|Research Paper 37|
|How to Diversify Internationally? A Comparison of Conditional and Unconditional Asset Allocation
BARRAS - HEC-University of Geneva and International Center FAME
Dušan ISAKOV - HEC-University
of Geneva and International Center FAME
2003 - Revised Version
This paper has now been published and is no longer
available as a part of our Research Paper Series. The reference to this paper is:
L., Isakov, D. (2003): "How To Diversify Internationally: A Comparison of Conditional and Unconditional
Asset Allocation Methods." Financial Markets and Portfolio Management, Vol. 17 (2), pp. 194-212.
obtain the maximum benefits from diversification, financial theory suggests that investors should invest
internationally because of the larger potential for risk reduction stemming from the lower correlation
exisiting between assets of different countries. The question that we raise in this paper is how to
choose the best mix of countries to diversify internationally? We compare several methods of asset allocation
from a Swiss perspective over the period 1988-2001. We simulate different investment policies and compare
conditional and unconditional methods. We find that conditional methods, that explicitly assume time-variation
in expected returns, outperform all other asset allocation methods.
Modern portfolio theory gives very precise indications
to an investor wishing to diversify internationally his portfolio. The theory shows that to get the
maximum benefits from diversification, the international investor should allocate his wealth to various
countries to obtain a maximal risk reduction, as assets from different countries are less correlated
than stocks originating from the same country. The question raised in this paper is how to select the
optimal portfolio of countries? At the first sight, this question seems to be irrelevant because financial
theory provides a normative framework for such choices and shows that investors try to maximize the
expected return of a portfolio for any given level of risk, represented by the standard deviation of
a portfolio. This, in turn, will provide the optimal weights to invest in each country. The practical
implementation of this theoretical framework raises several issues. It requires the estimation of a
vector of expected returns and of a covariance matrix of returns. This is usually done in an unconditional
framework, meaning that these moments are assumed to be constant through time, which leads to parameters
being estimated with the historical means, variances and covariances of returns. Unfortunately, this
procedure yields very poor results, as it does not provide the best mean-variance trade-off for future
returns. For this reason, more efficient approaches are called for. A reasonable alternative to this
approach is to assume that moments are changing through time and therefore to rely on a conditional
implementation of the model. One way to approach this issue is to use the results from empirical studies
on the predictability of stock returns that have found that returns can be partially predicted with
some economic variables such as the term spread, the default spread, the dividend yield and lagged stock
returns. These studies show that there is a linear relation between future stock returns and past observations
of the predictive variables. This relation, estimated by ordinary least squares (OLS), provides an alternative
and easy way to characterize the dynamics of returns. The goal of this paper is to give a comprehensive
view of all the main methods available to achieve an optimal international asset allocation and to implement
them from a Swiss perspective.
The different asset allocation methods
considered in this paper are: the classical unconditional model, an alternative version of this model
that improves estimates of the expected returns vector (Bayes-Stein) and two conditional methods. The
first involves the direct estimation of expected returns with predictive variables such as the U.S.
default spread, the local term spread and the lagged stock returns (OLS-based method). The second method
has stronger theoretical foundations as it is based on a conditional international asset pricing model
(APM-based method), which uses predictive variables to determine the risk premia on two factors: the
world market return and an exchange rate factor. The returns are simulated on a sample of 17 countries
that includes 11 developed markets and 6 emerging markets. We use weekly returns on MSCI indices over
the period 1988-2001. We allow the investor to hedge currency risk with future contracts. The optimal
weights invested in each country are obtained by maximizing the Sharpe ratio of the investor’s portfolio.
All the simulations are implemented in a truly out-of-sample approach as the parameters are first estimated
on a five-year window and then used as inputs to determine the optimal weights for subsequent periods.
We only model the expected return vector as the covariance matrix has been shown to be fairly stable
through time in the literature.
The results of our empirical analysis
show that the OLS-based conditional asset allocation outperforms in absolute terms all the other strategies
that have been investigated in the paper.
Over the simulation period 1995-2001, it yields
an average annualized returns of 32.31%. This average return is significantly above 14.37% which is
the average annualized return of the classical unconditional method. Other allocation methods yield
the following average return: 13.58% for the Bayes-Stein estimator and 8.45% for the APM-based conditional
allocation. The OLS-based conditional allocation also yields the best results in terms of risk– adjusted
return as its Sharpe ratio is 1.26 whereas all other methods have Sharpe ratios between 0.5 and 0.8.
We also compare the outcome of our strategies to standard benchmarks such as the MSCI World index and
the minimum variance portfolio and find that they are also dominated by the OLS-based conditional allocation.
We attribute the outstanding results obtained by this type of conditional allocation to its ability
to capture the effect of changing economic conditions on financial markets.