The Value of Financial Advisory Services

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IN THE FIELD OF TECHNOLOGY DEGREE PROJECT

INDUSTRIAL ENGINEERING AND MANAGEMENT AND THE MAIN FIELD OF STUDY

INDUSTRIAL MANAGEMENT, SECOND CYCLE, 30 CREDITS STOCKHOLM SWEDEN 2018,

The Value of Financial Advisory Services

VIKTOR CARLSON

KTH ROYAL INSTITUTE OF TECHNOLOGY

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The Value of Financial Advisory Services

by

Viktor Carlson

Master of Science Thesis TRITA-ITM-EX 2018:152 KTH Industrial Engineering and Management

Industrial Management SE-100 44 STOCKHOLM

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Värdet av finansiell rådgivning

Viktor Carlson

Examensarbete TRITA-ITM-EX 2018:152 KTH Industriell teknik och management

Industriell ekonomi och organisation SE-100 44 STOCKHOLM

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Master of Science Thesis TRITA-ITM-EX 2018:152 The Value of Financial Advisory Services

Viktor Carlson

Approved

2018-05-30

Examiner

Terrence Brown

Supervisor

Tomas Sörensson

Commissioner Contact person

Abstract

Financial advisory services currently face many challenges such as adapting to regulations, competing against robot advisors and offering qualitative advice. We use a utility function based on the clients' risk preferences and investigated the value added by advisory services. The data represents real clients that received financial advisory services from an advisory firm, which gives this thesis a unique accuracy. For the calculations we simulated outcomes of the portfolios and computed key values pertaining to the investors' financial positions. Our calculations show that investors on average gain corresponding 1.66 % per year in risk free return on their investments from advisory services. In addition, we show that the client's value of advisory service increased with respect to the investor's risk level and time horizon of investment.

Key-words: Financial Advisory Service, Utility Theory, Asset Allocation, Asset Location, Risk Aversion.

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Examensarbete TRITA-ITM-EX 2018:152 Värdet av finansiell rådgivning

Viktor Carlson

Godkänt

2018-05-30

Examinator

Terrence Brown

Handledare

Tomas Sörensson

Uppdragsgivare Kontaktperson

Sammanfattning

Aktörerna inom finansiell rådgivning står för närvarande inför flera utmaningar, att anpassas efter regleringar, konkurrera mot robotrådgivare och erbjuda hög kvalitet i rådgivningen. Vi har använt en nyttofunktion baserad på kunders riskpreferenser och utrett vilket värde som finansiell rådgivning tillför. De data som använts representerar verklig kunddata från ett rådgivningsföretag, vilket ger denna studie en unik träffsäkerhet. Beräkningarna av nyckeltal för investerarnas finansiella position har gjorts genom simulering av portföljer. Våra beräkningar visar att finansiell rådgivning ger investerare i genomsnitt motsvarande 1.66 % i ökad riskfri avkastning per år efter avgifter och skatter.

Dessutom vi visa att rådgivarnas tillförda värde ökar med avseende på investerarnas risknivå och tidshorisont.

Nyckelord Finansiell rådgivning, nyttofunktion, tillgångsallokering, skattemiljö, riskaversion.

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Acknowledgement

First of all, I want to thank my supervisor Tomas S¨orensson and the Department of In- dustrial Economics and Management at Royal Institute of Technology (KTH) for their valuable inputs during the working process. I also want to thank my supervisor at the financial institution that helped me with the data and suggested approaches for the analysis. Last but not least, thanks to my great friend Alexander Singer who helped proofread the language before publication.

Stockholm, May 2018 Viktor Carlson

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List of Figures

1 The Shape of Utility Functions . . . 10

2 Q-Q plots . . . 16

3 Distribution of Risk Aversion . . . 25

4 Yearly Value Added by Advisory Service . . . 31

5 Distribution of Risk Aversion . . . 43

6 Historical STIBOR and Swedish Bank Deposite Rate . . . 45

7 Residual of Regression 1 . . . 46

8 QQ-plot Regression 1 . . . 46

9 Residual of Adjusted Regression 1 . . . 47

10 QQ-plot Adjusted Regression 1 . . . 47

11 Residual of Regression 1 . . . 48

12 QQ-plot Regression 2 . . . 48

List of Tables

1 Result of Regression 1 . . . 28

2 Result of Adjusted Regression 1 . . . 29

3 Result of Regression 2 . . . 30

4 Result of Regression with Parallel Shift of Parameter ρ . . . 32

5 Parameter Values per Risk Group . . . 44

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1 Introduction

This section gives an introduction to the industry of financial advice and briefly compares human and robot advisors. Subsequently, the problem statement and purpose of this thesis is described. Finally, the research question with limitations will be presented.

1.1 Background

In the last couple of years, the financial industry has faced many regulatory challenges.

One of these is MiFID II which took effect on January 3rd 2018. MiFID II imposes comprehensive regulations that have a profound effect on the entire industry on different levels (Regulation EU, 2014). As a result of this there are new stricter requirements for financial advisors (ESMA, 2017). Furthermore, the financial advisory industry faces new challenges as a result of the establishment of many new participants who offer financial robot advice (EY, 2015). Therefore human financial advisors must both fulfill the quality requirements regulated by law and at the same time compete against robot advisors that can offer relatively low-price financial services. Robot advisors that rely on algorithms for customer recommendations can easily decrease the marginal cost to a level where physical advisors cannot compete. Therefore it is reasonable that the physical advisor’s primary competitive advantage is the offer of individually designed solutions for every particular customer’s specific needs on a level that is not possible for robots.

Many robot advisors focus on optimizing the customer’s portfolio by using some applica- tion of Markowitz (1952) Modern Portfolio Theory for mean-variance analysis. However, financial advice consists of more than portfolio optimization. There are many studies on this topic and it is common to divide financial advice into different categories based on the type of advice. One example is KinniryJr. et al. (2016) who compute the value of financial advice, which is referred to as Advisor’s Alpha in the Vanguard report. They divide it into the following components: Asset allocation, Cost-effective implementation, Rebalancing, Behavioral coaching, Asset location, Withdrawal order for client spending from portfolios and Total-return versus income investing. Afterwards, they estimate the value of Advisor’s Alpha for each component separately.

Beyond this Vanguard report, many other participants have estimated the value of financial advice. Another participant who has conducted similar research is Morningstar. They divide Financial advice into the following aspects: Asset Location and Withdrawal Sourc- ing, Total Wealth Asset Allocation, Annuity Allocation, Dynamic Withdrawal Strategy and Liability-Relative Optimization (Blanchett and Kaplan, 2013). Different organizations within the industry, who have interests in this field stemming from each organization’s own financial service offers, have conducted research with various results. Nevertheless, these different studies categorize financial advice into similar categories.

Most of the studies are similar in the regard that they analyze every category of financial advice separately. They also compute it in a context where no other parameters affect the result. For example, the common measure for the value of financial advice is the potential increase of expected return with constant risk. In this way, Rebalancing is computed from

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simulations of market data, but only with respect to measuring potential portfolio value.

Consequently, there are similar methods for the other categories (KinniryJr. et al., 2016).

When a financial advisor provides his services to clients he primarily conducts a background analysis of the client’s financial needs and goals, understands the client’s desired risk level and then provides his recommendations. The recommendations are based on the prior goal and risk assessment, therefore these are essential steps in the process. Pro- fessional advisors have computer programs with algorithms capable of recommending an optimal portfolio as the output in a model. The input in these programs often consists of financial mathematical parameters, which are necessary to conduct the calculations.

1.2 Problem Statement

Assessing the client’s risk level, is by nature non-trivial partly because there are several risk measure such as volatility, Value at Risk, Expected Shortfall etc, that measure different aspects of risk. Also, because the concept of risk is abstract and not easily defined, it is difficult for investors to translate their perception of risk to parameter values in a financial portfolio optimization model (Hult et al., 2012). Furthermore, in order to give correct and qualitative advice, the financial advisor must take into account that the client’s personal finances are influenced by more factors than just the portfolio’s development.

This statement is true for both the income- and expenditure side of the particular client’s personal income statement. This is especially applicable in the current situation where Swedish households’ average Leverage-to-Value (LTV) was 64 % in 2016 and the Swedish housing market has seen a steep rise in prices in recent years. Housing and the associated mortgage for many Swedish households a significant part of the personal balance sheet (Finansinspektionen, 2017a).

In addition to being complicated, translating the investor’s risk preferences to parameter values must be done with respect to the investor’s financial needs and goals. Normally, the advice is measured by expected return and risk. Although the assumptions of return and correlation between assets in a portfolio is not obvious, the method for computing for example expected return is straight-forward. However, because portfolio optimization only includes the specific portfolio, it does not provide the whole picture of the investor’s personal finances.

The added value for the customer that hires a financial advisor depends - for obvious reasons - on the skills of the advisor and the investor’s current financial position. For example, if the client currently holds a theoretically efficient portfolio that is well in line with his preferences, then the financial advisor would not be able to add value and therefore the financial position of the investor would not change as a result of the advisory services.

These aspects are also important when evaluating the value of financial advice.

As a result of the complexity of financial advisory services, there is a great interest in investigating how the investor’s entire financial position is affected by professional financial advice. This is essential when evaluating the value of these services. Therefore, there are many aspects of financial advisory services, many new competitors in the industry and

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new regulations. The future of the industry is strongly dependent of the value an advisor can provide to their clients. The problem is knowing whether or not financial advisors add value and the potential size of this value.

1.3 Purpose

The purpose of the study is to measure the accuracy and value of financial advice with respect to the client’s preferences.

1.4 Research Question

This thesis is based on following research question:

• How is the investor’s financial position affected by financial advice, under the condition that the investor adheres to the advisor’s recommendations?

In the question above, the investor’s financial position is defined as the position of investor’s portfolio, including current position of all non-financial assets such as real estate and debt of the investor. The change of the portfolio value is measured by the investor’s utility of potential outcomes depending on the advisory service.

1.5 Contribution

Since the new regulations MIFID II took effect on January 3rd 2018 (ESMA, 2017), the topic is currently of high interest within the industry. There are many prior studies regarding financial advice. Even though many of these studies are conducted by organizations with specific interests in the results, they provide a balanced and reasonable view on the value of financial advice. However, most of the studies are conducted from an American point of view and focus on the potential value of each category of financial advice, i.e. asset allocation, asset location etc. This thesis will not investigate the potential of financial advisory services, but how these advisory services affect the investor’s financial position.

We will use real customer data from a large participant in the industry which provides this thesis with a unique opportunity to achieve a high level of accuracy. This detailed data will allow us to analyze the entirety of the investors’ financial positions and not only their portfolios. We will focus on comparing investors’ financial positions with respect to the particular investor’s preference to risk and expected return. We will be the first ones to investigate real Swedish investors’ financial positions in this way.

1.6 Limitations

When we investigate how the investor’s financial position changes, we will use a model we have developed based on financial theory. For obvious reasons, it is not possible to apply a single advisory method that every advisor uses. In the same way, no universal method for simulating the future of the market exists. Because of its complexity and stochastic properties, different participants have different methods for simulation. We will use one acceptable way based on the available literature.

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1.7 Delimitations

Our assertion that we will include the investor’s entire personal finances is not entirely true. It is not possible to include all assets outside the portfolio since we do not have data for every investment. However, in the advisory process, the client states his relevant assets and loans. Thus, the available data that an advisory firm has access to is used. In addition, financial advisory service could include everything from pension withdrawal to savings. This thesis is limited to investment advice.

Another delimitation in this thesis is that we are not conducting any macroeconomic analysis. This will impact the advisory model because the recommendations will not depend on subjective beliefs in the market. Every advisor may have different views on the future of the markets. Also, we will not decide if some industries or categories of funds should be over- or underweighted. In our advisory model, we choose between some comprehensive funds where we assume that the particular fund is well diversified against different markets and industries.

2 Institutional Framework

This section states the laws and regulations applicable to the industry in which financial advisors operate. First, the tax options are described and subsequently regulations regarding the financial advisory process.

2.1 Tax Environment

For Swedish investors, there are three tax alternatives for the portfolio¹: Traditional Brokerage Account, Investment Savings Account (ISK) and Endowment Insurance. Below, these three alternatives will be explained.

2.1.1 Traditional Brokerage Account

The oldest way that is currently used to hold securities is in a traditional brokerage account. This tax environment is the standard and follows the laws for capital gains. In this segment, the taxes on capital gains is 30 % according to Inkomstskattelag (1999:1229) 65 chap. 7 §. In this law, 41 chap. 1-7 §§ regulates capital gains for financial assets.

The tax is levied based on the profit generated by an asset (44 chap. 13 §). Investors are entitled to deduct losses from their capital gains, which means that losses from one asset can with the same amount, reduce the tax from a profit of another asset. The taxation of the income is attributed to the calendar year the investor can access the cash, i.e.

when the investor has sold assets and received the cash. The deduction of losses is based on the year that the losses are definitive and cannot be postponed (44 chap. 26 §). If assets currently are held in a traditional brokerage account and are transferred to an ISK, the assets are considered to be sold and any gains or losses are taxable (44 chap. 8a §) (Sveriges.Rikes.Lag, 2017).

1We exclude pension savings accounts since these departs in many ways from the standard regulations and is not of interest in our research.

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Thus, capital gains from financial assets are calculated when they become accessible to the investor and then 30 % taxes are owed on the profit after losses are deducted. Another opportunity for investors when calculating their tax is to use The Standard Method, which can only be applied to shares of stock or index bonds. This method is favorable for the investor if the stock has increased in price by more than 400 % and is calculated as if the investor’s purchasing price was 20 % of the selling price. With both methods, the investors can deduct their brokerage commission and other charges related to the transactions (Skatteverket, 2018a). Furthermore, dividends are considered capital gains as above (57 chap. 2 §) (Sveriges.Rikes.Lag, 2017).

2.1.2 Investment Savings Account (ISK)

Investment Savings Account was introduced as an option for investors in Sweden in 2011 (Lag (2011:1268) om investeringssparkonto). Investors can hold cash and investment assets in their ISK according to 16 § (2011:1268) (Sveriges.Rikes.Lag, 2017). Assets that are acceptable in ISK is defined in 6 § as financial instruments that are traded on a regulated market or a similar market outside the European cooperation area, financial instrument that is traded on a MTF-platform or shares of a fund or special fund Lag (2017:700) (SFS 2017:1146).

The taxation of assets in ISK is calculated based on the entire capital regardless of profits or losses. The taxes are calculated in two steps: (1) calculate the standard income when holding assets in investment savings account and (2) capital gains are increased by this amount in the investors tax return. The taxes for capital gains are currently 30 % in Sweden (Inkomstskattelag (1999:1229) 65 chap. 7 §). The first step is performed by using a quarter of the sum of the market value for the following four categories, as defined in Inkomstskattelag (1999:1229) 42 chap. 37 §: assets that are kept in the ISK at the beginning of each quarter during the calendar year, cash transferred into the ISK during the calendar year, assets that are transferred into an ISK from another tax environment and assets that are transferred into an ISK from other investors. This sum is then multiplied by the government bond rate at the end of November the calender year before, increased by one percentage point (Inkomstskattelag (1999:1229) 42 chap. 36 §). There is one exception, which is that the lowest multiplication factor is 1.25 % according to Lag (2017:1250) (Sveriges.Rikes.Lag, 2017). I.e. if government bond rate is under 0.25 %, the multiplication factor 1.25 % is used. This is the standard income amount that is subsequently taxed by 30 %.

2.1.3 Endowment Insurance

Endowment Insurance is a life insurance where investors can hold assets. A crucial difference between ISK and traditional brokerage account is that the insurance company is the formal owner of the assets in the insurance. This means that the investor does not pay taxes when filing. Instead, the insurance company pays taxes for the Endowment Insurance and takes the corresponding amount of capital from the investor’s portfolio (Skatteverket, 2018b). Because of the fact that Endowment Insurance is an insurance agreement between

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the investor and an insurance company, the agreement can differ between participants. For example, there could be agreements locking in assets for a predetermined period of time.

Also, some charges can be associated with the agreement. It is easy to see the difference if one compares the offers of some participants on the Swedish market (Avanza, 2018).

The taxes that the insurance company have to pay and that are taken from the investors portfolio is calculated in the following way. The market value of the initial value of a calender year is added to every deposit during the first half of the year. Then half of the deposits in the second half of the year are added. This amount is computed at same way as for ISK, i.e. multiply it by the government bond rate plus one percentage point.

Finally 30 % of this amount is levied in tax (Avanza, 2018).

2.2 Advisory Service Regulations

The financial advisory industry is highly regulated. One of these regulations and the most important for this thesis is ”lag (2003:862) om finansiell r˚adgivning till konsumenter ”, which includes laws about the advisory service process to consumers (Lindeblad, 2015).

Recently, the regulation became more extensive due to MiFID II (Regulation EU, 2014).

In the financial advisory service process to clients, there are regulations regarding which financial instruments that are recommended. Two key concepts are that the client is deemed appropriate for trading with the recommended instruments and that these recommended instruments are in line with the client’s needs and desired risk level (Finansinspektionen, 2017c). Securities institutions must define target groups for each instrument with respect to the client’s risk tolerance, knowledge, experience and investment goals. This regulation also applies to distributors of financial instruments (Finansinspektionen, 2017b). The advisor must ensure that the advice is suitable for the client according to ”Lag (2007:528) om v¨ardepappersmarknaden” 9 chap. 28 §. The suitability explanation has to be documented (Sveriges.Rikes.Lag, 2017). Another aspect of the regulation according to MiFID II is that receiving commission from third parties is prohibited when providing independent financial advisory service (Lindeblad, 2015).

3 Literature Review

This section explains the concepts that will be used in this thesis. The first subsection describes some key aspects of how advisors can add value for investors, including wealth management and behavioral finance. The next subsection deals with properties of the stock market and some time series, while the final subsection introduces the risk measure toolbox.

3.1 Wealth Management

There are many ways for advisors to create value for investors. Some financial services that can potentially create value for investors are asset allocation, risk diversification, instructions discouraging purchases of assets deemed expensive or sales of assets deemed cheap (KinniryJr. et al., 2016). This thesis focuses on how the investors’ financial positions change when receiving financial advisory services and is limited to the theoretical positions

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on the day this service is received. Thus, not all aspects of financial advice, such as coaching and rebalancing of portfolios in the future, is relevant in this context. Below, the relevant theoretical aspects of this thesis will be introduced.

3.1.1 Risk Diversification and Asset Allocation

In the financial industry, one central concept is Risk Diversification. The simplest form of risk diversification is Markowitz (1952) mean-variance analysis, which assumes that an investor wants to maximize the expected return and minimize the variance of the portfolio.

If values of the assets’ expected returns, variance of returns and correlation of returns are given, one can solve the optimization problem above and compute the efficient frontier.

When combinations of assets are used, the total risk can significantly change compared to simply looking at one asset. Depending on the correlation between the assets, it is possible for two assets with high variance of return separately to have a low cumulative variance of return. In this way, the goal of risk diversification is achieved (Elton et al., 2014). However, in the process of risk diversification, there are almost infinitely many inputs of different assets because of the large supply of stocks on the market. This makes the truly optimal diversification difficult to find.

A similar concept to risk diversification is Asset Allocation which divides investments into different classes of assets. In the investment process, asset allocation is a key concept when adjusting a portfolio to a given risk. The same issue is present as in risk diversification with the large amount of asset on the market, which makes it difficult to create an optimal allocation. Nevertheless, given a set of assets, e.g. if the advisor or client limits the supply to a given input of assets, the asset allocation can be done (Elton and Gruber, 1999).

In this way, the value that a financial advisor can add to a investor’s portfolio can be computed if an efficient portfolio is composed from an investor’s risk preferences and subsequently compared to the investor’s actual portfolio.

In addition to the theoretical aspect of asset allocation at a given risk level and set of assets, when the concept is applied on advisory service, the risk level can be based on the investor’s risk tolerance or a combination of preferences and tolerance. Blanchett and Kaplan (2013) argue for the last one, a model where a combination of the investor’s risk preferences and risk tolerance should be the underlying metric for asset allocation.

There is potential value to be added to investors’ portfolios by asset allocation and risk diversification. How much value an advisor can add is not definitive, but participants in the market have made various calculations. KinniryJr. et al. (2016) determine the value added by asset allocation to be significant but there is too much variation between different investors to give any general number. Blanchett and Kaplan (2013) computed the value added for total wealth asset allocation, i.e. when including the investor’s total wealth and not just the portfolio. They found that advisory service of total wealth asset allocation can generate an additional 6.43 % of return to investors and corresponding risk adjusted return on 0.45 % per year. A similar approach where total wealth is investigated was conducted by Blanchett and Straehl (2015) who found that the difference in asset

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allocation when just optimizing the portfolio and including assets outside the portfolio is significant. In their approach, they sometimes found that the human capital accounted for the largest part of wealth, i.e. future income and non-financial assets. In these cases, the profit from financial advisory services will vary a lot depending on salary, industry etc. However, the conclusion is clearly that this aspect has a relevant impact on the profit generated by advisory services.

3.1.2 Asset Location

Another aspect of the financial advisory service is the asset location as this regulates the tax environment of the investment. One should note that because of the nature of asset location, different participants offer different services for investors. Thus, they have different interests that can influence their opinion. In essence, only these participants’

opinions and government investigations are available in this field. From the institutional framework, it appears that there are three options. Taxes in a traditional brokerage account are based on the profit and the other two options are taxed with respect to the total amount of capital. Furthermore, losses in a traditional brokerage account can be offset against profit. ISK has been the best option for most investments since it was introduced. The main reasons is because the government bond rate has been relatively low and the stock market has performed well in general. Therefore, because ISK is not taxed based on profit but by the total capital it has been the preferred tax environment (Finansdepartementet, 2017). Beyond these aspects, Hemberg (2015) also argues for the investor’s freedom when choosing ISK because the investor can sell and swap assets without declaring and paying taxes for the profit. Because of these advantages, Waldenstr¨om et al.

(2018) argue that this option is too attractive for investors and reach the conclusion that ISK and Endowment Insurance should be abolished.

The main aspect of the tax environment should be to maximize the wealth for investors, rather than minimize the taxes. Because taxes in a traditional brokerage account is paid when the investor sells his assets, an investor can infinitely hold assets in a traditional brokerage account without paying taxes. The result of this, under the condition that the value of assets increases, is that the deferred taxes in the personal balance sheet will increase and generate return. This is in contrast to ISK and Endowment Insurance, where the investor must pay taxes every year. Nyman (2018) uses this aspect and cites for scenarios where traditional a brokerage account is favorable for the investor. These scenarios are either if the investment decreases in value or shows small increases in value or if the investment’s time horizon is very long. However, in the most scenarios, where investors invest in the short and medium term and with high risk, ISK provides a favorable tax environment.

For investors, there is no doubt that they have many options and depending on the outcome, the choice of asset location could imply a large difference in wealth for the investors.

This also motivates the relevance of this aspect in financial advisory service.

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3.1.3 Behavioral Finance

One key aspect in modern financial research is the field behavioral finance which focuses on the psychology of investing (Rom, 2000). Because of the nature of the psychology of investing, it is a wide area which includes many aspects and different researchers have explained behavioral patterns with different models. One of these is Howard (1968) who generalizes decision-making with three approaches: normative-, descriptive- and prescrip- tive analysis. For the financial advisors, this field has become important because their clients may take emotional decisions which will not serve their interests or investment goals (Kahneman and Riepe, 1998).

One aspect of behavioral finance is overconfidence. This concept means that investors tend to overestimates their knowledge and abilities (Ackert and Deaves, 2010). Kahneman and Riepe (1998) describe the concept by constructing a thought experiment where the reader is asked to make a 98 % confidence interval of the value of the Dow Jones one month from now, where there is 1 % probability that the outcome is higher and consequently 1 % that the outcome is lower. If this confidence interval was well calibrated, 98 % of outcomes would be correct and 2 % would be surprising. They mean that studies of this kind show that in 15-20 % of cases, investors are overconfident of their estimates. A closely related concept to overconfidence is optimism. Optimists tend to both overestimate their skills and underestimate bad outcomes. In combination with overconfidence, investors with these characteristics underestimates risk and believe that they have more control than they in fact have (Kahneman and Riepe, 1998).

In addition to these beliefs of investors, studies have shown that investors tend to overreact to favorable events when occurring. One of the first studies in this field applied to the stock market is done by Bondt and Thaler (1985) who found that the best performing stocks in the past are underperforming in the future. From this result, they argue for the phenomena that most investors underestimate the mean reverting effect and overreact to historical return. The psychology behind it is that people tend to respond in a way where they believe the new information highly outweighs what was known before (Tversky and Kahneman, 1974). Bondt and Thaler (1985) mean that this is applicable to the stock market.

3.1.4 Utility Theory

The financial markets are complex. Markowitz (1952) developed the theory of mean- variance analysis for ‘rational’ investments. While the mean-variance analysis measures an investment’s quality, it does not include behavioral finance aspects, which is necessary when analyzing investor’s portfolio preferences. In this context, decision theory, which deals with investors’ portfolio preferences becomes relevant (Savage, 1954). One key concept of this field is expected utility theory. This theory is that one defines a utility function, u(X) which represents the behavior of the specific investor, then the expected utility E[u(X)] is calculated and finally the investment with highest expected utility is chosen (Hens and Bachmann, 2008). The input, X could for example be money or returns.

The utility function can take many shapes depending on the investor’s behavior. In Figure

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1, a general overview of three kinds of utility functions u(W ) with respect to return of wealth W is shown (Elton et al., 2014).

Figure 1: The Shape of Utility Functions

(1) represents the behavior of Risk-seeking investors, (2) represents the behavior of Risk neutral investors and (3) represents the behavior of Risk Averse investors. The plot is obtained from

Elton et al. (2014).

From the concept of expected utility, one can compare which of many investments options, with different risk levels and expected returns, an investor prefers to invest in. Thus, if two investment options are compared where one is to invest in risky assets and the other in risk free assets. Then the risk free asset can be derived from the inverse utility. This defines the certainty equivalent, which represents the amount of money or risk free return an investor requires for the same utility as investing it in risky assets. This concept was developed by inter alia Savage (1954) and Pratt (1964). The definition of certainty equivalents (CE) is shown below:

CE = u⁻¹(E[u(X)]) (1)

Hence, the choice of utility function is the key for successful investment decisions. Based on the standards in the industry, investors are assumed to follow general preferences.

Morningstar (2009) lists their assumptions that they use for their utility function and when Morningstar rates funds:

1. Investors’ preferences of expected wealth are strictly increasing, i.e. the utility function is positively sloped

2. Investors are risk averse

3. The utility function is independent of the distribution of risky assets

4. Investors’ risk preferences are independent of the investors’ amount of capital

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Note that the fourth assumption is arguable. Firstly, wealthy investors are most likely more tolerant towards risk than less wealthy investors. This gives wealthy investors the opportunity to take more risk. On this topic, McInish et al. (1993) showed a negative relationship between wealth and income and risk aversion. On the other hand, less wealthy investors with high goals may be forced to take high risk because of their expected return preferences. Paravisini et al. (2015) found in their study that more wealthy investors generally take less risk. Elton et al. (2014) describe this phenomena as if an investor, whose current wealth is $ 10,000 allocated 50 % in risky assets and 50 % in risk free assets, subsequently experiences an increase of wealth to $ 20,000 then the fourth assumption will only be true if he still prefers the same asset allocation.

Based on different assumptions about properties of investors’ risk aversion, different utility functions can be denoted. One of the most general ways is to define the utility function as the Hyperbolic Absolute Risk Aversion (HARA) function (Merton, 1971). There are many ways to express the HARA-family mathematically, e.g. Hult et al. (2012) denote it as:

u(x) =







1

γ−1(τ + γx)¹⁻¹^γ , γ 6= 1, 0;

log(τ + x) , γ = 1;

−τ exp (−^x_τ) , γ = 0

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Here, γ and τ are parameters of risk aversion and x is defined with dimension money. One special case of the HARA utility function is Constant Relative Risk Aversion (CRRA) function which follows the property that the risk aversion of investor is independent of the amount of wealth. There are some equivalent or closely related CRRA utility functions used in the literature, e.g. Gandelman and Hern´andez-Murillo (2015) define the CRRA utility function g(y) as below:

g(y) =

(_y1−ρ−1

1−ρ , ρ 6= 1,

log(y) , ρ = 1 (3)

Note that they denote the utility function as g(y) where y is money and ρ is the parameter for risk aversion, but the content is the same. The concept and property of constant relative risk aversion come from Pratt (1964) and Arrow (1965) and is called Arrow-Pratt measure of absolute risk aversion (ARA) which is defined as:

ARA(w) = −u⁰⁰(w)

u⁰(w) (4)

Where w is wealth and for the relative risk aversion, RRA(w) = ARA(w) ∗ w applied on definition 3 gives:

RRA(w) = ARA(w) ∗ w = wg⁰⁰(w) g0(w) =

(ρ , ρ 6= 1,

1 , ρ = 1 (5)

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3.1.5 Time Diversification

Another important aspect of portfolio management is the investor’s time horizon, which is defined as time diversification. In general, the industry’s common view of investments’

time horizons is that the portfolio should have the opportunity to manage more risk as the time horizon increases (Sanfilippo, 2002). This view has been established since the long-run performance of U.S. equities in the last century motivates the statement (Blanchett et al., 2013). However, the academic debate of this phenomenon shows that there has not been a clear commonly held view. Siegel (2008) argues in favor of the time diversification effect to decreasing risk. He concluded that investments in the stock market is the best approach in the long run when investors wants to accumulate returns. As an argument, he shows that the stability of the returns on the stock market are better in the long term compare to the short term. The implementation of this conclusion is that the fraction of portfolio’s risky assets such as shares of stock or funds of shares should be larger the longer time horizon of investment. In opposition, Samuelsson (1994) means that the risk of the investment does not decrease for longer time horizons because of utility theory which claims that investors prefer to maximize the expected utility over maximizing expected return. This opinion comes from mathematical theorems which are derived from the following assumptions: (1) Investors’ risk aversion is independent on wealth, (2) stock return follows a random walk and (3) the future wealth of investors is independent of other income than portfolio return. The debate has continued for a long period of time where academics have taken different positions. The differences depend on the assumptions that have been used (Bennyhoff, 2014). Fisher and Statman (1999) claim that the theory presented by Samuelsson (1994) is mathematical true under his stated utility assumption, but they mean that these assumptions are not true. Because these assumptions do not reflect the real market, the theory does not hold in general.

3.2 Simulation

Because investors have an interest in predicting the financial markets, it is natural that methods for this purpose have been developed. One way is to analyze historical data and compute the empirical value of the particular measure. Another way is to parameterize a model and simulate based on it. Regardless, there are many methods for this purpose and the methods have different strengths and weaknesses (Hult et al., 2012). A selection of the necessary theory to simulate models for this thesis’ purpose will be explained in this subsection.

3.2.1 Time Series

Time series analysis is important for modelling time series and when forecasting them.

A general linear approach is the ARMA(p,q)-process which is a combination of AR (Au- toregressive) and MA (Moving average) processes. The current jump in an autoregressive process AR(p) depends on the p earlier steps and the MA(q) process depends on the q:s earlier steps’ white noise. Below, MA(q), AR(p) are defined (Brockwell and Davis, 2002).

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{X_t} is a MA(q) process if:

{X_t} = Z_t+ θ₁Z_t−1+ · · · + θ_qZ_t−q (6) Where {Z_t} ∼ W N (0, σ²) is white noise and θ_i are constants.

{X_t} is a AR(p) process if:

{X_t} = φ₁X_t−1+ · · · + φ_pX_t−p+ Z_t (7) Where {Zt} ∼ W N (0, σ²) is white noise and φi are constants.

An extension to the linear ARMA-process is Bollerslev’s (1986) Generalized Autoregressive Conditional Heteroskedasity process (GARCH-process). This is a generalization of Engle’s (1982) ARCH process and defines as follows (Bollerslev, 1986):

_t|Ψ_t−1∼ N (0, h_t), (8)

ht= α0+

q

X

i=1

αi²_t−i+

p

X

i=1

βiht−i (9)

Where p ≥ 0, q > 0, α0 > 0, αi≥ 0 for i = 1 . . . q and β_i ≥ 0 for i = 1 . . . p.

3.2.2 Properties of Stock Market

Because of the complexity of the stock market, there is no common approach to forecast the future. There are many different approaches, which follow from different statistical findings and assumptions regarding the stock market (Bouchaudy et al., 2002). However, some specific parameters are commonly used. The simplest model uses parameters for expected return and are enough for mean-variance analysis (Markowitz, 1952). This approach is set up from normal conditions and may give a poor fit in the worst case scenarios (Jorion, 2007). An extension of this is to see the stock market as a time series model, where historical data shows two properties: fat tail and mean reversion (Brigo et al., 2007).

The concept of fat tails means that there is a tail dependence between many stocks.

The implementation of this property gives that large price drops in some stocks tend occurs at the same time, which has been shown in for example financial crises (Balla et al., 2012). One approach for fitting a model with this property is to use a GARCH- model where the volatility is stochastic (Brigo et al., 2007). GARCH was introduced by Bollerslev (1986) and is a general autoregressive process where the variance follows properties of heteroscedasticity. This approach is often used to get good fit of stochastic process of finance data (Brockwell and Davis, 2002). Hence, a GARCH model could be fitted to reflect the market volatility index (VIX), which historically has followed stochastic properties of a time series where it used have an expected range of variance and where the current VIX is dependent of the yesterday’s VIX (Whaley, 2008).

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In the long run, financial assets tend to have a mean reversion. The concept mean reversion means in theory that the assets’ price converges to a trend, but where it is allowed to move with some stochastics around that trend. This could be modelled by an autoregressive process, for example AR(1)-process (Brigo et al., 2007). AR(1) process is a stochastic time step process which only depends on the last step (Brockwell and Davis, 2002).

3.2.3 Monte Carlo Simulation

Monte Carlo Simulation is a common method in the financial industry. It is an approximation method where a large amount of outcomes are simulated. The simulations comes from a pre-specified probability distribution (Jorion, 2007). The method is to first simulate randomly and independently of a distribution, often using a uniform distribution.

Then, one can transform the outcome from uniform distribution to be outcomes represent- ing outcomes in the given model that one investigates. By taking a large enough sample size when simulating, the law of large numbers gives that the outcomes converges to the theoretical model. Thus, one can analyze an approximation of every possible outcome and its probability (Glasserman, 2003). The advantage of this method is that some calculations may be difficult or almost impossible to compute with an algebraic method. A computer that simulates for example tens of thousands of outcomes from the given model can easily cover the outcomes and compute some key values for the risk measure. Since this method approximates the solution, there is an error that can usually be calculated in accordance with Central Limit Theorem which says that the error decreases by 1/√

n for n simulations (Jorion, 2007).

3.2.4 Regression Analysis

One important type of regression analysis is Linear Multiple Regression. To conduct this analysis a model is set up with one dependent random variable y, which responds to the covariates x_iand the independent random residual . The standard model with parameters βi is defined as (Lang, 2015):

y = β₀+ x₁β₁+ · · · + x_kβ_k+ (10) Here, under almost perfect conditions, four assumptions are fulfilled:

1. y depends on the covariates and the residual

2. The residual is independent between observations and has the properties that the expected value is 0 and the variance is constant: E[i] = 0 and E[²_i] = σ²

3. The residual follows a normal distribution 4. There is no dependence between the covariates

Note that these four assumptions are in practice not always fulfilled. There could often be a correlation between different covariates or that y and the covariates have a mutual relationship for obvious reasons. For example, when modelling the log-wage with the

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covariates age [year], education [year] and working experience [year], there is reason to believe that assumption four above is not met because the relationship between the three covariates usually tends to be the following: age = 6 + education + experience². To deal with issues like this, there are some techniques where the aim is to minimize these errors.

It is rarely possible to fit a perfect model, but most important is that one minimizes the errors to fulfilling the four assumptions as much as possible and be aware of the limitations in the model (Lang, 2015).

When fitting models to data, there are many methods. One commonly used approach is the Least Square Estimator (LSE), which minimizes the sum of squared deviations between the quantiles of selected parametric distribution and the empirical quantiles. The method was founded around the turn of the century 1700/1800 (Stigler, 1981). A general way to estimate parameters βi in Equation 10 with LSE is shown in Equation 11 (Everitt and Howell, 2005):

β = (Xˆ ^TX)⁻¹X^TY (11)

Here, β, X and Y are defined as below:

X =







1 x_1,1 . . . x_1,k

... ...

1 xn,1 . . . xn,k





and Y =





 y₁

... yn





and ˆβ =





 βˆ₀

... βˆ_k







Where, xi,j represents the observations for variable and yi represents the observations of respeons variable in regression.

When investigating the goodness of fit for a model, one can analyze the shape of a quantile- quantile-plot (qq-plot). That is a plot where the empirical distribution is plotted against a reference distribution. The points in a qq-plot of the two dimensional scatter plot is defined follows (Hult et al., 2012):

{(F⁻¹(n − k + 1

n + k ), F_n⁻¹(n − k + 1

n + 1 )) : k = 1, . . . , n} (12) Where F⁻¹is the reference quantile function and F_n⁻¹ is the empirical quantile function of sample size n. If the shape of the scatter plot is linear, or almost linear, it is an indication of a well fitted model. Otherwise, if the plot curves up in the right tail it indicates that the empirical sample has a heavier right tail than the reference distribution, or in the same way, a S-sharpe indicates that the empirical distribution has a lighter tail. These phenomena are shown in Figure 2 (Hult et al., 2012).

2β0= 6 since the most children are 6 years old when starting the school.

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Figure 2: Q-Q plots

The left plot shows a q-q-plot for a two-degrees of freedom standard Student’s t distribution against a standard normal distribution. The right plot is a q-q plot of empirical data of Nasdaq Compossite log-return against a three degrees of freedom standard Student’s t distribution. The

plots are obtained from (Hult et al., 2012).

3.3 Risk Measures

Financial risk is a wide term without a strict definition. There are many generally accepted risk measures in the toolbox that compute different aspects of risk. Some of those will be introduced in this section. Acting on the financial market is related to potential losses that can occur for many different reasons like interest rate changes, changes in government policies or inflation. Generally, financial risk can be divided into four categories (Jorion, 2007):

• Market Risk, which represents losses from movement on the market.

• Liquidity Risk, which represents market product liquidity risk and cash flow risk.

• Credit Risk, which represents the risk that the counterpart cannot fulfill its obliga- tions in a financial contract.

• Operational Risk, which represents failure in internal processes.

The risk aspect of investment is of great interest for investors. Jorion (2007) motivates the investor’s need for tools that measure risk using the categories above and also lists some historical financial losses. Today, risk measure is one of the main tools of the financial market’s participants.

3.3.1 Properties of Good Risk Measures

When developing methods for risk measure, it is important that the measurements follow some natural properties that represent the behavior of investors. Below, a general risk measure is defined. Then, some requirements for good risk measures that follow from natural behavior of investors are presented (Artzner et al., 1999).

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Let X be random and represent the value of portfolio at time 1. Denote ρ as a function ρ(X) that measures the risk. The interpretation of ρ is that it represents the minimum capital that the investor needs to add to risk free assets in the portfolio X at time 0, to not make the position unacceptable, i.e. if and only if ρ ≤ 0, the position X at time 0 is acceptable. Below, the natural properties are defined (Hult et al., 2012).

1. Translation Invariance

Let c be a real number and R₀ be the return of a zero-coupon bond. Translation Invariance is defined as ρ(X + cR0) = ρ(X) − c

The translation Invariance property implies that the risk of the portfolio is reduced when adding the amount c of cash and it will be reduced by the same amount c.

In this case, the investor invest the added amount c in a risk free asset such as zero-coupon bond.

2. Monotonicity

Monotonicity is defined as if X2 ≤ X₁⇒ ρ(X₁) ≤ ρ(X2)

This property implies that if there is 100 % certainty that the first financial position has a greater value than the second one at time 1, then the first position is less risky.

3. Convexity

Let λ ∈ [0, 1] be a real number. Then, Convexity is defined as ρ(λX₁+ (1 − λ)X₂) ≤ λρ(X₁) + (1 − λ)ρ(X₂)

This implies that a position is less risky if a fraction of the initial capital value is invested in two different stocks that are less risky separately than a third stock, compare to investing the entire initial capital in the third stock.

4. Normalization

Normalization property is defined as ρ(0) = 0

This implies that an investor can always refrain from investing capital and hold a position that is acceptable from a risk perspective.

5. Positive Homogeneity

Let λ ≥ 0, then Positive Homogeneity is defined as ρ(λX) = λρ(X)

This property implies that the risk is linearly proportional to the size of position.

6. Subadditivity

Subadditivity defines as ρ(X1+ X2) ≤ ρ(X1) + ρ(X2)

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The subadditivity measure implies that diversification reduces risk. If an investor has two securities in the portfolio, the total risk is less than or equal to the aggregated risk of having the two securities separately. This holds when the two securities are uncorrelated.

If a risk measure fulfills the properties (1), (2) and (3) above, the measure is denoted as a convex risk measure. Furthermore, if a risk measure fulfills properties (1), (2), (5) and (6), it is called a Coherent Risk Measure (Artzner et al., 1999).

3.3.2 Volatility

One common financial risk measure is volatility. Volatility measures the variability of the returns of a portfolio, an asset or similar. Mathematically, the volatility is calculated by taking the square root of the return of the asset’s variance, i.e. equivalent to the standard deviation. The Volatility of an asset is expressed as σ and defines as follows:

σ =p

V ar(R) =p

E[(R − E[R])²] (13)

Where, R is the return of asset (Berk and DeMarzo, 2014). When a portfolio contains more than one asset, the volatility of the entire portfolio also depends on the correlation between the assets. The volatility of a portfolio is a key aspect of Markowitz’s (1952) mean-variance analysis and is defined as follows:

σp = (w^TΣw)^1/2 (14)

Where w = (w¹, . . . , w^d)^T is the portfolio weights of d assets and Σ is the covariance matrix of the asset’s return Rⁱ:

Σ = E[(R − E[R])(R − E[R])^T] =







Cov(R¹, R¹) . . . Cov(R¹, R^d) ... . .. ... Cov(R^d, R¹) . . . Cov(R^d, R^d)





 (15)

By definition, volatility measures the risk in normal cases but is a relatively poor measure when analyzing the extreme values of assets. For example in financial crises’, or similar large price drops on the stock market, assets tend to have some tail dependence that the parameter volatility is not catching. However, volatility is a good measure when measuring market risk because of its ability to catch market price movements (Jorion, 2007). It is currently more common that volatility is used as a risk measure in portfolio optimization when computing the efficient frontier (Berk and DeMarzo, 2014).

3.3.3 Value at Risk

Value at Risk at level p ∈ (0, 1) is a risk measure that represents the loss of an asset at the 1 − p worst case scenario and is written as V aRp(X), where X is the asset. VaR is

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likely the most commonly used risk measure in the financial industry. Mathematically, it has the following equivalent definitions:

V aR_p(X) = min{m : P (mR₀+ X < 0) ≤ p} (16)

V aRp(X) = F_L⁻¹(1 − p) (17)

Here, R₀ represents the return in percent of a risk-free asset, L denotes the losses of X, i.e. X = −L and F⁻¹ is the quantile function of distribution function F (Hult et al., 2012). Note that the measure says nothing about the parametrization or the assumptions of the used distribution in the model. This gives the measure flexibility to be useful independently of the investor’s subjective beliefs of tail dependence. This makes VaR applicable for every financial model (Jorion, 2007). Value at Risk is not coherent but has the characteristics of translation invariance, monotonicity and positive homogeneity (F¨ollmer and Schied, 2011).

3.3.4 Expected Shorfall

While VaR gives the quantile value of losses, the measure does not give any information about the left tail beyond the particular quantile value. One alternative to VaR is Expected Shortfall. Expected Shortfall at level p is written as (ES_p) and represents average Value at Risk at the left tail of p. Mathematically, the measure is defined as follows:

ESp(X) = 1 p

Z p 0

V aRu(X)du (18)

The strength of Expected Shortfall is that it takes all possible outcomes of the worst case scenario into account. Acerbi and Tasche (2002) show that the measure is a coherent risk measure, but not in general if there are discontinuities in the loss distributions.

3.3.5 Maximum Drawdown

In addition to the risk measure above, Maximum Drawdown (MDD) is a risk measure which is used to measure the gap between the peak and the following drop of a price. Thus, if one compute MDD of a time series, it represents the largest possible difference between two points in the series, where the bottom value is occurring after the top. Formally, for a time series from t to T of an asset with return r_i,t at time i, MDD is defined below (Gray and Vogel, 2013):

M DD = min

∀t,T(

T

Y

t

ri,t− 1) (19)

A strength of this risk measure is that MDD shows the worst possible scenario. Even though the outcome of an investment in a given time horizon has a positive return, it is possible that the wealth decreases during the time series (Gray and Vogel, 2013). Because of the phenomena that the pain of losses tend to be more painful than the satisfaction

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of similar gains, a large drawdown could affect the investment strategy and investors in general prefer portfolios where the value cannot fall under a certain level (Brunel, 2006).

4 Methodology

In the methodology, we create models based on the literature about the behavior of the stock market and of investors. Some considerations are taken in the model’s approach, which will be motivated where necessary. Furthermore, the effect of the choices we have made are analyzed briefly where eventual under- or overestimation is also described. A more in-depth analysis of potential errors in the result are analyzed in the results section.

4.1 Research design

The purpose of the thesis is to analyze how investors’ financial positions change when receiving financial advice. For this analysis, we need an approach for which measures that are relevant, how these are estimated and finally data to test significance. We have identified five main processes:

1. Asset Simulation Set-up 2. Advisory Model Set-up

3. Monte Carlo Simulation of Portfolios

4. Compute Key Values for the Financial Positions 5. Analyze Significance of Result

We believe every step above is necessary because of the nature of the research question.

To analyze how the investor’s financial position is changed by financial advisory service we use a Monte Carlo Simulation of potential outcomes of the advised portfolios and compare them to what the outcomes would have been if the portfolios had not been changed following the advice. From there, given risk measures can easily be computed.

Hence, the key is to have a valid simulation- and advisory process. When this is done, we will run it with data of investors financial positions. For that reason, we believe this is the natural model design to fulfill the purpose of the thesis. The steps above follow a general process where we first use the literature to develop a model and then the model is applied to the data. Per definition, that means that the process follows a deductive method (Hallin, 2017).

One should note that because of the complexity of stock market, there are not any commonly used ways in the industry for the two set-up-steps above. Therefore, we will explain the properties and limitations of our models in each section below and how these are related to the stock market. This complexity is also valid in step four because of the large amount of different risk measures, utility functions and parameters.

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4.1.1 Asset Simulation Set-up

One key task is to estimate each financial measure of the investors’ portfolio. For this approach we use a Monte Carlo simulation on their assets to simulate outcomes and compute risk measures and expected return of each allocation group separately. As a result of the large amount of assets on the stock markets and the fact that we do not intend to conduct valuations of every single asset, the portfolios that we are using when simulating are portfolios with different allocation between assets, where we assume proper risk diversification within the allocation groups.

We are simulating different asset allocations separately. The simulation model is built on the assumption that the future log-returns follow an autoregressive time series with monthly jumps in time. The time lag of one month is reasonable because of the balance between not overfitting for what is actually just noise and not missing relevant price moves.

In addition Brigo et al. (2007) apply this time length in their simulations when developing different simulation models. They also show that it is fitted well to the stock market.

Another difficulty in the autoregressive model is to use enough parameters to fit data but not too many because it could give an over-fitted model which is not preferable. It could certainly give good values of historical return but because of the many parameters, it will have poor predictive capacity (Lang, 2015). For the purpose of long term simulation, which we are using in this thesis, variables of fundamental economic value are the most important for the model (Griffioen, 2003). Certainly, there is no common model for this.

However, two key aspects of the stock market when simulating the long term are heavy tail and mean reverting properties (Brigo et al., 2007).

For this simulation approach, there are many options. A simple model is a Geometric Brownian Motion (GBM) which follows a Wiener Process with independent identically normally distributed variables (Jorion, 2007). Because of the independence between every time step in this process, this model assume that returns of one month is independent of the next month which will result in that the properties of mean reversion and heavy tail in the long run is lost. For handle this issue, Brigo et al. (2007) use, among other things, a Variance Gamma (VG) process, which is defined as:

d log S(t) = ¯µdt + ¯θdg(t) + ¯σdW (g(t)) (20) Here, S(0) = S0and ¯µ, ¯θ and ¯σ are constants. In this model, the g(t) parameter is charac- terizing market activity in time and is assumed to be a gamma process with parameter µ.

This gives the model a heavy tail. The other property, mean reverting over time is in the time series characteristics of AR(1)-processes when φ1 ≤ 1 from equation 7 (Brockwell and Davis, 2002). This property is found in a Vasicek’s (1977) Vasicek model which follows an Ornstein Uhlenbeck process for market simulation. This is a jump model where the jumps are estimated as:

dx_t= α(θ − x_t)dt + σdW_t (21)

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If this model is used in discrete time, this is equivalent to an AR(1)-process. Therefore it follows the mean reverting property. Also, the process is mean reverting in continuous time. Brigo et al. (2007) show that if one transforms a Vasicek process by taking its exponential, the result gives an Exponential Vasicek where the underlying process is mean reverting and heavy tailed for large positive values.

Our study investigates the financial positions of investors with respect to the investors’

financial goals, where the time horizon may vary. However, when simulating investments on time horizons that are at least five years, the properties of the stock market stated above are the most relevant for our model. Thus, we use a similar model as the Vasicek model, but where the log return is simulated as in equation 21 with the modification that xt is logarithmically transformed. That gives a kind of Exponential Vasicek, which Brigo et al. (2007) show has a slightly fatter tail. Also, the volatility parameter is stochastic as a result of the properties of the stock market. From this set up, we fit parameters from historical log returns and simulate by running the AR(1) process.

To summarize the properties of our time series, it is modelled to follow the following three properties of the stock market: heavy tailed, mean reverting and stochastic volatility. Our set up of the model follows that log-returns are a function of a parameter for the expected return, a parameter for mean reverting trend and a parameter for volatility of return.

4.1.2 Advisory Model Set-up

The advisory model is one of the most important parts of the study. Every calculation of the advisory effect is strongly dependent on the accuracy of this model. The goal is to use an advisory model that is as general as possible and represents how financial advice is provided. Thus, the result of this study will be generalizable. For this purpose, we use literature and assumptions of investor’s behavior to demonstrate the credibility of our used financial advisory model. One key assumption is that because of the fact that financial advisory service is a service to clients, it is important for the advisory model to give value to the clients. This means that the advisor has interest of minimizing the risk of dissatisfied clients. Based on this background, it is natural that the advisory model that we use will minimize the probability for the investor to receive a poorer return than the lowest acceptable drawdown of investors.

Our financial advice model must take into account both requirements and optimization considerations. Our approach is divided into three steps. The first step is to set up constraints, which follows from regulations and some behavioral finance aspects. If there are any conflicts between two constraints such as regulations by law and behavioral finance aspects, then the law reigns supreme when setting up the constraints. Secondly, after the set-up of constraints, investment theory is applied with the aim of optimizing the investor’s portfolio. The optimization is based on the asset simulation, i.e. if the aim is to maximize the expected return of the portfolio under some constraints, then our advisory model will recommend the portfolio which will receive the largest expected return in our simulation. Finally, depending on the outcome of our simulation, an asset location will also be recommended. The process will be described below.

The Value of Financial Advisory Services

The Value of Financial Advisory Services

VIKTOR CARLSON

The Value of Financial Advisory Services

by

Viktor Carlson

Värdet av finansiell rådgivning

Viktor Carlson

Acknowledgement

Contents

List of Figures

List of Tables

1 Introduction

2 Institutional Framework

3 Literature Review

4 Methodology