Commodity Trading Advisors (CTAs) have gained popularity due to their abilities to generate an absolute return strategy. Little is known about how CTAs work and what variables are important to tune in order to create a profitable strategy. Some investors use CTA-like strategies to leverage their portfolio and create positive returns in times when the spot market is falling. The report is written for Skandinaviska Enskilda Banken and aims to give the bank and readers an understanding on how changes of parameters in a CTA strategy change the outcome of it with focus on three main measurements: Sharpe ratio, drawdown and total return.  The foundation of CTAs is that they rely on signals from some given sets of assets and make investments decisions solely based on them. CTAs can be rule-based with a binomial signal, or they can use a continual signal, like in the report. The thesis aims to recreate a CTA using a continuous momentum signal and with the signal, invest accordingly. Some different variables were tested, most importantly the report focuses on the weights of the assets and investigates if the momentum signal is good as it is or if a risk parity weighting is needed on top of the signal in order to generate a return that matches the expectations of a low drawdown and a high Sharpe ratio.  Beyond the weight allocation, different lookback periods of both the signal and weight were tested. A shorter lookback generated a quicker return that was more sensible to short trends on the market. Which in some cases was profitable but it also lost more of it accumulated return when the trend was "false". The equally weighted signal that only takes the trend into account when allocating the weights of the assets was more volatile it its returns and benefited from a long signal. The CTA results presented can only be seen as an index since it is rebalanced every rebalancing point, the frequency of those points was examined and the strategy was performing well if rebalanced once a week or once a month, every day and once a year did not yield a better result.  As expected, the CTA benefits from trend on the market, no matter the direction of it. The best periods for the CTA were when the market was very volatile, mainly 2008 and 2022. When there is no clear trend, the CTA reacts too slowly and often loses money. One important conclusion is that the CTA never should be used as an investment strategy on its own, rather as a hedging strategy that allocates a fraction of a total long-only portfolio.

This research paper studies the Day-of-the-week effect in the cryptocurrency market. Using multiple regression, we analyze the effect using 12 counterfactual optimized portfolios of the cryptocurrencies, as well as the 10 cryptocurrencies alone. Our findings show that well-optimized cryptocurrency portfolios are not subject to Day-of-the-week effects. A positive Monday and a negative Thursday effect were confirmed in Bitcoin, Ethereum, and Ripple, as well as a negative Sunday effect for Ripple.

This diploma thesis deals with the problem of portfolio optimization in relation to the mean vector and the variance matrix of yields. The emphasis is put on Mar- kowitz model. In the thesis there are explored some possibilities of robustification based on the used parametric set. Beside the classic formulation of the task our focus is also devoted to the cases in which short sales are not allowed. The core of the thesis constitutes of a simulation study that models the impact of errors in the estimation of the input parameters of Markowitz model. It takes into account different types of risk aversions and different approaches to modelling parameter perturbations . Therefore it specifies the hypothesis of the dominating influence of the mean vector estimate which is valid only for a risk lover. 1

<p>Hedge funds are a debated subject in today’s financial industry. During 2008, despite hedge funds absolute return target, the global hedge fund industry showed a negative performance whilst the Swedish hedge fund market performed relatively well in comparison. Many studies have been made investigating the effect on incorporating hedge funds in a traditional portfolio though none focused separately on the Swedish market. In a global perspective it is quite easy to invest in hedge fund portfolios due to the existence of investable indices. To invest on the Swedish market is a more complex matter. SIX Harcourt HFXS Index is a Swedish hedge fund index representing the Swedish hedge fund market though it is not investable. Hence it would be interesting to see if it is possible to create an investable version of SIX Harcourt HFXS. When creating an investable index, several administrative costs will arise and in order to cover these costs it would be interesting to see whether or not it possible to optimize SIX Harcourt HFXS Index in purpose of achieving a outperformance which could cover any administrative costs for setting up the investable version. Also, since the optimized version must replicate the standard SIX Harcourt HFXS Index it must maintain a certain level of correlation.</p><p>This thesis, which is based on a positivistic epistemology, is built upon a quantitative case study where SIX Harcourt HFXS Index is optimized in purpose of achieving an outperformance in terms of the risk-adjusted return. The optimization uses an adjusted mean-variance methodology and is limited to a maintained correlation above 0,9 towards the standard SIX Harcourt HFXS Index. The optimization is created through the use of an Excel application created by Harcourt Investment Consulting.</p><p>Also, based on the outperformance by Swedish hedge funds compared to global hedge funds, this study aims to show the effect of incorporating Swedish hedge funds in a traditional portfolio consisting of equities and bonds. This effect is analyzed by the use of several performance-and risk measures.</p><p>The study shows that it is possible to optimize SIX Harcourt HFXS Index and produce an outperformance of approximately 1,5% per annum with a maintained correlation above 0,9. It also shows that the effect of incorporating Swedish hedge funds to a traditional portfolio is positive in regards to both risk and return.</p>

Hedge funds are a debated subject in today’s financial industry. During 2008, despite hedge funds absolute return target, the global hedge fund industry showed a negative performance whilst the Swedish hedge fund market performed relatively well in comparison. Many studies have been made investigating the effect on incorporating hedge funds in a traditional portfolio though none focused separately on the Swedish market. In a global perspective it is quite easy to invest in hedge fund portfolios due to the existence of investable indices. To invest on the Swedish market is a more complex matter. SIX Harcourt HFXS Index is a Swedish hedge fund index representing the Swedish hedge fund market though it is not investable. Hence it would be interesting to see if it is possible to create an investable version of SIX Harcourt HFXS. When creating an investable index, several administrative costs will arise and in order to cover these costs it would be interesting to see whether or not it possible to optimize SIX Harcourt HFXS Index in purpose of achieving a outperformance which could cover any administrative costs for setting up the investable version. Also, since the optimized version must replicate the standard SIX Harcourt HFXS Index it must maintain a certain level of correlation. This thesis, which is based on a positivistic epistemology, is built upon a quantitative case study where SIX Harcourt HFXS Index is optimized in purpose of achieving an outperformance in terms of the risk-adjusted return. The optimization uses an adjusted mean-variance methodology and is limited to a maintained correlation above 0,9 towards the standard SIX Harcourt HFXS Index. The optimization is created through the use of an Excel application created by Harcourt Investment Consulting. Also, based on the outperformance by Swedish hedge funds compared to global hedge funds, this study aims to show the effect of incorporating Swedish hedge funds in a traditional portfolio consisting of equities and bonds. This effect is analyzed by the use of several performance-and risk measures. The study shows that it is possible to optimize SIX Harcourt HFXS Index and produce an outperformance of approximately 1,5% per annum with a maintained correlation above 0,9. It also shows that the effect of incorporating Swedish hedge funds to a traditional portfolio is positive in regards to both risk and return.

The combination of two or more portfolio rules is theoretically convex in return-risk space, which provides for a new class of portfolio rules that gives purpose to the Mean-Variance framework out-of-sample. The author investigates the performance loss from estimation risk between the unconstrained Mean-Variance portfolio and the out-of-sample Global Minimum Variance portfolio. A new two-fund rule is developed in a specific class of combined rules, between the equally weighted portfolio and a mean-variance portfolio with the covariance matrix being estimated by linear shrinkage. The study shows that this rule performs well out-of-sample when covariance estimation error and bias are balanced. The rule is performing at least as good as its peer group in this class of combined rules.

全球經濟情況變動，壽險公司的資產快速增加，國內投資工具無法滿足壽險公司的投資需求，政府大幅增加了壽險公司的投資範圍，如開放壽險公司海外投資上限，希望能提升壽險公司的資金運用效率。然而金融海嘯過後，壽險公司的投資績效受到打擊，金融資產出現大幅跌價，面臨投資跌價損失、資產減損、投資報酬率下降等情況，投資獲利逐漸下滑，影響了壽險公司的整體營運，經營情況日趨嚴峻。於是近年來，國內壽險公司投資收益佔營收比重逐漸增加，資產配置策略及實務上如何進行資金運用操作，實關係著壽險公司經營穩健度及獲利能力。本論文以一個案人壽公司為例，透過MV模型分析2005年至2011年間，在現行法令限制下，壽險公司投資組合的報酬率與風險之影響為何，且既定風險情況下，分析其投資績效，並探討此壽險公司資產配置是否具效率，又可如何調整配置提升投資報酬率，藉以供作壽險業未來資金運用策略之參考。 / As life insurance company assets rapidly increase and vary with global economical situations, domestic investment means no longer satisfy investing needs of life insurance companies. The Government relaxes investment restrictions, financially and legally, aiming to improve the very investment benefit of life insurance companies. But after the financial tsunami, their investment performance decreased, financial assets declined, unrealized losses on investment and asset impairment occurred, and return on Investment went down. The life insurance company’s overall operating conditions became more and more severe. Thus, the facts that the increasing proportion of domestic life insurance companies’ income on investment, asset allocation policy and practice on how to fund operations, do influence the stability and profitability of life insurance companies. Employing the Markowitz portfolio model, this thesis will analyze the investment benefit of life insurance companies with a specific case of a life insurance company during the period between 2005 and 2011. It reassesses issues below: the relation between capital allocation efficiency and risk of life insurance companies under established risk situations, the efficiency of life insurance companies’ asset allocation, and the rearrangement of asset allocation in order to upgrade capital allocation efficiency. These analyses would provide some reference for life insurance companies’ investing strategies in uses of future funds.

>Magister Scientiae - MSc / In this thesis, we discuss methods for optimising the expected rate of return of a portfolio with minimal risk. As part of the work we look at the Modern Portfolio Theory which tries to maximise the portfolio's expected rate of return for a cer- tain amount of risk. We also use Quadratic Programming to optimise portfolios. Generally it is recognised that portfolios with a high expected return, carry higher risk. The Modern Portfolio Theory assists when choosing portfolios with the lowest possible risk. There is a nite number of assets in a portfolio and we therefore want to allocate them in such a way that we're able to optimise the expected rate of return with minimal risk. We also use the Markowian approach to allocate these assets. The Capital Asset Pricing Model is also used, which will help us to reduce our e cient portfolio to a single portfolio. Furthermore we use the Black-Litterman model to try and optimise our portfolio with a view to understanding the current market conditions, as well as considering how the market will perform in the future. An additional tool we'll use is Value at Risk. This enables us to manage the market risk. To this end, we follow the three basic approaches from Jorion [Value at Risk. USA: McGraw-Hills, 2001]. The Value at Risk tool has become essential in calcu- lating a portfolio's risk over the last decade. It works by monitoring algorithms in order to nd the worst possible scenarios within the portfolio. We perform several numerical experiments in MATLAB and Microsoft Excel and these are presented in the thesis with the relevant descriptions.

The thesis provides a comparison of different portfolio models and tests their performance on the financial markets. Our analysis particularly focuses on comparison of the classical Markowitz modern portfolio theory and the downside risk models of the post-modern portfolio theory. In addition, we consider some alternative portfolio models ending with total eleven models that we test. If the performance of different portfolio models should be evaluated and compared correctly, we must use a measure that is unbiased to any portfolio theory. We suggest solving this issue via a new approach based on the utility theory and utility functions. We introduce the unbiased method for evaluation of the portfolio model performance using the expected utility efficient frontier. We use the asymmetric behavioural utility function to capture the behaviour of the real market investors. The Markowitz model is the leading market practice. We investigate whether there are any circumstances in which some other models might provide better performance than the Markowitz model. Our research is for three reasons unique. First, it provides a comprehensive comparison of broad classes of different portfolio models. Second, we focus on the developed markets in United States and Germany but also on the local emerging markets in Czech Republic and Poland. These local markets have never been tested in such extent before. Third, the empirical testing is based on the broad data set from 2003 to 2012 which enable us to test how different portfolio model perform in different macroeconomic conditions.

This project investigates the applicability of the originalversion of Markowitz’s mean-variance model for portfoliooptimization to real-world modern actively managed portfolios.The method measures the mean-variance model’s capability toaccurately capture the riskiness of given portfolios, by invertingthe mathematical formulation of the model. The inversion of themodel is carried out both for fabricated data and real-world dataand shows that in the cases of real-world data the model lackscertain accuracy for estimating risk averseness. The method hascertain errors which both originate from the proposed estimationmethods of input variables and invalid assumptions of investors. / Projektet undersöker lämpligheten att använda den ursprungliga versionen av Markowitzs ”Mean-Variance model” för portföljoptimering för moderna aktivt förvaltade portföljer. Metoden mäter modellens förmåga att tillförlitligt beräkna risken för givna portföljer genom att invert-era den matematiska formuleringen av modellen. Inversionen av modellen utförs både för simulerad data och verklig data och visar att i fallet med verkliga data saknar modellen viss noggrannhet för att uppskatta riskpreferens. Metoden har vissa fel som både uppstår från de föreslagna uppskattningsmetoderna för inputvariabler och ogiltiga antaganden för investerare. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm