Managing marginal capital requirements in solvency II: Analysis of a real insurance portfolio

This thesis provides a complete analysis of the Standard Capital Requirements given by Solvency II for a real insurance portfolio. We analyze the investment portfolio of BPI Vida e Pensões, an insurance company affiliated with a Portuguese bank BPI, both at security, sub-portfolio and asset class levels. By using the Standard Formula from EIOPA, Total SCR amounts to 239M€. This value is mostly explained by Market and Default Risk whereas the former is driven by Spread and Concentration Risks. Following the methodology of Leblanc (2011), we examine the Marginal Contribution of an asset to the SCR which allows for the evaluation of the risks of each security given its characteristics and interactions in the portfolio. The top contributors to the SCR are Corporate Bonds and Term Deposits. By exploring further the composition of the portfolio, our results show that slight changes in allocation of Term and Cash Deposits have severe impacts on the total Concentration and Default Risks, respectively. Also, diversification effects are very relevant by representing savings of 122M€. Finally, Solvency II represents an opportunity for the portfolio optimization. By constructing efficient frontiers, we find that as the target expected return increases, a shift from Term Deposits/ Commercial Papers to Eurozone/Peripheral and finally Equities occurs.

A comparative review of risk based portfolio allocations: An empirical study throughout rising yields

Since the financial crisis, risk based portfolio allocations have gained a great deal in popularity. This increase in popularity is primarily due to the fact that they make no assumptions as to the expected return of the assets in the portfolio. These portfolios implicitly put risk management at the heart of asset allocation and thus their recent appeal. This paper will serve as a comparison of four well-known risk based portfolio allocation methods; minimum variance, maximum diversification, inverse volatility and equally weighted risk contribution. Empirical backtests will be performed throughout rising interest rate periods from 1953 to 2015. Additionally, I will compare these portfolios to more simple allocation methods, such as equally weighted and a 60/40 asset-allocation mix. This paper will help to answer the question if these portfolios can survive in a rising interest rate environment.

PERFORMANCE ANALYSIS OF A TACTICAL ASSET ALLOCATION – Evidence from the Black–Litterman model based fixed income portfolio

Over time the demand for quantitative portfolio management has increased among financial institutions but there is still a lack of practical tools. In 2008 EDHEC Risk and Asset Management Research Centre conducted a survey of European investment practices. It revealed that the majority of asset or fund management companies, pension funds and institutional investors do not use more sophisticated models to compensate the flaws of the Markowitz mean-variance portfolio optimization. Furthermore, tactical asset allocation managers employ a variety of methods to estimate return and risk of assets, but also need sophisticated portfolio management models to outperform their benchmarks. Recent development in portfolio management suggests that new innovations are slowly gaining ground, but still need to be studied carefully. This thesis tries to provide a practical tactical asset allocation (TAA) application to the Black–Litterman (B–L) approach and unbiased evaluation of B–L models’ qualities. Mean-variance framework, issues related to asset allocation decisions and return forecasting are examined carefully to uncover issues effecting active portfolio management. European fixed income data is employed in an empirical study that tries to reveal whether a B–L model based TAA portfolio is able outperform its strategic benchmark. The tactical asset allocation utilizes Vector Autoregressive (VAR) model to create return forecasts from lagged values of asset classes as well as economic variables. Sample data (31.12.1999–31.12.2012) is divided into two. In-sample data is used for calibrating a strategic portfolio and the out-of-sample period is for testing the tactical portfolio against the strategic benchmark. Results show that B–L model based tactical asset allocation outperforms the benchmark portfolio in terms of risk-adjusted return and mean excess return. The VAR-model is able to pick up the change in investor sentiment and the B–L model adjusts portfolio weights in a controlled manner. TAA portfolio shows promise especially in moderately shifting allocation to more risky assets while market is turning bullish, but without overweighting investments with high beta. Based on findings in thesis, Black–Litterman model offers a good platform for active asset managers to quantify their views on investments and implement their strategies. B–L model shows potential and offers interesting research avenues. However, success of tactical asset allocation is still highly dependent on the quality of input estimates.

A comprehensive portfolio construction under stochastic environment

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. ^ A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: (a) increase the efficiency of the portfolio optimization process, (b) implement large-scale optimizations, and (c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. ^ The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. ^ The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH). ^

A Comprehensive Portfolio Construction Under Stochastic Environment

Prior research has established that idiosyncratic volatility of the securities prices exhibits a positive trend. This trend and other factors have made the merits of investment diversification and portfolio construction more compelling. A new optimization technique, a greedy algorithm, is proposed to optimize the weights of assets in a portfolio. The main benefits of using this algorithm are to: a) increase the efficiency of the portfolio optimization process, b) implement large-scale optimizations, and c) improve the resulting optimal weights. In addition, the technique utilizes a novel approach in the construction of a time-varying covariance matrix. This involves the application of a modified integrated dynamic conditional correlation GARCH (IDCC - GARCH) model to account for the dynamics of the conditional covariance matrices that are employed. The stochastic aspects of the expected return of the securities are integrated into the technique through Monte Carlo simulations. Instead of representing the expected returns as deterministic values, they are assigned simulated values based on their historical measures. The time-series of the securities are fitted into a probability distribution that matches the time-series characteristics using the Anderson-Darling goodness-of-fit criterion. Simulated and actual data sets are used to further generalize the results. Employing the S&P500 securities as the base, 2000 simulated data sets are created using Monte Carlo simulation. In addition, the Russell 1000 securities are used to generate 50 sample data sets. The results indicate an increase in risk-return performance. Choosing the Value-at-Risk (VaR) as the criterion and the Crystal Ball portfolio optimizer, a commercial product currently available on the market, as the comparison for benchmarking, the new greedy technique clearly outperforms others using a sample of the S&P500 and the Russell 1000 securities. The resulting improvements in performance are consistent among five securities selection methods (maximum, minimum, random, absolute minimum, and absolute maximum) and three covariance structures (unconditional, orthogonal GARCH, and integrated dynamic conditional GARCH).

Sampled Control for Mean-Variance Hedging in a Jump Diffusion Financial Market

In this technical note we consider the mean-variance hedging problem of a jump diffusion continuous state space financial model with the re-balancing strategies for the hedging portfolio taken at discrete times, a situation that more closely reflects real market conditions. A direct expression based on some change of measures, not depending on any recursions, is derived for the optimal hedging strategy as well as for the ""fair hedging price"" considering any given payoff. For the case of a European call option these expressions can be evaluated in a closed form.

Agentes comerciais: modelos de avaliação de risco e rentabilidade

Dissertação para obtenção do grau de Mestre em Engenharia Electrotécnica na Área de Especialização de Energia

System Level Simulation and Radio Resource Management for Distributed Antenna Systems with Cognitive Radio and Multi-Cell Cooperation

4th International Conference on Future Generation Communication Technologies (FGCT 2015), Luton, United Kingdom.

Honey, I shrunk the sample covariance matrix

The central message of this paper is that nobody should be using the samplecovariance matrix for the purpose of portfolio optimization. It containsestimation error of the kind most likely to perturb a mean-varianceoptimizer. In its place, we suggest using the matrix obtained from thesample covariance matrix through a transformation called shrinkage. Thistends to pull the most extreme coefficients towards more central values,thereby systematically reducing estimation error where it matters most.Statistically, the challenge is to know the optimal shrinkage intensity,and we give the formula for that. Without changing any other step in theportfolio optimization process, we show on actual stock market data thatshrinkage reduces tracking error relative to a benchmark index, andsubstantially increases the realized information ratio of the activeportfolio manager.

Metsäteollisuusyhtiön liiketoimintaportfolion synergioiden määrittäminen ja optimointi: Case UPM-Kymmene Oyj

Tutkielmassa selvitettiin UPM-Kymmene Oyj:n liiketoimintaportfolion muodostamia synergioita julkisiin lähteisiin pohjautuen. Synergioiden määrittämistä varten muodostettiin malli, jonka avulla määritettiin synergiat montaa eri liiketoimintaa harjoittavalle yhtiölle. Synergianäkemystä hyödynnettiin portfolion optimoinnissa uudella lähestymistavalla. Synergian mittausmallissa arvotettavan yhtiön liiketoiminta-alueille valittiin vertailuyhtiöt, joiden taloudellista suoriutumista arvioimalla pystyttiin määrittämään arvio synergian määristä. Tutkielman aihe synergioiden muodostumisesta ja mittaamisesta on tärkeä, sillä montaa liiketoimintaa harjoittavat yhtiöt oikeuttavat olemassa olonsa vetoamalla liiketoimintojen välillä syntyviin hyötyihin ja synergioihin. Synergiat ja portfolion optimointi ovat johdolle tärkeä aihe, sillä portfolion hallinta on yrityksen liiketoiminnan jatkuvuuden, taloudellisen suoriutumisen ja olemassa olon kannalta erittäin keskeistä Tutkielman tulosten perusteella UPM:n liiketoimintaportfoliossa muodostuvien synergioiden voidaan arvioida olevan vuosittain 44 miljoonasta eurosta 117 miljoonaan euroon. Portfolion optimoinnin tuloksena ainoastaan paperin ja vaneriliiketoimintojen suhteellista painoarvoa tulee laskea, mikä johtuu lähinnä näiden liiketoimintojen jatkuvasta huonosta taloudellisesta suoriutumisesta.

Valuuttasuojaus kansainvälisissä osakeportfolioissa - eurosijoittajan näkökulma

Tämän tutkimuksen tarkoituksena on selvittää eurosijoittajan näkökulmasta tehokkain strategia kansainvälisen osakeportfolion valuuttariskin suojaamiseen. Tutkimuksessa tarkastellaan akateemisissa tutkimuksissa eniten käsiteltyjä valuuttasuojausstrategioita ja pyritään tunnistamaan niistä tieteellisesti valideimmat metodit tutkimuksen empiiriseen osioon. Valuuttasuojauksen tehokkuutta tullaan mittaamaan niin riskin kuin tuoton näkökulmista. Empiirisessä osiossa käytetään aineistona kahdeksan eri valtion osakemarkkinaindeksien ja valuuttojen spot- ja termiinikurssien kuukausittaisia tuottoja niin, että tarkastelu tapahtuu euroalueen sijoittajan näkökulmasta. Tutkimuksen aikaväli on 31.12.2004 - 31.12.2010. Tutkimuksessa päädyttiin suosittamaan 50 % valuuttariskin suojausastetta eurosijoittajan näkökulmasta. Kyseinen strategia alensi parhaiten kansainvälisen sijoittajan portfolion riskiä tutkitulla aikavälillä, eikä strategia myöskään heikentänyt merkittävästi portfolion tuottoa. Absoluuttisella kumulatiivisella tuotolla mitattuna suojaamaton osakeportfolio oli tutkimuksen aikavälillä paras, johtuen pääosin vuoden 2010 eurokriisistä, jonka vuoksi euro heikentyi voimakkaasti muita valuuttoja vastaan. Ennen kriisiä ”selektiivinen” valuuttasuojausstrategia oli tuotoilla (sekä kumulatiivinen että riskikorjattu) mitattuna paras.

Risk Parity: A Modern Tool for Diversification

The purpose of this study is to examine how well risk parity works in terms of risk, return and diversification relative to more traditional minimum variance, 1/N and 60/40 portfolios. Risk parity portfolios were constituted of five risk sources; three common asset classes and two alternative beta investment strategies. The three common asset classes were equities, bonds and commodities, and the alternative beta investment strategies were carry trade and trend following. Risk parity portfolios were constructed using five different risk measures of which four were tail risk measures. The risk measures were standard deviation, Value-at-Risk, Expected Shortfall, modified Value-at-Risk and modified Expected Shortfall. We studied also how sensitive risk parity is to the choice of risk measure. The hypothesis is that risk parity portfolios provide better return with the same amount of risk and are better diversified than the benchmark portfolios. We used two data sets, monthly and weekly data. The monthly data was from the years 1989-2011 and the weekly data was from the years 2000-2011. Empirical studies showed that risk parity portfolios provide better diversification since the diversification is made at the risk level. Risk based portfolios provided superior return compared to the asset based portfolios. Using tail risk measures in risk parity portfolios do not necessarily provide better hedge from tail events than standard deviation.

Varallisuudenhoito indeksiosuusrahastoilla

Tämä Pro gradu–työ on käytännönläheinen sijoittajalähtöinen tutkimus varallisuudenhoidosta indeksiosuusrahastoilla. Tavoitteena on selvittää indeksiosuusrahastojen olemusta, niiden hyötyjä sekä mahdollisia haittapuolia. Toisena tavoitteena on rakentaa indeksiosuusrahastoista aikaisemman tutkimuksen pohjalta mallisalkku. Kolmantena tavoitteena on luoda Excelin portfolio-optimoinnilla salkku, jossa tutkitaan indeksiosuusrahastojen suoriutumista markkinoilla. Tämä optimointimetodi on rakennettu Mika Vaihekosken (2002) mukaan. Tutkimusmenetelmänä on empiirinen tutkimus. Tarkastelen aihetta pääosin liiketaloustieteellisestä näkökulmasta. Tutkimuksessa käytetään myös paljon rahoitusmarkkinalähtöistä näkökulmaa. Tutkimusaineisto koostuu kolmestakymmenestäneljästä Yhdysvaltain markkinoiden osake-, joukkovelkakirja- sekä raaka-aineindeksiosuusrahastosta. Aineisto on vuosilta 2006 – 2011 sisältäen 34x69 havaintoa. Portfolio-optimoinnissa käytetään neljää hyperbola-kerrointa. Empiiristen tutkimustulosten mukaan indeksiosuusrahastojen menneisyyden hyvät tuotot ennustaisivat hyvin tulevaisuuden hyviä tuottoja ainakin tämän tutkimuksen aikavälillä tammikuusta 2006 syyskuuhun 2011. Valinta-aikavälin 2006 – 2008 aineistosta muodostettu tangenttiportfolio menestyi suhteellisen hyvin hallussapitoaikavälillä 2009 – 2011. Tangenttiportfolio osoittautui ainakin tässä tutkielmassa käyttökelpoiseksi työkaluksi indeksiosuusrahastojen varallisuudenhallinnassa.

Diversification benefits for a Finnish non-industrial private forest investor: Real Estate Investment Trusts in the USA

This thesis examined both domestic and international forest investment options for a Finnish non-industrial private forest investor. The focus was on forest-based investment instruments. The influence of movements of currency exchange rates on foreign returns were also taken into account. Annual data from 1995 to 2011 was used. The main portfolio optimization model in this study was the Mean-Variance model but the results were also validated by using the Value at Risk and Expected Shortfall models. In addition, the exchange rate risk hedging was established by using one-week-maturity forward contracts. The results suggested that 75 % of the total wealth should be invested in Finnish private forests and the rest, 25 %, to a US REIT, in this case Rayonier. With hedging, the total return on the portfolio was 7.21 % (NIPF 5.3%) with the volatility of 6.63 % (NIPF 7.9%). Taxation supported US investments in this case. As a conclusion, a Finnish private forest investor may, as evidenced, benefit in diversifying a portfolio using REITs in the US.

Dynamic linkages of real estate and stock markets in Finland

Traditionally real estate has been seen as a good diversification tool for a stock portfolio due to the lower return and volatility characteristics of real estate investments. However, the diversification benefits of a multi-asset portfolio depend on how the different asset classes co-move in the short- and long-run. As the asset classes are affected by the same macroeconomic factors, interrelationships limiting the diversification benefits could exist. This master’s thesis aims to identify such dynamic linkages in the Finnish real estate and stock markets. The results are beneficial for portfolio optimization tasks as well as for policy-making. The real estate industry can be divided into direct and securitized markets. In this thesis the direct market is depicted by the Finnish housing market index. The securitized market is proxied by the Finnish all-sectors securitized real estate index and by a European residential Real Estate Investment Trust index. The stock market is depicted by OMX Helsinki Cap index. Several macroeconomic variables are incorporated as well. The methodology of this thesis is based on the Vector Autoregressive (VAR) models. The long-run dynamic linkages are studied with Johansen’s cointegration tests and the short-run interrelationships are examined with Granger-causality tests. In addition, impulse response functions and forecast error variance decomposition analyses are used for robustness checks. The results show that long-run co-movement, or cointegration, did not exist between the housing and stock markets during the sample period. This indicates diversification benefits in the long-run. However, cointegration between the stock and securitized real estate markets was identified. This indicates limited diversification benefits and shows that the listed real estate market in Finland is not matured enough to be considered a separate market from the general stock market. Moreover, while securitized real estate was shown to cointegrate with the housing market in the long-run, the two markets are still too different in their characteristics to be used as substitutes in a multi-asset portfolio. This implies that the capital intensiveness of housing investments cannot be circumvented by investing in securitized real estate.