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Abstract:
This paper proposes a method of calculating a Liquidity Adjusted Value-at-Risk (L-VaR) measure. The traditional approaches that have been implemented assume that the financial markets are perfect and hence an investor can either buy or sell any amount of stock without causing significant price changes. However, this conjecture is not a realist one as most of the markets, especially the emerging ones, are illiquid. In the attempt to create a L-VaR measure that accounts for the spread variation, we estimate the components of the bid-ask spread in order to calculate accurately both the endogenous and the exogenous liquidity risk. Under the new framework, the liquidation price of a position will not be the midpoint of the spread, but at least the bid price and therefore the calculated Value-at-Risk number will be more realistic. We extend the Madhavan et al. (1997) model by incorporating the traded volume and find out that both the adverse selection component and the L-VaR measure exhibit a U-shape pattern throughout the day, while the percent of risk that is attributed to liquidity displays an inverse U-shape pattern. Finally, at higher confidence level, the liquidity component of the high-priced, high-capitalization stocks represents 3.40% of the total market risk, while for the low capitalization securities it equals to 11% and therefore cannot be neglected.

Liquidity Adjusted Value-at-Risk, Bid-Ask Spread, Asymmetry Information, Transaction

Abstract:
The fluctuation of shipping freight rates (freight rate risk) is an important source of market risk for all participants in the freight markets including hedge funds, commodity and energy producers. We measure the freight rate risk by the Value-at-Risk (VaR) approach. A range of parametric and non-parametric VaR methods is applied to various popular freight markets for dry and wet cargoes. Backtesting is conducted in two stages by means of statistical tests and a subjective loss function that uses the Expected Shortfall, respectively. We find that the simplest non-parametric methods should be used to measure freight rate risk. In addition, freight rate risk is greater in the wet cargoes markets. The margins in the growing freight derivatives markets should be set accordingly.

Backtesting, Expected Shortfall, Forward Freight Agreements, Freight Markets, Freight Rates, Value-at-Risk

Abstract:
Academics and practitioners have extensively studied Value-at-Risk (VaR) to propose a unique risk management technique that generates accurate VaR estimations for long and short trading positions and for all types of financial assets. However, they have not succeeded yet as the testing frameworks of the proposals developed, have not been widely accepted. A two-stage backtesting procedure is proposed to select a model that not only forecasts VaR but also predicts the losses beyond VaR. Numerous conditional volatility models that capture the main characteristics of asset returns (asymmetric and leptokurtic unconditional distribution of returns, power transformation and fractional integration of the conditional variance) under four distributional assumptions (normal, GED, Student-t, and skewed Student-t) have been estimated to find the best model for three financial markets, long and short trading positions, and two confidence levels. By following this procedure, the risk manager can significantly reduce the number of competing models that accurately predict both the VaR and the Expected Shortfall (ES) measures.

Backtesting, Value-at-Risk, Expected Shortfall, Volatility Forecasting, Arch Models

Abstract:
We evaluate the performance of an extensive family of ARCH models in modeling daily Value-at-Risk (VaR) of perfectly diversified portfolios in five stock indices, using a number of distributional assumptions and sample sizes. We find, first, that leptokurtic distributions are able to produce better one-step-ahead VaR forecasts; second, the choice of sample size is important for the accuracy of the forecast, whereas the specification of the conditional mean is indifferent. Finally, the ARCH structure producing the most accurate forecasts is different for every portfolio and specific to each equity index.

Value at Risk, GARCH estimation, Backtesting, Volatility forecasting, Quantile Loss Function

Abstract:
The accuracy of parametric, non-parametric and semi-parametric methods in predicting the one-day-ahead Value-at-Risk (VaR) of perfectly diversified portfolios in three types of markets (stock exchanges, commodities and exchange rates) is investigated, both for long and short trading positions. The risk management techniques are designed to capture the main characteristics of asset returns, such as leptokurtosis and asymmetric distribution, volatility clustering, asymmetric relationship between stock returns and conditional variance and power transformation of conditional variance. Based on backtesting measures and a loss function evaluation method, we find out that the modeling of the main characteristics of asset returns produces accurate VaR forecasts. Especially for the high confidence levels, a risk manager must employ different volatility techniques in order to forecast the VaR for the two trading positions.

Asymmetric Power ARCH model, Skewed-t Distribution, Value-at-Risk, Volatility Forecasting

Abstract:
Recently risk management has become a standard prerequisite for all financial institutions. Value-at-Risk is the main tool of reporting to the bank regulators the risk that the financial institutions face. As it is essential to estimate it accurately, numerous methods have been proposed in order to minimize the forecast error. This chapter provides a selective survey of the risk management techniques that have been applied and discusses potential improvements in estimating, evaluating and adjusting Value-at-Risk and Expected Shortfall.

Backtesting, Expected Shortfall, Value-at-Risk, Volatility Forecasting

Abstract:
We analyse the components of the bid-ask spread in the Athens Stock Exchange (ASE), which was recently characterised as a developed market. For large and medium capitalisation stocks, we estimate the adverse selection and the order handling component of the spreads as well as the probability of a trade continuation on the same side of either the bid or the ask price, using the Madhavan et al. (1997) model. We extend it by incorporating the traded volume and we find that the adverse selection component exhibits U-shape patterns, while the cost component pattern depends on the stock price. For high priced stocks, the usual U-shape applies, while for low-priced ones, it is an increasing function of time, mainly due to the order handling spread component. Furthermore, the expected price change and the liquidity adjustment to Value-at-Risk that is needed are higher in the low capitalisation stocks, while the most liquid stocks are the high priced ones. Moreover, by estimating the Madhavan et al. (1997) model for two distinct periods we explain why there are differences in the components of the bid-ask spread.

Abstract:
We analyze the components of the bid-ask spread in the Athens Stock Exchange (ASE), which was recently characterized as a developed market. For 18 large and 13 medium capitalization stocks, we estimate the adverse selection and the order handling component of the spreads as well as the probability of a trade continuation on the same side of either the bid or the ask price, using the Madhavan et al. (1997) model. We extend it by incorporating the traded volume and we find that the adverse selection component exhibits U-shape patterns, while the cost component pattern depends on the stock price. For high priced stocks, the usual U-shape applies, while for low-priced ones, it is an increasing function of time, mainly due to the different magnitude of the order handling spread component. Our analysis shows that the order handling component dominates inventory effects, particularly in the first and last half hour of the trading day and hence we observe economies of scale in trading. Furthermore, the expected price change is higher in the low capitalization stocks, while the most liquid stocks are the high priced ones. Moreover, by estimating the Madhavan et al. (1997) model for two distinct periods we explain why there are differences in the components of the bid-ask spread.

Bid-ask spread, asymmetry information, transaction costs, price impact

Abstract:
This paper analyses several volatility models by examining their ability to forecast the Value-at-Risk (VaR) for two different time periods and two capitalization weighting schemes. Specifically, VaR is calculated for large and small capitalization stocks, based on Dow Jones (DJ) Euro Stoxx indices and is modeled for long and short trading positions by using non parametric, semi parametric and parametric methods. In order to choose one model among the various forecasting methods, a two-stage backtesting procedure is implemented. In the first stage the unconditional coverage test is used to examine the statistical accuracy of the models. In the second stage a loss function is applied to investigate whether the differences between the models, that calculated accurately the VaR, are statistically significant. Under this framework, the combination of a parametric model with the historical simulation produced robust results across the sample periods, market capitalization schemes, trading positions and confidence levels and therefore there is a risk measure that is reliable.

Value-at-Risk, Asymmetric Power ARCH, Filtered Historical Simulation, Extreme Value Theory, Backtesting

Abstract:
This paper analyses the application of several volatility models to forecast daily Value-at-Risk (VaR) both for single assets and portfolios. We calculate the VaR number for 4 Greek stocks, 2 portfolios based on these securities and for Athens Stock Exchange General Index (ASE). We model VaR for long and short trading positions by employing non-parametric methods, such as historical and filtered historical simulation, and parametric ones. Especially for the later techniques we use a collection of ARCH models (GARCH, EGARCH and TARCH) based on three distributional assumptions (Normal, Student-T and Skewed Student-T), while we combine the Extreme Value Theory with a volatility updating technique (via GARCH type-modeling). In order to choose one model among the various forecasting methods, we employ a two-stage backtesting procedure. In the first one, we implement two backtesting criteria (unconditional and conditional coverage) to test the statistical accuracy of the models. In the second stage, we employ standard forecast evaluation methods in order to examine whether the diferences between the models, which have converged suficiently, are statistically significant.

Value-at-Risk, GARCH, Backtesting

Abstract:
We evaluate the performance of symmetric and asymmetric ARCH models in forecasting one-day-ahead Value-at-Risk (VaR) and realized intra-day volatility of two equity indices in the Athens Stock Exchange (ASE). Under the framework of three distributional assumptions, we find out that the most appropriate method for the Bank index in forecasting the one-day-ahead VaR is the symmetric model with normally distributed innovations, while the asymmetric model with asymmetric conditional distribution applies for the General index. On the other hand, the asymmetric model tracks closer the one-step-ahead intra-day realized volatility with conditional normally distributed innovations for the Bank index but with asymmetric and leptokurtic distributed innovations for the General index. Therefore, as concerns the Greek stock market, there are adequate methods for predicting market risk but it does not seem to be a specific model that is the most accurate for all the forecasting tasks.

Asymmetric Power ARCH model, Intra Day Realized Volatility, Skewed-t Distribution, Value-at-Risk, Volatility Forecasting

Abstract:
We evaluate the performance of symmetric and asymmetric ARCH models in forecasting one-day-ahead Value-at-Risk (VaR) and realized intra day volatility of two equity indices in the Athens Stock Exchange (ASE). Under the framework of three distributional assumptions, we find out that the most appropriate method for the Bank index in forecasting the one-day-ahead VaR is the symmetric model with normally distributed innovations, while the asymmetric model with asymmetric conditional distribution applies for the General index. On the other hand, the asymmetric model tracks closer the one-step-ahead intra day realized volatility with conditional normally distributed innovations for the Bank index but with asymmetric and leptokurtic distributed innovations for the General index. Therefore, as concerns the Greek stock market, there are adequate methods for predicting market risk but it does not seem to be a specific model that is the most accurate for all the forecasting tasks.

Asymmetric Power ARCH model, Intra Day Realized Volatility, Skewed-t Distribution, Value-at-Risk, Volatility Forecasting

Abstract:
In this study, the properties and portfolio management implications of the value- weighted idiosyncratic volatility in 24 emerging markets are examined. The paper provides evidence against the view that the rise of idiosyncratic risk is a global phenomenon. Furthermore, specific and market risks jointly predict market returns as there is a negative (positive) relation between idiosyncratic (market) risk and subsequent stock returns. Idiosyncratic volatility is the most important component of tracking error volatility and it does not exhibit either an upward or a downward trend. Thus, investors do not have to increase, on an average, the number of stocks that they hold, to keep the active risk constant.

Emerging markets, Idiosyncratic risk, Portfolio management, Tracking error

Abstract:
The proposition that idiosyncratic volatility may matter in asset pricing is currently a topic of research and controversy. Using data from the UK market we examine the predictive ability of various measures of idiosyncratic risk and provide evidence which suggests that: (a) it is the idiosyncratic volatility of small capitalization stocks that matters for asset pricing and (b) that small stocks idiosyncratic volatility predicts the small capitalization premium component of market returns and is unrelated to either "pure" market risk or the value premium. The predictive power of the aggregate idiosyncratic volatility of small stocks remains intact even after we control for the possible proxying effects of business cycle fluctuations and liquidity and is robust across time and different econometric specifications.

Idiosyncratic risk, stock market volatility and stock return predictability

Abstract:
In the light of recent evidence that liquidity and idiosyncratic risk may be priced factors in the cross section of expected stock returns and that market capitalization significantly affects investor behavior and liquidity, we explore the interactions between liquidity, idiosyncratic risk and return across time as well as across size-based portfolios of stocks listed in the London Stock Exchange. In a Vector Autoregressive (VAR) analytical framework, we find that volatility spills over from large cap stocks to small cap stocks and vice versa. Volatility shocks can be predicted by illiquidity shocks in both large cap as well as in the small cap portfolios. Illiquidity can be predicted by return shocks in small cap stocks. Finally, we document some evidence of asymmetric liquidity spillovers, from large cap stocks to small cap ones, supporting the intuition that common information is first incorporated in the trading behavior of large-cap investors and the liquidity of large cap stocks and is then transmitted in the trading of small stocks.

liquidity spillover, idiosyncratic risk, London Stock Exchange

Abstract:
The volatility prediction is the most important issue in finance, as it is the key ingredient variable in forecasting the prices of options, the VaR number and, in general, the risk that investors face. By estimating not only inter-day volatility models that capture the main characteristics of asset returns, such as the non-zero skewness, the excess kurtosis relative to that of the normal distribution and the fractional integration of the conditional variance, but also an intra-day model, we investigate their forecasting performance for three European equity indices. We find out that there is no consistent relation between the examined models and the specific purpose of volatility forecasts. Researchers cannot apply, not even for the same equity index, one model for all the forecasting purposes. However, if they want to choose one model, they must prefer an inter-day specification that accounts at least for volatility clustering and the leverage effect.

ARFIMA, ARCH, FIAPARCH, fractional integration, option pricing, skewed Student-t distribution, value at risk, volatility forecasting

Abstract:
The evidence on the inter-temporal relation between idiosyncratic risk and future stock returns is conflicting and confusing. We shed new light on the issue using a more flexible econometric approach based on Hamilton's (1989) regime switching model that accommodates the parameter instability of the forecasting relation between returns and financial variables. We find strong evidence suggesting that idiosyncratic risk is related to future stock market returns only in the low variance regime.

Idiosyncratic Risk, Stock Market Volatility and Regime Switching

Abstract:
This paper analyses the properties of idiosyncratic risk in the Greek Stock Market by disaggregating the total volatility of stocks at market, industry, and firm level. Idiosyncratic risk is much larger and represents a smaller component of total volatility in Greece compared with other developed markets, is persistent, shows no trend over time but tends to increase more in up-markets than in down markets. Average firm specific risk in Greece is best described by a two-state Markov process and during periods of high volatility (in 1987, in 1989-1990, in 1994 and 1998-2000) the average idiosyncratic variance is twice than that of the low variance regime. The implications for portfolio and risk management of changing idiosyncratic volatility are discussed.

Idiosyncratic Risk, Stock Market Volatility, Risk Management

Abstract:
The prices of Greek closed-end funds behave similarly to the prices of U.S. funds: They deviate substantially from their net asset values (NAVs), they are more volatile than their NAVs, they are overly-sensitive to the movements of the domestic stock market index, and their premia are: (i) positively correlated cross-sectionally, (ii) positively correlated with the future NAV returns, and (iii) negatively correlated with the future returns on the funds. This is true especially for larger CEF where mean reversion is exhibited even for the shortest sample period of one month but for all funds this behavior is confirmed for the longer periods of 9 and 12 months. The larger Greek closed-end funds are subsidiaries of banks and it appears that trading by the parent institutions initiate the earlier drop in sentiment.

Closed-End Fund, Net Asset Value, Fund Premium, Fund Discount, Mean Reversion, Excess Volatility, Common Factor, Predictive Ability, Over-Sensitivity, Noise Trading, Small Investor, Bank Subsidiary, Arbitrage, Measurement Error, Market Friction

Abstract:
Greek public pension funds can invest up to 23% into risky assets and are not allowed to invest outside Greece. This paper seeks to investigate the costs of investment constraints on pension fund portfolios. In particular we try to quantify the losses that portfolios suffer due to under-diversification and sub-optimal asset allocation. We find that the high concentration of Greek equity portfolios imposes a substantial return and utility loss which is further increased when the lack of international diversification is taken into account. Restricting the weight of equities to 23% of the total portfolio, leads to sub-optimal asset allocation that costs as much as 2% (3%) per annum compared to a balanced domestic (global) benchmark.

Portfolio Efficiency, Idiosyncratic Risk, Asset Allocation, Utility Loss, Pension Funds.

Abstract:
This paper considers the task of forming a portfolio of assets that outperforms a benchmark index, while imposing a constraint on the tracking error volatility. We examine three alternative formulations of active portfolio management. The first one is a typical set up in which the fund manager myopically maximizes excess return. The second formulation is an attempt to set a limit on the total risk exposure of the portfolio by adding a constraint that forces a priori the risk of the portfolio to be equal to the benchmark's. The third formulation, presented in this paper, directly maximizes the efficiency of active portfolios, while setting a limit on the maximum tracking error variance.

In determining optimal active portfolios, we incorporate additional constraints on the optimization problem, such as a limit on the maximum number of assets included in the portfolio (i.e. the cardinality of the portfolio) as well as upper and lower bounds on asset weights. From a computational point of view, the incorporation of these complex,though realistic, constraints becomes a challenge for traditional numeric optimization methods, especially when one has to assemble a portfolio from a big universe of assets. To deal properly with the complexity and the roughness of the solution space, we use particle swarm optimization, a population-based evolutionary technique. As an application, we select portfolios of different cardinality that actively reproduce the performance of the FTSE/ATHEX 20 Index of the Athens Stock Exchange. Our empirical study reveals important results as concerns the efficiency of common practices in active portfolio management and the incorporation of cardinality constraints.

active portfolio management, tracking error, particle swarm optimization