunity set. Using the myopic asset-liability
model (M-ALM thereafter), HMSS nd signicant differences in the portfolio
allocations of investors who ignore liabilities.
Our principal contribution in this paper is that we develop a model which results in a
closed-form solution for the dynamic multi-period portfolio choice problem in the
presence of liabilities (D-ALM thereafter). Our model nests the asset-only model of JV.
It is analytically tractable and hence allows the study and interpretation of factors
affecting optimal portfolio choice in an ALM framework. The model we propose can
accommodate any number of assets and state variables. To develop the proposed model
we build on JV and HMSS. Our representative investor is endowed with power utility
over the ratio of assets and liabilities, as opposed to over assets only, at a xed horizon;
she can invest in many risky assets and a riskless asset. The investment opportunity set is
time-varying and captures the variation in risk premia, interest rates and the state
variables. The optimal investment policy that we derive has a simple structure; it is
comprised of myopic and intertemporal hedging terms. The novel feature of our model is
that we show analytically how the intertemporal hedging demand which appears in the
asset-only multi-period portfolio choice literature is also driven by the correlation
between the innovations of liabilities and the innovations in the changes of the state
variables.
In our empirical investigation we take into account practical considerations. We
incorporate short-sales or borrowing constraints, as in Brandt et al. (2009). We also
1
ALM based on stochastic programming and used in practice include the RusselYasuda
Kasai model described in Cari~
no et al. (1998) and the Towers PerrinTillinghast ALM
approach presented in Mulvey et al. (2000).
© 2016 John Wiley & Sons, Ltd.
256 Daniel Giamouridis, Athanasios Sakkas and Nikolaos Tessaromatis

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