Robust multivariate portfolio choice with stochastic covariance in the presence of ambiguity

This paper provides the optimal multivariate intertemporal portfolio for an ambiguity averse investor, who has access to stocks and derivative markets, in closed form. The stock prices follow stochastic covariance processes and the investor can have different levels of uncertainty about the diffusion parts of the stocks and the covariance structure. We find strong evidence that the optimal exposures to stock and covariance risks are significantly affected by ambiguity aversion. Welfare analyses show that investors who ignore model uncertainty incur large losses, larger than those suffered under the embedded one-dimensional cases. We further confirm large welfare losses from not trading in derivatives as well as ignoring intertemporal hedging, we study the impact of ambiguity in that regard and justify the importance of including these factors in the scope of portfolio optimization. Conditions are provided for a well-behaved solution in general, together with verification theorems for the incomplete market case.     

Robustness of the inference procedures for the global minimum variance portfolio weights in a skew-normal model

In this paper, we study the influence of skewness on the distributional properties of the estimated weights of optimal portfolios and on the corresponding inference procedures derived for the optimal portfolio weights assuming that the asset returns are normally distributed. It is shown that even a simple form of skewness in the asset returns can dramatically influence the performance of the test on the structure of the global minimum variance portfolio. The results obtained can be applied in the small sample case as well. Moreover, we introduce an estimation procedure for the parameters of the skew-normal distribution that is based on the modified method of moments. A goodness-of-fit test for the matrix variate closed skew-normal distribution has also been derived. In the empirical study, we apply our results to real data of several stocks included in the Dow Jones index.     

Dynamic factor long memory volatility

In this paper, we develop a long memory orthogonal factor (LMOF) multivariate volatility model for forecasting the covariance matrix of financial asset returns. We evaluate the LMOF model using the volatility timing framework of Fleming et al. [J. Finance, 2001, 56, 329–352] and compare its performance with that of both a static investment strategy based on the unconditional covariance matrix and a range of dynamic investment strategies based on existing short memory and long memory multivariate conditional volatility models. We show that investors should be willing to pay to switch from the static strategy to a dynamic volatility timing strategy and that, among the dynamic strategies, the LMOF model consistently produces forecasts of the covariance matrix that are economically more useful than those produced by the other multivariate conditional volatility models, both short memory and long memory. Moreover, we show that combining long memory volatility with the factor structure yields better results than employing either long memory volatility or the factor structure alone. The factor structure also significantly reduces transaction costs, thus increasing the feasibility of dynamic volatility timing strategies in practice. Our results are robust to estimation error in expected returns, the choice of risk aversion coefficient, the estimation window length and sub-period analysis.     

Portfolio analysis of intraday covariance matrix in the Greek equity market

The intraday nonparametric estimation of the variance–covariance matrix adds to the literature in portfolio analysis of the Greek equity market. This paper examines the economic value of various realized volatility and covariance estimators under the strategy of volatility timing. I use three types of portfolios: Global Minimum Variance, Capital Market Line and Capital Market Line with only positive weights. The estimators of volatilities and covariances use 5-min high-frequency intraday data. The dataset concerns the FTSE/ATHEX Large Cap index, FTSE/ATHEX Mid Cap index, and the FTSE/ATHEX Small Cap index of the Greek equity market (Athens Stock Exchange). As far as I know, this is the first work of its kind for the Greek equity market. Results concern not only the comparison of various estimators but also the comparison of different types of portfolios, in the strategy of volatility timing. The economic value of the contemporary non-parametric realized volatility estimators is more significant than this when the covariance is estimated by the daily squared returns. Moreover, the economic value (in b.p.s) of each estimator changes with the volatility timing.     

Improved estimation of the covariance matrix of stock returns with an application to portfolio selection

This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing estimators: the sample covariance matrix and single-index covariance matrix. This method is generally known as shrinkage, and it is standard in decision theory and in empirical Bayesian statistics. Our shrinkage estimator can be seen as a way to account for extra-market covariance without having to specify an arbitrary multifactor structure. For NYSE and AMEX stock returns from 1972 to 1995, it can be used to select portfolios with significantly lower out-of-sample variance than a set of existing estimators, including multifactor models.     

Parameter uncertainty in portfolio selection: Shrinking the inverse covariance matrix

The estimation of the inverse covariance matrix plays a crucial role in optimal portfolio choice. We propose a new estimation framework that focuses on enhancing portfolio performance. The framework applies the statistical methodology of shrinkage directly to the inverse covariance matrix using two non-parametric methods. The first minimises the out-of-sample portfolio variance while the second aims to increase out-of-sample risk-adjusted returns. We apply the resulting estimators to compute the minimum variance portfolio weights and obtain a set of new portfolio strategies. These strategies have an intuitive form which allows us to extend our framework to account for short-sale constraints, transaction costs and singular covariance matrices. A comparative empirical analysis against several strategies from the literature shows that the new strategies often offer higher risk-adjusted returns and lower levels of risk.     

On the performance of the minimum VaR portfolio

Alexander and Baptista [2002. Economic implications of using a mean-value-at-risk (VaR) model for portfolio selection: A comparison with mean–variance analysis. Journal of Economic Dynamics and Control 26: 1159–93] develop the concept of mean-VaR efficiency for portfolios and demonstrate its very close connection with mean–variance efficiency. In particular, they identify the minimum VaR portfolio as a special type of mean–variance efficient portfolio. Our empirical analysis finds that, for commonly used VaR breach probabilities, minimum VaR portfolios yield ex post returns that conform well with the specified VaR breach probabilities and with return/risk expectations. These results provide a considerable extension of evidence supporting the empirical validity and tractability of the mean-VaR efficiency concept.     

An exact test on structural changes in the weights of the global minimum variance portfolio

In the paper, a finite sample test is suggested for detecting changes in the composition of the global minimum variance portfolio. The exact density of the test statistic is calculated. It appears that under the null hypothesis of no change, it is independent of the parameters of the asset returns distribution. The testing procedure is implemented in a situation that is practically relevant. We show that ignoring the uncertainty about the estimated weights of the holding portfolio leads to misleading results, i.e. to a more frequent reallocation of the investor's wealth.     

A performance evaluation of portfolio managers: tests of micro and macro forecasting

This study examines the performance of Irish domiciled funds over the period 1988 to 2000. The study specifically examines whether Irish portfolio managers, particularly in light of the small and thinly traded domestic market, can effectively partake in micro or macro forecasting. Four alternative models are used to jointly assess micro and macro forecasting, while a fifth non-parametric model is used to solely examine market timing effects. The results reveal consistent evidence of poor micro forecasting/stock selection ability across the funds examined. The macro forecasting results are more varied, with some evidence of positive timing ability in two of the models. In addition, significant correlations are generally found between the funds micro and macro forecasting ability, while diagnostic tests reveal limited evidence of mis-specification in the models used.     

The information content of portfolio performance history and persistence in fund performance: An examination of rollover funds

This paper examines the relation between past and future performance and explores the optimal past performance information set for a subset of Australian investment funds, namely, rollover funds. Four categories of funds are examined: fixed interest; multi-sector yield; multi-sector balanced; and multi-sector growth. This study extends the performance persistence literature through the use of three methodologies (1) regression analysis;(2) non-parametric contingency tables; and (3) top (and bottom) quartile rankings to explore the information content of fund performance history for groups of funds differentiated by investment objective. The results of the regression analysis suggest that there is evidence in support of persistence in performance for the fixed interest funds (particularly when performance is measured in terms of Jensen Alpha) but much more ambiguous evidence in relation to the multi-sector funds. Contingency table analysis of fund performance histories of varying lengths reveals quite different results depending upon whether raw or risk-adjusted returns are used. Use of raw returns creates an overall impression of performance reversals, whereas use of risk-adjusted returns suggests the existence of performance persistence. Finally, the use of prior period top-quartile and bottom-quartile ranking are found to show strong evidence of persistence in respect to the risk-adjusted performance of fixed-interest funds.     

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.      

Bias-correcting the realized range-based variance in the presence of market microstructure noise

Market microstructure noise is a challenge to high-frequency based estimation of the integrated variance, because the noise accumulates with the sampling frequency. This has led to widespread use of constructing the realized variance, a sum of squared intraday returns, from sparsely sampled data, for example 5- or 15-minute returns. In this paper, we analyze the impact of microstructure noise on the realized range-based variance and propose a bias correction to the range-statistic. The new estimator is shown to be consistent for the integrated variance and asymptotically mixed Gaussian under simple forms of microstructure noise. We can select an optimal partition of the high-frequency data in order to minimize its asymptotic conditional variance. The finite sample properties of our estimator are studied with Monte Carlo simulations and we implement it using Microsoft high-frequency data from TAQ. We find that a bias-corrected range-statistic often leads to much smaller confidence intervals for the integrated variance, relative to the realized variance. We should like to thank an anonymous referee and the associate editor for insightful comments on an earlier draft. Parts of this paper were written while Kim Christensen was at the University of California, San Diego, whose hospitality is gratefully acknowledged. Mark Podolskij received financial support from CREATES funded by the Danish National Research Foundation, and Mathias Vetter was supported by the Deutsche Forschungsgemeinschaft grant SFB 475 “Reduction of Complexity in Multivariate Data Structures.” The code for this paper was written in the Ox programming language, due to Doornik (2002). All views expressed here are those of the authors and do not necessarily represent the views of Nordea.     

Exploring the benefits of using stock characteristics in optimal portfolio strategies

I examine the benefits of using stock characteristics to model optimal portfolio weights in stock selection strategies using the characteristic portfolio approach of Brandt, Santa-Clara, and Valkanov. [2009. “Parametric Portfolio Policies: Exploiting Characteristics in the Cross-section of Equity Returns.” Review of Financial Studies 22: 3411–3447]. I find that there are significant out-of-sample performance benefits in using characteristics in stock selection strategies even after adjusting for trading costs, when investors can invest in the largest 350 UK stocks. Imposing short selling restrictions on the characteristic portfolio strategy leads to more consistent performance. The performance benefits are concentrated in the earlier part of the sample period and have disappeared in recent years. I find that there no performance benefits in using stock characteristics when using random subsets of the largest 350 stocks.     

A minimum variance benchmark to measure the performance of pension funds in Mexico

We propose the use of the minimum variance portfolio as weighting method in a strategy benchmark for pension funds performance in Mexico. By performing three discrete event simulations with daily data from January 2002 to May 2013, we test this benchmark's weighting method against the Max Sharpe ratio one and a linear combination of both benchmarks (minimum variance and Max Sharpe). With the Sharpe ratio, the Jensen's alpha significance test and the Huberman and Kandel’ (1987) spanning test, we found that the three benchmarks have a statistically equal performance. By using Bailey's (1992) risk exposure, market representativeness and turnover benchmark quality criteria, we found that the min variance is preferable for the publicly traded Mexican defined contribution pension funds.     

Discussions on the spurious hyperbolic memory in the conditional variance and a new model

This paper studies the spurious hyperbolic memory in the conditional variance caused by the Markov Regime-Switching GARCH (MRS-GARCH) process. We firstly propose an illustrative cause of this spuriousness and provide simulation evidence. An MRS Hyperbolic GARCH (MRS-HGARCH) model is then developed to successfully address it. Related statistical properties including the stationarity conditions and asymptotic behaviours of the maximum likelihood estimators of the MRS-HGARCH process are also investigated. An empirical study of the S&P 500 and TOPIX indexes returns is then conducted which demonstrates that our MRS-HGARCH model can provide a more reliable estimator of the hyperbolic-memory parameter and outperform both the HGARCH and MRS-GARCH models.     

A macroeconomic hedge portfolio and the cross section of stock returns

We use a stock's returns on days when important macroeconomic news is released to form a hedge portfolio, which is long (short) in stocks which have a sensitive (insensitive) reaction to the surprise component of the macroeconomic news. This macroeconomic hedge portfolio (MHP) earns a risk premium of about 5% p.a. over time and a similar premium when used as a risk factor in an asset pricing model. This premium can be interpreted as a cost of an insurance against unexpected changes in an investor's marginal utility. We show that risk premiums associated with the MHP are estimated with a higher precision than traditional macroeconomic tracking portfolios. Furthermore, when the MHP is present in a common factor model, risk factors like high minus low lose much of their ability to explain the cross section of stock returns.     

Financial integration and the price of world covariance risk: Large- vs. small-cap stocks

We investigate whether recent country-level evidence of global pricing is particular to large-cap stocks. Specifically, we examine cross-country return correlations and conduct asset pricing tests on three size-based stock portfolios for nine developed countries over the period from 1980 to 2004. We find that large-cap stocks realize significant comovements across countries, whereas small-cap stocks realize smaller average correlations (relative to both large-cap stocks and small-cap stocks across countries). More important, asset pricing tests suggest that while large-cap stocks are priced globally, global pricing is rejected for most small-cap stocks. Finally, the evidence indicates that financial integration deepened in recent years primarily for large-cap stocks. Overall, the results suggest that the global pricing pertains chiefly to large-cap stocks.     

Stock market volatility, excess returns, and the role of investor sentiment

Using the Investors' Intelligence sentiment index, we employ a generalized autoregressive conditional heteroscedasticity-in-mean specification to test the impact of noise trader risk on both the formation of conditional volatility and expected return as suggested by De Long et al. [Journal of Political Economy 98 (1990) 703]. Our empirical results show that sentiment is a systematic risk that is priced. Excess returns are contemporaneously positively correlated with shifts in sentiment. Moreover, the magnitude of bullish (bearish) changes in sentiment leads to downward (upward) revisions in volatility and higher (lower) future excess returns.     

Re-examining the small-cap myth: problems in portfolio formation and liquidation

This study investigates the realizable returns on portfolios at the turn-of-the-year. Using an intraday simulation that accounts for the volumes offered or wanted at market bid-ask prices, large-capitalization securities significantly outperform small-capitalization securities by 2.4% and 6.5%, depending on whether the portfolios were formed on the last day of the taxation year or were formed over the last month of the trading year. In no one year could the small-capitalization portfolio be completely divested by the end of the holding period, suggesting that investors are not remunerated for the illiquidity in this portfolio. Results based on returns calculated by using the mean of the bid-ask spread show that the results are not derived solely from transaction costs.