The introduction of a private pension funds in conjunction with the public social security system is the essence of pension system reform that was implemented in Lithuania. The performance of private funds is mainly presented by fund's net asset value and few classical risk estimates. Such evaluation shows the management company's ability to profitably invest funds, but does not give the evidential riskreturn evaluation. This paper refers to the overall statistical analysis of 26 private pension funds over a certain time period. The objective of the research is to determine the risk-return profile of pension funds and to answer the question whether the categories specified based on investment strategy in equities reflect fund's empirical behaviour. Research methodology includes the statistical analysis, risk measuring, performance ratio estimation, and K-means clustering. The conclusions obtained by the research allow determining whether the distinct pension funds have beaten a low risk reference and are adequately assigned to a certain risk category.

The paper proposes a new approach to investigating the dynamics of hourly exchange rates of two currenciesthe Euro (EUR) and US dollar (USD). The dynamics of foreign exchange (forex) rate is a complex process that can be better understood through a study of its characteristics, such as for instance volatility. In this article the exchange rate fluctuation is analysed by calculating the sum of absolute differences (SAD) of a time series per hour. It has been shown empirically that a new time series constructed from SAD values is more suitable for predicting exchange rate volatility if it takes into account only the magnitude of the exchange rate fluctuation and ignores its direction. The analysis of EUR/USD exchange rate data at major financial centers has revealed that both exchange rates undergo periodical intraday variations; therefore, both additive and multiplicative versions of Holt-Winters exponential smoothing techniques have been applied in the analysis and predict of exchange rate volatility. These methods are appropriate for a time series with a linear trend and seasonal variations. Since a time series of SAD values does not have a clear trend, simplified versions (without changes in trend) of the Holt-Winters model were applied. Two different statistics-mean absolute error (MAE) and root mean squared error (RMSE)-were applied to select the optimal parameters of four versions of the Holt-Winters model. The study showed that volatility is best predicted by a simplified version of the multiplicative Holt-Winters model.

In this paper we consider the problem of choosing the optimal pension fund in the second pillar of Lithuanian pension system by providing some guidelines to individuals with defined contribution pension plans. A multistage risk-averse stochastic optimization model is proposed that can be used to plan a long-term pension accrual under two different cases: minimum and maximum accumulation plans as possible options in the system. The investment strategy of personal savings is based on the optimal solutions over possible scenario realizations generated for a particular participant. The concept of the risk-averse decision-maker is implemented by choosing the Conditional Value at Risk (CVaR) as the risk measure defined by a nested formulation that guarantees the time consistency in the multistage model. The paper focuses on three important decision-making moments corresponding to the duration of periods to be modelled. The first period is a short-term accumulation, while the second period is a long-term accumulation with possibly high deviation of objective function value. The third period is designed to implement the concept of Target Date Fund in the second pillar pension scheme as the subsequent need to protect against potential losses at risky pension funds. The experimental findings of this research provide insights for individuals as decision-makers to select pension funds, as well as for policy-makers by revealing the vulnerability of pension system.

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