Population-based continuous optimization, probabilistic modelling and mean shift

Evolutionary algorithms perform optimization using a population of sample solution points. An interesting development has been to view population-based optimization as the process of evolving an explicit, probabilistic model of the search space. This paper investigates a formal basis for continuous, population-based optimization in terms of a stochastic gradient descent on the Kullback-Leibler divergence between the model probability density and the objective function, represented as an unknown density of assumed form. This leads to an update rule that is related and compared with previous theoretical work, a continuous version of the population-based incremental learning algorithm, and the generalized mean shift clustering framework. Experimental results are presented that demonstrate the dynamics of the new algorithm on a set of simple test problems.

Liquidity and portfolio optimisation

This thesis presents research within empirical financial economics with focus on liquidity and portfolio optimisation in the stock market. The discussion on liquidity is focused on measurement issues, including TAQ data processing and measurement of systematic liquidity factors (FSO). Furthermore, a framework for treatment of the two topics in combination is provided. The liquidity part of the thesis gives a conceptual background to liquidity and discusses several different approaches to liquidity measurement. It contributes to liquidity measurement by providing detailed guidelines on the data processing needed for applying TAQ data to liquidity research. The main focus, however, is the derivation of systematic liquidity factors. The principal component approach to systematic liquidity measurement is refined by the introduction of moving and expanding estimation windows, allowing for time-varying liquidity co-variances between stocks. Under several liability specifications, this improves the ability to explain stock liquidity and returns, as compared to static window PCA and market average approximations of systematic liquidity. The highest ability to explain stock returns is obtained when using inventory cost as a liquidity measure and a moving window PCA as the systematic liquidity derivation technique. Systematic factors of this setting also have a strong ability in explaining a cross-sectional liquidity variation. Portfolio optimisation in the FSO framework is tested in two empirical studies. These contribute to the assessment of FSO by expanding the applicability to stock indexes and individual stocks, by considering a wide selection of utility function specifications, and by showing explicitly how the full-scale optimum can be identified using either grid search or the heuristic search algorithm of differential evolution. The studies show that relative to mean-variance portfolios, FSO performs well in these settings and that the computational expense can be mitigated dramatically by application of differential evolution.

International stock portfolio selection and performance measures recognizing higher moments of return distributions

Since the seminal works of Markowitz (1952), Sharpe (1964), and Lintner (1965), numerous studies on portfolio selection and performance measure have been based upon the mean-variance framework. However, several researchers (e.g., Arditti (1967, and 1971), Samuelson (1970), and Rubinstein (1973)) argue that the higher moments cannot be neglected unless there is reason to believe that: (i) the asset returns are normally distributed and the investor's utility function is quadratic, or (ii) the empirical evidence demonstrates that higher moments are irrelevant to the investor's decision. Based on the same argument, this dissertation investigates the impact of higher moments of return distributions on three issues concerning the 14 international stock markets.^ First, the portfolio selection with skewness is determined using: the Polynomial Goal Programming in which investor preferences for skewness can be incorporated. The empirical findings suggest that the return distributions of international stock markets are not normally distributed, and that the incorporation of skewness into an investor's portfolio decision causes a major change in the construction of his optimal portfolio. The evidence also indicates that an investor will trade expected return of the portfolio for skewness. Moreover, when short sales are allowed, investors are better off as they attain higher expected return and skewness simultaneously.^ Second, the performance of international stock markets are evaluated using two types of performance measures: (i) the two-moment performance measures of Sharpe (1966), and Treynor (1965), and (ii) the higher-moment performance measures of Prakash and Bear (1986), and Stephens and Proffitt (1991). The empirical evidence indicates that higher moments of return distributions are significant and relevant to the investor's decision. Thus, the higher moment performance measures should be more appropriate to evaluate the performances of international stock markets. The evidence also indicates that various measures provide a vastly different performance ranking of the markets, albeit in the same direction.^ Finally, the inter-temporal stability of the international stock markets is investigated using the Parhizgari and Prakash (1989) algorithm for the Sen and Puri (1968) test which accounts for non-normality of return distributions. The empirical finding indicates that there is strong evidence to support the stability in international stock market movements. However, when the Anderson test which assumes normality of return distributions is employed, the stability in the correlation structure is rejected. This suggests that the non-normality of the return distribution is an important factor that cannot be ignored in the investigation of inter-temporal stability of international stock markets. ^

From efficiency to optimality in proportional reinsurance under group correlation

Based on our recent discovery of closed form formulae of efficient Mean Variance retentions in variable quota-share proportional reinsurance under group correlation, we analyzed the influence of different combination of correlation and safety loading levels on the efficient frontier, both in a single period stylized problem and in a multiperiod one.

Managing marginal capital requirements in solvency II: Analysis of a real insurance portfolio

This thesis provides a complete analysis of the Standard Capital Requirements given by Solvency II for a real insurance portfolio. We analyze the investment portfolio of BPI Vida e Pensões, an insurance company affiliated with a Portuguese bank BPI, both at security, sub-portfolio and asset class levels. By using the Standard Formula from EIOPA, Total SCR amounts to 239M€. This value is mostly explained by Market and Default Risk whereas the former is driven by Spread and Concentration Risks. Following the methodology of Leblanc (2011), we examine the Marginal Contribution of an asset to the SCR which allows for the evaluation of the risks of each security given its characteristics and interactions in the portfolio. The top contributors to the SCR are Corporate Bonds and Term Deposits. By exploring further the composition of the portfolio, our results show that slight changes in allocation of Term and Cash Deposits have severe impacts on the total Concentration and Default Risks, respectively. Also, diversification effects are very relevant by representing savings of 122M€. Finally, Solvency II represents an opportunity for the portfolio optimization. By constructing efficient frontiers, we find that as the target expected return increases, a shift from Term Deposits/ Commercial Papers to Eurozone/Peripheral and finally Equities occurs.

Portafolio selection with skewness: a comparison of methods and a generalized two fund separation result

This contribution compares existing and newly developed techniques for geometrically representing mean-variances-kewness portfolio frontiers based on the rather widely adapted methodology of polynomial goal programming (PGP) on the one hand and the more recent approach based on the shortage function on the other hand. Moreover, we explain the working of these different methodologies in detail and provide graphical illustrations. Inspired by these illustrations, we prove a generalization of the well-known two fund separation theorem from traditionalmean-variance portfolio theory.

Honey, I shrunk the sample covariance matrix

The central message of this paper is that nobody should be using the samplecovariance matrix for the purpose of portfolio optimization. It containsestimation error of the kind most likely to perturb a mean-varianceoptimizer. In its place, we suggest using the matrix obtained from thesample covariance matrix through a transformation called shrinkage. Thistends to pull the most extreme coefficients towards more central values,thereby systematically reducing estimation error where it matters most.Statistically, the challenge is to know the optimal shrinkage intensity,and we give the formula for that. Without changing any other step in theportfolio optimization process, we show on actual stock market data thatshrinkage reduces tracking error relative to a benchmark index, andsubstantially increases the realized information ratio of the activeportfolio manager.

Optimization of the sampling scheme for maps of physical and chemical properties estimated by kriging

The sampling scheme is essential in the investigation of the spatial variability of soil properties in Soil Science studies. The high costs of sampling schemes optimized with additional sampling points for each physical and chemical soil property, prevent their use in precision agriculture. The purpose of this study was to obtain an optimal sampling scheme for physical and chemical property sets and investigate its effect on the quality of soil sampling. Soil was sampled on a 42-ha area, with 206 geo-referenced points arranged in a regular grid spaced 50 m from each other, in a depth range of 0.00-0.20 m. In order to obtain an optimal sampling scheme for every physical and chemical property, a sample grid, a medium-scale variogram and the extended Spatial Simulated Annealing (SSA) method were used to minimize kriging variance. The optimization procedure was validated by constructing maps of relative improvement comparing the sample configuration before and after the process. A greater concentration of recommended points in specific areas (NW-SE direction) was observed, which also reflects a greater estimate variance at these locations. The addition of optimal samples, for specific regions, increased the accuracy up to 2 % for chemical and 1 % for physical properties. The use of a sample grid and medium-scale variogram, as previous information for the conception of additional sampling schemes, was very promising to determine the locations of these additional points for all physical and chemical soil properties, enhancing the accuracy of kriging estimates of the physical-chemical properties.

Chasing performance persistence of hedge funds

The thesis examines the performance persistence of hedge funds using complement methodologies (namely cross-sectional regressions, quantile portfolio analysis and Spearman rank correlation test). In addition, six performance ranking metrics and six different combinations of selection and holding periods are compared. The data is gathered from HFI and Tremont databases covering over 14,000 hedge funds and time horizon is set from January 1996 to December 2007. The results suggest that there definitely exists performance persistence among hedge funds and the strength and existence of persistence vary among fund styles. The persistence depends on the metrics and combination of selection and prediction period applied. According to the results, the combination of 36-month selection and holding period outperforms other five period combinations in capturing performance persistence within the sample. Furthermore, model-free performance metrics capture persistence more sensitively than model-specific metrics. The study is the first one ever to use MVR as a performance ranking metric, and surprisingly MVR is more sensitive to detect persistence than other performance metrics employed.

Risk Parity: A Modern Tool for Diversification

The purpose of this study is to examine how well risk parity works in terms of risk, return and diversification relative to more traditional minimum variance, 1/N and 60/40 portfolios. Risk parity portfolios were constituted of five risk sources; three common asset classes and two alternative beta investment strategies. The three common asset classes were equities, bonds and commodities, and the alternative beta investment strategies were carry trade and trend following. Risk parity portfolios were constructed using five different risk measures of which four were tail risk measures. The risk measures were standard deviation, Value-at-Risk, Expected Shortfall, modified Value-at-Risk and modified Expected Shortfall. We studied also how sensitive risk parity is to the choice of risk measure. The hypothesis is that risk parity portfolios provide better return with the same amount of risk and are better diversified than the benchmark portfolios. We used two data sets, monthly and weekly data. The monthly data was from the years 1989-2011 and the weekly data was from the years 2000-2011. Empirical studies showed that risk parity portfolios provide better diversification since the diversification is made at the risk level. Risk based portfolios provided superior return compared to the asset based portfolios. Using tail risk measures in risk parity portfolios do not necessarily provide better hedge from tail events than standard deviation.

Hedge-rahastojen menestyksen pysyvyyden empiirinen tarkastelu sijoittajan näkökulmasta

This study examines performance persistence of hedge funds from investor's point of view and look at the methods by which an investor could choose the successful hedge funds to the portfolio. This study was used the data from HFI & Tremont databases on period 1998-2007. In this study used the 36-month combination (24-month selection and 12-month prediction periods). As the research methods used the Sharpe index, raw returns, MVR (mean variance ratio), GSC-clustering, the SDI index and the new combination of metrics. The evaluation criterions of the results used the volatility, excess returns and the Sharpe index. This study compared different results from the 7 time series with each other, and commenting the problems on a portfolio loss of funds.

Hedge-rahastojen menestyksen pysyvyys ja suhteellinen suoriutuminen sijoittajan näkökulmasta

The purpose of the thesis is to examine the long-term performance persistence and relative performance of hedge funds during bear and bull market periods. Performance metrics applied for fund rankings are raw return, Sharpe ratio, mean variance ratio and strategy distinctiveness index calculated of the original and clustered data correspondingly. Four different length combinations for selection and holding periods are employed. The persistence is examined using decile and quartile portfolio formatting approach and on the basis of Sharpe ratio and SKASR as performance metrics. The relative performance persistence is examined by comparing hedge portfolio returns during varying stock market conditions. The data is gathered from a private database covering 10,789 hedge funds and time horizon is set from January 1990 to December 2012. The results of this thesis suggest that long-term performance persistence of the hedge funds exists. The degree of persistence also depends on the performance metrics employed and length combination of selection and holding periods. The best results of performance persistence were obtained in the decile portfolio analysis on the basis of Sharpe ratio rankings for combination of 12-month selection period and the holding period of equal length. The results also suggest that the best performance persistence occurs in the Event Driven and Multi strategies. Dummy regression analysis shows that a relationship between hedge funds and stock market returns exists. Based on the results, Dedicated Short Bias, Global Macro, Managed Futures and Other strategies perform well during bear market periods. The results also indicate that the Market Neutral strategy is not absolutely market neutral and the Event Driven strategy has the best performance among all hedge strategies.

Dynamic linkages of real estate and stock markets in Finland

Traditionally real estate has been seen as a good diversification tool for a stock portfolio due to the lower return and volatility characteristics of real estate investments. However, the diversification benefits of a multi-asset portfolio depend on how the different asset classes co-move in the short- and long-run. As the asset classes are affected by the same macroeconomic factors, interrelationships limiting the diversification benefits could exist. This master’s thesis aims to identify such dynamic linkages in the Finnish real estate and stock markets. The results are beneficial for portfolio optimization tasks as well as for policy-making. The real estate industry can be divided into direct and securitized markets. In this thesis the direct market is depicted by the Finnish housing market index. The securitized market is proxied by the Finnish all-sectors securitized real estate index and by a European residential Real Estate Investment Trust index. The stock market is depicted by OMX Helsinki Cap index. Several macroeconomic variables are incorporated as well. The methodology of this thesis is based on the Vector Autoregressive (VAR) models. The long-run dynamic linkages are studied with Johansen’s cointegration tests and the short-run interrelationships are examined with Granger-causality tests. In addition, impulse response functions and forecast error variance decomposition analyses are used for robustness checks. The results show that long-run co-movement, or cointegration, did not exist between the housing and stock markets during the sample period. This indicates diversification benefits in the long-run. However, cointegration between the stock and securitized real estate markets was identified. This indicates limited diversification benefits and shows that the listed real estate market in Finland is not matured enough to be considered a separate market from the general stock market. Moreover, while securitized real estate was shown to cointegrate with the housing market in the long-run, the two markets are still too different in their characteristics to be used as substitutes in a multi-asset portfolio. This implies that the capital intensiveness of housing investments cannot be circumvented by investing in securitized real estate.

TAKING ADVANTAGE OF THE LOCAL ADVANTAGE? - Investment value of the analyst local advantage in the Finnish stock market in 2006–2014

An investor can either conduct independent analysis or rely on the analyses of others. Stock analysts provide markets with expectations regarding particular securities. However, analysts have different capabilities and resources, of which investors are seldom cognizant. The local advantage refers to the advantage stemming from cultural or geographical proximity to securities analyzed. The research has confirmed that local agents are generally more accurate or produce excess returns. This thesis tests the investment value of the local advantage regarding Finnish stocks via target price data. The empirical section investigates the local advantage from several aspects. It is discovered that local analysts were more focused on certain sectors generally located close to consumer markets. Market reactions to target price revisions were generally insignificant with the exception to local positive target prices. Both local and foreign target prices were overly optimistic and exhibited signs of herding. Neither group could be identified as a leader or follower of new information. Additionally, foreign price change expectations were more in line with the quantitative models and ideas such as beta or return mean reversion. The locals were more accurate than foreign analysts in 5 out of 9 sectors and vice versa in one. These sectors were somewhat in line with coverage decisions and buttressed the idea of local advantage stemming from proximity to markets, not to headquarters. The accuracy advantage was dependent on sample years and on the measure used. Local analysts ranked magnitudes of price changes more accurately in optimistic and foreign analysts in pessimistic target prices. Directional accuracy of both groups was under 50% and target prices held no linear predictive power. Investment value of target prices were tested by forming mean-variance efficient portfolios. Parallel to differing accuracies in the levels of expectations foreign portfolio performed better when short sales were allowed and local better when disallowed. Both local and non-local portfolios performed worse than a passive index fund, albeit not statistically significantly. This was in line with previously reported low overall accuracy and different accuracy profiles. Refraining from estimating individual stock returns altogether produced statistically significantly higher Sharpe ratios compared to local or foreign portfolios. The proposed method of testing the investment value of target prices of different groups suffered from some inconsistencies. Nevertheless, these results are of interest to investors seeking the advice of security analysts.

TAKING ADVANTAGE OF THE LOCAL ADVANTAGE? - Investment value of the analyst local advantage in the Finnish stock market in 2006–2014

An investor can either conduct independent analysis or rely on the analyses of others. Stock analysts provide markets with expectations regarding particular securities. However, analysts have different capabilities and resources, of which investors are seldom cognizant. The local advantage refers to the advantage stemming from cultural or geographical proximity to securities analyzed. The research has confirmed that local agents are generally more accurate or produce excess returns. This thesis tests the investment value of the local advantage regarding Finnish stocks via target price data. The empirical section investigates the local advantage from several aspects. It is discovered that local analysts were more focused on certain sectors generally located close to consumer markets. Market reactions to target price revisions were generally insignificant with the exception to local positive target prices. Both local and foreign target prices were overly optimistic and exhibited signs of herding. Neither group could be identified as a leader or follower of new information. Additionally, foreign price change expectations were more in line with the quantitative models and ideas such as beta or return mean reversion. The locals were more accurate than foreign analysts in 5 out of 9 sectors and vice versa in one. These sectors were somewhat in line with coverage decisions and buttressed the idea of local advantage stemming from proximity to markets, not to headquarters. The accuracy advantage was dependent on sample years and on the measure used. Local analysts ranked magnitudes of price changes more accurately in optimistic and foreign analysts in pessimistic target prices. Directional accuracy of both groups was under 50% and target prices held no linear predictive power. Investment value of target prices were tested by forming mean-variance efficient portfolios. Parallel to differing accuracies in the levels of expectations foreign portfolio performed better when short sales were allowed and local better when disallowed. Both local and non-local portfolios performed worse than a passive index fund, albeit not statistically significantly. This was in line with previously reported low overall accuracy and different accuracy profiles. Refraining from estimating individual stock returns altogether produced statistically significantly higher Sharpe ratios compared to local or foreign portfolios. The proposed method of testing the investment value of target prices of different groups suffered from some inconsistencies. Nevertheless, these results are of interest to investors seeking the advice of security analysts.