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.

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.

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.