Monte Carlo Hypothesis Testing with The Sharpe Ratio

The purpose of this master thesis was to perform simulations that involve use of random number while testing hypotheses especially on two samples populations being compared weather by their means, variances or Sharpe ratios. Specifically, we simulated some well known distributions by Matlab and check out the accuracy of an hypothesis testing. Furthermore, we went deeper and check what could happen once the bootstrapping method as described by Effrons is applied on the simulated data. In addition to that, one well known RobustSharpe hypothesis testing stated in the paper of Ledoit and Wolf was applied to measure the statistical significance performance between two investment founds basing on testing weather there is a statistically significant difference between their Sharpe Ratios or not. We collected many literatures about our topic and perform by Matlab many simulated random numbers as possible to put out our purpose; As results we come out with a good understanding that testing are not always accurate; for instance while testing weather two normal distributed random vectors come from the same normal distribution. The Jacque-Berra test for normality showed that for the normal random vector r1 and r2, only 94,7% and 95,7% respectively are coming from normal distribution in contrast 5,3% and 4,3% failed to shown the truth already known; but when we introduce the bootstrapping methods by Effrons while estimating pvalues where the hypothesis decision is based, the accuracy of the test was 100% successful. From the above results the reports showed that bootstrapping methods while testing or estimating some statistics should always considered because at most cases the outcome are accurate and errors are minimized in the computation. Also the RobustSharpe test which is known to use one of the bootstrapping methods, studentised one, were applied first on different simulated data including distribution of many kind and different shape secondly, on real data, Hedge and Mutual funds. The test performed quite well to agree with the existence of statistical significance difference between their Sharpe ratios as described in the paper of Ledoit andWolf.

Searching for return: How Google search engine query data can beat the market

Throughout the last years technologic improvements have enabled internet users to analyze and retrieve data regarding Internet searches. In several fields of study this data has been used. Some authors have been using search engine query data to forecast economic variables, to detect influenza areas or to demonstrate that it is possible to capture some patterns in stock markets indexes. In this paper one investment strategy is presented using Google Trends’ weekly query data from major global stock market indexes’ constituents. The results suggest that it is indeed possible to achieve higher Info Sharpe ratios, especially for the major European stock market indexes in comparison to those provided by a buy-and-hold strategy for the period considered.

Essays in equilibrium asset pricing

This thesis consists of four essays in equilibrium asset pricing. The main topic is investors' heterogeneity: I investigates the equilibrium implications for the financial markets when investors have different attitudes toward risk. The first chapter studies why expected risk and remuneration on the aggregate market are negatively related, even if intuition and standard theory suggest a positive relation. I show that the negative trade-off can obtain in equilibrium if investors' beliefs about economic fundamentals are procyclically biased and the market Sharpe ratio is countercyclical. I verify that such conditions hold in the real markets and I find empirical support for the risk-return dynamics predicted by the model. The second chapter consists of two essays. The first essay studies how het¬erogeneity in risk preferences interacts with other sources of heterogeneity and how this affects asset prices in equilibrium. Using perceived macroeconomic un¬certainty as source of heterogeneity, the model helps to explain some patterns of financial returns, even if heterogeneity is small as suggested by survey data. The second essay determines conditions such that equilibrium prices have analytical solutions when investors have heterogeneous risk attitudes and macroeconomic fundamentals feature latent uncertainty. This approach provides additional in-sights to the previous literature where models require numerical solutions. The third chapter studies why equity claims (i.e. assets paying a single future dividend) feature premia and risk decreasing with the horizon, even if standard models imply the opposite shape. I show that labor relations helps to explain the puzzle. When workers have bargaining power to exploit partial income insurance within the firm, wages are smoother and dividends are riskier than in a standard economy. Distributional risk among workers and shareholders provides a rationale to the equity short-term risk, which leads to downward sloping term structures of premia and risk for equity claim. Résumé Cette thèse se compose de quatre essais dans l'évaluation des actifs d'équilibre. Le sujet principal est l'hétérogénéité des investisseurs: J'étudie les implications d'équilibre pour les marchés financiers où les investisseurs ont des attitudes différentes face au risque. Le première chapitre étudie pourquoi attendus risque et la rémunération sur le marché global sont liées négativement, même si l'intuition et la théorie standard suggèrent une relation positive. Je montre que le compromis négatif peut obtenir en équilibre si les croyances des investisseurs sur les fondamentaux économiques sont procyclique biaisées et le ratio de Sharpe du marché est anticyclique. Je vérifier que ces conditions sont réalisées dans les marchés réels et je trouve un appui empirique à la dynamique risque-rendement prédites par le modèle. Le deuxième chapitre se compose de deux essais. Le première essai étudie com¬ment hétérogénéité dans les préférences de risque inter agit avec d'autres sources d'hétérogénéité et comment cela affecte les prix des actifs en équilibre. Utili¬sation de l'incertitude macroéconomique perù comme source d'hétérogénéité, le modèle permet d'expliquer certaines tendances de rendements financiers, même si l'hétérogénéité est faible comme suggéré par les données d'enquête. Le deuxième essai détermine des conditions telles que les prix d'équilibre disposer de solutions analytiques lorsque les investisseurs ont des attitudes des risques hétérogènes et les fondamentaux macroéconomiques disposent d'incertitude latente. Cette approche fournit un éclairage supplémentaire à la littérature antérieure où les modèles nécessitent des solutions numériques. Le troisième chapitre étudie pourquoi les equity-claims (actifs que paient un seul dividende futur) ont les primes et le risque décroissante avec l'horizon, mme si les modèles standards impliquent la forme opposée. Je montre que les relations de travail contribue à expliquer l'énigme. Lorsque les travailleurs ont le pouvoir de négociation d'exploiter assurance revenu partiel dans l'entreprise, les salaires sont plus lisses et les dividendes sont plus risqués que dans une économie standard. Risque de répartition entre les travailleurs et les actionnaires fournit une justification à le risque à court terme, ce qui conduit à des term-structures en pente descendante des primes et des risques pour les equity-claims.

Portfolio choice and the effects of liquidity

This paper shows how to introduce liquidity into the well known mean-variance framework of portfolio selection. Either by estimating mean-variance liquidity constrained frontiers or directly estimating optimal portfolios for alternative levels of risk aversion and preference for liquidity, we obtain strong effects of liquidity on optimal portfolio selection. In particular, portfolio performance, measured by the Sharpe ratio relative to the tangency portfolio, varies significantly with liquidity. Moreover, although mean-variance performance becomes clearly worse, the levels of liquidity onoptimal portfolios obtained when there is a positive preference for liquidity are much lower than on those optimal portfolios where investors show no sign of preference for liquidity.

Understanding portfolio efficiency with conditioning information

We show that unconditionally efficient returns do not achieve the maximum unconditionalSharpe ratio, neither display zero unconditional Jensen s alphas, when returns arepredictable. Next, we define a new type of efficient returns that is characterized by thoseunconditional properties. We also study a different type of efficient returns that is rationalizedby standard mean-variance preferences and motivates new Sharpe ratios and Jensen salphas. We revisit the testable implications of asset pricing models from the perspective ofthe three sets of efficient returns. We also revisit the empirical evidence on the conditionalvariants of the CAPM and the Fama-French model from a portfolio perspective.

Portable alphas from pension mispricing

We introduce a new dynamic trading strategy based on the systematic misspricing of U.S. companies sponsoring Defined Benefit pension plans. This portfolio produces an average return of 1.51% monthly between 1989 and 2004, with a Sharpe Ratio of 0.26. The returns of the strategy are not explained by those of primary assets. These returns are not related to those of benchmarks in the alternative investments industry either. Hence, we are in the presence of a "pure alpha" strategy that can be ported into a large variety of portfolios to significantly enhance their performance.

Beyond the carry trade: Optimal currency portfolios

Author's Pre-print

Credit default swap (CDS) prediction model & trading strategy

This project focuses on the study of different explanatory models for the behavior of CDS security, such as Fixed-Effect Model, GLS Random-Effect Model, Pooled OLS and Quantile Regression Model. After determining the best fitness model, trading strategies with long and short positions in CDS have been developed. Due to some specifications of CDS, I conclude that the quantile regression is the most efficient model to estimate the data. The P&L and Sharpe Ratio of the strategy are analyzed using a backtesting analogy, where I conclude that, mainly for non-financial companies, the model allows traders to take advantage of and profit from arbitrages.

Evidence of market anomalies in the Eurozone: A practical implementation

A Work Project, presented as part of the requirements for the Award of a Master’s Double Degree in Finance and Financial Economics from NOVA – School of Business and Economics and Maastricht University

Trading the differences in expectations between the CDS and bond markets

This paper uses the framework developed by Vrugt (2010) to extract the recovery rate and term-structure of risk-neutral default probabilities implied in the cross-section of Portuguese sovereign bonds outstanding between March and August 2011. During this period the expectations on the recovery rate remain firmly anchored around 50 percent while the instantaneous default probability increases steadily from 6 to above 30 percent. These parameters are then used to calculate the fair-value of a 5-year and 10- year CDS contract. A credit-risk-neutral strategy is developed from the difference between the market price of a CDS of the same tenors and the fair-value calculated, yielding a sharpe ratio of 3.2

Aplicação da teoria moderna do portfólio à selecção de canais de marketing digital

O intuito desta dissertação é investigar em que medida a Teoria Moderna do Portfólio pode ser aplicada à selecção de um portfólio de canais ou de tácticas de Marketing Digital, de modo a obter o melhor compromisso entre o retorno esperado do investimento e o respectivo risco. Anteriores aplicações da teoria do portfólio ao Marketing, enquanto meio de racionalizar a selecção do portfólio, concentraram-se no uso deste modelo em decisões relacionadas com portfólios de produtos, de clientes e segmentos de clientes, de formatos de retalho e de promoções de preço. Não se encontraram evidências de que a abordagem proposta neste texto tenha já sido tentada. A evolução tecnológica nas últimas duas décadas trouxe a adopção generalizada de smartphones e tablets e também a revolução da internet, originando a proliferação do e-mail, dos blogs e dos sites de redes sociais. Devido à infinidade de meios para chegar aos consumidores, os marketers enfrentam actualmente grandes desafios no planeamento e na definição das suas estratégias de Marketing. Em resposta, consultoras detêm ferramentas para a análise de portfólios de canais de Marketing que permitem às empresas e aos marketers, em particular, melhorar o desempenho da sua actividade e maximizar o rendimento da sua despesa de Marketing. Contudo, além de dispendiosas e estritamente analíticas, estas ferramentas são muito sofisticadas, baseando-se em algoritmos e raciocínios complexos que nem sempre são evidentes para os marketers, o que dificulta a sua compreensão e consequentemente a sua adopção. Sem uma ferramenta de análise, é frequente os marketers fundamentarem as suas decisões nos resultados das campanhas online anteriores, registados pelas Web Analytics, e na sua experiência profissional. Assim, crê-se que a Teoria Moderna do Portfólio, baseando-se em conceitos estatísticos simples, possa representar para os marketers uma ferramenta útil no apoio à selecção do conjunto de canais ou de tácticas de Marketing Digital que melhor se adequa aos interesses e aos objectivos estratégicos das organizações. A Teoria Moderna do Portfólio tem como principais vantagens a análise e selecção de portfólios com base na sua combinação de retorno esperado e risco de investimento (retorno ajustado ao risco), por oposição a considerar exclusivamente o retorno esperado, e a simplicidade estatística do modelo, por oposição aos softwares das consultoras. O presente estudo fundamentou-se na literatura existente acerca da Teoria Moderna do Portfólio, concebida em 1952 por Harry Markowitz, bem como no conceito de Sharpe Ratio, por William Sharpe, tendo-se revisto também conceitos genéricos de Marketing e Marketing Digital. Dado que a medição do retorno financeiro do investimento em Marketing – central ao estudo – não é tão linear quanto a medição dos retornos de activos financeiros, revelou-se necessário introduzir algumas alterações à teoria do portfólio original. Estas alterações tomaram em consideração as principais conclusões dos estudos anteriores sobre a aplicação do modelo a outras áreas. Para desenvolver o modelo proposto, utilizou-se o Microsoft Excel. Seguidamente, procedeu-se à sua prova de conceito através de uma abordagem empírica, utilizando dados de uma empresa portuguesa de Marketing Digital. Concluiu-se que é possível aplicar a Teoria Moderna do Portfólio à selecção de canais ou tácticas de Marketing Digital de uma empresa, com as devidas adaptações, para determinar as parcelas do orçamento de comunicação de uma organização a alocar a cada tipo de canal ou táctica.

Introducing spin-off stocks into the NSP’s risk parity strategy

Field lab: Nova Student Portfolio

Trading the changes of stock market index composition: Evidence from European markets

This paper studies the changes in European stock market indexes composition from 1995 to 2015. It was found that there are mixed price effects producing abnormal returns around the effective replacement of added and deleted stocks. The price pressure hypothesis seems to hold for added stocks in some indexes but not for deleted stocks as there is not a clear inversion of behaviour after the replacement. Finally, the building and back testing of a trading strategy aiming to capture some of those abnormal returns shows it yields a Sharpe Ratio of 1.4 and generates an annualised alpha of 11%.

Using artificial neural networks to generate trading signals for crude oil, copper and gold futures

In this thesis, a feed-forward, back-propagating Artificial Neural Network using the gradient descent algorithm is developed to forecast the directional movement of daily returns for WTI, gold and copper futures. Out-of-sample back-test results vary, with some predictive abilities for copper futures but none for either WTI or gold. The best statistically significant hit rate achieved was 57% for copper with an absolute return Sharpe Ratio of 1.25 and a benchmarked Information Ratio of 2.11.

Covariance Matrix Estimation and Mean-Variance Optimization in application to International Diversification

Tutkimus keskittyy kansainväliseen hajauttamiseen suomalaisen sijoittajan näkökulmasta. Tutkimuksen toinen tavoite on selvittää tehostavatko uudet kovarianssimatriisiestimaattorit minimivarianssiportfolion optimointiprosessia. Tavallisen otoskovarianssimatriisin lisäksi optimoinnissa käytetään kahta kutistusestimaattoria ja joustavaa monimuuttuja-GARCH(1,1)-mallia. Tutkimusaineisto koostuu Dow Jonesin toimialaindekseistä ja OMX-H:n portfolioindeksistä. Kansainvälinen hajautusstrategia on toteutettu käyttäen toimialalähestymistapaa ja portfoliota optimoidaan käyttäen kahtatoista komponenttia. Tutkimusaieisto kattaa vuodet 1996-2005 eli 120 kuukausittaista havaintoa. Muodostettujen portfolioiden suorituskykyä mitataan Sharpen indeksillä. Tutkimustulosten mukaan kansainvälisesti hajautettujen investointien ja kotimaisen portfolion riskikorjattujen tuottojen välillä ei ole tilastollisesti merkitsevää eroa. Myöskään uusien kovarianssimatriisiestimaattoreiden käytöstä ei synnytilastollisesti merkitsevää lisäarvoa verrattuna otoskovarianssimatrisiin perustuvaan portfolion optimointiin.