Pawel Sakowski

Quasi-Experimental Estimates of Class Size Effect in Primary Schools in Poland.

In this paper we analyze class size effects in the case of primary schools in Poland. We use two empirical strategies to avoid endogeneity bias. First, we use average class size in a grade as an instrumental variable for actual class size. This allows us to control for within school selection of pupils with different abilities to classes of different sizes. Additionally, we estimate fixed effects for schools to control for differences between them. Second, we exploit the fact that there is an informal maximum class size rule. We estimate class size effect only for those enrollment levels where some schools decide to add a new class and thus dramatically lower class sizes. For such enrollment levels variance of class size is mainly exogenous and we argue that this allows to estimate quasi-experimental class size effects. In this case we again use average class size as an instrument with enrollment as a key control variable. Using both strategies we obtain similar findings. We found that the positive effects observed with OLS regression disappear when we use instrumental variables. If we avoid endogeneity bias, then class size negatively affects student achievement. However, this effect is rather small. We discuss methodology, possible bias of results and the importance of our findings to current policy issues in Poland.

Investment Strategies Beating the Market: What Can We Squeeze from the Market?

The paper presents the new approach to optimizing automatic transactional systems. We propose the multi-stage technique which enables us to find investment strategies beating the market. Additionally, new measures of combined risk and returns are applied in the process of optimization. Moreover, we define new elements of risk control system based on volatility measures and consecutive signals confirmation. As the result, we formulate three complex investment systems, which maximize returns and simultaneously minimize risk in comparison to all other alternative investments (IR=2, Maximum Drawdown

Option Pricing Models with HF Data – a Comparative Study. The Properties of Black Model with Different Volatility Measures

This paper compares option pricing models, based on Black model notion (Black, 1976), especially focusing on the volatility models implied in the process of pricing. We calculated the Black model with historical (BHV), implied (BIV) and several different types of realized (BRV) volatility (additionally searching for the optimal interval Δ, and parameter n - the memory of the process). Our main intention was to find the best model, i.e. which predicts the actual market price with minimum error. We focused on the HF data and bidask quotes (instead of transactional data) in order to omit the problem of non-synchronous trading and additionally to increase the significance of our research through numerous observations. After calculation of several error statistics (RMSE, HMAE and HRMSE) and additionally the percent of price overpredictions, the results confirmed our initial intuition that that BIV is the best model, BHV being the second best, and BRV – the least efficient of them. The division of our database into different classes of moneyness ratio and TTM enabled us to observe the distinct differences between compared pricing models. Additionally, focusing on the same pricing model with different volatility processes results in the conclusion that point-estimate, not averaged process of RV is the main reason of high errors and instability of valuation in high volatility environment. Finally, we have been able to detect “spurious outliers” and explain their effect and the reason for them owing to the multi-dimensional comparison of the pricing error statistics.

Midquotes or Transactional Data? The Comparison of Black Model on HF Data

The main idea of this research is to check the efficiency of the Black option pricing model on the basis of HF emerging market data. However, liquidity constraints - a typical feature of an emerging derivatives market - put severe limits for conducting such a study. That is the reason why Kokoszczynski et al., 2010, have conducted their earlier research on midquotes data treating them as potential transactional data. They have got some intriguing conclusions about implementing different volatility processes into the Black option model. Nevertheless, taking into account that midquotes do not have to be the proper representation of market prices as probably transactional data do, we decide to compare in this paper the results of the research conducted on HF transactional and midquotes data. This comparison shows that the results do not differ significantly between these two approaches and that BIV model significantly outperforms other models, especially BRV model with the latter producing the worst results. Additionally, we provide the discussion of liquidity issue in the context of emerging derivatives market. Finally, after exclusion of spurious outliers we observe significant patterns in option pricing that are not visible on the raw data.

Volatility as a New Class of Assets? The Advantages of Using Volatility Index Futures in Investment Strategies

This paper investigates the changes in the investment portfolio performance after including VIX. We apply different models for optimal portfolio selection (Markowitz and Black-Litterman) assuming both the possibility of short sale and the lack of it. We also use various assets, data frequencies, and investment horizons to get a comprehensive picture of our results’ robustness. Investment strategies including VIX futures do not always deliver higher returns or higher Sharpe ratios for the period 2006-2013. Their performance is quite sensitive to changes in model parameters. However, including VIX significantly increases the returns in almost all cases during the recent financial crisis. This result clearly emphasizes potential gains of having such an asset in the portfolio in case of very high volatility in financial markets.

CROSS-SECTIONAL RETURNS WITH VOLATILITY REGIMES FROM A DIVERSE PORTFOLIO OF EMERGING AND DEVELOPED EQUITY INDICES

Abstract This article aims to extend evaluation of the classic multifactor model of Carhart (1997) for the case of global equity indices and to expand analysis performed in Sakowski et. al. (2015). Our intention is to test several modifications of these models to take into account different dynamics of equity excess returns between emerging and developed equity indices. Proposed extensions include a volatility regime switching mechanism (using dummy variables and the Markov approach) and the fifth risk factor based on realized volatility of index returns. Moreover, instead of using data for stocks of a particular market (which is a common approach in the literature), we check performance of these models for weekly data of 81 world investable equity indices in the period of 2000-2015. Such an approach is proposed to estimate an equity risk premium for a single country. Empirical evidence reveals important differences between results for classical models estimated on single stocks (either in international or US-only frameworks) and models evaluated for equity indices. Additionally, we observe substantial discrepancies between results for developed countries and emerging markets. Finally, using weekly data for the last 15 years we illustrate the importance of model risk and data overfitting effects when drawing conclusions upon results of multifactor models.

Does Historical Volatility Term Structure Contain Valuable Information for Predicting Volatility and Index Futures

We suggest that the term structure of volatility futures (e.g. VIX futures) shows a clear pattern of dependence on the current level of VIX index. At the low level of VIX (below 20) the term structure is highly upward sloping; at the high VIX level (over 30) it is strongly downward sloping. We use those features to better predict future volatility and index futures. We begin by introducing some quantitative measures of volatility term structure (VTS) and volatility risk premium (VRP). We use them further to estimate the distance between the actual value and the fair (model) value of the VTS. We find that this distance has significant predictive power for volatility futures and index futures and we use this feature to design a simple strategy to invest in VIX index futures and S&P500.

Options Delta Hedging with No Options at All

The adjustment speed of delta hedged options exposure depends on the market realized and implied volatility. We observe that by consistently hedging long and short positions in options we can eventually end up with pure exposure to volatility without any options in the portfolio at all. The results of such arbitrage strategy is based only on speed of adjustment of delta hedged option positions. More specifically, they rely on interrelation between realized volatility levels calculated for various time intervals (from daily to intraday frequency). Theoretical intuition enables us to solve the puzzle of the optimal frequency of hedge adjustment and its influence on hedging efficiency. We present results of a simple hedge strategy based on the consistent hedging of a portfolio of options for various worldwide equity indice

Which Option Pricing Model is the Best? High Frequency Data for Nikkei225 Index Options

Option pricing models are the main subject of many research papers prepared both in academia and financial industry. Using high-frequency data for Nikkei225 index options, we check the properties of option pricing models with different assumptions concerning the volatility process (historical, realized, implied, stochastic or based on GARCH model). In order to relax the continuous dividend payout assumption, we use the Black model for pricing options on futures, instead of the Black-Scholes-Merton model. The results are presented separately for 5 classes of moneyness ratio and 5 classes of time to maturity in order to show some patterns in option pricing and to check the robustness of our results. The Black model with implied volatility (BIV) comes out as the best one. Highest average pricing errors we obtain for the Black model with realized volatility (BRV). As a result, we do not see any additional gain from using more complex and time-consuming models (SV and GARCH models. Additionally, we describe liquidity of the Nikkei225 option pricing market and try to compare our results with a detailed study for the emerging market of WIG20 index options (Kokoszczynski et al. 2010b).