Equally Weighted vs. Long‐Run Optimal Portfolios

Published date01 September 2015
Date01 September 2015
Equally Weighted vs. Long-Run
Optimal Portfolios
Carolina Fugazza
University of Milano-Biccocca and CeRP-Collegio Carlo Alberto
E-mail: carolina.fugazza@unimib.it
Massimo Guidolin
IGIER, Bocconi University
E-mail: massimo.guidolin@unibocconi.it
Giovanna Nicodano
University of Turin, CeRP-Collegio Carlo Alberto and Netspar
E-mail: giovanna.nicodano@unito.it
Out-of-sample experiments cast doubt on the ability of portfolio optimising
strategies to outperform equally weighted portfolios, when investors have a
1-month time horizon. This paper examines whether this nding holds for longer
investment horizons over which the optimising strategy exploits linear
predictability in returns. Our experiments indicate that investors with longer
horizons on average would have beneted, ex post, from an optimising strategy
over the period 19952009. We analyse performance sensitivity to investor risk
aversion, to the number of predictors included in the forecasting model and to the
deduction of transaction costs from portfolio performance.
Keywords: equally weighted portfolios, strategic asset allocation, Real Estate
Investment Trusts (REITs), return predictability, parameter uncertainty
JEL classification: G11, L85
We would like to thank the editor John Doukas and an anonymous referee for their helpful
commentsand suggestions. We are grateful to Dirk Brounen, Bradley Case, Mathijsvan Dijck,
Gonçalo Faria, Lorenzo Garlappi, Bruno Gerard, Loriana Pelizzon, Andrea Tortora, Luis
Viceira,and Grigory Vilkov for suggestions and discussions.We also thank for their comments
participants at the AREUEA meetings in Atlanta, the Conference on Money, Banking, and
Finance (Rome), the Conference of the Swiss Society for Financial Market Research, the
European FinanceAssociation in Frankfurt, IREBS Conferencein Regensburg, the ReCapNet
Conference in Mannheim, the Financial Management Association in Atlanta, and the
Workshop on Applied Finance and Financial Econometrics (Berlin). Giovanni Bissolino,
Raffaele Corvino,and Yu Man Tam provided excellent research assistance.Financial support
from the Italian Research Department (PRIN) is gratefully acknowledged.
European Financial Management, Vol. 21, No. 4, 2015, 742789
doi: 10.1111/eufm.12042
© 2014 John Wiley & Sons Ltd
1. Introduction
Finance scholars and practitioners have long recognised that the out-of-sample, ex post
performance of ex ante optimal portfolios may be worse than that of simpler strategies,
which are sub-optimal from an in-sample, ex ante perspective (see, e.g., Bawa
et al., 1979; Friend and Blume, 1970; Jorion, 1985).
In particular, Brown (1976),
Duchin and Levy (2009), DeMiguel et al. (2009a), and Jacobs et al. (2009), among
others, report that equally weighting available assets (the so-called 1/N strategy)
consistently outperforms almost every optimising model they scrutinise. This is very
troublesome evidence for the entire portfolio management industry, indicating that
simple rules-of-thumbmay lead to higher realised ex post performance than do
optimising asset management strategies. However, this evidence refers overwhelmingly
to short (typically, 1 month) investment horizons, while several institutions and many
households invest for the long-term and care about portfolio properties associated with
longer time horizons.
Our paper shows that this startling, out-of-sample performance by the naïve, equally
weighted strategy (i.e., portfolios where each asset has the same weight) fails to generally
extend to longer-term portfolio strategies, when asset return predictability is taken into
account. This nding, which to our best knowledge is new in the literature, implies that
portfolio management methods become increasingly valuable to investors as their
planned time horizon grows. This insight seems of relevance to mutual and pension fund
managers, who should reect in their portfolio optimising decisions the length of the
horizons of their shareholders.
Our emphasis on investorshorizons, which we set from 1 to 60 months in this paper,
guides several aspects of our research design. First, we allow for predictable risk premia
and parameter uncertainty, since these features need to be taken into account by
managers of long-term portfolios; at the same time these very features ensure that time
horizon affects optimal asset allocation (see, e.g., Barberis, 2000; Campbell et al., 2002).
Second, we model, by assuming power utility, an investor who has preferences with
regard to skewness and kurtosis of wealth. This setting simplies to mean variance
preferences, as assumed in most of the literature, for short horizons only. Third, our long-
horizon emphasis affects the choice of both the type of problem and the asset menu.
While many papers study stock selection, we focus on strategic asset allocation, because
asset allocation has been shown to be the main determinant of portfolio performance
(see, e.g., Cumming et al., 2014; Ibbotson and Kaplan, 2000). As a consequence, we
include real estate in the asset menu alongside traditional assets, given the presence of
this asset class in long-term investorsportfolios. Finally, we model T-bills as a risky
asset, because long-term investors clearly face re-investment risk (see, e.g., Campbell
et al., 2001).
In-sample, ex ante analyses assume that investors know precisely the necessary input
parameters for portfolio optimisation, which is of course not realistic, as parameter
uncertainty may play a major role (see Brown, 1976; Klein and Bawa, 1976; Zellner and
Chetty, 1965). In contrast, out-of-sample, ex post analyses test the performance of
optimisation methods under realistic conditions in which only information (including
parameter estimates, when needed) at time tis used to solve the portfolio problem at time t,
and the subsequently realised performance is recorded and investigated.
© 2014 John Wiley & Sons Ltd
Equally Weighted vs. Long-Run Optimal Portfolios 743
Our baseline experiment uses US monthly returns on stocks, publicly traded equity
real estate vehicles (REITs), long-term government bonds, and T-bills, for the sample
period 19722007. However, in Section 5 we analyse both shorter and longer sample
periods, to include data from the recent nancial crisis and to test the robustness of our
results. Our data consist of well-known indices that are investable by private investors at
low cost via exchange-traded funds. Our key nding is that an investor with a long
horizon obtains higher ex post realised utility from optimising strategies when that
investor takes into account the predictability of real returns. Such predictability is
captured by simple vector autoregressive (VAR) models that link asset returns to past
values of variables (such as dividend yield and the term spread) that are commonly used
to capture the state of the economy. The superior performance holds when compared to
both naïve strategies and portfolios of intermediate complexity, which derive from an
optimisation but ignore predictability. It is thus prediction of returns that leads to
substantial improvement in the investors ex post welfare. These conclusions, which
hold uniformly for intermediate-to-high investor risk aversion, are robust to changes
in the asset menu (with and without REITs), to whether parameter uncertainty is
taken into account during the optimisation (i.e., whether we compute Classical or
Bayesian portfolios), and to the presence of transaction costs: a long-horizon investor
always prefers an optimised portfolio to a naïve, equally weighted strategy when such
investor uses the best predictive model. These results emphasise the potential
irrationality of the observed behaviour of individual investors, who nevertheless
allocate their wealth by equally weighting assets (see, e.g., Benartzi and Thaler, 2001;
Brown et al., 2007).
For short-horizon problems, our results align with the earlier mean-variance literature,
despite the different experimental design: equal weighting provides 1-month-horizon
investors with higher ex post realised utility than optimal portfolios under constant risk
premia. Given the ndings of DeMiguel et al. (2009a) that naïve diversication leads to
lower performance than a mean variance strategy if the sample size exceeds a critical
value (which increases in the number of assets), our key nding obtains because the
number of assets is relatively small but the sample size is large.
This paper contributes to the literature by providing a systematic decomposition of the
economic and statistical drivers behind our results. The key driver is indeed the
predictability of returns using VAR models at horizons in excess of 24 months. Although
such predictability is weak at shorter horizons (consistent with a growing literature, e.g.,
Welch and Goyal, 2008), especially in the case of stocks and to some extent REITs, at a
5-year horizon it becomes sufciently strong to outperform models that forecast returns
using recursive means. Interestingly, in relative terms, such predictive power is always
rather weak, yet it may give a long-run portfolio optimiser an economically valuable
hedge. Given the complex, non-linear relationship between risk premium forecasts and
portfolio weights when the investor has power utility, such results are far from obvious.
Although adopting an asset menu that includes real estate is realistic, we show that this
choice is not critical to our results. In fact, in some experiments, the economic value an
investor may derive from exploiting predictability is actually larger for a traditional asset
menu that includes only stocks, bonds, and T-bills. Importantly, our results are not
signicantly affected when we impute ex post transaction costs related to realised
portfolio turnover. This evidence indicates that our key ndings do not derive from
predictability-based strategies that lead investors to trade at an absurdly intense
frequency. The degree of risk aversion plays a limited role in the sense that under low risk
© 2014 John Wiley & Sons Ltd
744 Carolina Fugazza, Massimo Guidolin and Giovanna Nicodano

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