本文包含關於估計風險與動態資產配置的兩篇研究。第一篇研究主要就當須估計的投資組合其投入參數具有高維度特質的觀點下，探究因忽略不確定性通膨而對資產配置過程中帶來的估計風險。此研究基於多重群組架構下所發展出的新投資決策法則，能夠確實地評價不確定性通膨對資產報酬的影響性，並在應用於建構大規模投資組合時，能有效減少進行最適化投資決策過程中所需的演算時間與成本。而將此模型應用於建構全球ETFs投資組合的實證結果則進一步顯示，若在均值變異數架構下，因建構大型投資組合時須估計高維度投入參數而伴隨有大量估計風險時，參數估計方式建議結合採用貝氏估計方法來估算資產報酬的一階與二階動差，其所對應得到的投資組合樣本外績效會比直接採用歷史樣本動差來得佳。此實證結果亦隱含：在均值變異數架構下，穩定的參數估計值比起最新且即時的參數估計資訊對於投資組合的績效來得有益。同時，若當投入參數的樣本估計值波動很大時，增加放空限制亦能有利投組樣本外績效。 第二篇文章則主要處理當處於對數常態證券市場下時，投資組合報酬率不具有有限動差並導致無法在均值變異數架構下發展出最適化封閉解時的難題。本研究示範此時可透過漸近方法的應用，有效發展出在具有放空限制下，考量了估計風險後的簡單投資組合配置法則，並且展示如何將其應用至實務上的資產配置過程以建構全球投資組合。本文的數值範例與實證模擬結果皆顯示，估計風險的存在對於最適投資組合的選擇有實質的影響，無估計風險下得出的最適投資組合，不必然是存有估計風險下的最適投資組合。此外，實證模擬結果亦證明，當存有估計風險時，本文所發展的簡單法則，能使建構出的投資組合具有較佳的樣本外績效表現。 / This dissertation consists of two essays on dynamic asset allocation with regard to dealing with estimation risk as being in different uncertainties in the mean-variance framework. The first essay concerns estimation errors from disregarding uncertain inflation in terms of the need in estimating high-dimensional input parameters for portfolio optimization. This study presents simplified and valid criteria referred to as the EGP-IMG model based on the multi-group framework to be capable of pricing inflation risk in a world of uncertainty. Empirical studies shows the proposed model indeed provides a smart way in picking worldwide ETFs that serves well to reduce the amount of costs and time in constructing a global portfolio when facing a large number of investment products. The effect of Bayesian estimation on improving estimation risk as the decision maker is subject to history sample moments for input parameters estimations is meanwhile examined. The results indicate portfolios implementing the Stein estimation and shrinkage estimators offer better performance compared with those applying the history sample estimators. It implicitly demonstrates that yielding stable estimates for means and covariances is more critical in the MV framework than getting the newest up-to-date parameters estimates for improving portfolio performance. Though short-sales constraints intuitively should hurt, they do practically contribute to uplift portfolio performance as being subject to volatile estimates of returns moments. The second essay undertakes the difficulty that the probability distribution of a portfolio's returns may not have finite moments in a lognormal-securities market, and thus leads to the arduous problem in solving the closed-form solutions for the optimal portfolio under the mean-variance framework. As being in a lognormal-securities market, this study systematically delivers a simple rule in optimization with regard to the presence of estimation risk. The simple rule is derived accordingly by means of asymptotic properties when short sales are not allowed. The consequently numerical example specifies the detailed procedures and shows that the optimal portfolio with estimation risk is not equivalent to that ignoring the existence of estimation risk. In addition, the portfolio performance based on the proposed simple rule is examined to present a better out-of-sample portfolio performance relative to the benchmarks.

國內壽險公司面臨資金不斷累積與同業間激烈競爭，加上全球經濟動盪不安，國際金融偶有黑天鵝事件發生，尤以2008年金融海嘯重創全球產業為最，壽險業亦難以倖免，肇致壽險業者經營益顯艱困。因此，為維繫公司永續經營，規劃長期財務穩健性至關重要。是故，如何訂定投資策略與妥適資產配置，並兼顧風險管理，為當前壽險公司重要課題。 本研究分析郵政壽險資產配置行為，歸納影響公司資產配置之內、外在因素，例如流動性風險、利率風險、信用風險、資本適足率、匯率風險及法令規範等因素，皆影響資產配置策略。另為建構最佳資產配置，提升獲利，逐步改善財務結構，在現行法令限制下，運用Markowitz之投資組合理論為分析工具，導出效率前緣線，再運用夏普指標績效分析，來建立最佳投資組合。 另外分析壽險公司必須正視未來「國際會計準則」（International Financial Reporting Standards, IFRS）IFRS 4第二階段適用公平價值評估負債，利差損問題會更加嚴重，對業務發展與負債評價將產生巨大衝擊。尤其我國壽險業發行商品大都以長年期終身險為主，若壽險商品負債評價與資產不一致時，其缺口將因利率變化影響損益波動。 / Abstract Domestic life insurers are in a challenging environment with increasing asset size to manage and fierce competition within the industry. Moreover, the world economy is going down a bumpy path. Every now and then in the global financial system, we encounter a black swan event. Among them, the financial tsunami of 2008 hit global industries most severely. The financial tsunami of 2008 also left life insurers having an increasingly difficult time running the business. It is crucial to have sound long-term financial plans in order to ensure business sustainability. Therefore, how to form an investment strategy, determine asset allocation and manage risks at the same time becomes a critical issue for life insurers. The research studies the asset allocation behavior of Chunghwa Post insurance sector and lists both the internal and the external factors affecting asset allocation. Factors like liquidity risk, interest rate risk, credit risk, capital adequacy, currency risk and regulations all have some influence on the asset allocation strategy. Meanwhile, the research constructs efficient frontier with Markowitz Portfolio Theory and adopts Sharpe ratio as the performance measure to build an optimal portfolio under current regulations with the goal of optimizing asset allocation, boosting profits and gradually improving the financial structure. The research also studies the tremendous impact of IFRS 4 on business development and liability valuation of life insurance companies. The implementation of IFRS 4 Phase II will require fair value measurement of liabilities, which will exacerbate the negative interest spread problem. When the liability valuation approach of insurance products is not in line with asset valuation, the gap will intensify the income fluctuations from interest rate movements, especially for domestic life insurers whose main products are long-term whole life policies.

因為股票市場常具有厚尾、偏態和峰態的特性且在國際的股票市場之間，股票報酬長存在有尾端相依的情況，所以我們的資產模型不能選用Gaussian分配。 近幾年來，常用GH 分配建構單維度的股票報酬。這篇文章將利用多元仿射JD、多元仿射VG 和多元仿射NIG分配去建構風險性資產的報酬並請應用到資產配置。 建構風險性資產的報酬後，我們提供兩種不同形式的投資組合並且可以導出投資組合的期望值、變異數、偏態和峰態。我們嘗試以投資組合的期望值、變異數、偏態和峰態當成我們的目標函數，然後得出未來最佳的投資組合的權重。為了讓我們的資產配置更加動態和有效率，我們重新估計模型的參數、選擇最佳的投資組合權重，然後重新評估最佳的資產配置在每個決策日期。實證結果發現當股票市場的表現好的時候，我們建議資產配置應使用偏態當成我們的目標函數，但是當股票市場的表現太好的時候，我們建議資產配置應使用變異數當成我們的目標函數。 / Since the stock markets always have the characteristics of heavy-tailness, skewness and kurtosis and there exists tail dependence among the international stock markets, we can’t use the Gaussian distribution as our model. Recently, the generalized hyperbolic (GH) distribution has been suggested to fit the single stock returns. This article will use the multivariate affine JD (MAJD), multivariate affine variance gamma (MAVG) and multivariate affine normal inverse Gaussian (MANIG) distributions to construct the risky asset returns, and apply them to asset allocation. After constructing the risky asset returns, we provide two different forms of portfolio and obtain the mean, variance, skewness, kurtosis of portfolio. We can try to select the optimal weights of portfolio by using the mean, variance, skewness, kurtosis of portfolios as our objective functions. To make our asset allocation more dynamic and efficient, we re-estimate all parameters for our models, select the optimal weights of portfolio, and re-assess the optimal asset allocation at each decision date. Empirically, when the performances of stock markets are good, we suggest that our asset allocation uses the skewness as the objective function. When the performances of stock markets are not good, we suggest that our asset allocation uses the variance as the objective function.

我國勞工退休金新制自2005年7月1日開始實施，由過去的確定給付制改為具有確定提撥特色的「個人帳戶制」。對於勞工而言，確定提撥制和過去確定給付制不同之處在於承擔退休金投資風險的責任將由雇主轉由個人承擔。如何透過退休機制的設計以降低退休金的投資風險是近年來的重要議題，因此本文主要從個人偏好與風險的觀點探討保證投資收益率制度與制度轉換選擇權等兩個降低確定提撥制投資風險的重要配套措施。 在本論文的第一篇研究中發現，資產配置與國際投資對保證成本的影響頗大，在個人可選擇資產配置的情況下，高投資風險的資產選擇將造成政府未來龐大的或有負債。為了解決政府保證成本過高造成代內與代間的財富移轉，本文從使用者付費與個人效用的觀點探討保證投資收益率制度的設計，發現藉由設立保證投資收益上限可提升風險趨避者、損失趨避者與後悔趨避者等偏好下的預期效用，且能降低個人管理下方風險所需的提撥成本與退休計畫參加者所需繳交的保證費用，故建議政府可將投資收益率上限納入保證投資收益率制度，供退休計畫參加者選擇合於本身偏好的保證收益率上限。 在近來許多國家的公、民營退休體系由過去以確定給付制改為確定提撥制，為了降低在確定提撥制下的退休金投資風險，在美國的佛羅里達州之公務人員退休體系中，存在著可供個人選擇是否轉換到確定給付制的機制。在我國勞退新制中除了從過去的確定給付制改為確定提撥制外，亦輔以「年金保險制」供勞工選擇與轉換，若年金保險制具有確定給付制的特徵，則勞工等於是擁有一個從確定提撥轉換轉到確定給付制的選擇權，因此制度選擇權的探討對我國而言亦是相當地重要。在本論文的第二篇研究中發現，當風險趨避程度越高則轉換至確定給付制的機率越高，轉換到確定給付制的高峰期會出現在開始工作的初期與屆臨退休之際等兩段期間。隨著工作期間的延長，個人轉換到確定給付制的機率越低，但仍可有效地提升退休金的所得替代率與達到降低退休金下方風險的效果，在加入退休制度初期不得轉換的限制之後，會降低轉換到確定給付制的機率。 / The Labor Retirement Pension Act enacted in 2005 introduced defined contribution (DC) pension plan for substituting the traditional defined benefit (DB) pension plan. In the defined contribution pension plan, the investment risk is transferred to the participants. However, the design of rate of return guarantee makes the investment risk less severe for participants. In the first essay, we find that the asset allocation and foreign investment have large impact on the guarantee cost: the high risky investment may result in large potential liability of the government in the future if participants have the investment portfolio choice. This study develops a framework to analyze design of rate of return guarantee from the financial engineering and user paid principle view. We find that the cap of investment return guarantee not only increases the expected utility of risk aversion, loss aversion and regret aversion, but also decreases the contribution cost to participant associated with managing the downside risk. Around the world, the defined contribution (DC) plans have been the primary trend of pension reform in the both public and private sector. In an attempt to decrease the investment risk associated with DC plan, the public employees are provided with an option to buy back DB plan in the Florida State of U.S.A. In the second essay, we find that the higher level of risk aversion is, the higher probability to buy back DB plan is. During the employee’s early years of service and as the employees near retirement, the probability to exercise the option is the highest. The probability to exercise the option is decreasing with the years of service being increasing; the option also increase the pension replacement rate as well as decrease the downside risk of pension. The probability to exercise the option is lower, when the option to buy back the DB plan is prohibited during the employee’s early years of service.

Made available in DSpace on 2010-04-20T21:00:18Z (GMT). No. of bitstreams: 3 martincasalsturma2003.pdf.jpg: 11517 bytes, checksum: 930c75c74ff8269d877983110854646d (MD5) martincasalsturma2003.pdf: 975293 bytes, checksum: f41cfd3a5f3e659d07e2861acf4e23d4 (MD5) martincasalsturma2003.pdf.txt: 107784 bytes, checksum: e96ad0fb809a12f13ba7d3f08e24c1ee (MD5) Previous issue date: 2006-02-15T00:00:00Z / O objetivo deste trabalho é analisar a alocação de investimentos no mercado acionário brasileiro, utilizando a teoria do prospecto de Tversky e Kahneman (1979) e o conceito de Aversão a Perdas Míope (Myopic Loss Aversion) proposto por Benartzi e Thaler (1995). Foram levantados através de experimento de laboratório os parâmetros da função de valor e da função de ponderação de probabilidades da teoria do prospecto e foi verificada a alocação de investimentos entre ações e renda fixa que maximizam a utilidade. Chegamos à conclusão que o total de recursos atualmente direcionados ao mercado de ações no Brasil, que é de aproximadamente 2,7% para pessoas físicas e de 6,0% para pessoas jurídicas, é compatível com a teoria do prospecto. / The objective of this study is to analyze the investment allocation in the Brazilian stock market, using Tversky and Kahneman’s prospect theory (1979) and the concept of myopic loss aversion proposed by Benartzi and Thaler (1995). We run a laboratory experiment to obtain the parameters of the value function and the probability weighting function of the prospect theory and identify the allocation that maximizes utility in the Brazilian Market We conclude that the actual allocation of investment in the stock market, of around 2.7% for individuals and around 6% for all the segments, is in accordance with the prospect theory.

Modern financial asset pricing theory is a broad, and at times, complex field. The literature review in this study covers many of the asset pricing techniques including factor models, random walk models, correlation models, Bayesian methods, autoregressive models, moment-matching models, stochastic jumps and mean reversion models. An important topic in finance is portfolio opti-misation with respect to risk and reward such as the mean variance optimisation introduced by Markowitz (1952). This study covers optimisation techniques such as single period mean variance optimisation, optimisation with risk aversion, multi-period stochastic programs, two-fund separa- tion theory, downside optimisation techniques and multi-period optimisation such as the Bellman dynamic programming model. The question asked in this study is, in the context of investing for South African individuals in a multi-asset portfolio, whether an active investment strategy is signi cantly di erent from a passive investment strategy. The passive strategy is built using stochastic programming with moment matching methods for non-Gaussian asset class distributions. The strategy is optimised in a framework using a downside risk metric, the conditional variance at risk. The active strategy is built with forward forecasts for asset classes using the time-varying transitional-probability Markov regime switching model. The active portfolio is finalised by a dynamic optimisation using a two-stage stochastic programme with recourse, which is solved as a large linear program. A hypothesis test is used to establish whether the results of two strategies are statistically different. The performance of the strategies are also reviewed relative to multi-asset peer rankings. Lastly, we consider whether the findings reveal information on the degree of effi ciency in the market place for multi-asset investments for the South African investor. / Operations Management / M. Sc. (Operations Research)

Le but de cette thèse est de construire un modèle de détection des changements de phase -passages de marché haussier à baissier et vice versa - du marché des actions américaines cotées, en utilisant un nombre relativement important de variables à la fois fondamentales (macroéconomiques et microéconomiques) et issues de l’analyse technique.Le modèle statistique retenu est la régression logistique statique, avec un retard pour les variables explicatives allant de zéro à trois mois. Les huit variables les plus significatives parmi vingt candidatesont été sélectionnées à partir des données mensuelles du S&P500 sur la période 1963-2003. Le modèle obtenu a été testé sur 2004-2013 et sa performance a été supérieure à celles de la stratégie Buy & Holdet d’un modèle univarié utilisant la variable ayant le plus fort pouvoir de détection - ce dernier modèle ayant fait l’objet d’une étude dans la littérature.Il a également été montré que des variables non encore considérées dans la littérature - la moyenne mobile sur les six derniers mois des créations nettes d’emplois non-agricoles, la base monétaire et le Composite Leading Indicator de l’OCDE - ont un pouvoir de détection significatif pour notre problématique. D'autre part, la variable binaire indiquant la position du S&P500 par rapport à sa moyenne mobile des dix derniers mois - variable de type analyse technique - a un pouvoir prédictif beaucoup plus élevé que les variables fondamentales étudiées. Enfin, les deux autres variables les plus statistiquement significatives sont macroéconomiques : l'écart entre les taux à dix ans des T-bonds et à trois mois des T-bills et la moyenne mobile des créations d’emplois non-agricoles. / The goal of this thesis is to build a model capable of detecting the reversals - shift from bull market to bear market or vice versa - of the American stock market, by using a relatively large number of explanatory variables, both of fundamental (macroeconomic and microeconomic) and of ‘technical analysis’ types.The statistical model used is static logistic regression, with lags for the independent variables ranging from zero to three months. Starting with twenty variables, the eight most significant ones have been selected on a training set consisting of monthly data of the S&P500 between 1963 and 2003. There sulting model has been tested over the 2004-2013 period and its performance was better than those of a buy & hold strategy and of a univariate model based on the variable with the highest predictive power – the latter model being the focus of a paper in the current literature. Another contribution of the thesis is that some variables not yet studied in the literature – the six month moving average of net non-farm job creations, the monetary base and the OECD Composite Leading Indicator – are statistically significant for our problem. Moreover, the predictive power of the binary variable indicating whether the S&P500 is above or below its ten-month moving average – a technical analysis variable – is much higher than that of the fundamental variables which have been considered. Finally, the two other most significant variables are macroeconomic ones: the spread between the ten-year T-bond and three-month T-bill rates and the moving average of non-farm jobs creations.

Le premier chapitre examine les caractéristiques statistiques à long terme des rendements financiers en France et aux USA. Les propriétés des différents actifs font apparaître qu’à long terme les actions procurent un risque sensiblement moins élevé. En outre, les propriétés de retour à la moyenne des actions justifient qu’elles soient utilisées dans une stratégie de cycle de vie comme « option par défaut » de plans d’épargne retraite. Le chapitre deux fournit une explication au débat sur l'hypothèse d’efficience des marchés. La cause du débat est souvent attribuée à la petite taille des échantillons et à la faible puissance des tests statistiques dédiés. Afin de contourner ce problème, nous utilisons l'approche développée par Campbell et Viceira (2005) qui utilisent une méthode VAR pour mettre en évidence l’existence de retour vers la moyenne dans le cours des actifs risqués.Le troisième chapitre évalue la vitesse de convergence des cours des actions. Un moyen classique pour caractériser la vitesse de retour vers la moyenne est la « demi-vie ». En comparant les indices boursiers de quatre pays développés (États-Unis, Royaume-Uni, France et Japon) sur la période 1950-2014, nous établissons une vitesse de convergence significative, avec une demi-vie entre 4,0 et 5,8 ans.Le dernier chapitre présente les résultats d'un modèle conçu pour étudier les interactions entre la démographie et les régimes de retraite. Afin d’étudier les risques inhérents à l’utilisation des revenus du capital pour financer les retraites, nous utilisons un « Trending OU process » au lieu d’un MBG classique pour modéliser les rendements. Pour un épargnant averse au risque le marché pourrait concurrencer les régimes par répartition. / Chapter one examines the long run statistical characteristics of financial returns in France and the USA for selected assets. This study clearly shows that the returns’ distributions diverge from the Gaussian strategy as regards longholding periods. Thereafter we analyze the consequences of the non-Gaussian nature of stock returns on default-option retirement plans.Chapter two provides a reasonable explanation to the strong debate on the Efficient Market Hypothesis. The cause of the debate is often attributed to small sample sizes in combination with statistical tests for mean reversion that lackpower. In order to bypass this problem, we use the approach developed by Campbell and Viceira (2005) who have settled a vectorial autoregressive methodology (VAR) to measure the mean reversion of asset returns.The third chapter evaluates the speed of convergence of stock prices. A convenient way to characterize the speed of mean reversion is the half-life. Comparing the stock indexes of four developed countries (US, UK, France and Japan) during the period 1950-2014, we establish significant mean reversion, with a half-life lying between 4,0 and 5,8 years.The final chapter provides some results from a model built in order to study the linked impacts of demography and economy on the French pension scheme. In order to reveal the risks that are contained in pension fund investment, we use a Trending Ornstein-Uhlenbeck process instead of the typical GBM for modeling stock returns. We find that funded scheme returns, net of management fees, are slightly lower thanthe PAYG internal rate of return.

Bakgrund: Kapital på börsen förflyttas fram och tillbaka mellan olika tillgångar, vilket ären naturlig del av diversifieringen i portföljer. När osäkerheten ökar i marknaden väljerinvesterare normalt att förflytta kapital från aktier till säkrare tillgångar som exempelvisobligationer, vilket beskrivs som Flight to Quality (FTQ). Däremot har räntorna efter denglobala finanskrisen 2008 varit historiskt låga och under vissa perioder negativa, vilket i sintur försvagar förflyttningen. Sverige har här utmärkt sig, genom att till skillnad från USA,fortsatt att sänka räntan och legat på låga nivåer under en väldigt lång tid. Därmed uppstårfunderingar kring hur förflyttningar av kapital har sett ut i Sverige de senaste 30 åren, samthur det senaste lågränteklimatet påverkar. Syfte: Syftet med studien är att undersöka förhållandet mellan avkastningen på noteradeobligationer och aktier i Sverige från 1993 till 2022. Studien ska även undersöka hur enlågräntemiljö påverkar förhållandet. Metod: OMXSPI samt BMSD10Y har använts för att beräkna avkastningen på aktierrespektive obligationer från databaserna Refinitiv Eikon samt Refinitiv Datastream. Urvaleti studien uppgick till 7271 respektive 1526 observationer. Genom en kvantitativ metod ochdeduktiv ansats har studien utgått från teorin gällande FTQ för att undersöka hurkorrelationen förändrats. Vidare har regressioner använts för att säkerställa påverkan pånivån av korrelationen samt hur ett lågränteklimat påverkar styrkan i FTQ. Slutsats: Studiens resultat påvisar att korrelationen mellan aktier och obligationer undertidsperioden har varit svagt negativ med fyra olika strukturella förändringar under perioden.Vidare visar studiens resultat att ett lågränteklimat under perioden har försvagat styrkan iFTQ:er som inträffat i Sverige mellan 1993 och 2022. Studien bidrar till litteraturen inomområdet korrelation mellan aktier och obligationers avkastningar, samt litteraturen kringlågränteklimats påverkan på finansiella marknader. / Background: Capital on the stock exchange is moved back and forth between differentassets, which is a natural part of the diversification of portfolios. When uncertainty increasesin the market, investors normally choose to move capital from equities to safer assets such asbonds, which is described as Flight to Quality (FTQ). On the other hand, interest rates afterthe global financial crisis in 2008 have been historically low and in some cases negative,which in turn weakens the capital movement. Sweden has distinguished itself, in that unlikethe United States, it has continued to lower its interest rates and have kept them at low levelsfor a very long time. This raises concerns about how capital movements over the past 30 yearshave developed in Sweden, and how the recent low interest rate climate is affecting. Purpose: The purpose of the study is to investigate the relationship between returns onstocks and bonds in Sweden from 1993 to 2022. The study will also investigate how a lowyield environment effects the relationship. Method: OMXSPI and BMSD10Y have been used to calculate the return on stocks andbonds from the databases Refinitiv Eikon and Refinitiv Datastream, respectively. The samplein the study amounted to 7271 and 1526 observations. Through a quantitative method anddeductive approach, the study has been based on the theory regarding FTQ to investigatehow the correlation has changed. Furthermore, regressions have been used to ensure theimpact on the level of the correlation and how a low interest rate climate affects the strengthof the FTQ. Conclusion: The result shows a weak negative correlation between returns on stocks andbonds during the time period, with four different structural breaks during the period.Furthermore, the results show that a low yield environment has weakened the strength of theFlights to Quality that have occurred in Sweden between 1993 and 2022. This studycontributes to the literature in the field of stock-bond return correlation and the field of lowyield effects on financial markets.

In this study within quantitative portfolio optimization, stochastic programming is investigated as an investment decision tool. This research takes the direction of scenario based Mean-Absolute Deviation and is compared with the traditional Mean-Variance model and widely used Risk Parity portfolio. Furthermore, this thesis is done in collaboration with the First Swedish National Pension Fund, AP1, and the implemented multi-asset portfolios are thus tailored to match their investment style. The models are evaluated on two different fund management levels, in order to study if the portfolio performance benefits from a more restricted feasible domain. This research concludes that stochastic programming over the investigated time period is inferior to Risk Parity, but outperforms the Mean-Variance Model. The biggest aw of the model is its poor performance during periods of market stress. However, the model showed superior results during normal market conditions. / I denna studie inom kvantitativ portföljoptimering undersöks stokastisk programmering som ett investeringsbeslutsverktyg. Denna studie tar riktningen för scenariobaserad Mean-Absolute Deviation och jämförs med den traditionella Mean-Variance-modellen samt den utbrett använda Risk Parity-portföljen. Avhandlingen görs i samarbete med Första AP-fonden, och de implementerade portföljerna, med era tillgångsslag, är därför skräddarsydda för att matcha deras investeringsstil. Modellerna utvärderas på två olika fondhanteringsnivåer för att studera om portföljens prestanda drar nytta av en mer restrektiv optimeringsmodell. Den här undersökningen visar att stokastisk programmering under undersökta tidsperioder presterar något sämre än Risk Parity, men överträffar Mean-Variance. Modellens största brist är dess prestanda under perioder av marknadsstress. Modellen visade dock något bättre resultat under normala marknadsförhållanden.