Detta arbete syftar till att undersöka relationen mellan företagsstorlek och dess aktieavkastning,annars känt som storlekseffekten, inom halvledarsektorn. Vi använder oss av två portföljer bestående av de tio största och tio minsta halvledarbolagen och görutfallstestet under perioden 2004–2015. Tre olika allokeringsstrategier tillämpas: equal weight, meanvariance och equal risk contribution samt tre olika ombalanseringsperioder. Vårt resultat visar på ett negativt samband mellan företagsstorlek och riskjusterad avkastning oavsettallokeringsstrategi. Resultaten tyder på att effekten inte är en proxy för fundamentala skillnader ellerberor på en felspecificering av β. / This thesis aims to examine the relationship between firm size and stock return, otherwise known asthe size effect, within the semiconductor industry. We construct two portfolios each comprising the ten largest and smallest semiconductor companiesand conduct a back test between 2004-2015. We examine three allocation strategies: equal weight,mean variance, and equal risk contribution along three difference rebalancing periods. Our results show a negative relationship between firm size and risk adjusted return regardless ofallocation strategy. The results also show that size effect is not a proxy for fundamental differencesnor a misspecification of β.

Even though the framework of mean-variance analysis is convincing, in practice, investors encounter serious drawbacks. Understandably, a more stable and rather simple method to make investment decisions without depending on the expected returns would obviously be preferred by some investors. In this study, we adopt a newly proposed equally-weighted risk contribution portfolio (ERC), without the assumption of expected returns, in order to observe its risk and return, as well as the timing of use compared to different benchmarks, the Taiwan 50 index (TWN50) and Taiwan weighted index (Y9997). For comparison, we adopt the other two commonly used methods, the minimum variance portfolio (MVP) and the equal weight portfolio (EW). It is interesting to observe the ERC¡¦s risk and return profile because, similar to the EW, it invests in every asset in a portfolio while adjusting weights to consider the marginal risk between each component. Therefore, no individual asset¡¦s risk contribution is dominated by an other and they all have the same risk contribution. In addition, to strike a balance between risk control and pursuing excess return, we incorporate arbitrage portfolios into the standard ERC portfolio; to satisfy the standard of the passive funds, we combine the minimum tracking error portfolio with the standard ERC portfolio by a specific ratio. From the TWN50 and the Y9997 cases, we presume that the problem relating to whether or not the benchmark is a full sample or a partial sample and whether it¡¦s replicable, affects the performance of the ERC. If our benchmark is a partial sample like the TWN50, the ERC strategy can outperform the benchmark and even provides some degree of defensive ability when the market trend is down.

Mean variance optimization has shortcomings making the strategy far from optimal from an investor’s perspective. The purpose of the study is to conduct an empirical investigation as to how modern methods of portfolio optimization address the shortcomings associated with mean variance optimization. Equal risk contribution, the Most diversified portfolioand a modification of the Minimum variance portfolio are considered as alternatives to the mean variance model. Portfolio optimization models introduced are explained in detail and solved using the optimization algorithms Cyclical coordinate descent and Alternating direction method of multipliers. Through implementation and backtesting using a diverse set of indices representing various asset classes, the study shows that the mean variance model suffers from high turnover and sensitivity to input parameters in comparison to the modern alternatives. The sophisticated asset allocation models equal risk contribution and the most diversified portfolio do not rely on expected return as an input parameter, which is seen as an advantage, and are not affected to the same extent by the shortcomings associated with mean variance optimization. The paper concludes by discussing the findings critically and suggesting ideas for further research. / Maximering av avkastning i samband med minimering av varians, på engelska kallat Mean variance optimization, är inte optimalt ur en investerares synpunkt. Syftet med denna uppsats är att genomföra en empirisk studie av hur moderna metoder för portföljallokering adresserar de problem som är förknippade med Mean variance optimization. Mer specifikt undersöks allokeringsstrategierna Equal risk contribution, Most diversified portfolio samt en variant av Minimum variance som ersättare till Mean variance optimization. Allokeringsmetoderna beskrivs detaljerat och löses med optimeringsalgoritmerna Cyclical coordinate descent och Alternating direction method of multipliers. Genom implementering och historisk simulering med ett antal index som representerar olika tillgångsslag visar studien att Mean variance optimization innebär hög portföljomsättning och har en större känslighet för ingångsparametrar i jämförelse med de moderna alternativen. De sofistikerade allokeringsmodellerna Equal risk contribution och Most diversified portfolio bygger inte på ingångsparametern förväntad avkastning, vilket ses som en fördel, och drabbas inte i samma utsträckning av problemen associerade med Mean variance optimization. Studien avslutas med att diskutera resultatet kritiskt och ge förslag på vidare studier som bygger på den teori och det resultat som har presenterats.

Allocation to private infrastructure debt investments has increased in the recent years [15]. For managers of multi-asset portfolios, it is important to be able to assess the risk of the total portfolio and the contribution to risk of the various holdings in the portfolio. This includes being able to explain the risk of having private infrastructure debt investments in the portfolio. The modelling of private infrastructure debt face many challenges, such as the lack of private data and public indices for private infrastructure debt. In this thesis, two approaches for modelling private infrastructure debt in a parametric risk factor model are proposed. Both approaches aim to incorporate revenue risk, which is the risk occurring from the type of revenue model in the infrastructure project or company. Revenue risk is categorised into three revenue models; merchant, contracted and regulated, as spread level differences can be distinguished for private infrastructure debt investments using this categorisation. The difference in spread levels between the categories are used to estimate β coefficients for the two modelling approaches. The spread levels are obtained from a data set and from a previous study. In the first modelling approach, the systematic risk factor approach, three systematic risk factors are introduced where each factor represent infrastructure debt investments with a certain revenue model. The risk or the volatility for each of these factors is the volatility of a general infrastructure debt index adjusted with one of the β coefficients. In the second modelling approach, the idiosyncratic risk term approach, three constant risk terms for the revenue models are added in order to capture the revenue risk for private infrastructure debt investments. These constant risk terms are estimated with the β coefficients and the historical volatility of a infrastructure debt index. For each modelling approach, the commonly used risk measures standalone risk and risk contribution are presented for the entire block of the infrastructure debt specific factors and for each of the individual factors within this block. Both modelling approaches should enable for better explanation of risk in private infrastructure debt investments by introducing revenue risk. However, the modelling approaches have not been backtested and therefore no conclusion can be made in regards to whether one of the proposed modelling approaches actually is better than current modelling approaches for private infrastructure debt. / Investeringar i privat infrastrukturskuld har ökat de senaste åren [15]. För βägare av portföljer med investeringar i samtliga tillgångsslag är det viktigt att kunna urskilja risken från de olika innehaven i portföljen. Det finns många utmaningar vad gäller modellering av privat infrastrukturskuld, så som den begränsade mängden privat data och publika index för privat infrastrukturskuld. I denna uppsats föreslås två tillvägagångssätt för att modellera privat infrastrukturskuld i en parametrisk riskfaktormodell. Båda tillvägagångssätten eftersträvar att inkorporera intäktsrisk, vilket är risken som beror på den underliggande intäktsmodellen i ett infrastrukturprojekt eller företag. Intäksrisk delas in i intäksmodellerna "merchant", "contracted" och "regulated", då en skillnad i spreadnivå mellan privata infrastrukturskuldinvesteringar kan urskiljas med denna kategorisering. Skillnaden i spreadnivå mellan de olika kategorierna används för att estimera β -koefficienter som används i båda tillvägagångssätten. Spreadnivåerna erhålls från ett dataset och från en tidigare studie. I det första tillvägagångssättet, den systematiska riskfaktor-ansatsen, introduceras tre systematiska riskfaktorer som representerar infrastrukturskuldinvesteringar med en viss intäktsmodell. Risken eller volatiliten för dessa faktorer är densamma som volatiliteten för ett index för infrastrukturskuld justerat med en av β -koefficienterna. I det andra tillvägagångssättet, den idriosynktratiska riskterm-ansatsen, adderas tre konstanta risktermer för intäktsmodellerna för att fånga upp intäktsrisken i de privata infrastrukturinvesteringarna. De konstanta risktermerna är estimerade med β -koefficienterna och en historisk volatilitet för ett index för infrastrukturskuld. För båda tillvägagångssätten presenteras riskmåtten stand-alone risk1 och risk contribution2. Riskmåtten ges för ett block av samtliga faktorer för infrastrukturskuld och för varje enskild faktor inom detta block. Båda tillvägagångssätten borde möjliggöra bättre förklaring av risken för privata infrastrukturskuldinvesteringar i en större portfölj genom att ta hänsyn till intäktsrisken. De två tillvägagångssätten för modelleringen har dock ej testats. Därför kan ingen slutsats dras med hänsyn till huruvida ett av tillvägagångssätten är bättre än de som används för närvärande för modellering av privat infrastrukturskuld.

近年來金融市場情勢瞬息萬變且波動劇烈而令投資人難以捉摸，導致被動式投資重獲投資人的青睞。市值加權法是最普遍被使用的指數編製方法，傳統市值加權指數的缺點，主要有投資組合主要集中於特定成份股與暴露於不會吸引風險溢價的各類風險因子中，這些缺點促成Smart Beta策略的發展，未來將有許多具備不同風險與報酬水準的指數供投資人參考。本研究選用近幾年提出不需仰賴預期報酬假說的等量風險貢獻度投資組合(ERC)建構方式，以台灣50為基準，利用其成份股建構投資組合，探討權重與風險分散特性，並且檢視其績效表現與報酬風險輪廓。為了有比較上的基礎，除了與台灣50做比較外，也另外選用以風險分散角度所配置的投資組合建構方法：等權重投資組合(EW)作對照。 　　研究結果發現全樣本時期，等量風險貢獻度投資組合在事後相較於台灣50擁有較低的波動度。當市場趨勢向下時，除了能維持其低波動的特性，還能提供某種程度上的抗跌能力。然而，以報酬率和Sharpe Ratio指標來看，表現皆不如台灣50，但優於等權重投資組合。同時，依不同經濟狀況與時間區間檢視投資組合績效表現，等量風險貢獻度投資組合能將波動度控制在較低水準，但績效表現上較不穩定。 　　本文透過HHI指數及吉尼係數衡量持股集中度與風險集中度。以持股權重分配的特性來說，台灣50極端集中於少數股票上，等量風險貢獻度投資組合和等權重投資組合則相對較平均。以風險權重分配的特性來說，台灣50風險權重過於集中，風險權重較平均分散的組合則為等量風險貢獻度投資組合。 / Traditional capitalization-weighted approaches are the most common ways to construct indexes. However, during market up turns, the capitalization-weighted indexes may be influenced by a small number of large-cap stocks. Smart beta indexes have recently prompted great interest among academic researchers and market practitioners. Risk-based indexes are an important category of smart beta. In this article, we explore equal risk contribution portfolio (ERC), which is risk-parity based smart beta. The portfolio implies to determine the weights so as to obtain the same risk contribution for each asset. The aim is to minimize the concentration in terms of risk contributions. In this paper, we examine whether or not ERC portfolio can outperform a buy and hold, capitalization-weighted and equally-weighted allocation in different economic environments. We also compute the parity in portfolio “risk allocation” and parity in “asset class allocation” using HHI index and Gini coefficient. 　　We consider here real-life applications with stock universe: the Yuanta /P-shares Taiwan Top 50 ETF. We compute smart beta portfolios by using the one-year empirical covariance matrix of stock returns. Empirical applications show that ERC portfolios generally are inferior in terms of return performance and Sharpe ratios. It does have some characteristics such as balanced risk allocation and less volatile performance characteristics. It also exposes to lower maximum drawdown. ERC portfolio provides the best ex ante and ex post “parity “in asset class risk contribution. On the other hand, the capitalization-weighted portfolio is concentrated in terms of weights and risk contributions. The statistics suggest to us that the capitalization-weighted portfolio’s superior Sharpe ratio is largely due to its higher returns.

In risk management one important aspect is the allocation of total portfolio risk into its components. This can be done by measuring each components' risk contribution relative to the total risk, taking into account the covariance between components. The measurement procedure is straightforward under assumptions of elliptical distributions but not under the commonly used multivariate log-normal distributions. Two portfolio strategies are considered, the "buy and hold" and the "constant mix" strategy. The profits and losses of the components of a generic portfolio strategy are defined in order to enable a proper definition of risk contribution for the constant mix strategy. Then kernel estimation of risk contribution is performed for both portfolio strategies using Monte Carlo simulation. Further, applications for asset and risk management with risk contributions are discussed in the context of life insurance. / En viktig aspekt inom riskhantering är tilldelning av total portföljrisk till tillångsportföljens beståndsdelar. Detta kan åstadkommas genom att mäta riskbidrag, som även kan ta hänsyn till beroenden mellan risktillgångar. Beräkning av riskbidrag är enkel vid antagande om elliptiska fördelningar så som multivariat normalfördelning, men inte vid antagande om multivariat log-normalfördelning där analytiska formler saknas. Skillnaden mellan riskbidragen inom två portföljstrategier undersöks. Dessa strategier är "buy and hold" och "constant mix" (konstant ombalansering). Tilldelning av resultaten hos de olika beståndsdelarna med en generisk portföljstrategi härleds för att kunna definiera riskbidrag för "constant mix" portföljstrategin. "Kernel estimering" används för att estimera riskbidrag genom simulering. Vidare diskuteras applikationer för tillgångs- och riskhantering inom ramen för livförsäkringsbolag.

截至2016年的統計資料，我國產險與壽險業的保險公司家數來到54家，保險業資產總額佔了全台灣所有金融機構總資產的31.78%，資產規模來到新台幣22.6兆元，在如此龐大的資產規模下，保險公司的投資組合管理變成相當的重要，重點漸漸的從投資在什麼樣的商品可以讓資金獲取最大效益轉移到了投資後的管理與部位的調整，以避免不必要的非系統性風險，有鑑於此，台灣在2003年實施了RBC制度，讓保險公司的投資組合的分配有所依據，不過仍然免不了過度集中在某些資產的問題，所以本研究的目的在於能否運用風險集中度的概念來判斷投資組合是否過度集中，而不僅僅只有投資金額的比例來做判斷。 本論文的研究方法會根據各家保險公司的實際投資組合以每半年或每年的型式分別計算Marginal Risk Contribution(MRC)的値，並且進行分析後再以Herfindahl-Hirschman Index(HHI)與 Gini Index 來檢視長期資產組合集中度的趨勢，最後的研究結果可以發現若是從邊際風險貢獻的比例來看，各保險公司的風險分布主要是集中在國內上市普通股與ETF、海內外不動產投資、國外已開發國家或新興市場上市普通股與ETF以及A評等的國外固定收益債券，而利用HHI與Gini Index兩個指標來看，各保險公司的資產集中度是逐年上升的。 / According to the statistical data in 2016, there are 54 insurance companies which includes property and casualty insurance company and life insurance company. And the scale of insurance asset is NTD 2,260 billion, accounting for 31.78% of whole asset of financial institution in Taiwan. Under huge amount of asset, the portfolio management for insurance company become more and more important. The key points of this issue are transferring to the ratio of portfolio management from choosing asset class to get maximum profit in order to avoid the nonsystematic risk gradually. Therefore, the Risk-based Capital policy has established in 2003 in Taiwan. The ratio of the insurance companies’ portfolio had the reference to allocate. However, there were some issues about the excessive concentration of some asset classes. So, the target of this study is using the concept of the risk concentration to judge the portfolio too concentrated or not. Not just judge it by its amount invested. The research process of this thesis is to calculate the marginal risk contribution value of the insurance companies’ portfolio every half a year or every year. Moreover, using the Herfindahl-Hirschman Index (HHI) & Gini Index to observe the trend of long term portfolio concentration. From the marginal risk contribution ratio. We can found the result of this study is the risk concentrated on the domestic listed common stock & ETF, domestic or foreign Real Estate, foreign developed market or emerging market listed common stock & ETF and fixed income bond (A rating). Besides, using the Herfindahl – Hirschman index and Gini index. The concentrated ratio of insurance companies’ portfolio were raising recent years.