تجزیه و تحلیل پرتفوی ماتریس کواریانس روزانه در بازار سرمایه یونان

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.

The accurate volatility forecasts are very important both theoretically and empirically in portfolio analysis. The main objective of this paper is the evaluation of volatility and covariance forecasts with economic criteria in a portfolio framework. In specific, it is examined whether it is better estimating volatility and covariance estimators with intraday or daily data. Volatility has recently been analyzed by Evans and Speight, 2010 and Haniff and Pok, 2010, and Kitamura (2010). In broad terms, they analyze specific characteristics of volatility in an intraday frequency. These characteristics include interdependence, spillovers, periodicities and announcement effects. It is also examined which of the estimators is better in the volatility timing strategy. The present paper is based on the methodology of the volatility timing strategy introduced by Fleming et al. (2003) – FKO (2003) hereafter. Another relative and more recent paper is Kyj et al. (2009). However, the present paper is the first using so many realized volatility estimators in volatility-timing strategy. It is also among the few papers examining the significance of the Greek equity market to a portfolio manager. Data concern three major indices of the Greek equity market (Athens Stock Exchange; ASE): FTSE/ATHEX 20 index, FTSE/ATHEX Mid Cap index, and FTSE/ATHEX Small Cap index. Kyrtsou and Terraza (2000), Niarchos and Alexakis (2003) and Panas (2005) study the properties of either the intraday data or the volatility in the ASE. Volatility in the Greek equity market have also been recently examined by Diamandis et al. (2007) and Kenourgios and Samitas (2008). The results are supportive of using the realized volatility estimators instead of daily squared returns as well as the significance of the economic value of the volatility timing strategy. An investor is willing to pay annually up to 1014 basis points in order to profit from the estimators of the variance and covariance matrix that use intraday data. The economic value is further improved when the high-frequency intraday sampling frequency is the optimal one. The bias correction for the microstructure noise of the intraday data improves results as well. The use of intraday data in forecasting the variance–covariance matrix across the three major ASE indices reveals significant economic gains. The plan of the rest of the paper is as follows. Section 2 presents the methodology concerning the volatility estimators, the types of portfolios and the economic evaluation criteria of both the volatility forecasts and the volatility timing strategy. Section 3 describes the data used in this paper. Section 4 discusses the results and Section 5 gives the concluding remarks with some plausible extensions of the present analysis.

Estimating and forecasting the variance–covariance matrix with various types of realized volatility estimators gives significant portfolio profits. Significant profits exist in the Greek equity market. High values of all evaluation criteria reveal these conclusions. There are some conclusive results regarding the portfolio statistics and others regarding the performance fees. The CML-Long portfolio type and mostly the CML portfolio type as well have the highest performance fees and the best portfolio statistics. Moreover, the dominance of the CML portfolio type towards the GMV portfolio type is compatible with both the portfolio theory and the Capital Asset Pricing Model (CAPM). The gains from using the realized volatility estimators instead of the squared daily returns are very significant, concerning both the portfolio statistics and performance fees, in all three portfolio types. The correction of the bias coming from the microstructure noise of the intraday data is more significant than the selection of the optimal sampling frequency. The selection of the optimal sampling frequency improves results only for the CML portfolio type. However, the bias-correction improves the results in all three portfolio types. FKO (2003) also report that the bias-correction improves the portfolio statistics (μ, σ and SR) as well as the performance fees. Though, according to the results of this paper, there are some cases where the selection of the optimal sampling frequency is more significant than the bias-correction. This is true only for some performance fees. The highest performance fees are for the CML portfolio type as well as when there is bias-correction. When there is not any bias-correction, the performance fees exist only for the CML-Long portfolio type. This is also reported by de Pooter et al. (2008) under the framework of Partial and Global Minimum Variance portfolio types. The rankings of the covariances regarding portfolio statistics and performance fees are: greek-3, greek-1 and greek-2. An important result, concerning the portfolio weights, is that there are not extreme weights in any type of portfolio or estimator. The weights in Cash are always positive. The weights in FTSEM are larger than those in FTSE, which in their turn are larger than those in FTSES. Though, the inclusion of the FTSE index improves the performance of the portfolios with either the FTSEM or the FTSES. This result is more significant for the CML portfolio type and also when the criteria used are the portfolio statistics. Nevertheless, the inclusion of the FTSEM and FTSES indices gives better portfolio statistics and performance fees. This is true because the correlation coefficients between the two indices and between each of them and the FTSE index have negative values (0 < p ≤ −1) as well as different volatility range. 8 Interesting is also that the constraint of only positive weights for the CML portfolio type (as proposed by Jagganathan and Mu, 2003) not only does not lessen the portfolio performance but in some cases it also improves the portfolio performance, regardless the evaluation criteria and the realized volatility estimator used. This result is very important if we think that this constraint really holds in the Greek equity market (ASE); a market in crisis for near two years (from 2008 – Lehman crisis – to 2010 – the end of dataset). The overall portfolio performance of the Greek equity market is quite significant. It is up to future research to examine whether other contemporary non-parametric realized volatility estimators can improve the portfolio performance or not. Moreover, it would have been ambitious to see whether the portfolio performance changes with the use of different economic evaluation criteria or not, under the volatility timing strategy. Also, could we get better results where portfolio components may be either capitalization indices of a more developed equity market, or international equity indices, or even different assets? Finally, examining the economic value of country stock markets’ major indices across a set of either European only or international stock markets seems influential. Comparing the economic value of European stock markets’ portfolios to the value of the international ones before, during and after the recent (from 2008) financial crises seems interesting as well.