Asset pricing models have been of interest since their origin in modern finance. The Capital Asset Pricing Model is a widely used tool and is one of the early developed asset pricing models in modern finance. There are continual improvements of this model with the evident multifactor models of Fama and French (2015), Carhart (1997) and the South African two – factor arbitrage pricing models of Van Rensburg (2002) and Laird-Smith et al. (2016). This research empirically investigates the performance of eight-different multi-factor asset pricing models in describing average portfolio returns in the South African Johannesburg Stock Exchange. We find that the Carhart (1997) four factor model comprising of the market factor, size factor, value factor and the momentum factor is the most parsimonious model and thus better explains the average portfolio returns in the South African JSE. This model is an improvement of the Fama and French (1992) three factor model. Additionally, we investigate the performance of the two factor Asset Pricing Theory (APT) model of Laird-Smith et al. (2016) and Van Rensburg (2002) that consists of the South African Financial Index (SAFI) and the South African Resources Index (SARI). We observe that the model performs better than the traditional CAPM that is widely used in industry. Adding the SAFI and the SARI to the six-factor model results in an eight-factor model that has a significant improvement in explaining average returns. The results indicate that the market factor, the South African Financial Index and the South African Resources Index (SARI) poorly explain each other but their linear combination improves the eight-factor asset pricing model in explaining average portfolio returns in the South African market. The eight – factor model comprises of the market, size, value, investment, profitability, momentum factors and the two South African indices namely, the South African Financials Index (SAFI) and the South African Resources Index (SARI).

El principal objetivo de la presente investigación es promover, intensificar, dilucidar qué criterios deben considerar los inversionistas para estimar de manera adecuada la tasa de descuento a utilizar, en función a los diversos sectores económicos, el entorno en la que se desarrollará la actividad a invertir, además de considerar el plazo del proyecto. Asimismo, es imprescindible recalcar que, a pesar de no existir en la actualidad una tasa de descuento determinante en el mercado, es vital y preponderante que los inversores, evaluadores, etc., estimen tasas reales, aterrizadas en función a la información derivada del análisis del proyecto o inversión a realizar, más aún, tomando en cuenta el impacto que dichas decisiones tendrán en el ámbito de desarrollo tanto económico para el inversionista y sobre todo al medio ambiente para las futuras generaciones. En ese sentido, es preciso considerar que las valuaciones de proyectos de inversión, de adquisición de bienes o de activos debe de contemplar variables económicas como: VPN, COSC, CAPM, WACC o WARA, las mismas que deben ser ajustadas al riesgo, según el tipo de proyecto o de adquisición, tomando como modelos referentes a los mercados desarrollados, variables que si bien ayudan a mitigar riesgo, también contribuyan a valorar y coberturar los daños al medio ambiente, dado que, las repercusiones productos de las decisiones tomadas en el tiempo han generado perjuicios calamitosos a los recursos naturales y al ecosistema, afectando así la herencia para las futuras generaciones, daños que muchas veces a pesar de la cuantificación económica son irreversibles, impacto ocasionados por el sector minero, infraestructura, por la explotación de tala, además de valorar las adquisiciones de medicinas o pruebas para el sector salud en harás del bienestar de la población de un país. / The main objective of this research is to promote, intensify, elucidate what criteria investors should consider to estimate adequately the discount rate to be used, depending on the different economic sectors, the environment in which the activity to be developed will be developed, besides considering the term of the project. Likewise, it is essential to emphasize that, although there is currently no significant discount rate in the market, it is vital and preponderant that investors, evaluators, etc., estimate real rates, based on the information derived from the analysis of the project or investment to be made, even more so, taking into account the impact that these decisions will have on the development environment both economically for the investor and especially the environment for future generations. In this sense, it is necessary to consider that the valuations of investment projects, of acquisition of assets or of assets must contemplate economic variables such as: VPN, COSC, CAPM, WACC or WARA, which must be adjusted to the risk, according to the type of project or acquisition, taking as models referring to developed markets, variables that although help to mitigate risk, also contribute to assess and cover the damage to the environment, given that, the repercussions have generated calamitous damages to natural resources and the ecosystem, affecting the inheritance for future generations, damages that often, despite economic quantification, are irreversible, impact caused by the mining sector, infrastructure, exploitation of logging, in addition to assessing the acquisition of medicines or tests for The health sector in the welfare of the population of a country. / Trabajo de Suficiencia Profesional

[pt] O IBrX é um índice que mede o retorno de uma carteira teórica composta em média por 100 ações selecionadas entre as mais negociadas na Bovespa (Bolsa de Valores de São Paulo). Esta pesquisa utilizou, como banco de dados, os ativos que compuseram o índice IBrX no período de maio de 2002 a dezembro de 2007, examinando a influência do comportamento das variáveis beta, valor de mercado, índice preço/lucro e índice valor contábil/valor de mercado no mercado brasileiro, confrontando-se o resultado com outras pesquisas realizadas no Brasil. Ao investigar a influência da variável beta, este trabalhou buscou verificar se as premissas adotadas pelo CAPM ( Capital Asset Pricing Model) são válidas no modelo proposto por este estudo. As técnicas de estimação utilizadas nesta pesquisan para avaliar o grau de influência das variáveis, foram o SUR (Seemingly Unrelated Regression) e o TSCS (Time Series Cross-Sectional Analysis). Os resultados apontaram significância para as variáveis índice Preço/Lucro e valor de mercado. Porém, a variável o índice valor contábil/valor de mercado foi a que apresentou maior estabilidade, sendo significante em todos os modelos propostos. Em relação ao CAPM (Capital Asset Pricing Model), a pesquisa apontou que todas as variáveis analisadas apresentaram algum grau de influência nas variações cross-section das rentabilidades médias das ações, sinalizando que além do beta, outros fatores podem estar associados ao comportamento dos ativos. / [en] The IBrX is an index that evaluates the return of a theoretical portfolio composed of one a hundred stocks selected as the most trader as the São Paulo Stock Exchange. This research has made use of stocks that composed the IBrX index during the period between May of 2002 until December 2007 as its database, examining the influence of beta, market value, price/earnings ratio and book to market ratio, on Brazilian market performance, comparing the results obtained with other research done in Brazil. In investigating the influence of beta, this study aimed to verify if the premises made by CAPM( Capital Asset Pricing Model) should be considered valid in the model here proposed. The estimation techniques used in this study to estimate the degree of influence of variables were SUR (Seemingly Unrelated Regression) and TSCS (Time Series Cross-Sectional Analysis). The results point out the price/earnings ratio and market value variables, as being significant. However, the book value/market value index was the variable that presented the strongest stability, being significant in all models proposed. In relation to CAPM (Capital Asset Pricing Model) the study point out that all analyzed variables have presented in some extent a degree of influence in cross-section variations of average stock returns, signalizing that in addition to beta, other factors are associated with stock performance.

Escolheu-se o método GMM a fim de testar os modelos CAPM não-condicionais (Sharpe-Litner e zero-beta) no mercado de capitais brasileiro, pois as séries dos log-retornos diários de ações analisadas não se mostraram normais e IID. Este trabalho é pioneiro em testar a validade do modelo CAPM zero-beta via GMM no mercado brasileiro. Constatamos que o modelo CAPM de SL, tanto em termos da SELIC como do CDI, não pode ser rejeitado ao nível de 5% para o período de 2/1/00 até 31/12/04. Já para os períodos de 2/1/95 até 31/12/99 e de 2/1/95 até 31/12/04, tal modelo foi rejeitado ao nível de 5%. Dessa forma, para o modelo CAPM de SL, tanto em termos da SELIC como do CDI, o índice BOVESPA se comportou como um portfólio eficiente somente no período de 2/1/00 até 31/12/04. Já para o modelo CAPM zero-beta, verifica-se a sua não rejeição ao nível de 5% nos três períodos analisados acima. / The GMM method have been chosen in order to test non-conditional CAPM (Sharpe-Lintner and zero-beta) model in Brazilian security market, because the daily log-returns series of the analyzed shares did not showed itselves as normal and IID. This dissertation will be pioneer in testing the validity of the CAPM zero-beta model by GMM. We have realized that the SL CAPM model, either in terms of SELIC rate as of CDI rate (risk-free assets), can not be rejected at 5% level for the period from 2/1/00 until 31/12/04. For the periods from 2/1/95 until 31/12/99 and from 2/1/95 until 31/12/04, the given model was rejected at the 5% level. This way, for the SL CAPM model, either in terms of SELIC rate as of CDI rate, the BOVESPA index has behaved as an efficient portfolio only on the period from 2/1/00 until 31/12/04. For the zero-beta CAPM model, it can be verified that we cannot reject it at the 5% level in none of the three periods analyzed above.

As técnicas utilizadas pelas empresas atualmente para a avaliação econômica dos projetos de investimento em condições de risco, com destaque para a análise de cenários, apresentam três importantes limitações: não fornecem o capital no risco, utilizam uma taxa mínima da atratividade (TMA) única para a empresa em seu todo, desprezando as particularidades de cada caso, e tratam o risco isoladamente, fora do contexto amplo da diversificação eficiente. Diante desse contexto, o presente estudo propôs a aplicação de três modelos originários do mercado de capitais: o valor no risco (VAR), o modelo de precificação dos ativos de capital (CAPM) e a teoria de precificação por arbitragem (APT). Os resultados obtidos mostram que tais modelos são capazes de: fornecer o capital no risco dos projetos de investimento (VAR), utilizar uma TMA própria, segundo as particularidades de cada projeto de investimento (CAPM e APT), e tratar o risco em projetos de investimento no contexto amplo da diversificação eficiente (VAR, CAPM e APT). / The techniques used now by the companies for the economic evaluation of the investment projects in risk conditions, with prominence for the analysis of sceneries, present three important limitations: they don\'t supply the capital in the risk, they use an attractiveness of minimum rate (TMA) only for the company in its whole, despising the particularities of each case, and they treat the risk separately, out of the wide context of the efficient diversification. Before of that context, the present study proposed the application of three original models of the market of capitais: the value at risk (VAR), the capital asset pricing model (CAPM) and the arbitrage pricing theory (APT). The obtained results showed that such models are capable of: to supply the capital in the risk of the investment projects (VAR), to use an own TMA, according to the particularities of each investment project (CAPM and APT), and to treat the risk in investment projects in the wide context of the efficient diversification (VAR, CAPM and APT).

Essa dissertação procura analisar se as variações dos retornos de carteiras setoriais formadas por ações do Índice teórico da Bolsa de Valores de São Paulo (Ibovespa), do primeiro quadrimestre de 2010, podem ser explicadas pelo CAPM condicional não-paramétrico proposto por Wang (2002) e também por quatro variáveis de informação disponíveis aos investidores: (i) percentual de variação do nível de produção industrial brasileira; (ii) percentual de variação do monetário agregado M4; (iii) percentual de variação da inflação representada pelo Índice de Preços ao Consumidor Amplo (IPCA); e (iv) percentual de variação da taxa de câmbio real-dólar, obtida pela cotação do dólar PTAX. O estudo compreendeu as ações listadas na Bolsa de Valores de São Paulo no período de janeiro de 2002 a dezembro de 2009. Utilizou-se a metodologia de teste desenvolvida por Wang (2002) e replicada para o contexto mexicano por Castillo-Spíndola (2006). Foram utilizados os excessos de retornos mensais para as ações, carteiras e prêmio de mercado. Ainda, para estimar a influência das variáveis de informação, foram calculados seus respectivos percentuais de variação mensal, para o período de janeiro de 2002 a novembro de 2009. A fim de validar a aplicação do CAPM condicional não-paramétrico para o mercado acionário brasileiro, foram estimados os diversos parâmetros do modelo e testada sua validade estatística para cada variável de informação avaliando-se o p-value. Os resultados observados indicam que o modelo condicional não-paramétrico é relevante na explicação dos retornos das carteiras da amostra considerada para duas das quatro variáveis testadas, M4 e dólar PTAX. / This dissertation seeks to analyze if the variations of returns from sector portfolios, formed by shares of the São Paulo Stock Exchange Index (Ibovespa), in the first four months of 2010, could be explained by the nonparametric conditional Capital Asset Pricing Model (CAPM), suggested by Wang (2002), and also by four variables of information available to the investors: (i) percentage variation of the Brazilian industrial production level; (ii) percentage variation of broad money supply M4; (iii) percentage variation of the inflation represented by the Índice de Preços ao Consumidor Amplo (IPCA); and (iv) percentage variation in the real-dollar exchange rate, obtained by PTAX dollar quotation. This study comprised the shares listed in São Paulo Stock Exchange throughout January 2002 to December 2009. The test methodology developed by Wang (2002) and retorted to the Mexican context by Castillo-Spíndola (2006) was used. The excess of monthly returns for the shares, portfolios, and market premium were used. Still, aiming to estimate the influence of information variables, their monthly percentage variations were calculated for the period from January 2002 to November 2009. In order to validate the nonparametric conditional CAPM application for the Brazilian stock market, the models several parameters were estimated and its statistic validity was tested for each information variable, evaluating the p-value. The observed results indicate that the nonparametric conditional model is relevant in explaining the portfolios returns of the sample considered for two among the four tested variables, M4 and PTAX dollar.

[pt] Em uma indústria sujeita à regulamentação, o Custo Médio Ponderado de Capital - CMPC é parâmetro fundamental para a determinação da remuneração justa dos fornecedores de capital das empresas reguladas (investidores e credores), bem como para determinar a tarifa módica para o consumidor dos produtos ou serviços. Sabendo que as indústrias reguladas prestam, em geral, serviços básicos e de infra- estrutura, toda a sociedade é atingida pelas decisões a respeito desse custo, e sua determinação é parte importante das atividades do regulador. A teoria que suporta o conceito do CMPC remonta ao final da década de 50 e se encontra consagrada nos meios acadêmicos, empresariais e normativos. Entretanto, a metodologia para a determinação dos seus componentes prospectivos, ou seja, a determinação de qual será o CMPC no futuro, encontra divergências entre os principais autores e apresenta dificuldades operacionais. Essas dificuldades aumentam em um mercado de capitais pequeno quando comparado a outros países e em um ambiente político com uma curta história de estabilidade. O objetivo do presente trabalho é discutir a metodologia empregada pela Agência Nacional de Energia Elétrica - ANEEL para determinar o CMPC para empresas de distribuição de energia elétrica no Brasil à luz das melhores práticas e do conhecimento teórico sobre o tema. / [en] In regulated industries, estimating the weighted average cost of capital (CMPC) is important to the regulatory framework in order to establish both the fair return to the capital providers (investors and creditors) of the regulated companies, as well the reasonable price of goods or services for the customers. The regulated industries provide, in general, basic or infrastructure services and, as the whole society is affected by decisions about this cost, the determination of such is an important part of the regulators activities. The theoretical foundations supporting the concept of the weighted average cost of capital (CMPC) date back to the 1950 s and are solidly established in the academic and business circles, as well as in the regulating entities. The methodologies applied to estimate the expected weighted average cost of capital (CMPC) in future years generate, however, some controversy among the authors. In addition, difficulties exist in gathering the necessary data, especially in emerging markets with small capital markets and a short history of political stability. The objective of this dissertation is to analyze the methodology employed by Agência Nacional de Energia Elétrica - ANEEL (Brazilian National Agency for Electricity - the country s regulator of electricity generation, transmission and distribution) in the calculation of the weighted average cost of capital (CMPC) used in the tariff review process for the electricity distribution companies.

<p>I denna uppsats<strong> </strong>undersöker jag huruvida CAPM eller APT modellerna ger resultat på den svenska aktiemarknaden mellan 1998 och 2007. Jag undersöker om någon av dessa modeller passar in i den svenska aktiemarknaden och hurdan är resultatet. Det som gör uppsatsen intressant är att jag använder båda modellerna i en och samma studie och jämför resultatet av uppskattningar av modellerna. Som markandsindex har jag använt OMXS30 index och som makroekonomiska variabler i APT-modellen har jag använt inflation, oljepris, industriproduktionsindex och ränta. Resultatet av studien är att med de makroekonomiska variablerna, som jag har använt, ger både CAPM och APT likvärdiga resultat. Slutsatsen av min studie är att APT med de rätta variablerna är en bättre modell att skatta priset på aktier än CAPM.</p> / <p>In this essay, I examine whether CAPM or APT models give results on the Swedish stock market between 1998 and 2007. I examine if either CAMP or APT or both of these models fits in on the Swedish stock market and what the result is. What makes this essay interesting is that I use both models in one and the same study and compare the result of my estimates with these two models. As market index, I have used the OMXS30 index and as macroeconomic variables in APT model, I have used inflation, oil price, industry production index and interest. The result of the study is that with the macroeconomic variables, that I have used with APT and CAPM, gives CAPM and APT equivalent results. The conclusion of the study is that APT, with the correct variables, is better model for estimating the stock prices than CAPM.</p>

<p>An efficient market implies that the use of fundamental analysis should not result in excess return, and that any return exceeding the market average can be explained by compensation for risk, accord-ing to The Capital Asset Pricing Model (CAPM). The focus of this study is to test whether the suc-cessful investment strategy developed by Piotroski (2000) generates excess return on American data, after risk adjustment by using Fama & French’s (1993) 3-factor and Carhart’s (1997) 4-factor CAPM. Initially we form stock portfolios based on companies characterized by high book-to-market values, additionally, we divide them into different performance classes by ranking them with Piotroski’s (2000) measure of financial performance, F_SCORE. Furthermore, we measure the actual return which these portfolios generates, using an one- and two-year buy-and-hold strategy, and calculate what theoretical return that is motivated by 3- and 4-factor CAPM, on the same sample. Our results show that Piotroskis (2000) investment strategy generates an average excess return for all the portfo-lios we construct, which cannot be explained by either 3- or 4-factor CAPM.</p>

An efficient market implies that the use of fundamental analysis should not result in excess return, and that any return exceeding the market average can be explained by compensation for risk, accord-ing to The Capital Asset Pricing Model (CAPM). The focus of this study is to test whether the suc-cessful investment strategy developed by Piotroski (2000) generates excess return on American data, after risk adjustment by using Fama &amp; French’s (1993) 3-factor and Carhart’s (1997) 4-factor CAPM. Initially we form stock portfolios based on companies characterized by high book-to-market values, additionally, we divide them into different performance classes by ranking them with Piotroski’s (2000) measure of financial performance, F_SCORE. Furthermore, we measure the actual return which these portfolios generates, using an one- and two-year buy-and-hold strategy, and calculate what theoretical return that is motivated by 3- and 4-factor CAPM, on the same sample. Our results show that Piotroskis (2000) investment strategy generates an average excess return for all the portfo-lios we construct, which cannot be explained by either 3- or 4-factor CAPM.