Med hjälp av årlig prisstatistik avseende försäljningar av skogsfastigheter (1995-2020) bedömer studien skogliga investeringars marknadsrisk samt estimerar dess diskonteringsränta. Analysen sker inom de teoretiska ramverken Capital Asset Pricing Theory (CAPM) samt Arbitrage Pricing Theory (APT). Utöver korrelation med marknaden analyseras ett antal riskfaktorer så som inflation, förändringar i bostadspriser, BNP samt förändringar i virkespriser. CAPM beräknas för olika löptider där den riskfria räntan matchas mot investeringens tidshorisont. Resultatet ligger i linje med tidigare forskning och visar att skogliga investeringar har en låg marknadsrisk och troligen kan ge ett skydd mot inflation. Val av korrekt löptid för den riskfria räntan har betydande effekt på den estimerade diskonteringsräntan.

This study investigates the cryptocurrency called bitcoin. A cryptocurrency is a type of currency that depends on cryptography to issue new units instead of depending on government decree like fiat currencies. The study will first explain some of the technical details that make bitcoin work. This is necessary to lay groundwork to get to the actual aim of the study, namely investigating the economic aspects of bitcoin. The study will evaluate bitcoin, and other cryptocurrencies, along with fiat currencies against certain definitions. In the process it will introduce a new subclass of cryptocurrency - the sovereign cryptocurrency. Bitcoin’s implied monetary policy will also be discussed, as well as the problems it creates for central banks. A hypothesis on the behaviour of the bitcoin price will be explained and research will be provided to support the acceptance of the hypothesis. Using this hypothesis, a stochastic pricing model for bitcoin will be derived. Arbitrage trading strategies will also be provided that explain certain price constraints that operate in the bitcoin market. The dissertation will also introduce a means to improve the anonymity of a user of bitcoin and will reason that improvements such as these and others will increase the use of bitcoin. Therefore, improvements to anonymity will increase the economic relevance of bitcoin and increase its competitive edge over the traditional banking system. It will be reasoned, based on the possible problems created by bitcoin’s monetary policy, as well as the growth projections implied by the stochastic pricing model, and the increased economic relevance due to improvements in anonymity, that central banks would need to create their own cryptocurrency that conforms to certain requirements – the previously introduced sovereign cryptocurrency. The study will conclude by explaining the technical changes needed for a fork of bitcoin to become a sovereign cryptocurrency, as well as a mathematical model to control the monetary policy of the sovereign cryptocurrency. As its aim, adaptive monetary policy will have stable prices for the economy using the sovereign cryptocurrency to price its goods and services. Please note, that while every effort was made to use published references, the field of cryptocurrencies is very young and changing constantly. Thus, most publications on the subject are simply placed on websites on the internet. This is especially true for the work relating to the founding of the field, and the data sources of the operation of the cryptocurrencies. Therefore a lot of the references do refer to websites on the internet. / Dissertation (MSc)--University of Pretoria, 2019. / Mathematics and Applied Mathematics / MSc / Unrestricted

The installed capacity of electricity produced from solar power has increased over the years and will do so even further. A lot of companies are investing in so-called solar parks to create large scale electricity production from solar power. With intermittent energy sources such as solar power comes challenges for the electricity net where storage systems can play an important role to handle these challenges. Storage systems connected to renewable energy can also be a way to increase the economic benefits of a system.  This study investigates whether a lithium-ion battery system connected to a solar park is economically profitable, and in that case under which circumstances. This is done by focusing on a solar park in Uppsala, Sweden, owned by Vasakronan AB. Different grid-connected services provided by the battery that could generate income were identified and chosen for the study which were arbitrage, a local flexibility market and frequency regulation. The usage of the battery for each and a combination of these services were modelled and simulated in Matlab (2020). Each individual case was created as its own model for three different battery capacities (2, 4 & 8 MWh). To investigate whether a case was profitable or not, the internal rate was calculated for each model. This was also done for a longer lifetime of the battery and for lower investment costs as a sensitivity analysis. The results show that a system of this kind is only profitable for one case which is if a 2 MWh battery is used for the frequency regulation services FFR and FCR-D. This results in an internal rate of 6% which is higher than the rate of return of 5% that Vasakronan requires. The conclusions of the study is that it is difficult to make an investment in a battery system that is only charged from a solar park profitable.

We use an adversarial expert based online learning algorithm to learn the optimal parameters required to maximise wealth trading zero-cost portfolio strategies. The learning algorithm is used to determine the relative population dynamics of technical trading strategies that can survive historical back-testing as well as form an overall aggregated portfolio trading strategy from the set of underlying trading strategies implemented on daily and intraday Johannesburg Stock Exchange data. The resulting population time-series are investigated using unsupervised learning for dimensionality reduction and visualisation. A key contribution is that the overall aggregated trading strategies are tested for statistical arbitrage using a novel hypothesis test proposed by Jarrow et al. [31] on both daily sampled and intraday time-scales. The (low frequency) daily sampled strategies fail the arbitrage tests after costs, while the (high frequency) intraday sampled strategies are not falsified as statistical arbitrages after costs. The estimates of trading strategy success, cost of trading and slippage are considered along with an offline benchmark portfolio algorithm for performance comparison. In addition, the algorithms generalisation error is analysed by recovering a probability of back-test overfitting estimate using a nonparametric procedure introduced by Bailey et al. [19]. The work aims to explore and better understand the interplay between different technical trading strategies from a data-informed perspective.

Mortgage loans are the major assets securitised by South African banks. Arguments from the literature indicate that the use of securitisation as an instrument for regulatory arbitrage weakened banks’ soundness and caused, at least partially, the 2007-2008 Global Financial Crisis. In this regard, financial institutions continually took advantage of the loopholes in the Basel regulation, principally that of Basel I. Undertaken from both the empirical and theoretical angles, this thesis investigated whether regulatory capital arbitrage under Basel II and III regulations, was a driver of mortgage loans securitisation by South African banks. Additionally, the effect of mortgage loans securitisation on the South African banks’ stability was analysed. Furthermore, the project built upon the case of mortgage loans securitisation to deepen the insight on banks’ behaviour towards risk, by considering a rare contractual relationship where banks are regarded as agents acting on behalf of regulators. The theoretical examination was carried out by means of perspectives from Agency and Institutional Theories. The South African banking system is essentially monopolistic with five banks holding more than 90% of total assets, out of which four, with 70% of the assets, consistently report outstanding volume of mortgage loans securitised. Based on the data collected from these four major banks, this research project is the first in many regards. It involves an emerging economy, considers the influence of both Basel II and III regulations, covers the period 2008 to 2015, and focuses on well-capitalised banks exclusively. Moreover, it extends regulatory capital arbitrage analysis to the evidence of loans expansion, includes CAMELS as bank stability proxy and brings in Agency Theory and Institutional Theory to explain banks’ behaviour with regards to risk in this particular context. In contrast, other studies were concentrated on Europe and America, mostly under Basel I, limited to one or two baseline models for regulatory capital arbitrage and often only the Z-score measure was used for bank stability. In three major steps, this study first employed the Ordinary Least Squares statistical methodology to test the capital arbitrage theory of securitisation and other of its features whereby it causes the decrease of capital with little or no reduction of risk. The estimation results indicated that securitisation of mortgage loans lessened South African banks’ regulatory capital, increased their overall risk level and moreover, suggested that the proceeds from securitisation were used to expand their loans portfolios. These outcomes tentatively imply that South African banks securitise mortgage loans for regulatory capital arbitrage. The second step explored the impact of securitisation of mortgage loans on South African banks’ stability. Two different measures of bank stability were involved: the CAMELS and the Z-score. CAMELS stands for C: capital (leverage ratio and not the regulatory capital); A: assets quality; M: management efficiency; E: earning; L: liquidity; and S: sensitivity to market risk (interest risk). The Two Stage Least Squares and the Ordinary Least Squares statistical methods were used respectively for the analysis of the relationship between the two bank stability indicators and the outstanding volume of mortgage securitised. The empirical results from CAMELS showed that mortgage loans securitised negatively affected the level of capital proxied by the leverage ratio, eroded assets quality and increased South African banks’ overall costs. However, they had a positive effect on South African banks’ profit, they seemed to be an additional source of liquidity and represented a useful tool to curtail market risk sensitivity, especially the interest risk as they increased net interest income. With regards to the analysis with the Z-score, the results indicated a negative impact of mortgage securitised on South African banks’ stability. The outcome remained unchanged when retained interests in the form of subordinated loans were included in the analysis, but retained interest had a positive influence on the Z-score. The last step of this study pertained to the theoretical analysis based on the concepts of Agency Theory and Institutional Theory. Acting as regulators’ agents in an agency relationship, the simple model of Agency Theory in its extended form explained that South African banks were first and foremost risk-taking players. They were more interested in the risk/reward trade-off in their decision-making attitude towards risk than pursuing the regulators’ goal of the stability of the banking system. In that sense, it was not a surprise that they engaged in regulatory capital arbitrage despite knowing that it was risky but could provide gains in liquidity and profit. In addition to goals conflict, Agency Theory indicated asymmetry of information between banks and regulators as the indirect origin of regulatory capital arbitrage, where the opacity of banks’ activities, such as securitisation, rendered regulations ineffective and thus easy to shirk. Furthermore, it was found that the essentials of the behaviour-oriented contract suggested by the theory as the optimal contract, were already included in the formulation of the latest Basel Accords. However, the researcher believes that one key element, which is the reward or compensation that should benefit the banks (the agent) when they abide by the terms of the contract, is missing. Regulators should therefore include incentives in the regulations and combine the behaviour and outcome-oriented contracts to optimize their relationship with banks even though, as explained by the theory, the outcome of bank stability will remain partially uncertain due to uncontrollable factors such as the economic conditions. The concept of legitimacy, from Institutional Theory, explicated that banks’ legitimacy came from their ability to comply with the regulations. From this stance, the results suggested that regulatory capital arbitrage seemed instead to undermine the legitimacy of South Africa banks well-capitalised position.

A thesis submitted to the School of Economic and Business Sciences, Faculty of Commerce, Law and Management, University of the Witwatersrand in fulfilment of the requirements for the degree of Master of Commerce (M.Com) in Finance, Johannesburg June 2017 / Traditional finance theory surrounding the risk-return relationship is underpinned by the CAPM which posits that a single risk factor, specifically market risk, is priced into asset returns. Even though it is a popular asset pricing model, the CAPM has been widely criticised due to its unrealistic assumptions and the APT was developed to address the CAPM’s weaknesses. The APT framework allows for a multitude of risk factors to be priced into asset returns; implying that it can be used to model returns using either macroeconomic or microeconomic factors. As such, the APT allows for non-traditional factors, such as investor sentiment, to be included. A macroeconomic APT framework was developed for nine countries using the variables outlined by Chen, Roll, and Ross (1986) and investor sentiment was measured by the FEARS index (Da, Engelberg, & Gao, 2015). Regression testing was used to determine whether FEARS is a statistically significant explanatory variable in the APT model for each country. The results show that investor sentiment is a statistically significant explanatory variable for market returns in five out of the nine countries examined. These results add to the existing APT literature as they show that investor sentiment has a significant explanatory role in explaining asset prices and their associated returns. The international nature of this study allows it to be extended by considering the role that volatility spill-over or the contagion effect would have on each model. / XL2018

This project uses software development to investigate the link between software and finance. The focus of the work is developing and implementing a trading algorithm which seeks to make profit by making trades based on arbitrage opportunities between currencies. Specifically, the sets of currencies examined are two fiat currencies and one cryptocurrency. Trades are made by combining a blockchain system, which maintains the cryptocurrency, and the live foreign exchange market, which enables fiat currency exchange. The main methodologies for carrying out the research are test-driven development and the use of a simulation to facilitate trades. By passing all of the unit tests, the software is verified. In addition, data gathered during runs of the simulation show that the algorithm successfully identifies arbitrage opportunities and turns a profit on average over many runs. This project proposes an interesting topic for further research in the field of blockchain technology used for financial trading. / Detta projekt bygger på mjukvaruutveckling för att undersöka kopplingen mellan programvara och finans. Arbetet fokuserar på att utveckla och implementera en algoritm för valutahandel som försöker skapa vinst genom att genomföra handel baserade på arbitragemöjligheter mellan valutor. Specifikt är de uppsättningar valutakurserna som undersöks två ordinarie valutor och en kryptovaluta. Handel utförs genom att kombinera ett s.k. blockchain-system, som upprätthåller kryptovalutan, och den ordinarie valutamarknaden för vanlig valutaväxling. De viktigaste metoderna för att genomföra undersökningen är testdriven utveckling och användande av simulering för att genomföra valutahandel. Mjukvaran verifieras med hjälp av en uppsättning enhetstester. Dessutom visar datan som samlats under simuleringar att algoritmen framgångsrikt identifierar arbitragemöjligheter och i genomsnitt ger en vinst över många körningar. Detta projekt utgör på så sätt ett intressant ämne för vidare forskning inom blockchain- teknik för finansiell handel.

Final qualifying work (master's thesis) is devoted to the study of various methods of hedging using options. The subject of the study are the economic relations arising in the process of studying the methods of hedging on the basis of option contracts. The main purpose of the master's thesis is to study the theoretical and practical ways of hedging and arbitrage potential of the investment portfolio using options, in conclusion, the recommendations for improving the arbitrage opportunities of the investment portfolio using options. / Выпускная квалификационная работа (магистерская диссертация) посвящена исследованию различных методов хеджирования с использованием опционов. Предметом исследования выступают экономические отношения, возникающие в процессе изучения методов хеджирования на основе опционных контрактов. Основной целью магистерской диссертации является изучить теоретические и практические способы хеджирования и арбитражный потенциал инвестиционного портфеля с использованием опционов. В заключении обозначены рекомендации по совершенствованию арбитражных возможностей инвестиционного портфеля с использованием опционов.

The Heath-Jarrow-Morton (HJM) model represents the latest in powerful arbitrage-free technology for modeling the term structure and managing interest rate risk. Yet risk management strategies in the form of immunization portfolios using duration, convexity, and M-square are still widely used in bond portfolio management today. This study addresses the question of how traditional risk measures and immunization strategies perform when the term structure evolves in the HJM manner. Using Monte Carlo simulation, I analyze four HJM volatility structures, four initial term structure shapes, three holding periods, and two traditional immunization approaches (duration-matching and duration-and-convexity-matching). I also examine duration and convexity measures derived specifically for the HJM framework. In addition I look at whether portfolios should be constructed randomly, by minimizing their M-squares or using barbell or bullet structures. I assess immunization performance according to three criteria. One of these criteria corresponds to active portfolio management, and the other two correspond to passive portfolio management. Under active portfolio management, an asset portfolio is successfully immunized if its holding period return is greater than or equal to the holding period return of the liability portfolio. Under passive portfolio management, the closer the returns of the asset portfolio to the returns of the liability portfolio, the better the immunization performance. The results of the study suggest that, under the active portfolio management criterion, and with the duration matching strategy, HJM and traditional duration measures have similar immunization performance when forward rate volatilities are low. There is a substantial deterioration in the immunization performance of traditional risk measures when there is high volatility. This deterioration is not observed with HJM duration measures. These results could be due to two factors. Traditional risk measures could be poor risk measures, or the duration matching strategy is not the most appropriate immunization approach when there is high volatility because yield curve shifts would often be large. Under the active portfolio management criterion and with the duration and convexity matching strategy, the immunization performance of traditional risk measures improves considerably at the high volatility segments of the yield curve. The improvement in the performance of the HJM risk measures is not as dramatic. The immunization performance of traditional duration and convexity measures, however, deteriorates at the low volatility segments of the yield curve. This deterioration is not observed when HJM risk measures are used. Overall, with the duration and convexity matching strategy, the immunization performance of portfolios matched with traditional risk measures is very close to that of portfolios matched with the HJM risk measures. This result suggests that the duration and convexity matching approach should be preferred to duration matching alone. Also the result shows that the underperformance of traditional risk measures under high volatility is not due to their being poor risk measures, but rather due to the reason that the duration matching strategy is not an appropriate immunization approach when there is high volatility in the market. Under the passive portfolio management criteria, the performances of traditional and HJM measures are similar with the duration matching strategy. Less than 29% of the duration matched portfolios have returns within one basis point of the target yield, whereas almost all are within 100 basis points of the target yield. These results suggest that the duration matching strategy might not be sufficient to generate cash flows close to those of the target bond. The duration measure assumes a linear relation between the bond price and the yield change, and the nonlinearities that are not captured by the duration measure might be important. When the duration and convexity matching strategy is used, more than 36% of the portfolios are within one basis point of the target with HJM risk measures. This dramatic improvement in the immunization performance of HJM measures is not guaranteed for traditional risk measures. In fact, there are certain cases in which the performance of traditional risk measures deteriorates with the duration and convexity matching strategy. In this respect, choosing the correct risk measure is more important than the immunization strategy when passive portfolio management is pursued. Under active portfolio management criterion, there is no significant difference among bullet, barbell, minimum M-square, and random portfolios with both duration matching and duration and convexity matching strategies. Under the passive portfolio management criterion, bullet portfolios produce closer returns to the target for short holding periods when the duration matching strategy is used. With the duration and convexity matching strategy, bullet, barbell and minimum M-square portfolios produce closer returns to the target for short holding periods. Random portfolios perform as well as bullet, barbell and minimum M-square portfolios for medium to long holding periods. These results suggest that when the duration matching strategy is used, bullet portfolios are preferable to other portfolio formation strategies for short holding periods. When the duration and convexity matching strategy is used, no portfolio formation strategy is better than the other. Under the active portfolio management criterion, minimum M-square portfolios are successfully immunized under each yield curve shape and volatility structure considered. Under the passive portfolio management criterion, minimum M-square portfolios perform better for short holding periods, and their performance deteriorates as the holding period increases, irrespective of the volatility level. This suggests that the performance of minimum M-square portfolios is more sensitive to the holding period rather than the volatility. Therefore, minimum M-square portfolios would be preferred in the markets when there are large changes in volatility. Overall, the results of the study suggest that, under the active portfolio management criterion and with the duration matching strategy, traditional duration measures underperform their HJM counterparts when forward rate volatilities are high. With the duration and convexity matching strategy, this underperformance is not as dramatic. Also no particular portfolio formation strategy is better than the other under the active portfolio management criterion. Under the passive portfolio management criterion, the duration matching strategy is not sufficient to generate cash flows closer to those of the target bond. The duration and convexity matching strategy, however, leads to substantial improvement in the immunization performance of the HJM risk measures. This improvement is not guaranteed for the traditional risk measures. Under the passive portfolio management criterion, bullet portfolios are preferred to other portfolio formation strategies for short holding periods. For medium to long holding periods, however, the portfolio formation strategy does not significantly affect immunization performance. Also, the immunization performance of minimum M-square portfolios is more sensitive to the holding period rather than the volatility. / Ph. D.

Models of the term structure of interest rates play a central role in the modern theory of pricing bonds and other interest rate claims. Term structure models based on the principle of no-arbitrage, especially those of the Heath-Jarrow-Morton (1992) class, have become very popular recently, both with academics and practitioners. Surprisingly however, although the implied volatility function plays a crucial role in these no-arbitrage term structure models, there is little systematic evidence to guide optimal model specification within this broad class. We study the implied volatility in the Heath-Jarrow-Morton framework using Eurodollar futures options data. We estimate a daily time series of forward rates within the HJM framework such that, by construction, the predicted futures prices from our model exactly match the observed futures prices. Next, we estimate a daily time series of volatility parameters such that the sum of squared errors between futures options prices predicted by the model and observed futures options prices is minimized. We use the six different volatility specifications suggested by Amin and Morton (1994) within the HJM class of models to price interest rate claims. Since the volatilities are the only unobservables, we use these models to infer the volatilities from the market prices of Eurodollar futures options over the 1987-1998 periods. The minimized sum of squared errors in the option prices is used as the measure of accuracy of each specific model. Each model differs from the others in its ability to match the market option prices and the time required for the computation. We compare the performances of the six volatility specifications in the accuracy-versus-computation time tradeoff. We document the systematic biases between the model and market prices as a function of option type, maturity, and moneyness. We also examine alternative numerical implementations of HJM models using the six volatility specifications. In particular, we analyze the impact on accuracy and computation time of using different numbers of time-steps. We also examine the effect of using time-steps of varying lengths within the same estimation procedure, and of ordering the time-steps in different ways. / Ph. D.