Dynamic Investment Strategy with Factor Models Under Regime Switches

A model for dynamic investment strategy is developed where assets’ returns are represented by multiple factors. In a mean–variance framework with factor models under regime switches, we derive a semi-analytic solution for the optimal portfolio with transaction costs. Due to the existence of transaction costs, the optimal portfolio is characterized as a linear combination of current and target portfolios, the latter of which maximizes the value function in the current regime. For some special cases of interest, we also derive simplified analytical solutions. To see the effect of regime switches, the proposed model is applied to US equity market in which small minus big and high minus low are employed as factors. Investment strategy based on our model demonstrates empirically that the regime switching models exhibit superior performance over the single regime model for such performance measures as realized utility and Sharpe ratio which are of particular interest in practice. Taking a close look at the time series of portfolio returns, the result shows the usefulness of the regime switching model as investors flexibly optimize asset allocations depending on the state of the market.     

An Empirical Investigation of Eastern European Bond Markets

We examine the value of Eastern European emerging bond markets to global fixed income managers. In an environment where bonds from traditional developed markets are offering modest yields, emerging market bonds with attractive yields are becoming more popular with institutional managers. Furthermore, the returns on these bonds exhibit low correlations with traditional fixed income investments and thus offer opportunities for portfolio diversification. We develop a multifactor forecasting model and estimate its parameters using a dynamic Kalman filter procedure. The forecasts are then used to construct optimal mean–variance portfolios with and without emerging market bonds. We find that the portfolios that include emerging market bonds have significantly higher Sharpe ratios.     

Cross‐sectional Tests of Conditional Asset Pricing Models: Evidence from the German Stock Market

We study the performance of conditional asset pricing models and multifactor models in explaining the German cross‐section of stock returns. We focus on several variables, which (according to previous research) are associated with market expectations on future market excess returns or business cycle conditions. Our results suggest that the empirical performance of the Capital Asset Pricing Model (CAPM) can be improved when allowing for time‐varying parameters of the stochastic discount factor. A conditional CAPM using the term spread explains the returns on our size and book‐to‐market sorted portfolios about as well as the Fama‐French three‐factor model and performs best in terms of the Hansen‐Jagannathan distance. Structural break tests do not necessarily indicate parameter instability of conditional model specifications. Another major finding of the paper is that the Fama‐French model – despite its generally good cross‐sectional performance – is subject to model instability. Unconditional models, however, do a better job than conditional ones at capturing time‐series predictability of the test portfolio returns.     

Are TIPS the “real” deal?: A conditional assessment of their role in a nominal portfolio

This paper documents predictable time-variation in the real return beta of US Treasury Inflation Protected Securities (TIPS) and in the Sharpe ratios of both indexed and conventional bonds. The conditional mean and volatility of both bonds and their conditional correlation first are estimated from predetermined variables. These estimates then are used to compute conditional real return betas and Sharpe ratios. The time-variation in real return betas and the correlation between TIPS and nominal bonds coincides with major developments in the fixed-income market. One implication of this predictability is that portfolio managers can assess more efficiently the risk of investing in TIPS versus conventional bonds. Conditional Sharpe ratios indicate that over the sample period, TIPS had superior volatility-adjusted returns relative to nominal bonds. This finding is striking in view of the absence of a major inflation scare during the sample period from February 1997 through August 2001, but is loosely consistent with the possibility that TIPS elevated rather than reduced Treasury borrowing costs. On the other hand, mean–variance spanning tests indicate that TIPS did not enhance the mean–variance efficiency of diversified portfolios.     

Risk Reduction and Mean-Variance Analysis: An Empirical Investigation

Abstract:  I examine the performance of global minimum variance (GMV) and minimum tracking error variance (TEV) portfolios in UK stock returns using different models of the covariance matrix. I find that both GMV and TEV portfolios deliver portfolio risk reduction benefits in terms of significantly lower volatility and tracking error volatility relative to passive benchmarks for every model of the covariance matrix used. However, the GMV (TEV) portfolios do not provide significantly superior Sharpe (1966) (adjusted Sharpe) performance relative to passive benchmarks except for the restricted GMV portfolios. I find that a number of alternative covariance matrix models can improve the performance of the restricted TEV portfolio formed using the sample covariance matrix but not the restricted GMV portfolio. I also find that simpler covariance matrix models perform as well as the more sophisticated models.     

Using industry momentum to improve portfolio performance

Minimum-variance portfolios, which ignore the mean and focus on the (co)variances of asset returns, outperform mean–variance approaches in out-of-sample tests. Despite these promising results, minimum-variance policies fail to deliver a superior performance compared with the simple 1/N rule. In this paper, we propose a parametric portfolio policy that uses industry return momentum to improve portfolio performance. Our portfolio policies outperform a broad selection of established portfolio strategies in terms of Sharpe ratio and certainty equivalent returns. The proposed policies are particularly suitable for investors because portfolio turnover is only moderately increased compared to standard minimum-variance portfolios.     

Limits to mutual funds' ability to rely on mean/variance optimization

Our evidence suggests that estimation error in the required statistics is an important factor inhibiting investors' ability to rely on mean/variance analysis. We compare the returns reported by mutual funds to the returns obtained from a mean/variance optimized portfolio of fund holdings. The results suggest that funds tend to outperform the optimized portfolio out-of-sample (when means/variances/covariances are unknown), but under-perform in-sample (when the required statistics in the optimization are known). Therefore, a popular assumption in asset pricing models that investors rely on a basic mean/variance analysis with known underlying statistics is likely to be grossly violated in the case of mutual funds.     

Volatility‐Managed Portfolios

Managed portfolios that take less risk when volatility is high produce large alphas, increase Sharpe ratios, and produce large utility gains for mean‐variance investors. We document this for the market, value, momentum, profitability, return on equity, investment, and betting‐against‐beta factors, as well as the currency carry trade. Volatility timing increases Sharpe ratios because changes in volatility are not offset by proportional changes in expected returns. Our strategy is contrary to conventional wisdom because it takes relatively less risk in recessions. This rules out typical risk‐based explanations and is a challenge to structural models of time‐varying expected returns.     

On the stability of portfolio selection models

One of the main issues in portfolio selection models consists in assessing the effect of the estimation errors of the parameters required by the models on the quality of the selected portfolios. Several studies have been devoted to this topic for the minimum variance and for several other minimum risk models. However, no sensitivity analysis seems to have been reported for the recent popular Risk Parity diversification approach, nor for other portfolio selection models requiring maximum gain–risk ratios.Based on artificial and real-world data, we provide here empirical evidence showing that the Risk Parity model is always the most stable one in all the cases analyzed with respect to the portfolio composition. Furthermore, the minimum risk models are typically more stable than the maximum gain–risk models, with the minimum variance model often being the preferable one. The Risk Parity model seems to be the most stable one also with respect to profitability when measured by the Sharpe ratio. However, the maximum gain–risk models, although quite sensitive to the input data, generally appear to attain better profitability results.     

Characteristic-based mean-variance portfolio choice

We study empirical mean-variance optimization when the portfolio weights are restricted to be direct functions of underlying stock characteristics such as value and momentum. The closed-form solution to the portfolio weights estimator shows that the portfolio problem in this case reduces to a mean-variance analysis of assets with returns given by single-characteristic strategies (e.g., momentum or value). In an empirical application to international stock return indexes, we show that the direct approach to estimating portfolio weights clearly beats a naive regression-based approach that models the conditional mean. However, a portfolio based on equal weights of the single-characteristic strategies performs about as well, and sometimes better, than the direct estimation approach, highlighting again the difficulties in beating the equal-weighted case in mean-variance analysis. The empirical results also highlight the potential for ‘stock-picking’ in international indexes using characteristics such as value and momentum with the characteristic-based portfolios obtaining Sharpe ratios approximately three times larger than the world market.     

(Almost) Model‐Free Recovery

Under mild assumptions, we recover the model‐free conditional minimum variance projection of the pricing kernel on various tradeable realized moments of market returns. Recovered conditional moments predict future realizations and give insight into the cyclicality of equity premia, variance risk premia, and the highest attainable Sharpe ratios under the minimum variance probability. The pricing kernel projections are often U‐shaped and give rise to optimal conditional portfolio strategies with plausible market timing properties, moderate countercyclical exposures to higher realized moments, and favorable out‐of‐sample Sharpe ratios.     

Deciphering robust portfolios

Robust portfolio optimization has been developed to resolve the high sensitivity to inputs of the Markowitz mean–variance model. Although much effort has been put into forming robust portfolios, there have not been many attempts to analyze the characteristics of portfolios formed from robust optimization. We investigate the behavior of robust portfolios by analytically describing how robustness leads to higher dependency on factor movements. Focusing on the robust formulation with an ellipsoidal uncertainty set for expected returns, we show that as the robustness of a portfolio increases, its optimal weights approach the portfolio with variance that is maximally explained by factors.     

Small caps in international equity portfolios: the effects of variance risk

We show that predictable covariances between means and variances of stock returns may have a first order effect on portfolio composition. In an international asset menu that includes both European and North American small capitalization equity indices, we find that a three-state, heteroskedastic regime switching VAR model is required to provide a good fit to weekly return data and to accurately predict the dynamics in the joint density of returns. As a result of the non-linear dynamic features revealed by the data, small cap portfolios become riskier in bear markets, i.e., display negative co-skewness with other stock indices. Because of this property, a power utility investor ought to hold a well-diversified portfolio, despite the high risk premium and Sharpe ratios offered by small capitalization stocks. On the contrary, small caps command large optimal weights when the investor ignores variance risk, by incorrectly assuming joint normality of returns.      

Normative portfolio theory

In this paper, we correct the adverse impact of estimation risk on both portfolio weights and performance with two new equity allocation methods we implement with estimation-free and estimated ex-ante returns. Portfolios with estimation-free ex-ante returns and systematic-to-unsystematic risk weights have statistically higher Sharpe ratios than both similar portfolios with estimated ex-ante returns and 1/N′th portfolios. Optimal portfolio methods with well-behaved weights guide investors in a way not hitherto possible (normative portfolio theory).     

The coskewness puzzle

We propose a novel approach to testing non-linear stochastic discount factor (SDF) specifications that arise in rational representative investor models. Our approach does not require overly-restrictive assumptions about the shape of investors’ preferences, typically imposed by the extant literature, and is based instead on restrictions that rule out “good deals”, i.e., arbitrage opportunities as well as unduly large Sharpe ratios. We apply this framework to test the empirical admissibility of 3 and 4-moment versions of the CAPM. We find that, while coskewness and cokurtosis risk help price a number of stock strategies and portfolios, including static strategies based on a fine industry-level diversification, momentum strategies and portfolios managed on the basis of available information, the CAPM and its 3 and 4-moment versions cannot provide an exhaustive account of observed asset returns.     

Weighing asset pricing factors: a least squares model averaging approach

Empirical evidence has demonstrated that certain factors in asset pricing models are more important than others for explaining specific portfolio returns. We propose a technique that evaluates the factors included in popular linear asset pricing models. Our method has the advantage of simultaneously ranking the relative importance of those pricing factors through comparing their model weights. As an empirical verification, we apply our method to portfolios formed following Fama and French [A five-factor asset pricing model. J. Financ. Econ., 2015, 116, 1–22] and demonstrate that models accommodated to our factor rankings do improve their explanatory power in both in-sample and out-of-sample analyses.     

International portfolio diversification: Is there a role for the Middle East and North Africa?

We examine the issue of possible portfolio diversification benefits into seven Middle East and North African (MENA) stock markets. We construct international portfolios in dollars and local currencies. Ex ante weights are obtained by plugging five optimization models and two risk measures into a rolling block-bootstrap methodology. This allows us to derive 48 monthly rebalanced ex post portfolio returns. We analyze the out-of-sample performance based on Sharpe and Sortino ratios and the Jobson–Korkie statistic. Our results highlight outstanding diversification benefits in the MENA region, both in dollar and local currencies. Overall, we show that these under-estimated, under-investigated markets could attract more portfolio flows in the future.     

Long-Run Performance Persistence of Investment Funds

This article analyzes the long-run persistence of returns and risk of investment in the assets of money, bound, and stock funds recorded on the Polish market in 2000–12. Portfolios of safe, hybrid, and stock classes are formed on the basis of tested funds. The persistence of returns and the Sharpe ratio are investigated in rolled five-year sub-periods, with one year step. Also, persistence in performance is assessed using classic CAPM and Fama and French models, which allow for evaluating management skills. We find the occurrence of the Sharpe ratio long-run persistence of money and bound funds. The study does not explicitly show long-run persistence in hybrid and stock fund portfolios. The CAPM and Fama and French models simulations of returns on stock and hybrid funds indicate varying management skills during five-year periods.     

The output gap and stock returns: Do cyclical fluctuations predict portfolio returns?

This study examines whether the output gap leads portfolio stock returns. The paper conducts in-sample and out-of-sample forecasting of US stock portfolios formed on the basis of size and value. First, the paper finds cross-sectional portfolios are predictable in-sample by the output gap. Out-of-sample evidence is weaker but still generally supports the finding that the historical average benchmark can be beaten. Secondly and most importantly, we find mixed evidence that the Fama–French factor mimicking portfolios can be forecasted by the output gap. In particular, there is some out-of-sample predictability of the size effect (SMB) suggesting this lags the output gap. However, the output gap, a key business cycle indicator, cannot predict the value effect (HML) either in-sample or out-of-sample. Our results add to the prior literature which finds that the factor mimicking returns are related contemporaneously (Petkova and Zhang, 2005) or lead (Liew and Vassalou, 2000) economic indicators.     

Reduction of estimation risk in optimal portfolio choice using redundant constraints

It is well known that when the moments of the distribution governing returns are estimated from sample data, the out-of-sample performance of the optimal solution of a mean–variance (MV) portfolio problem deteriorates as a consequence of the so-called “estimation risk”. In this document we provide a theoretical analysis of the effects caused by redundant constraints on the out-of-sample performance of optimal MV portfolios. In particular, we show that the out-of-sample performance of the plug-in estimator of the optimal MV portfolio can be improved by adding any set of redundant linear constraints. We also illustrate our findings when risky assets are equally correlated and identically distributed. In this specific case, we report an emerging trade-off between diversification and estimation risk and that the allocation of estimation risk across portfolios forming the optimal solution changes dramatically in terms of number of assets and correlations.