Yes / This paper uses a novel numerical optimization technique – robust optimization – that is well suited to solving the asset–liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximize the Sharpe ratio. We disaggregate pension liabilities into three components – active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme’s projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes–Stein and Black–Litterman models as well as the actual USS investment decisions. Over a 144-month out-of-sample period, robust optimization is superior to the four benchmarks across 20 performance criteria and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks.

A dissertação aborda e compara as características dos índices de Sharpe (SR) e suas variantes, SRc e SRd, Sharpe generalizado (GSR ) e potencial de investimento (IP), sendo os índices GSR e IP associados a alguma função de utilidade. Pelo fato de o GSR e o IP serem idênticos, testes empíricos foram realizados entre SRc e o GSR. Ambos foram avaliados teoricamente sob dois aspectos, o que definimos de análise retrospectiva, i.e., análise de séries de log-retornos mensais observados, e a análise prospectiva, i.e., séries a ocorrer. No âmbito prospectivo, ex ante facto, o SRc (índice de Sharpe com variável de estado normal) e o SRd (índice de Sharpe com variável de estado lognormal), por estarem associados à função de utilidade quadrática, apresentam distorções como o ponto bliss e o agente econômico bomba de dinheiro. O mesmo ocorre no âmbito retrospectivo, ex post facto, com o GSR (potencial de desempenho de ativos de risco para indivíduos com função de utilidade HARA) quando o coeficiente de aversão ao risco é igual a um negativo, gama=-1. No entanto, o GSR pode ser associado a funções de utilidade diferentes da quadrática evitando seus efeitos indesejáveis. Sob a suposição de movimento browniano geométrico (MBG) e da utilidade HARA para o preço mensal ajustado de ações brasileiras e americanas e para pontos mensais de índices brasileiros e americanos, entre janeiro de 2000 e março de 2008, obtivemos os seguintes resultados: (1) o índice GSR para utilidade quadrática apresentou elevada correlação com o SRc; (2) a menor correlação de GSR com SRc ocorreu para utilidade logarítmica; (3) para a utilidade exponencial, o GSR apresenta elevado grau de correlação com o SRc. Os resultados mostraram que o GSR com utilidade exponencial é o índice que menos se aproxima do comportamento do GSR com utilidade quadrática. Sabendo-se das distorções da utilidade quadrática, a adoção do GSR com gama=1 parece mais adequado para a classificação de ativos de risco. / This master dissertation studies and compares the characteristics of Sharpe ratio and its variants, SRc and SRd, generalized Sharpe ratio (GSR) and investment potential (IP), both GSR and IP associated to any utility function. By the fact that GSR and IP are identical indexes, empiric tests were conducted between SRc and GSR. The indexes were evaluated theoretically under two different aspects: retrospective analysis, i.e., analyze the observed monthly log-returns, and prospective analysis, i.e., series to occur. Under prospective view, ex ante facto, SRc (Sharpe ratio with normal state variable) and SRd (Sharpe ratio with lognormal state variable), for being associated to the quadratic utility function, show the inherent problems to utility functions such as the bliss point and the pump money economic agent. The same happens in a retrospective view, ex post facto, with the GSR (performance potential with HARA utility function family) when the risk aversion coefficient equals minus one, gama=-1. Therefore, the GSR can be associated to different utility functions avoiding the undesirable effects. Under the GBM (geometric Brownian motion) condition and HARA utility function for the Brazilian and American adjusted monthly stock prices and indexes monthly points during January 2000 and March 2008, we reached the following: (1) results indicate that GSR for quadratic utility has high correlation level with SRc; (2) while the logarithmic utility showed lowest correlation level between GSR and SRc; (3) exponential utilities showed a high level of correlation between GSR and SRc. The results showed that GSR with exponential utility kept the biggest behavior difference for the GSR with quadratic utility. Based on the knowing problems of the quadratic utility, GSR with gama=1 seems to be a better index choice for risk assets classification.

A dissertação aborda e compara as características dos índices de Sharpe (SR) e suas variantes, SRc e SRd, Sharpe generalizado (GSR ) e potencial de investimento (IP), sendo os índices GSR e IP associados a alguma função de utilidade. Pelo fato de o GSR e o IP serem idênticos, testes empíricos foram realizados entre SRc e o GSR. Ambos foram avaliados teoricamente sob dois aspectos, o que definimos de análise retrospectiva, i.e., análise de séries de log-retornos mensais observados, e a análise prospectiva, i.e., séries a ocorrer. No âmbito prospectivo, ex ante facto, o SRc (índice de Sharpe com variável de estado normal) e o SRd (índice de Sharpe com variável de estado lognormal), por estarem associados à função de utilidade quadrática, apresentam distorções como o ponto bliss e o agente econômico bomba de dinheiro. O mesmo ocorre no âmbito retrospectivo, ex post facto, com o GSR (potencial de desempenho de ativos de risco para indivíduos com função de utilidade HARA) quando o coeficiente de aversão ao risco é igual a um negativo, gama=-1. No entanto, o GSR pode ser associado a funções de utilidade diferentes da quadrática evitando seus efeitos indesejáveis. Sob a suposição de movimento browniano geométrico (MBG) e da utilidade HARA para o preço mensal ajustado de ações brasileiras e americanas e para pontos mensais de índices brasileiros e americanos, entre janeiro de 2000 e março de 2008, obtivemos os seguintes resultados: (1) o índice GSR para utilidade quadrática apresentou elevada correlação com o SRc; (2) a menor correlação de GSR com SRc ocorreu para utilidade logarítmica; (3) para a utilidade exponencial, o GSR apresenta elevado grau de correlação com o SRc. Os resultados mostraram que o GSR com utilidade exponencial é o índice que menos se aproxima do comportamento do GSR com utilidade quadrática. Sabendo-se das distorções da utilidade quadrática, a adoção do GSR com gama=1 parece mais adequado para a classificação de ativos de risco. / This master dissertation studies and compares the characteristics of Sharpe ratio and its variants, SRc and SRd, generalized Sharpe ratio (GSR) and investment potential (IP), both GSR and IP associated to any utility function. By the fact that GSR and IP are identical indexes, empiric tests were conducted between SRc and GSR. The indexes were evaluated theoretically under two different aspects: retrospective analysis, i.e., analyze the observed monthly log-returns, and prospective analysis, i.e., series to occur. Under prospective view, ex ante facto, SRc (Sharpe ratio with normal state variable) and SRd (Sharpe ratio with lognormal state variable), for being associated to the quadratic utility function, show the inherent problems to utility functions such as the bliss point and the pump money economic agent. The same happens in a retrospective view, ex post facto, with the GSR (performance potential with HARA utility function family) when the risk aversion coefficient equals minus one, gama=-1. Therefore, the GSR can be associated to different utility functions avoiding the undesirable effects. Under the GBM (geometric Brownian motion) condition and HARA utility function for the Brazilian and American adjusted monthly stock prices and indexes monthly points during January 2000 and March 2008, we reached the following: (1) results indicate that GSR for quadratic utility has high correlation level with SRc; (2) while the logarithmic utility showed lowest correlation level between GSR and SRc; (3) exponential utilities showed a high level of correlation between GSR and SRc. The results showed that GSR with exponential utility kept the biggest behavior difference for the GSR with quadratic utility. Based on the knowing problems of the quadratic utility, GSR with gama=1 seems to be a better index choice for risk assets classification.

Made available in DSpace on 2015-03-05T19:11:30Z (GMT). No. of bitstreams: 0 Previous issue date: 21 / Nenhuma / A indústria de fundos de investimento no Brasil está concentrada no segmento de renda fixa. Dos cerca de R$ 220 bilhões depositados em fundos, hoje, R$ 200 bilhões aproximadamente estão nesse segmento e R$ 20 bilhões em carteiras de renda variável. Observou-se que no primeiro semestre de 2002, os fundos de investimento em geral tiveram alguns problemas que diminuíram bastante os seus retornos. A mudança da métrica de avaliação dos fundos, da chamada Curva de Juros para a Marcação a Mercado, provocou profundas transformações em termos de mensuração de valor dos fundos de renda fixa. Neste contexto, verificou-se a performance das 17 maiores administradoras de fundos no período 1997-2003 com dados diários. O método empregado foi a Análise de Dados em Painel. A hipótese de que as administradoras de fundos nacionais privadas obtêm igual relação risco-retorno em suas carteiras do que as administradoras de fundos nacionais estatais e as administradoras de fundos estrangeiras não foi comprovada. As administradoras es / The industry of investment fund in Brazil is concentrated in the segment of fixed income. About R$ 220 billion are deposited in funds nowadays, from which R$ 200 billion approximately are in the fixed income segment and R$ 20 billion in variable income portfolios. In the first semester of 2002 it was observed that investment funds in general had substantially reduced their returns. In the wake of the change of the evaluation metrics of funds from yield curves to mark-to-market, caused profound transformation in the value of fixed income funds. In this context, the performance of the 17 biggest asset management firms in the period 1997-2000 in a daily basis has been assessed. The hypothesis that private Brazilian asset management firms have a similar risk-return performance in their portfolios as state and foreign firms has been rejected. Foreign asset management firms had a superior performance with respect to Brazilian private firms, while private firms sustained a superior performance vis-à-vis state firms

This paper gives an estimation of efficient frontiers for investment portfolios, they include stocks from Lima Stock Exchange General Index, Dow Jones Industrial Average, Gold, Cooper, Fixed Income Instruments of Peruvian government and savings in Peruvian financial institutions. The paper concludes that risk of investment in local portfolio reduces as a consequence of diversification, gold is an important asset and contributes to reduce portfolio risk. / El presente trabajo estima la frontera eficiente, en portafolios de inversión diversificados en acciones que componen el Índice General de la Bolsa de Valores de Lima (IGBVL), acciones que componen el Dow Jones Industrial Average (DJIA), oro, cobre, instrumentos de renta fija del Gobierno peruano e instrumentos de ahorro bancario. Se concluye que el riesgo de portafolios de inversión de acciones que componen el IGVBL disminuye como consecuencia de la diversificación; un activo relevante es el oro que contribuye a disminuir significativamente el riesgo del portafolio.

Submitted by Felipe Merlo Nascimento (felipemerlo.eng@gmail.com) on 2017-09-20T03:09:26Z No. of bitstreams: 1 Dissertação Felipe Merlo.pdf: 2654948 bytes, checksum: e4b83bed5e52b01c178db39bc7f862a1 (MD5) / Approved for entry into archive by Thais Oliveira (thais.oliveira@fgv.br) on 2017-09-20T17:57:59Z (GMT) No. of bitstreams: 1 Dissertação Felipe Merlo.pdf: 2654948 bytes, checksum: e4b83bed5e52b01c178db39bc7f862a1 (MD5) / Made available in DSpace on 2017-09-21T12:47:01Z (GMT). No. of bitstreams: 1 Dissertação Felipe Merlo.pdf: 2654948 bytes, checksum: e4b83bed5e52b01c178db39bc7f862a1 (MD5) Previous issue date: 2017-08-25 / In this paper, we present empirical evidence to investigate whether the propositions of the model of Frazzini and Pedersen (2014) apply to the Brazilian stock market. Using data from the year 2000 up to the first quarter of 2017, we find that the SML of this Market had a lower slope than that predicted by CAPM. In fact, it turned out to be negative, and this result was observed both in the time-series and in the cross-sectional analyzes. As a methodology to raise this evidence, 10 portfolios were created, organized in ascending order according to their respective betas. We calculated the returns relative to each portfolio and, with them, it was possible to verify that the portfolios with the highest beta performed less excess returns. In addition, we found that the Sharpe ratio was higher the lower the beta of the portfolios. Another proposition verified empirically in the Brazilian stock market, and in the considered period, was that the return of the BAB portfolios was positive. In addition, it was the largest one compared to others portfolios, and had the highest expected excess of return per unit of risk. Regarding the alpha, it was expected that the portfolios with higher beta had lower alpha. It was possible to verify this trend, but not in an undeniable way. This motivated us to make a small change in the model of Frazzini and Pedersen, which created a relation between the return of each one of the portfolios and the one of the BAB portfolio. The mathematical prediction, derived from the modified model, says that the coefficient of this relation is smaller the bigger the beta. It was possible to raise this empirical evidence in a clear way. This point was the great differential of this work, since we were the first to raise such evidence and to show that the BAB portfolios can be used as explanatory variable. / Neste trabalho, levantamos evidencias empíricas para investigar se as proposições do modelo de Frazzini e Pedersen (2014) se aplicam ao mercado acionário brasileiro. Utilizando dados que retomam o ano de 2000 até o primeiro trimestre de 2017, verificamos que a SML deste mercado é menos inclinada que a prevista pelo CAPM. De fato, ela chegou a ser negativa, sendo este resultado observado tanto nas analises em séries de tempo quanto nas em corte transversal. Como metodologia para levantar estas evidencias, foram criadas 10 carteiras, organizadas em ordem crescente segundo seus respectivos betas. Calculamos os retornos relativos a cada carteira e, com eles, foi possível verificar que os portfolios com maior beta realizaram menor retorno em excesso. Além disso, verificamos que o índice de Sharpe foi maior quanto menor foi o beta das carteiras. Outra proposição verificada empiricamente no mercado acionário brasileiro, e no período considerado, foi que o retorno das carteiras BAB foi positivo. Além disso, foi o maior entre todas as carteiras, ficando inclusive com o maior retorno esperado em excesso por unidade de risco. No que tange ao alfa, era esperado que as carteiras com maior beta tivessem menor alfa. Foi possível verificar esta tendência, mas não de maneira incontestável. Isso nos motivou a fazer uma pequena alteração no modelo de Frazzini e Pedersen, a qual criou uma relação entre o retorno de cada uma das carteiras e o da carteira BAB. A previsão matemática, oriunda do modelo modificado, diz que o coeficiente desta relação é menor quanto maior for o beta. Foi possível levantar esta evidencia empírica de maneira clara. Este ponto foi o grande diferencial deste trabalho, uma vez que fomos os primeiros a levantar tal evidencia e a mostrar que as carteiras BAB podem ser utilizadas como variável explicativa.

Made available in DSpace on 2010-04-20T20:51:08Z (GMT). No. of bitstreams: 3 154942.pdf.jpg: 18952 bytes, checksum: 23e574558dce7d0f2a386af838a81bbe (MD5) 154942.pdf: 506907 bytes, checksum: 04eae2214c9bdd57e0cbeb2bb4459728 (MD5) 154942.pdf.txt: 81444 bytes, checksum: 047630fc773c90c68757120835adddab (MD5) Previous issue date: 2006-02-15T00:00:00Z / Mutual funds performance evaluation is, traditionally, made using Sharpe Ratio that considers only the first and the second moments of the return distribution (mean and variance), but it requires assumptions on the normality of the returns distribution and on the investor’s utility function as quadratic. However, it is well known that a quadratic utility function is inconsistent with investor behavior and some funds, like hedge funds, have returns distributions far from a normal distribution Keating and Shadwick (2002a, 2002b) proposed a new measure called Omega that incorporates all the moments of the distribution, and has the advantage of requiring no assumptions on the returns distribution or on the utility function of a risk averse investor. The purpose of this work is to verify if this measure has a greater forecast power than other performance measures, like Sharpe and Sortino Ratios. The empiric study indicated that Omega measure makes a ranking, most of the time, different from the other measures. Despite the portfolios constructed with Omega have had an average return greater than the average return of the portfolios constructed using the other measures, in almost all the tests, this difference of averages of returns was significant only in some cases. In spite of this, there is a light indication that Omega measure is the most appropriate for the use of investors when is made the performance evaluation of mutual funds. / A avaliação de desempenho de fundos de investimentos é, tradicionalmente, realizada utilizando-se o Índice de Sharpe, que leva em consideração apenas os dois primeiros momentos da distribuição de retornos (média e variância), assumindo as premissas de normalidade da distribuição de retornos e função quadrática de utilidade do investidor. Entretanto, é sabido que uma função de utilidade quadrática é inconsistente com o comportamento do investidor e que as distribuições de retornos de determinados fundos, como os hedge funds, estão longe de serem uma distribuição normal. Keating e Shadwick (2002a, 2002b) introduziram uma nova medida denominada Ômega que incorpora todos os momentos da distribuição, e tem a vantagem de não ser necessário fazer premissas sobre a distribuição dos retornos nem da função de utilidade de um investidor avesso ao risco. O objetivo deste trabalho é verificar se esta medida Ômega tem um poder de previsibilidade maior que outras medidas de avaliação de desempenho, como o Índice de Sharpe e o Índice de Sortino. O estudo empírico indicou que a medida Ômega gera um ranqueamento, na maioria das vezes, relativamente diferente das outras medidas testadas. Apesar das carteiras formadas com base na medida Ômega terem gerado um retorno médio maior que o retorno médio das carteiras formadas pelas outras medidas em praticamente todos os testes, esta diferença entre as médias dos retornos só foi significativa em alguns casos. Mesmo assim, há uma leve indicação de que a medida Ômega é a mais apropriada para utilização do investidor ao fazer a avaliação de desempenho dos fundos de investimentos.

L’objectif principal de cette thèse est d’apporter de nouveaux résultats théoriques concernant la performance d’investissements basés sur des modèles stochastiques. Pour ce faire, nous considérons la stratégie optimale d’investissement dans le cadre d’un modèle d’actif risqué à volatilité constante et dont la tendance est un processus caché d’Ornstein Uhlenbeck. Dans le premier chapitre,nous présentons le contexte et les objectifs de cette étude. Nous présentons, également, les différentes méthodes utilisées, ainsi que les principaux résultats obtenus. Dans le second chapitre, nous nous intéressons à la faisabilité de la calibration de la tendance. Nous répondons à cette question avec des résultats analytiques et des simulations numériques. Nous clôturons ce chapitre en quantifiant également l’impact d’une erreur de calibration sur l’estimation de la tendance et nous exploitons les résultats pour détecter son signe. Dans le troisième chapitre, nous supposons que l’agent est capable de bien calibrer la tendance et nous étudions l’impact qu’a la non-observabilité de la tendance sur la performance de la stratégie optimale. Pour cela, nous considérons le cas d’une utilité logarithmique et d’une tendance observée ou non. Dans chacun des deux cas, nous explicitons la limite asymptotique de l’espérance et la variance du rendement logarithmique en fonction du ratio signal-sur-bruit et de la vitesse de retour à la moyenne de la tendance. Nous concluons cette étude en montrant que le ratio de Sharpe asymptotique de la stratégie optimale avec observations partielles ne peut dépasser 2/(3^1.5)∗100% du ratio de Sharpe asymptotique de la stratégie optimale avec informations complètes. Le quatrième chapitre étudie la robustesse de la stratégie optimale avec une erreur de calibration et compare sa performance à une stratégie d’analyse technique. Pour y parvenir, nous caractérisons, de façon analytique,l’espérance asymptotique du rendement logarithmique de chacune de ces deux stratégies. Nous montrons, grâce à nos résultats théoriques et à des simulations numériques, qu’une stratégie d’analyse technique est plus robuste que la stratégie optimale mal calibrée. / The aim of this thesis is to study the robustness of the optimal trading strategy. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein-Uhlenbeck process. In the first chapter, the background and the objectives of this study are presented along with the different methods used and the main results obtained. The question addressed in the second chapter is the estimation of the trend of a financial asset, and the impact of misspecification. Motivated by the use of Kalman filtering as a forecasting tool, we study the problem of parameters estimation, and measure the effect of parameters misspecification. Numerical examples illustrate the difficulty of trend forecasting in financial time series. The question addressed in the third chapter is the performance of the optimal strategy,and the impact of partial information. We focus on the optimal strategy with a logarithmic utility function under full or partial information. For both cases, we provide the asymptotic expectation and variance of the logarithmic return as functions of the signal-to-noise ratio and of the trend mean reversion speed. Finally, we compare the asymptotic Sharpe ratios of these strategies in order to quantify the loss of performance due to partial information. The aim of the fourth chapter is to compare the performances of the optimal strategy under parameters mis-specification and of a technical analysis trading strategy. For both strategies, we provide the asymptotic expectation of the logarithmic return as functions of the model parameters. Finally, numerical examples find that an investment strategy using the cross moving averages rule is more robust than the optimal strategy under parameters misspecification.

Housing is both a durable good and an investment vehicle, which makes it importantin people’s daily life aswell as for a nation’s economy. This thesis innovatively applies the Sharpe ratio on evaluating the performance of the US residentialhousing market within the time period from 2005:Q1 to 2019:Q3, andinvestigates how this performance would react upon macroeconomic shocks,including sudden changes in GDP growth rate and personal income growthrate, by establishing a vector auto-regression model with the lag order of four.The main results are that: (1)in the long run, direct residential investments are not significantly more profitable than treasury bills but not disappointing compared to the market portfolio of Dow Jones Industrial Average; (2)the performance of residential investments seem to slightly and positively co-move withGDP and personal income growth rate; (3)the long-term impacts that sudden GDP and personal income growths have on the performance seem inconspicuous and tend to mitigate within about three years and (4) limited evidence supports the hypothesis that current housing market performance can help predictfuture GDP growth rate. Based on housing’s two purpose of consumption andinvestment and the empirical results showing that direct investments on residentialproperties have similar risk-adjusted return level to short-term treasurybills, I suggest that financially feasible households purchase their own houseinstead of renting for a long time, and that speculative investors avoid puttingmoney in residential properties unless they have access to inside information. / Bostäder kan betraktas både som en hållbar vara och som ett investeringsinstrument.De är essentiella för människors vardag och har en viktig roll förett lands ekonomi. Denna avhandling använder innovativt Sharpe-förhållandet för att utvärdera hur den amerikanska bostadsmarknaden presterade under perioden2005: kvartal 1 till 2019: kvartal 3. Den försöker även undersöka om denna prestation påverkas av makroekonomiska chocker inklusive plötsligaförändringar i BNP-tillväxttakt och personliga inkomsttillväxthastighet. Detta görs genom att upprätta en vektor autoregression modell med en fördröjningsordningför fyra. De viktigaste resultaten är att: (1) på långsikt är direktabostadsinvesteringar inte betydligt mer lönsamma än statsskuldväxlar dock är det hellre inte en besvikelse jämfört med en marknadsportföljen av Dow JonesIndustrial Average; (2) Prestationen av bostadsinvesteringar verkar vara svagt och samverkar positivit både med BNP och tillväxttakten för personinkomst.(3) De långsiktiga effekterna av plötsliga tillväxter av BNP och personliga inkomster har på utvecklingen verkar vara vaga och tenderar att mildra inomcirka tre år och (4) begränsade bevis stöder hypotesen om att nuvarande bostadsmarknadsresultat kan bidra till att förutsäga framtida BNP-tillväxttakten.Baserat på bostädernas två syften inom konsumtion och investeringar, visar deempiriska resultaten att direkta investeringar i bostadsfastigheter har en liknande riskjusterad avkastningsnivå som kortfristiga statsskuldväxla. Därför föreslår jag att ekonomisk stabila hushåll borde köpa ett eget hus istället för att hyraunder en lång tid, och att spekulativa investerare borde undvika att satsa pengar inom bostadsfastigheter såvida de inte har tillgång till insider-information.

During the past few decades, social responsible investing (SRI) has rapidly grown to become a renowned investment strategy. Because of the contradictory findings on how successful this strategy is in terms of financial return, the aim of this thesis is to compare the performance of sustainable and conventional funds in four different geographical areas during the last three years. With the use of regression analysis, the correlation between the Portfolio Sustainability Score of a fund, which is a Morningstar-provided rating that represents how well a fund incorporates ESG, and its risk-adjusted return is determined. The final results of this analysis varies among the four geographical regions. The correlation between the two variables is positive in USA and Asia ex-Japan, whereas a negative relationship is found in Europe and the Nordic region. However, the obtained findings are not of statistical significance, implying that there is no difference between the risk-adjusted returns of sustainable versus conventional funds. / Under de senaste årtionden har hållbara investeringar ökat och på senare tid även blivit en väletablerad investeringsstrategi. Då tidigare studier inom området uppvisat motstridiga resultat gällande hur effektiv denna strategi är inom värdeskapande, fokuserar denna rapport på att klargöra ifall hållbara alternativt vanliga fonder är fördelaktiga utifrån ett finansiellt perspektiv. Mer specifikt undersöks fyra geografiska områden över en tidsperiod på tre år. Genom regressionsanalys bestäms korrelationen mellan en fonds Portfolio Sustainability Score, ett betyg som erhålls av Morningstar som representerar hur väl den specifika fonden inkorporerar ESG, och dess riskjusterade avkastning. De slutgiltiga resultaten av denna analys varierar i de fyra geografiska områdena. I USA och Asien där Japan exkluderas är korrelationen positiv medan en negativ korrelation råder i Europa och Norden. Dock är resultaten inte av statistisk signifikans vilket indikerar att det inte är någon skillnad i den riskjusterade avkastningen mellan hållbara och vanliga fonder.