Emerging Markets and the Global Economy: A Handbook
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About this ebook
Emerging Markets and the Global Economy investigates analytical techniques suited to emerging market economies, which are typically prone to policy shocks. Despite the large body of emerging market finance literature, their underlying dynamics and interactions with other economies remain challenging and mysterious because standard financial models measure them imprecisely.
Describing the linkages between emerging and developed markets, this collection systematically explores several crucial issues in asset valuation and risk management. Contributors present new theoretical constructions and empirical methods for handling cross-country volatility and sudden regime shifts. Usually attractive for investors because of the superior growth they can deliver, emerging markets can have a low correlation with developed markets. This collection advances your knowledge about their inherent characteristics.
Foreword by Ali M. Kutan
- Concentrates on post-crisis roles of emerging markets in the global economy
- Reports on key theoretical and technical developments in emerging financial markets
- Forecasts future developments in linkages among developed and emerging economies
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Emerging Markets and the Global Economy - Mohammed El Hedi Arouri
Part 1: COUNTRY-SPECIFIC EXPERIENCES
Chapter 1: Robust Measures of Hybrid Emerging Market Mutual Funds Performance
Mohamed A. Ayadi mayadi@brocku.ca Department of Finance, Operations, and Information Systems, Goodman School of Business, Brock University, St. Catharines, ON, Canada
Abstract
This chapter uses the fundamental asset pricing theorem to derive new conditional stochastic discount factor-based performance measures. The proposed setting is suitable to perform (un)conditional evaluations of fixed-weight and dynamic strategies of hybrid emerging market mutual funds. The empirical framework and the associated performance statistical tests in a GMM framework are also developed and discussed.
Keywords
Risk management; Stochastic discount factor; Emerging markets; Hybrid mutual funds; Performance measures
JEL Classification Codes
G11; G12
Acknowledgment
Financial support from the Brock University SSHRC funds is gratefully acknowledged.
1: Introduction
Emerging market mutual funds are investment portfolios that offer foreign investors opportunities to invest in alternative markets in Asia, Latin America, and Eastern Europe. These funds are particularly attractive to both individual and institutional investors seeking to increase their returns and diversify risks. Such funds have experienced a rapid growth over the past 20 years following the liberalization of economic and financial policies in various countries in Asia, Latin American, and Eastern Europe. ¹
The growing literature on emerging market investments and mutual funds has addressed several issues, and the ultimate objective of such a literature was to assess the selectivity, timing, and persistence performance of these portfolios (van der Hart et al., 2003; Gottesman and Morey, 2007; Huij and Post, 2011; Banegas, 2011). Other studies in this research stream have also examined the determinants of stock returns, the potential role of risk factors in the underlying return generating process of these special investment funds, and the validity of the benchmark models (Harvey, 1995; Rouwenhorst, 1999; Abel and Fletcher, 2004; Phylaktis and Xia, 2006; Iqbal et al., 2007, 2010). However, most of the academic and practitioners’ attention has focused on equity or bond (fixed-income) funds rather than balanced or hybrid funds. This class of emerging market funds is very popular with risk-averse investors because these funds offer lower volatility and moderate returns. In addition, such funds have experienced strong inflows ever since the last financial crisis.
The literature on US-based balanced mutual funds is very limited and consists of a few articles that rely on traditional multifactor asset pricing models adapted to equity and fixed-income pricing. These articles also extend the basic market-timing models used in the performance measurement of equity funds. For example, Aragon (2005) derives new performance measures from a theoretical model with multiple market exposures and finds balanced funds show a positive (negative) timing (selection) ability over the period 1976–2004. Using a multifactor benchmark specification, Comer (2006) reports significant timing performance over the period 1992–2000 for a large sample of US hybrid and asset allocation mutual funds. More recently, Comer et al. (2009) recommend using bond indices and factors to evaluate the performance of managed portfolios with substantial holdings in fixed-income securities.
All of these papers derive performance metrics by comparing the portfolio’s average excess return to that implied by a benchmark model that reflects the risks related to equity and fixed-income exposures. These benchmark models fail to deliver reliable measures of performance and sometimes generate misleading inferences where the rankings can change essentially due to the choice and efficiency of the chosen benchmarks. Other potential sources of false performance inferences include possible misspecifications of the proposed return dynamics. Finally, the proposed tests are based on unconditional performance metrics that fail to produce a robust measure of abnormal performance when the expected returns and/or risk are time-varying. It is because these metrics are not able to isolate the impact of the superior abilities of portfolio managers from inherent time variation in the underlying assets. All of these problems suggest the need to develop an asset pricing model-free measure, which can control for conditioning information to assess the performance of this hybrid type of emerging market funds.
This alternative methodology relies on the fundamental asset-pricing theorem known as the stochastic discount factor (SDF) representation of asset prices introduced by Harrison and Kreps (1979). The above-cited theorem states that any gross return discounted by a market-wide random variable has a constant conditional expectation. Furthermore, the proposed framework allows for an integration of the role of conditioning information with various structures (Hansen and Richard, 1987).
Thus, the objective of this chapter is to introduce a conditional SDF that is adapted to performance evaluation of emerging market hybrid funds. This SDF efficiently accounts for the time variation in expected returns and risk, and does not rely on the linear information scaling used in most SDF-based performance tests reported in the literature. This approach has the advantage of not being dependent on any asset pricing model or any distributional assumptions. The proposed SDF is further differentiated from most of the existing SDF models owing to its a unique structure that reflects the nonlinear interdependences between its conditional and unconditional versions caused essentially by the time variability in the optimal risky asset allocation. The framework is also suitable for performing unconditional evaluations of fixed-weight strategies and (un)conditional evaluations of dynamic strategies of hybrid emerging market mutual funds. ² We also develop the appropriate empirical framework for estimating the performance measures. We advocate the use of a flexible estimation methodology using Hansen’s (1982) (un)conditional Generalized Method of Moments (GMM). We estimate the empirical performance measures and perform their associated tests. The estimation of the GMM system is discussed and relies on a one-step method.
The remainder of the chapter is organized as follows: Section 2 presents the general asset-pricing framework and we derive the SDF in the presence of time-varying returns. An (un)conditional portfolio performance evaluation using the developed normalized pricing operator is carried out in Section 3. In Section 4, we develop and explain the econometric methodology and the performance tests. Finally, Section 5 concludes the chapter.
2: Stochastic Discount Factors and Benchmark Models
The fundamental theorem of asset pricing states that the price of a security is determined by the conditional expectations of its discounted future payoffs in frictionless markets. The stochastic discount factor (SDF) is a random variable that reflects the fundamental economy-wide sources of risk. The basic asset pricing equation is written using gross returns as:
si1_e(1)
The conditional expectation is defined with respect to the sub-sigma field on the set of states of nature, si2_e , which represents the information available to investors at time si3_e . si4_e is the price of asset si5_e at time si3_e , si7_e represents a gross return at time si8_e , defined as the ratio of a future payoff si9_e on the price of asset si5_e si11_e , and si12_e is the SDF or the pricing kernel. ³ The prices, returns, and discount factors can be real or nominal, and the general assumption is that the asset payoffs have finite second moments. ⁴
2.1: The Model
When investment opportunities are time-varying, the SDFs or the period weights can be interpreted as the conditional marginal utilities of an investor with isoelastic preferences described by a power utility function that exhibits constant relative risk aversion (CRRA), given by ⁵ :
si13_ewhere si14_e is the level of wealth at si3_e , and si16_e is the relative risk aversion coefficient. In a single period model, the uninformed investor who holds the benchmark portfolio composed of emerging markets securities (the risky asset) maximizes the conditional expectation of the utility of his or her terminal wealth:
si17_e (2)
The conditional expectation is based upon the information set si2_e .
The investor with such preferences decides on the fraction si19_e of wealth to allocate to the risky asset (hybrid or balanced portfolio of emerging markets of equity and fixed-income securities) with gross return si20_e , and any remaining wealth is invested in a risk-free security. The return on wealth is given by:
si21_e(3)
where si22_e is the gross return on the benchmark portfolio of the balanced investment from si3_e to si24_e . si25_e and si26_e are the gross returns on the equity and fixed-income portfolios, respectively. si27_e is the proportion of investment in the equity portfolio. si28_e is the gross risk-free rate from si3_e to si8_e that is known one period in advance at time si3_e ; and si19_e is the proportion of total wealth invested in the benchmark portfolio.
The optimal risky asset allocation or portfolio policy is no longer a constant parameter when emerging market asset returns are predictable. Harvey (1995) and Iqbal et al. (2010) document evidence of significant return predictability for long and short horizons where the means and variances of asset returns are time-varying and depend on some key variables such as lagged returns, dividend yield, term structure variables, and interest rate variables. Moreover, Brennan et al. (1997), Brandt (1999), and Aït-Sahalia and Brandt (2001) show that the optimal portfolio weight is a function of the state variable(s) that forecast the expected returns when stock returns are predictable. It follows that the optimal portfolio weight is a random variable measurable with respect to the set of state or conditioning variables and is consistent with a conditional Euler equation ⁶ :
si33_e (4)
Thus, considering a constant optimal portfolio weight when returns are predictable affects the construction of any measure based on this variable and distorts inferences related to the use of such a measure. In addition, the functional form and the parameterization of the optimal portfolio allocation depend on the relationship between asset returns and the predicting variables. ⁷
2.2: Robust Performance Measures
Assuming initial wealth at time si3_e equals one, the conditional optimization problem for the uninformed investor, as described in Brandt (1999), Aït-Sahalia and Brandt (2001), and Ayadi and Kryzanowski (2005), is:
si35_e(5)
The first-order condition gives the conditional Euler equation:
si36_e(6)
Now define
si37_e, which is a strictly positive conditional SDF consistent with the no-arbitrage principle. This ensures that if a particular fund has a higher positive payoff than another fund, then it must have a higher positive performance. Grinblatt and Titman (1989), Chen and Knez (1996) stress the importance of this positivity property in providing reliable performance measures. si38_e can be normalized such that:
si39_e(7)
The new conditional normalized SDF plays a central role in the construction of the portfolio performance measure. The unconditional normalized SDF is given by:
si40_e(8)
Let si41_e be the (un)conditional portfolio performance measure, depending on the use of the appropriate SDF. It is an admissible positive performance measure with respect to Chen and Knez’s (1996) definition. If si42_e is the excess return on any particular portfolio si43_e , then:
si44_e(9)
si45_e(10)
It follows that the expected performance measure reflects an average value plus an adjustment for the riskiness of the portfolio measured by the covariance of its excess return with the appropriate normalized SDF.
3: Performance Evaluation of Managed Portfolios
3.1: Unconditional Setting
When uninformed investors do not incorporate public information, the portfolio weights are fixed or constant. The gross return on such a portfolio is: si46_e , with si47_e being an si48_e -vector of gross security returns, and si49_e being an si48_e -vector of ones. We define
si51_e. We assume that the portfolio weights si52_e are chosen one period before. The corresponding unconditional performance measure is:
si53_e(11)
This suggests that the risk-adjusted return on the passive portfolio held by the uninformed investor is equal to the risk-free rate.
The parameters of si54_e are chosen such that si55_e . If si56_e is of dimension si57_e , then si58_e and si59_e . Informed investors, such as possibly some mutual fund managers, trade based on private information or signals implying non-constant weights for their portfolios. The gross return on an actively managed portfolio is given by:
si60_ewhere si61_e and si62_e represent public and private information sets, respectively.
The unconditional performance measure is given by:
si63_e(12)
When informed investors optimally exploit their private information or signals, this measure is expected to be strictly positive.
3.2: Conditional Setting
When uninformed investors use publicly known information, si61_e , in constructing their portfolios, the weights are a function of the information variables. The gross return is given by:
si65_eConsistent with the semi-strong form of the efficient market hypothesis, the conditional SDF prices the portfolio such that:
si66_e(13)
To model conditioning information, we define si67_e , where si68_e is a si69_e -vector of the conditioning variables containing unity as its first element. The conditional expectations are analyzed by creating general managed portfolios with linear scaling and then examining the implications for the unconditional expectations as in Cochrane (1996). The new scaled returns can be interpreted as payoffs to managed portfolios or conditional assets. The payoff space is expanded to si70_e dimensions to represent the number of trading strategies available to uninformed investors.
The conditional performance measure can be written as:
si71_e(14)
si72_e (15)
Assuming stationarity and applying the law of iterated expectations yields:
si73_e(16)
si74_e (17)
where si75_e is the Kronecker product obtained by multiplying every asset return by every instrument. These two conditions ensure that the conditional mean of the SDF is one, and that these managed portfolios are correctly priced. The conditional normalized SDF is only able to price any asset or portfolio whose returns are attainable from the dynamic trading strategies of the original si48_e assets with respect to the defined conditioning information set.
The conditional performance for the actively managed portfolio is given by:
si77_e(18)
This conditional test determines whether the private information or signal contains useful information beyond that which is publicly available, and whether or not this information has been used profitably.
4: Econometric Methodology and Tests
In this section, the empirical framework for the estimation of the performance measures and for the tests of the different hypotheses and specifications using Hansen’s (1982) generalized method of moments (GMM) is detailed. Important issues associated with the estimation procedure and the optimal weighting or distance matrix are also dealt with.
4.1: The General Framework
The estimation of the performance of actively managed portfolios (such as mutual funds) is based on a one-step method using a GMM system approach. The one-step method jointly and simultaneously estimates the normalized SDF parameters and the performance measures by augmenting the number of moment conditions in the initial system with the actively managed fund(s) or portfolio(s) of funds. ⁸ This multivariate framework incorporates all of the cross-equation correlations. By construction, such estimations account for the restriction on the mean of the normalized (un)conditional SDF, ⁹ which Dahlquist and Soderlind (1999), Farnsworth et al. (2002), and Ayadi and Kryzanowski (2005) show is important in order to obtain reliable estimates.
We now present the general steps and expressions leading primarily to the general case of conditional GMM estimation relevant for the conditional evaluation of dynamic trading-based portfolios. The unconditional GMM estimation is obtained as a special case.
Let si78_e be the vector of unknown SDF parameters to be estimated. Our model implies the following conditional moment restriction:
si79_e(19)
such that si80_e .
Now define
si81_eas an si48_e -vector of residuals or pricing errors, which depends on the set of unknown parameters, the excess returns on the benchmark portfolio(s), the conditioning variables, and the excess returns on passive trading strategy-based portfolios.
Assume that the dimensions of the benchmark excess return and the conditioning variables are si57_e and si69_e , respectively. Then, the dimension of the vector of unknown parameters is si85_e . We then have:
si86_e(20)
Define
si87_e. Our conditional and unconditional moment restrictions can be written as:
si88_e(21)
si89_e(22)
Because the model is overidentified, the GMM system is estimated by setting the si85_e linear combinations of the si70_e moment conditions equal to zero. When the system estimation of the performance measures is completed in one step, the number of moment conditions si92_e and the number of unknown parameters si93_e are augmented.
Following Hansen (1982), the GMM estimator is obtained by selecting si94_e that minimizes the sample quadratic form si95_e given by ¹⁰ :
si96_e (23)
where si97_e is a symmetrical and non-singular positive semi-definite si98_e weighting matrix and si99_e is given by si100_e .
Let si101_e be the minimized value of the sample quadratic form. ¹¹ When the optimal weighting matrix or the inverse of the variance-covariance matrix of the orthogonality conditions is used, si103_e has an asymptotic standard central chi-square distribution with si104_e degrees of freedom. This is the well-known Hansen si95_e -statistic. This estimation can handle the assumption that the vector of disturbances exhibits non-normality, conditional heteroskedasticity, and/or serial correlation even with an unknown form.
4.2: The Estimation Procedure and the Optimal Weighting Matrix
The estimates of the portfolio performance measure are obtained by minimizing the GMM criterion function constructed from a set of moment conditions in the system. This requires a consistent estimate of the weighting matrix that is a general function of the true parameters, at least in an efficient case. Hansen (1982) proves that the GMM estimator is asymptotically efficient when the weighting matrix is chosen to be the inverse of the variance-covariance matrix of the moment conditions. ¹² This covariance matrix is defined as the zero-frequency spectral density of the pricing errors vector si106_e . A consistent estimate of this spectral density is used herein to construct a heteroskedastic and autocorrelation consistent (HAC) or robust variance-covariance matrix in the presence of heteroskedasticity and autocorrelation of unknown forms. Chen and Knez (1996), Dahlquist and Soderlind (1999), Farnsworth et al. (2002), Ayadi and Kryzanowski (2005, 2008) construct robust t-statistics for their estimates of performance by using the modified Bartlett kernel proposed by Newey and West (1987) to construct a robust estimator for the variance-covariance matrix. ¹³
The variance-covariance matrix of si107_e can be written as:
si108_e (24)
where
si109_eis the si110_e th autocovariance matrix of si106_e .
This expression is difficult to estimate with an infinite number of terms. An estimate of si112_e is obtained by using a finite number of lags and by replacing the true autocovariances by their sample analogs, or:
si113_e(25)
where:
si114_efor si115_e ; and si116_e for si117_e . A small sample correction si118_e may be used instead of si119_e .
In the absence of serial correlation, a consistent estimate of si112_e is equal to the sample autocovariance of order zero. More formally:
si121_e(26)
However, two difficulties are associated with the estimation of the general expression. First, the sample autocovariance matrix si122_e is not a consistent estimator of the true autocovariance matrix si123_e for some si110_e with respect to the sample size si102_e . ¹⁴ Second, the estimated variance-covariance matrix may not be positive definite, particularly for finite samples. We estimate the zero-frequency spectral density and overcome difficulties in the estimation by using a non-parametric or kernel-based approach.
A non-parametric or kernel-based robust estimator has the following general expression:
si126_e (27)
where si127_e is a real-valued kernel, weighting function, or lag window, ¹⁵ and si128_e is a data-dependent bandwidth or lag truncation parameter. This particular structure imposes different weights on different sample autocovariances. Several estimators associated with different kernel functions are proposed in the spectral density function estimation literature. Only kernels that are relevant for portfolio performance measurement are presented next.
Newey and West (1987) use the modified Bartlett or triangular kernel to construct a robust estimator of the variance-covariance matrix. They demonstrate that this estimator, unlike the truncated kernel-based one, is positive definite given the assigned weighting structure. This property (together with its simple tractability) results in the popular use of this estimator for the estimation of portfolio performance evaluation models. Examples include Chen and Knez (1996), Ferson and Schadt (1996), Farnsworth et al. (1999), Dahlquist and Soderlind (1999), Abel and Fletcher (2004), and Ayadi and Kryzanowski (2005, 2008, 2011).
4.3: Optimal Risky Asset Allocation Specifications
In a conditional setting, the optimal risky asset allocation of the uninformed investor is a function of the conditional moments of asset returns. We assume that these conditional moments are linear in the state variables:
si129_e (28)
where si130_e is a vector of unknown parameters, and si68_e is a vector of instruments (including a constant) with a dimension equal to that of the retained conditioning variables. When an unconditional evaluation is conducted, the uninformed investor’s portfolio policy is a constant.
5: Conclusion
This paper uses the general asset-pricing or SDF framework to derive a conditional SDF that is suitable for measuring the performance of emerging market hybrid funds. Our approach reflects the predictability of this group of asset returns and accounts for conditioning information. Three robust performance measures are constructed and are related to the unconditional evaluation of fixed-weight strategies, and the unconditional and conditional evaluations of dynamic strategies. An appropriate empirical framework for estimating and implementing the proposed performance measures and their associated tests using the GMM method is developed.
Our approach may be extended in various directions. First, we can adopt a continuous SDF methodology adapted to the pricing of hybrid emerging market securities. Second, we can examine potential relationships between the performance measures and some business cycle indicators to determine more effectively if the performance of active portfolio management differs during periods of expansion and contraction in emerging markets. Third, we may assess the market-timing behavior of emerging market fund managers, and identify the determinants of fund flows based on several fund characteristics. These alternative directions are opportunities for future research.
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