Quadratic programming versus second order con programming in portfolio optimization

Despite the extensive literature in finding new models to replace the Markowitz model or trying to increase the accuracy of its input estimations, there is less studies about the impact on the results of using different optimization algorithms. This paper aims to add some research to this field by comparing the performance of two optimization algorithms in drawing the Markowitz Efficient Frontier and in real world investment strategies. Second order cone programming is a faster algorithm, appears to be more efficient, but is impossible to assert which algorithm is better. Quadratic Programming often shows superior performance in real investment strategies.

Three essays on the psychology of investment and financial markets

Préface My thesis consists of three essays where I consider equilibrium asset prices and investment strategies when the market is likely to experience crashes and possibly sharp windfalls. Although each part is written as an independent and self contained article, the papers share a common behavioral approach in representing investors preferences regarding to extremal returns. Investors utility is defined over their relative performance rather than over their final wealth position, a method first proposed by Markowitz (1952b) and by Kahneman and Tversky (1979), that I extend to incorporate preferences over extremal outcomes. With the failure of the traditional expected utility models in reproducing the observed stylized features of financial markets, the Prospect theory of Kahneman and Tversky (1979) offered the first significant alternative to the expected utility paradigm by considering that people focus on gains and losses rather than on final positions. Under this setting, Barberis, Huang, and Santos (2000) and McQueen and Vorkink (2004) were able to build a representative agent optimization model which solution reproduced some of the observed risk premium and excess volatility. The research in behavioral finance is relatively new and its potential still to explore. The three essays composing my thesis propose to use and extend this setting to study investors behavior and investment strategies in a market where crashes and sharp windfalls are likely to occur. In the first paper, the preferences of a representative agent, relative to time varying positive and negative extremal thresholds are modelled and estimated. A new utility function that conciliates between expected utility maximization and tail-related performance measures is proposed. The model estimation shows that the representative agent preferences reveals a significant level of crash aversion and lottery-pursuit. Assuming a single risky asset economy the proposed specification is able to reproduce some of the distributional features exhibited by financial return series. The second part proposes and illustrates a preference-based asset allocation model taking into account investors crash aversion. Using the skewed t distribution, optimal allocations are characterized as a resulting tradeoff between the distribution four moments. The specification highlights the preference for odd moments and the aversion for even moments. Qualitatively, optimal portfolios are analyzed in terms of firm characteristics and in a setting that reflects real-time asset allocation, a systematic over-performance is obtained compared to the aggregate stock market. Finally, in my third article, dynamic option-based investment strategies are derived and illustrated for investors presenting downside loss aversion. The problem is solved in closed form when the stock market exhibits stochastic volatility and jumps. The specification of downside loss averse utility functions allows corresponding terminal wealth profiles to be expressed as options on the stochastic discount factor contingent on the loss aversion level. Therefore dynamic strategies reduce to the replicating portfolio using exchange traded and well selected options, and the risky stock.

Behavioral aspects of investment fund's markets: are good managers lucky or skilled?

It is generally accepted that financial markets are efficient in the long run a lthough there may be some deviations in the short run. It is also accepted that a good portfolio manager is the one who beats the market persistently along time, this type of manager could not exist if markets were perfectly efficient According to this in a pure efficient market we should find that managers know that they can not beat the market so they would undertake only pure passive management strategies. Assuming a certain degree of inefficiency in the short run, a market may show some managers who tr y to beat the market by undertaking active strategies. From Fama’s efficient markets theory we can state that these active managers may beat the market occasionally although they will not be able to enhance significantly their performance in the long run. On the other hand, in an inefficient market it would be expected to find a higher level of activity related with the higher probability of beating the market. In this paper we follow two objectives: first, we set a basis to analyse the level of efficiency in an asset invest- ment funds market by measuring performance, strategies activity and it’s persistence for a certain group of funds during the period of study. Second, we analyse individual performance persistence in order to determine the existence of skilled managers. The CAPM model is taken as theoretical background and the use of the Sharpe’s ratio as a suitable performance measure in a limited information environment leads to a group performance measurement proposal. The empiri- cal study takes quarterly data from 1999-2007 period, for the whole population of the Spanish asset investment funds market, provided by the CNMV (Comisión Nacional del Mercado de Valores). This period of study has been chosen to ensure a wide enough range of efficient market observation so it would allow us to set a proper basis to compare with the following period. As a result we develop a model that allows us to measure efficiency in a given asset mutual funds market, based on the level of strategy’s activity undertaken by managers. We also observe persistence in individual performance for a certain group of funds

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Strategic investment appraisal; extended real options approach

Tutkielma keskittyy lisäämään investointiarviointiprosessien rationaalisuutta strategisten investointien arvioinnissa duopoli- / oligopolimarkkinoilla. Tutkielman päätavoitteena on selvittää kuinka peliteorialla laajennettu reaalioptioperusteinen investointien arviointimenetelmä, laajennettu reaalioptiokehikko, voisi mahdollisesti parantaa analyysien tarkkuutta. Tutkimus lähestyy ongelmaa investoinnin ajoituksen sekä todellisten investoinnin arvoattribuuttien riippuvuuksien kautta. Laajennettu reaalioptiokehikko on investointien analysointi- ja johtamistyökalu, joka tarjoaa osittain rajoitetun (sisältää tällä hetkellä ainoastaan parametrisen ja peliteoreettisen epävarmuuden) optimaalisen arvovälin investoinnin todellisesta arvosta. Kehikossa, ROA kartoittaa mahdolliset strategiset hyödyt tunnistamalla investointiinliittyvät eri optiot ja epävarmuudet, peliteoria korostaa ympäristön luomia paineita investointiin liittyvän epävarmuuden hallitsemisessa. Laajennettu reaalioptiokehikko tarjoaa rationaalisemman arvion strategisen investoinnin arvosta, koska se yhdistää johdonmukaisemmin option toteutuksen ja siten myös optioiden aika-arvon, yrityksen todellisiin rajoitettuihin (rajoituksena muiden markkinatoimijoiden toimet) polkuriippuvaisiin kyvykkyyksiin.

A Reappraisal of the Allocation Puzzle through the Portfolio Approach

Paradoxically, high-growth, high-investment developing countries tend to experience capital outflows. This paper shows that this allocation puzzle can be explained simply by introducing uninsurable idiosyncratic investment risk in the neoclassical growth model with international trade in bonds, and by taking into account not only TFP catch-up, but also the capital wedge, that is, the distortions on the return to capital. The model fits the two following facts, documented on a sample of 67 countries between 1980 and 2003: (i) TFP growth is positively correlated with capital outflows in a sample including creditor countries; (ii) the long-run level of capital per efficient unit of labor is positively correlated with capital outflows. Consistently, we show that the capital flows predicted by the model are positively correlated with the actual ones in this sample once the capital wedge is accounted for. The fact that Asia dominates global imbalances can be explained by its relatively low capital wedge.

Performance Comparison of Behavioral Finance -based Investment Strategies in the Finnish Stock Market 1996-2010

In this thesis traditional investment strategies (value and growth) are compared to modern investment strategies (momentum, contrarian and GARP) in terms of risk, performance and cumulative returns. Strategies are compared during time period reaching from 1996 to 2010 in the Finnish stock market. Used data includes all listed main list stocks, dividends and is adjusted in case of splits, and mergers and acquisitions. Strategies are tested using different holding periods (6, 12 and 36 months) and data is divided into tercile portfolios based on different ranking criteria. Contrarian and growth strategies are the only strategies with improved cumulative returns when longer holding periods are used. Momentum (52-week high price1) and GARP strategies based on short holding period have the best performance and contrarian and growth strategies the worst. Momentum strategies (52-week high price) along with short holding period contrarian strategies (52-week low price2) have the lowest risk. Strategies with the highest risk are both growth strategies and two momentum strategies (52-week low price). The empirical results support the efficiency of momentum, GARP and value strategies. The least efficient strategies are contrarian and growth strategies in terms of risk, performance and cumulative returns. Most strategies outperform the market portfolio in all three measures. 1 Stock ranking criterion (current price/52-week highest price) 2 Stock ranking criterion (current price/52-week lowest price)

Performance of active portfolio management and the effect of stock market trend

Purpose of the study is to evaluate performance of active portfolio management and the effect of stock market trend on the performance. Theory of efficient markets states that market prices reflect all available information and that all investors share a common view of future price developments. This view gives little room for the success of active management, but the theory has been disputed – at least the level of efficiency. Behavioral finance has developed theories that identify irrational behavior patterns of investors. For example, investment decisions are not made independent of past market developments. These findings give reason to believe that also the performance of active portfolio management may depend on market developments. Performance of 16 Finnish equity funds is evaluated during the period of 2005 to 2011. In addition two sub periods are constructed, a bull market period and a bear market period. The sub periods are created by joining together the two bull market phases and the two bear market phases of the whole period. This allows for the comparison of the two different market states. Performance of the funds is measured with risk-adjusted performance by Modigliani and Modigliani (1997), abnormal return over the CAPM by Jensen (1968), and market timing by Henriksson and Merton (1981). The results suggested that in average the funds are not able to outperform the market portfolio. However, the underperformance was found to be lower than the management fees in average which suggests that portfolio managers are able to do successful investment decisions to some extent. The study revealed substantial dependence on the market trend for all of the measures. The risk-adjusted performance measure suggested that in bear markets active portfolio managers in average are able to beat the market portfolio but not in bull markets. Jensen´s alpha and the market timing model also showed striking differences between the two market states. The results of these two measures were, however, somewhat problematic and reliable conclusions about the performance could not be drawn.

Diversification benefits for a Finnish non-industrial private forest investor: Real Estate Investment Trusts in the USA

This thesis examined both domestic and international forest investment options for a Finnish non-industrial private forest investor. The focus was on forest-based investment instruments. The influence of movements of currency exchange rates on foreign returns were also taken into account. Annual data from 1995 to 2011 was used. The main portfolio optimization model in this study was the Mean-Variance model but the results were also validated by using the Value at Risk and Expected Shortfall models. In addition, the exchange rate risk hedging was established by using one-week-maturity forward contracts. The results suggested that 75 % of the total wealth should be invested in Finnish private forests and the rest, 25 %, to a US REIT, in this case Rayonier. With hedging, the total return on the portfolio was 7.21 % (NIPF 5.3%) with the volatility of 6.63 % (NIPF 7.9%). Taxation supported US investments in this case. As a conclusion, a Finnish private forest investor may, as evidenced, benefit in diversifying a portfolio using REITs in the US.

Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.

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.

PERFORMANCE ANALYSIS OF A TACTICAL ASSET ALLOCATION – Evidence from the Black–Litterman model based fixed income portfolio

Over time the demand for quantitative portfolio management has increased among financial institutions but there is still a lack of practical tools. In 2008 EDHEC Risk and Asset Management Research Centre conducted a survey of European investment practices. It revealed that the majority of asset or fund management companies, pension funds and institutional investors do not use more sophisticated models to compensate the flaws of the Markowitz mean-variance portfolio optimization. Furthermore, tactical asset allocation managers employ a variety of methods to estimate return and risk of assets, but also need sophisticated portfolio management models to outperform their benchmarks. Recent development in portfolio management suggests that new innovations are slowly gaining ground, but still need to be studied carefully. This thesis tries to provide a practical tactical asset allocation (TAA) application to the Black–Litterman (B–L) approach and unbiased evaluation of B–L models’ qualities. Mean-variance framework, issues related to asset allocation decisions and return forecasting are examined carefully to uncover issues effecting active portfolio management. European fixed income data is employed in an empirical study that tries to reveal whether a B–L model based TAA portfolio is able outperform its strategic benchmark. The tactical asset allocation utilizes Vector Autoregressive (VAR) model to create return forecasts from lagged values of asset classes as well as economic variables. Sample data (31.12.1999–31.12.2012) is divided into two. In-sample data is used for calibrating a strategic portfolio and the out-of-sample period is for testing the tactical portfolio against the strategic benchmark. Results show that B–L model based tactical asset allocation outperforms the benchmark portfolio in terms of risk-adjusted return and mean excess return. The VAR-model is able to pick up the change in investor sentiment and the B–L model adjusts portfolio weights in a controlled manner. TAA portfolio shows promise especially in moderately shifting allocation to more risky assets while market is turning bullish, but without overweighting investments with high beta. Based on findings in thesis, Black–Litterman model offers a good platform for active asset managers to quantify their views on investments and implement their strategies. B–L model shows potential and offers interesting research avenues. However, success of tactical asset allocation is still highly dependent on the quality of input estimates.

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.