Strategic Asset Allocation with Mean-Variance Optimization

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Literature Review

The literature that will be used in this study will be collected throughout the research process, however primarily at the beginning. Firstly, a general search on topics regard-ing pension funds, hedge funds and low interest rate environment will be performed and will be narrowed down and become more specific as we identify relevant topics. These searches will be performed in search engines including KTH Primo, Google Scholar, Diva portal and SSRN. Furthermore, articles and journals will also be part of our literature review. To increase validity of the study we will perform the searches in both Swedish and English in order to capture what research that have been con-ducted in the Swedish financial market as well as the foreign, in particular American market. We are aware that there are diﬀerences in the Swedish and foreign markets as size and regulations diﬀer and will therefore account for those diﬀerences in our study.
The following search words will be used in this study:
Pension funds, Hedge fund, Hedge fund allocation, Pension fund allocation in low interest rate environment, Hedge funds and low interest rate environment, Hedge funds and macro-economic variables, Optimal hedge fund allocation, Optimal portfolio theory, Eﬃcient frontier, Mean-variance framework, Expected Shortfall and Eﬃcient frontier

Data Collection

An important part of this study will be based on historical data. The data that will be required for this study are: information on asset allocation from pension fund’s annual reports for the studied period, historical; hedge fund-, bond-, real estate- and stock- prices.

Sample Time

To increase the validity of the study we will select historical data with a time horizon of 10-years in order to capture diﬀerent macro-economical states, including periods of: a prolonged decline of interest-rates, generally rising stock-prices, and generally de-clining stock-prices – starting from 2006. This selection is due to the impact all these states have on overall performance for investors and their strategic asset allocation.

Pension Fund’s Annual Reports

To get information on pension funds strategic allocation and how these have changed during the time period, the collection of their annual reports and the interpretations of these are to be conducted. This will help us answer research question 1. Swedish pension funds are obligated by Swedish regulations to provide an annual report to Länsstyrelsen and these reports are public and can be acquired from Länsstyrelsen. This fact supports the reliability of the study since the data gathering are fully replicable. Stockholms Länsstyrelse only store annual reports dated five years back in time and the rest is stored in Stadsarkivet. This means that Stockholm based pension fund’s annual reports will need to be acquired from Stadsarkivet. Since Länstyrelsen have a database of all Swedish pension funds, we will request a list of all pension funds with market capitalization information. We will then sort the list and collect the twenty largest – in terms of market capitalization – pension funds. Once the list is obtained we will contact Länsstyrelsen and Stadsarkivet and request the annual reports for each pension fund in our obtained list. From the annual reports we will be able to extract important information about allocation for each pension fund. We have chosen a time frame of 10 years, between 2006 and 2015, in order to recognize if the allocation policy have changed over time. The pension funds that will be studied can be observed in the table below.

Historical Prices

In order to answer our second research question; “what hedge fund allocation policy contribute to the highest risk-adjusted return for pension funds? », we will need to replicate a pension fund portfolio which typically consists of the asset classes: fixed income, real estate, stocks and hedge funds. Through the analysis of the annual reports we will be able to get information on the asset class allocation structure for pension funds. Index data will be used as a proxy for each asset class. This implies that our study will be based on secondary data (Collis and Hussey, 2013) meaning that we will need to use reliable databases. Since we will use index data for our study, we will need to ensure that their way of collecting data can be trusted and we will need to assure that we use indices that represent Swedish pension fund’s allocation strategies by using the correct markets. This is an important aspect to consider since we want to make a comparable study. Furthermore, monthly data will be used for each asset class.
Stocks & Equity Funds
When replicating a pension fund’s portfolio we will group stocks and equity funds together. We will however diﬀerentiate between domestic and foreign stocks and eq-uity funds.
Swedish stocks and equity funds will be represented by OMX Stockholm PI In-dex. This is an all-share index that represents the publicly traded stocks on the Stockholm Stock Exchange with the aim to represent the overall development of the market (NASDAQ, 2017).
Since Swedish pension funds allocate heavily towards Swedish stocks and equity funds we will choose to separate Swedish and foreign stocks and have two diﬀerent indices. Foreign stocks and equity funds will be represented by MSCI World Index . This index captures large and mid cap companies across 23 developed markets, including Sweden. With that said, we are aware that our replicating portfolio will be somewhat over-weighted towards Swedish stocks investments since MSCI World Index include Sweden, and this is something the reader should be aware of. We will not try to iden-tify the exact weighting towards each instrument that will give the best risk-adjusted return, we are rather looking to find the best allocation strategy.
The reason we will pick developed markets is because pension funds are risk averse and emerging markets could be regarded as high risk. Picking emerging markets would not represent a Swedish pension fund’s asset allocation in a correct manner.
Bonds
Domestic bond investments will be represented by OMRX All Bond Index. The OMRX index represents the value growth for liquid interest-bearing Swedish bonds. The composite is based on bonds issued by the Swedish National Debt Oﬃce and Swedish mortgage institutions (NASDAQ, 2010)
Foreign bond investments will be represented by Citibank’s World Government Bond Index (WGBI). This index measures the performance of fixed-rate, local cur-rency, investment grade sovereign bonds. It is a widely used benchmark that currently comprises sovereign debt from over 20 countries, denominated in a variety of curren-cies. The WGBI provides a broad benchmark for the global sovereign fixed income market (Citi, 2017).
Real Estate
Real estate investments will be represented by NASDAQ OMX Valueguard-KTH Housing INDEX (HOX). This index is based on hedonistic price model that is updated monthly. HOX collects that data from Mäklarstatistik AB and is based on actual transactions. However, HOX collects data only on residential real estate that are sold as single family homes.
Hedge Funds
Hedge Fund investments will be represented by Nordic Hedge Index Composite (NHX). NHX tracks Nordic hedge fund manager’s performance on a monthly basis. It is important to highlight that NHX is representative for the industry and not of an investment hedge fund strategy in particular. In this study, we have delimited the use of particular hedge fund strategies and used NHX as overall representation of the asset class. The index is an equally weighted index towards the following hedge fund strategies:
• Equity focused funds – funds trading equity and equity derivatives 3.
• Fixed Income funds – funds trading fixed income and derivatives3.
• Multi-strategy funds – funds are classified as multi-strategy if less than 80% of the fund’s activities comes from one particular classification category3.
• Managed Futures/CTAs – funds trading listed financial and commodity futures and foreign exchange, usually employing a systematic, model-driven approach3.
• Fund of hedge funds – funds investing in other hedge funds, regardless of fee structure3.

Quantitative analysis

The collected data from the annual reports will give us information about pension funds allocation policies, i.e. weightening towards each asset class. In order to get un-derstanding and inference about the risk-return structure for pension funds allocation policies, this information will be used together with portfolio theory (as explained in Section 3.4). And together with the collected historical data from the indices we will be able to calculate eﬃcient frontiers, which are an integral aspect in portfolio theory for the risk-return analysis.
By analyzing the eﬃcient frontier we will be able to analyze what type of hedge fund allocation policy that contribute to the highest risk-adjusted return for corpo-rate pension funds. One can state that portfolio A outperforms portfolio B if the expected return of portfolio A is greater than the expected return of portfolio B while the risk of portfolio A is lower or equal to portfolio B. It is therefore of interest to investigate the shape of the eﬃcient frontier for the purpose of this study. By definition, no rational mean-variance investor would choose to hold any portfolio that is not located on the eﬃcient frontier. The eﬃcient frontier can be defined as the locus of all non-dominated portfolios in the mean-variance space (Danthine and Donaldson, 2005).
Using historical data to predict future outcomes is a common approach but still an assumption that needs to be highlighted. We will use historical data as a proxy for future outcomes, meaning that we will assume that historical information is a good indication of future outcomes. Furthermore, we wish to highlight that these results will be an approximation as there are other risks that needs to be accounted for such as currency risk, illiquidity risk, and market risk.
The calculations for the quantitative analysis are to be conducted in MatLab. The built in PortfolioCVaR() function are used to create a PortfolioCVaR object for con-ditional value-at-risk portfolio optimization and analysis. The PortfolioCVaR object workflow for creating and modeling a CVaR portfolio is:
– first create the object using function PortfolioCVaR(),
– define the asset returns and scenarios using function setScenarios(),
– specify the CVaR portfolio constraints and bounds using functions setDefault-Constraints() and setBounds(),
– specify probability level which the conditional value-at-risk is to be minimized using function setProbabilityLevel(),
– and estimating the eﬃcient portfolios and frontiers using function estimateFron-tier().

Statistical tools

In the quantitative study there are certain statistical assumptions that has to be investigated. To assure that the inference from the quantitative analysis are valid following statistical tools will be used in the calculations.
Skewness
Skewness is a statistical measure used to describe the asymmetry of a distribution around the mean. A negative skew indicates that the tail on the left side of the probability density function is longer or fatter than the right side. Conversely, positive skew indicates that the tail on the right side is longer or fatter than the left side. Skewness measure does not distinguish between the shape of the distribution, i.e. long or fat. As a consequence, skewness does not obey a simple rule. For instance, a skewness value of zero means that the tails on both sides even out overall implying a symmetric distribution. However, this could also mean that one tail is long but thin and the other being short but fat.
Kurtosis
Kurtosis is another statistical measure used to describe the shape of a given distri-bution. This measure is related to the tails of a distribution and a higher kurtosis number is the result of infrequent extreme deviations (or outliers), as opposed to frequent modestly sized deviations.
Drawdown
Drawdown is a common risk measure that measures any time the cumulative returns dips below the maximum cumulative return. Drawdowns are measured as a percent-age of the maximum cumulative return, in eﬀect, measured from peak (top) to the subsequent trough (bottom).

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Source Criticism

One way to ensure the use of high quality sources is by finding three separate sources of information that leads to the same conclusion. This method will be used to the highest degree possible throughout this study. In the case where three sources are diﬃcult to find, we will at least use two diﬀerent sources that leads to the same conclusion. A single source that cannot be confirmed by another will thus not be used. We will use published books and articles as our primarily sources.

Reliability

According to Collis and Hussey (2013) results are considered to be reliable if a re-peat study obtains the same results as the original study. For an empirical study of quantitative nature it is therefore important to clearly describe the research design. The first part of this study is based on annual reports that can be obtained from Länsstyrelsen and Stadsarkivet as they are open to the public. This means that any-one would be able to obtain the same results given that the same pension funds are analyzed. However, some minor deviations might happen since interpretations and assumptions on what investment category an investment should represent will need to be made when none or limited information is available about a specific investment.
The second part of the study would also fulfill the reliability requirement as we have specified each index that will be used to represent each investment category. We have also specified the studied period and the research design, i.e. maximizing the risk adjusted return based on an appropriate risk measure. Although some deviations regarding the exact weighting towards each asset class might take place, the same conclusions will be obtained. This means that this study is reliable and repeatability can be achieved.

Validity

Validity refers to the quality of a test and if it measures what is purported to measure (Collis and Hussey, 2013). In a quantitative study an important part is the use of a suitable method. In this study, we will investigate the assumptions of the mean-variance framework and based on the results choose appropriate risk-measure that account for the nature of the distributions of the returns for the studied asset classes.

Literature & Theoretical Framework

In this section we will present background information about Hedge funds and Pension funds, review previous research on low-interest environments and on asset allocation to hedge funds during such conditions, and lastly present relevant theory connected to the subject to be studied.

What is a Hedge Fund

Hedge funds are a part of the investment category that are seen as ‘alternative’ when compared to traditional asset class investments, e.g. mutual funds, equity and fixed income. Generally, alternative investments has more unregulated investment policies (AIFM – Directive 2011/61/EU). Hedge funds began as investment partnerships that could take long and short positions. Since then they have evolved into multifaceted organizational structures that are diﬃcult to put into simple definitions. However, a number of features that characterizes hedge funds includes flexible investment strate-gies, relatively sophisticated investors, substantial managerial investments, and strong managerial incentives (Ackermann et al., 1999).
Ackermann et al. (1999) continues explaining that, due to a limited number of in-vestors, hedge funds typically are largely unregulated. This allows them to be ex-tremely flexible in their investment options allowing them to use short selling, lever-age, derivatives, and highly concentrated investment positions, in order to enhance returns or reduce systematic risk. They also have the option to move quickly across diverse asset classes in an attempt to time the market.
These structural aspects of hedge funds are in sharp contrast to the organizational structure of the more common investment option in mutual funds. Mutual funds are often regulated by the the financial supervisory authority4 and have prospectus disclosure requirements, in order to keep their investors informed about their invest-ments and also limit potentially risky activities. These regulations and disclosure requirements generally limits mutual funds of using derivatives, short selling, and concentrate investments.
A downside for this flexibility that hedge funds are favoured by, can be that they are faced with advertising restrictions together with general capital inflow diﬃculties. Mutual funds and other traditional investment institutions can gather a lot of fund investors by promoting simple understandable strategies. Mass selling of hedge fund strategies tend to be more diﬃcult to promote since these strategies usually are too complex for the typical investor to comprehend (Stulz, 2007). Hedge funds there-fore typically attract mainly institutions and wealthy individual investors. These are investors who agrees to conditions which include higher minimum investment limits and liquidity lock-up periods.
Hedge funds are also characterized by strong performance incentives. Lan et al. (2013) studies the economics of hedge funds and in particular the management com-pensation. In their paper they explain that the typical management compensation for hedge funds features both management fee and performance-based incentive fees. The management fee is charged as a fraction of the Asset Under Management (AUM), e.g., 2%. However, what often diﬀerentiates hedge funds from mutual funds is the incentive fee. This fee is calculated as a fraction of the fund profit, e.g., 20%. The “two-twenty” compensation is often viewed as a industry norm.
Fung and Hsieh (1997) investigates the characteristics of the dynamic trading strate-gies of hedge funds, where they also discuss compensation structures as an underlying factor of the fund performance. For mutual funds, most managers have investment mandates with relative return targets. As they are typically limited to low or no leverage and also constrained to hold assets in a well-defined number of asset classes, their mandates are to meet or exceed the returns on these asset classes, e.g., a stock market benchmark index (Fung and Hsieh, 1997; Al-Sharkas, 2005). Knowing that the fund inflows have been going to the top-rated funds, rated according to their re-spective benchmark, and that mutual fund managers are compensated based on the amount of AUM. Thus, managers have an incentive to outperform their benchmark in order to increase their AUM and ultimately their compensation. This implies that they are likely to generate returns that tend to be highly correlated to the return of these benchmarks.
Hedge fund managers on the other hand derive a great deal of their compensation from incentive fees, paid only when the manager makes positive return. Also, a com-mon addition in their incentive contracts is the “high-water-mark” (HWM) feature, which keeps track of the maximum value of the invested capital and requires them to make up all previous losses before an incentive fee is paid (Fung and Hsieh, 1997). These conditions typically gives hedge fund managers investment mandates with ab-solute return targets, regardless of the market environment. To achieve absolute return they utilize their more flexible investment options that allows them to choose among more asset classes and to employ dynamic trading strategies that frequently involve leverage, short sales, and derivatives. This implies that these managers are more likely to generate absolute returns, contrary to mutual funds more relative re-turn.
Since hedge funds have a greater flexibility in their investment options it allows man-agers to employ various investment strategies. In order to compare performance, risk and other characteristics, it is helpful to categorize hedge funds by investment strategies. A common way to classify hedge funds was described by Fung and Hsieh (1997) as a distinction of the “style” and “location” of the fund. Here, “style” refers to the type of position the fund manager is taking, such as taking long and/or short security positions e.g., betting on particular type of corporate events, or maintaining market neutrality. The concept of style is not relevant with mutual funds since im-plicitly this categorization has buy-and-hold, long-only style. A standard style here would then be something like; small cap value stock or large cap growth stocks. The stylistic diﬀerences for mutual funds involve only the location variable. With “loca-tion” it is referred to which assets and asset classes the strategy is applied to, such as equity, fixed income, currencies, commodity, as well as the geographical location. Another related approach is to separate hedge funds according to whether they are directional or market neutral (Connor and Woo, 2004). Directional funds take bets on market movements and consequently have a return strongly correlated with the market. Market neutral funds on the contrary keep a low correlation with the overall market return by applying derivatives and short positions. Hedge fund strategies are continually changing, limiting the attempts of establishing any formal classification for hedge funds. Hedge Fund Research (HFR), one of the main hedge fund databases, has however constructed a ‘Strategy Classification System’ for all investment man-agers present in their HFR Database, grouping them under five broad themes: equity hedge, event driven, relative driven, macro, and fund of hedge funds.

Table of contents :

1 Introduction
1.1 Background
1.2 Problematization
1.3 Purpose
1.4 Research Questions
1.5 Expected Contribution
1.6 Assumptions and Delimitations
1.7 Subsequent Chapters
2 Methodology
2.1 Research Process
2.2 Literature Review
2.3 Data Collection
2.3.1 Sample Time
2.3.2 Pension Fund’s Annual Reports
2.3.3 Historical Prices
2.4 Quantitative analysis
2.4.1 Statistical tools
2.5 Source Criticism
2.6 Reliability
2.7 Validity
3 Literature & Theoretical Framework 1
3.1 What is a Hedge Fund
3.2 What is a Pension Fund
3.3 Previous Research
3.3.1 Allocation towards Hedge Funds
3.3.2 Responses to Low Interest-Rate Environment
3.4 Portfolio Theory
3.4.1 Strategic Asset Allocation with Mean-Variance Optimization
3.4.2 The Assumptions of Mean-Variance Optimization
3.5 Conditional Value-at-Risk
4 Results
4.1 Studied Pension Funds
4.2 Pension Fund’s Asset Allocation
4.3 Distribution of Asset Returns
4.4 Cumulative Return of Indices
4.5 Efficient Frontier
4.6 Cumulative Portfolio Return
4.7 Drawdown
5 Discussion
5.1 Pension Funds Asset Allocation During the Period
5.1.1 Comparison to Previous Research and Theory
5.1.2 Analysis of Method
5.2 Optimal Allocation Policy
5.2.1 Comparison to Previous Research
5.2.2 Analysis of Method
6 Conclusion, Implication and Future Research
6.1 Answering the Research Questions
6.2 Implications
6.3 Future Research
References
A Appendices