The Performance and Risk Analysis of Danish Mutual Funds and Turkish Mutual Funds, and Their Comparison Msc Finance and International Business

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1 1. INTRODUCTION A mutual fund is an investment tool which includes several shares or investment opportunities in it. It diversifies the risk of the fund by containing several shares. Pozen (1998, p.55) says that mutual fund asset is first mentioned in 1868 by The Foreign and Colonial Government Trust in London by dividing an investment tool into several different stocks. In addition, in March 1924, The Massachusetts Investor Trust started a portfolio which included 45 stocks with amount of $50,000 was the first open-end mutual-fund. The attractive side of mutual fund asset as an investment tool is attracts small investors because of no need of high amount of capital. Even a small-size investor can be a part of a mutual fund. However, lack of industry regulation, in great depression in 1929, mutual fund industry was severely affected. The acts that enacted by Security Exchange Commission in 1933 and 1934 and all rules in mutual fund industry were defined and regulations to protect investors had been declared (Pozen, 1998). Growth of mutual funds was relatively small in 50 s and 60 s. In 70 s tax-exemption in mutual funds emerged and triggered the growth of mutual fund and its share in all financial investment tool. In 90 s, due to vast impact of IT industry on the worldwide financial investments with the help of internet-based business, the amount of mutual fund assets were increased from $800 billion in 1987 to $4 trillion in 1997 where this increase can be seen as bull market (Pozen, 1998). Haslem (2003, p. 3) classifies funds in two categories: Open-end (diversified) funds and closed-end (non-diversified) funds. Open-end funds are called mutual funds. Open-end funds are portfolios with effective diversification in order to reduce the risk level and managed by investment advisors. Haslem (2003, p. 3) claims that open-end funds can be sold and redeemed by financial intermediaries which canalize savings to production activities. Hence, the funds that are used in this paper are open-end (diversified) funds. According to studies of Ercetin (1997), Karacabey (1999), Gursoy and Erzurumlu (2001), Kilic (2002), Canbas and Kandir (2002), Vuran (2002), and Arslan (2005), comparative analysis of Turkish mutual Funds performances is relatively low to other countries mutual funds performances (Arslan & Arslan, 2010). On the other hand, Christensen (2003) claims that Danish mutual funds have weak performances. Those funds either perform neutral or negative. Therefore, Danish and Turkish mutual fund assets are proper to make a comparison between them. 1

2 1.1.Motivation The main reason of preparing this study is to see whether Turkey, as a developing country, is ready to European Union in terms of financial aspects which include mutual fund assets. Due to mutual fund assets have high amount in financial markets in the world, i.e. have reached to the peak in the third quarter in 2007 as $26 trillion and in the first quarter of 2011 have reached to $23.07 trillion 1, those assets can be a good indicator of an country s financial performance and its risk level. As an EU country, Danish mutual funds are chosen to make a comparison with Turkey s mutual funds Problem Statement The general aim of the present paper is to analyze the performances and to measure risks of Danish mutual funds and Turkish mutual funds. In addition to the problem statement above, we want to find which mutual funds perform better. Danish or Turkish? We will analyze Danish and Turkish mutual funds over 5-years time horizon with daily prices of all mutual funds included (60 Danish mutual funds and 65 Turkish Mutual Funds). With the help of data we have, performance evaluation methods and risk evaluation methods will be tested and will find a solution to the problem of whether the results are model specific or not, and in the end, overall comparison will be done according to each method we use in the tests. In this paper, part 2, we draw a general picture of overall performance and risk analysis techniques and give some information about mutual fund industries if Denmark and Turkey. Part 3 is the methodology in which all performance measurement and risk analysis techniques are deeply analysed and explained how those methods can be applied in the study. Part 4 involves the information of data which is used in the study, how many funds have been used, where those funds have been found, etc. In part 5, we give the results of all performance and risk measurements methods. Parts 6 include the comparison of the results that found in part 6 in terms of performance and risk. At last, part 7 is the conclusion which includes overall conclusion and some comments about whether hypothesis that is mentioned in problem statement part is rejected or not. 1 Worldwide Mutual Fund Assets and Flows, Fourth Quarter 2011, Investment Company Institute 2

3 1.3. Delimitations We use daily historical prices for 5-years time horizon so we delimited number of mutual funds with those who have daily historical prices between The mutual fund assets which first served into the market after the beginning of 2006 have been excluded in the paper. We delimit ourselves in just looking from performance and risk point of view. The other aspects of a mutual fund industry such as legislations, regulations, moral values are not considered in order not to deviate from our main purpose of analysis in the tests. In addition, we delimit ourselves in historical daily prices by matching the data in a certain date with the exact match in its benchmark index. By doing this, return of a fund (a change in historical price, with the help of ln function in excel) exactly matches return of the relevant index at a certain date. With the help of matching, a special financial event which affects overall market index also affects the return of the fund at that certain day and coherence has been provided in the link between a mutual fund and the index that is used as the benchmark. 2. LITERATURE REVIEW Coolidge (1946) argues that diversification is needed in order to be influenced by risk concept. In addition, risk is diffused by using small-sized and great number of trust. Coolidge (1946) also says occasionally selected funds from the market such as Dow Jones have greater yields than those funds which are accepted that have average return level.. At last, Coolidge (1946) pays attention on a very crucial question whether a gain from a fund should be treated as a capital gain or income. The decision of distinction between a capital gain and income should be made properly. According to Brown & Vickers (1963), there are two types of comparisons in mutual fund industry: Among types of funds and among individual funds within type. The data includes information between 1953 and In terms of types of funds, there is an increase from 47.8% to 75.6% in share of common-stock fund net inflow. On the other side, share of net inflow in balanced funds declined from 46.2% to 21.5%. In addition, in an individual fund within type, if a mutual fund has purpose of growth, there would be fabulous performance and has the highest increase in absolute inflows and in share of flow. 3

4 Treynor (1965) argues that the performance of mutual funds can be analyzed and compared in different risk policies of open-end funds and market instability. His study creates a unique path to evaluate the impact of investment management on the performance of mutual funds. He compared the rate of return of a fund with rate of return of the market (characteristic line). As a result, Treynor (1965) says that although there are some fluctuations in short-term period rate of returns, characteristic line tends to be stationary (stagnant). Portfolio-possibility lines are drawn with help of characteristic line in order to rank the mutual funds and the significance of the differences in those rankings is high for individual investors 2. Sharpe (1966) claims that the forecasting of the performance of a mutual fund is done by taking account to both average return and risk. However, still there are some discrepancies among funds because of the differences in expense ratios (efficient capital market) and diversification with a reason of influential managerial skills which relies on risk analysis. Sharpe (1966) finds an inverse relationship between expense ratio of a fund and its results obtained by the investors. Mao (1970) says that before making the investment in a mutual fund, number of securities should be decided. In order to do that, simple selection criteria method and expended selection criteria method are used. The latter one gives better results with a conclusion of finding an optimal portfolio which means changing a security and its amount in the portfolio will not be profitable. In an imperfect market that includes different optimal portfolios, the risk is dependent on the allocation of securities in the portfolio and the weight of the index used in the portfolio. There are mainly two investment decisions in mutual fund industry. First, an investor should buy a fund that includes shares with relatively high earnings growth. It means that earnings of the shares should grow faster than the profits of those companies. Second, shares with lower price-earnings ratio relative to the market should be chosen (Posen,2009, p ). Ippolito (1987) focuses on turnover concept within mutual funds and pension funds. According to his study, there is not any relation between bad effects of stock turnover and mutual funds. The mutual funds that include shares between 65% and 90% of the portfolio have insignificant impact on turnover rate even there is a positive correlation between stock s percentage level in the portfolio and turnover possibility. 2 Treynor (1965) 4

5 Gil-Bazo & Ruiz Verd (2009) explains the relationship between the price of a mutual funds settled and pre-fee performance of the fund. The result is when latter is better, former decreases which mean an inverse relationship between price and historical performance. In addition, Cristoffersen & Musto (2002) emphasize non-sensitive investors against historical performances of mutual funds. Whether a fund s past performance is good or bad, non-sensitive investors invest according to price of the fund. Because of this reason, bad-performed fund may have relatively higher than the other mutual funds. Massa & Patigiri (2009) have a study for the link between contractual incentives and performance of mutual funds. According to their study, when the incentive amount in a contract increases, the management of the fund takes more risk, instinctively in order to earn high returns for covering the incentive amount. By doing so, the possibility of bankruptcy of the mutual fund rises. On the other hand, higher risk causes higher return and results in a noticeable great performance. In brief, the shares in the mutual fund should be balanced properly in order not to fail and not to spook riskaversive investors Danish Mutual Fund Industry In Denmark, first fund of investment was seen in the end of 1960s of Sparinvest & Bankinvest. Then, in 1980s, there was a trend to invest on foreign investment vehicles due to liberalization and tax incentives. After Black Monday in 1987, savings of Danish inhabitants decreased dramatically and the trend of decline in investment tools had been started. After restructuring of Danish Tax System in the end of 1980s, the decrease of investment in mutual funds stabilized in Bechmann and Rangvid (2007) mention that in 1995 the number of Danish mutual funds was not higher than 100 but ten years later it was more than 350. The more important aspect is that in 2005, around 25% Danish households invested in Danish mutual funds which can be a good indicator of the popularity of mutual funds as investment vehicle in Denmark. 3 The Federation of Danish Investment Associations 5

6 According to the article of Christensen (2005), active Danish mutual fund assets are in a rival against foreign ones. In addition, he claims Danish mutual funds provide lower yields than benchmark such as OMXC or OMX20. Therefore, an investor should be careful while selecting a fund to invest. Also, mutual funds of investment-grade bonds are not preferable due to high costs. Instead of using those bonds as mutual fund, equities and high-yield bonds should be selected to involve into a mutual fund 4. There is not any cheaper mutual fund in Europe than Danish mutual funds due to several reasons which are, having third lowest expenses of bond funds and equity funds, actively or passively managed funds and having annually high savings of investors in actively managed Danish equity funds 5. In last 10 years, Danish mutual fund industry showed a steady growth rate in sense of total volume. Except year 2008, trade volume of mutual funds in Denmark increased. Especially, between years 2003 and 2005, total volume of Danish funds raised 101% from 364,272 to 733,896, respectively (in million DKK). The summary of total volume of Danish funds from 2000 to 2010 can be seen in figure 1 below: Figure 1 Total Value of Danish Mutual Fund: (in million DKK) 1,500,000 Total Values of Danish Mutual Funds: (in million DKK) 1,000, , Source: The Federation of Danish Investment Associations 4 Christensen M., manager at Finansbanken, 2005, May 25 th 5 6

7 In the end of 2010, total volume of Danish funds exceeded 1,000,000 (in million DKK). In my opinion, in 2008, decline in total volume occurred due to US originated global sub-prime mortgage crisis. The reason is it was the only decrease in overall increase trend Turkish Mutual Fund Industry Turkey is an emerging (developing) country in economic point of view so its economy is an emerging economy. Emerging economies suffer several economic crises during their economic loops (peaks and bottoms) just like in Mexico and Turkey in 1994, Russian Federation and Brazil in 1997, Turkey in 2001, Argentina between 1999 and Kaminsky, Leons & Schmukler (2001) claim that equity based investments raised during 1990s and were majorly done via mutual funds. They also argue that the sensitivity of mutual funds to financial crisis in emerging markets was extremely high in 1990s. This claim is valid to Turkish financial market. In 1994 and 2001, two financial crises occurred in Turkey due to political instability, high inflation rate and huge domestic debt. In addition, those problems resulted in a decline in total volume of investment tools such as mutual funds. In figure 2, it is also seen that after recovery of financial crisis in February 2001, the total volume of Turkish mutual funds increased vastly. In 2001 February 21 th, ISE 100 index of Istanbul Stock Exchange declined 6.94% in one day 6. Rougier-Brierre et al (2006) assess that the first mutual fund was seen in 1987 in Turkey and in terms of net asset value, the growth rate is around 25% after They claim that there are 12 categories of mutual funds in Turkey depending on asset allocation and the composition of the portfolio. Statistics of Capital Market Board (CMB) in Turkey indicates the growth of Turkish mutual fund industry as in Figure 2 7 : CMB bulletin in January

8 As seen in Figure 2, the portfolio value of mutual funds in Turkey has been almost quadrupled in between 2002 & 2005 due to recovery of Turkish economy from the financial crisis of February In February 2001, because of administrative mismanagement of Turkish government and lack of administrative regulations in liberal economy since 1980s, Turkish lira faced with a great loss (55% loss in a night), and according to Turkish Statistical Institute, between 2000 and 2001, income declined from $2,965 to $2,123, gross national product (GNP) decreased from 6.3% to -9.5%. In recovery era (after 2001), inflation rate declined from 54.4% in 2001 to 10.1% in 2005 (Erbas & Turan, 2009). Figure 2 Portfolio Value of Turkish Mutual Fund: (in billion US $) Portfolio Values of Turkish Mutual Funds: (in billion US $) Source: Capital Market Bank of Turkey According to Gozbasi & Citak (2010), in 2008, number of mutual funds was 335 and the net asset value (NAV) was 23,972,348 TL (in thousands) in total and number of investors was 2,938,904 in Turkey. Gozbasi & Citak (2010) claim that almost 80% of all mutual funds invested in Turkey are liquid funds. It means that fund diversification could not be provided. They also claim that while 48% of all types of funds in the world are equity funds which it is 3% in Turkey. In the end, Gozbasi & Citak (2010) attribute to a very crucial aspect which is in Turkish mutual fund industry, most of the founders of mutual funds are commercial banks which have professionals who decide about the features of the funds. 8

9 Imisiker & Ozlale (2008) explain that there are two types of mutual funds: A Type and B Type. The former type of fund includes at least 25% equities in its asset. However, the latter one does not have such a rule. Type B funds involve mainly bonds. Imisiker & Ozlale (2008) attribute to a corporate tax law that was enacted in the 8 th article of that law and 94 th article of the Income Tax Law. By these laws, investors gained a tax advantage in investing mutual funds. Because of this reason, the portfolio value of Turkish mutual funds increased 300% between the terms of the beginning of year 2000 and the beginning of year METHODOLOGY The main concern in investment is why an investor should put money into an investment tool such as mutual fund. Investor should gain some benefits like earning some money, or risk exposure via investment. When there is no investment, an individual can add value to his money with the help of market return. In addition, the risk of non-invested money is calculated via risk-free interest rate (e.g., T-bills). Therefore, an investor can be better of if the return of a portfolio is higher than market return and the risk of the portfolio should be higher than the risk free rate. A portfolio has to be selected properly and carefully. Two aspects of a portfolio are expected return (performance) which can be predicted, so called desirable and variance of return (risk) which cannot be predicted (Markowitz, 1952). According to Lee & Lerro (1973), an investor s willingness to invest a portfolio involves two important concepts: Relatively lower risk and higher return than the average risk and return levels in the market, which can be observed via market index. Also, instable economy increases the concerns of the managers of portfolio owners in terms of the risk taken and its respective return. In this paper, the returns will be found by taking logarithms of daily prices of mutual funds with previous day s price. After, the earnings will be calculated via substracting the returns of mutual funds from related risk-free interest rate, either Danish risk-free rate or Turkish risk-free rate. Because the excess amount over risk-free rate is going to give real earnings that an investor has. Also, the amount of earnings can be negative which means a loss. Then, the earnings will be compared to market indices which are relative benchmarks. This comparison is going to show the performance of a mutual fund as a portfolio. By doing this, different opportunities will be provided 9

10 to investors. In addition, descriptive statistics will be calculated in order to find skewnesses, kurtosis and standard deviations in order to use in Value-at-Risk (VAR) calculations which will give information about the risk levels of the mutual funds. Furthermore, if the amounts in skewnesses and kurtosis are too high, modified VAR (Cornish-Fisher Model) will be used in order to get rid of the misleading affect of high kurtosis and skewness amount Capital Asset Pricing Model (CAPM) Capital Asset Pricing Model (CAPM) is a model that explains the relationship between the risk of a portfolio and its return in which are connected with β. β indicates how expected excess return of an asset to the expected excess return of the market. According to Brealey & Myers (2000), the equation of capital asset pricing model is: E(R i ) R f = β im [E(R m ) R f ] (1) where, E(R i ): expected return of the asset i, R f : risk-free rate of return, E(R m ): expected return of the market, E(R i ) R f : risk premium, β im = cov (R i, R m ) / var (R m ) (2) Sharpe (1964) claims that a well-diversified optimal portfolio exists in any point along (tangent) capital market line (CML). Capital Market line is a line shows the feasible (optimal) region for risky assets and starts from risk-free rate of return which means that when the risk of a portfolio is zero, the return that an investor is faced with is risk-free rate of return. In other words, all wealth is in risk-free asset. Rogalski & Tinic (1978) explain how capital market theory tries to explain equilibrium prices of assets under uncertainty. While explaining, they listed the characteristics of Sharpe and Lintner s explanations of capital market theory. According to Sharpe (1964) and Lintner (1965), investors 10

11 aim to maximize their utility while they are risk aversive, investors make their decisions in accordance with expected return and standard deviation of returns, investment horizons of the investors are all the same and in the same period, there is no restriction in borrowing or lending risk-free rate of interest, there is full diversification over any portfolio, some part of a portfolio can be bought or sold by investors, assumed that there are no taxes or transaction costs over portfolios, single investor can not affect the price of a security and all investors have similar expectations over the investment. Rogalski & Tinic (1972) define all those features as Sharpe-Lintner Version of Capital Market Theory. Market portfolio is tangent to capital market line (security market line). Therefore, market portfolio is a well-diversified optimal portfolio that can be invested.. All the assumptions mentioned above about CAPM are not feasible. The reason is in real world, investors willingness s are not homogeneous, there is no perfect market, taxes and transaction costs exist. On the other hand, the model gives us the basic ideas about how to select the assets in our portfolio in terms of risk-return relationship. The concept of risk premium, the amount of excess return above the risk-free rate, is the initial criteria about portfolio selection case. As last parameter, the expected return of the market is very important because β (sensitivity between expected market return and expected return of an asset) is calculated with the help of expected market return. In this paper, the benchmarks selected to use have deep impact on performance and risk evaluations of Danish and Turkish mutual funds Arbitrage Pricing Theory (APT) In simple terms, arbitrage pricing theory (APT) is an advanced version of capital asset pricing model. The founder of APT concept is Stephen Ross. Ross (1976) claims that in order to make CAPM model (single-factor model) more realistic, some expected return should be modeled by various factors. In other words, more parameters have to be involved. Ross (1976) thinks that the investors needs are not homogenous and affected by various indicators in overall economy. By doing so, different investment actions have been taken. According to Ross (1976), the APT model (multi-factor model) is: x i = E i + β i1 δ β ik δ k + ε i (3) 11

12 where E i : Expected return of asset i δ k : Systematic factor β ik : Volatility (Sensitivity) of asset i to factor k ε i : Idiosyncratic random shock of the risky asset (assumed to have a mean of zero) In Arbitrage Pricing Theory, the economic factors which may affect the portfolio can be inflation rate of the country, exchange rates, price of crude oil, price of gold, etc. An investor s priorities and expectations from the investment decide the weight of those factors in APT model. In addition, investors may differ in terms of being risk-aversive or risk-seeking. Unlike CAPM, APT does not have very strict assumptions. As mentioned above, there are various parameters which affect the investments, investors are more heterogeneous. Each investor holds a special portfolio which includes different betas. A changing in an economic factor may have a vast effect on expected return of a portfolio with the indication of weight of systematic factor in the portfolio. In this paper, APT model is not used due to its complexity and the aim of keeping simple and clear of the research. In investor s point of view, it is easy to analyze a portfolio s performance and risk aspects with the help of CAPM Performance Evaluation Methods There are several techniques in order to evaluate the performance of a portfolio. In this paper, four techniques have been used which are: Sharpe ratio, Treynor ratio, Modigliani and Modigliani measure (M 2 ) and Jensen s alpha single-factor model Sharpe Ratio Haslem (2003, pg. 254) defines Sharpe Ratio (Index) as reward-to-variability ratio. In Sharpe ratio a benchmark is used which is based on capital market line (CML). 12

13 As Jiang & Zhu (2009) mention, Sharpe Ratio measures the relationship between risk and return or standard deviation of a fund with no connection of any other specific models. Sharpe (1966) generated a ratio in order to evaluate the performances of funds. Although this ratio is known with Sharpe s name, it is a ratio of reward-to-variability. The main formula is: S = (µ p - R f ) / σ p (4) where µ p : average return of the portfolio (or fund) R f : return of the benchmark (in this paper, risk-free rate of return) σ p : standard deviation of the portfolio (or fund) The nominator of the formula of Sharpe ratio indicates portfolio excess return. According to Berk & DeMarzo (2007), the highest Sharpe ratio gives the tangent portfolio. Sharpe (1966) ranked thirty-four mutual funds during the period of with the help of sharpe ratio (Sharpe called it R / V ratio). In findings, Sharpe found that funds that have low rank in the beginning period tend to have low ranking in the later period. This fact shows that differences in performances of funds can be predicted. In other words, past performance is a good but not a perfect indicator. In this paper, three types of Sharpe ratios have been calculated for each mutual fund which covers different time periods (1-year, 3-years and 5-years). The purpose of doing this is to learn whether the performance of a mutual fund changes in long-time horizon or not. As mentioned above, the higher the Sharpe ratio, the higher the performance of a mutual fund. Sharpe ratio may give negative results which mean that the average return of a portfolio for a certain time horizon would be negative. Danish mutual funds and Turkish mutual funds will be compared in terms of Sharpe ratios in different time periods in order to see which mutual fund industry have better performance. 13

14 3.3.2 Treynor Ratio Treynor Ratio (Treynor Measure) is a risk-adjusted performance measurement. Treynor (1965) demonstrated that there are risks that are inevitable (systematic, non-diversified) risks that an investor would be faced with such as general market fluctuations or volatility of the stock market. To some extent, an investment which has only systematic risk would generate an excess return to the investor. Haslem (2003, pg. 253) defines Treynor Ratio (index) as reward-to-volatility ratio. It means that there is a relationship between portfolio s risk and its return. Treynor Measure uses systematic risk instead of total risk as the risk indicator. The formula of Treynor Measure as follows: T = (µ p - R f ) / β p (5) where µ p : average return of the portfolio (or fund) R f : return of the benchmark (in this paper, risk-free rate of return) β p : beta of the portfolio (or fund) As the equation (2), in our case β is calculated by dividing covariance of the return of mutual fund and market index with the variance of the market index. The nominator of the Treynor Ratio indicates the excess return of the mutual fund. Treynor Ratio s only difference from Sharpe Ratio is the usage systematic risk instead of total risk. The higher the Treynor Ratio, the better the performance of the mutual fund. In this paper, Treynor Measure is used for 5-years data. The importance of Treynor measure is the measurement of systematic risks effects on Danish mutual funds and Turkish mutual funds. 14

15 3.3.3 Modigliani and Modigliani Measure (M 2 ) Modigliani & Modigliani (1997) state that a managed portfolio can be measured with a relevant, unmanaged portfolio. The unmanaged portfolio may be the total market or benchmark used in the analysis. The main characteristic of M 2 measure is the managed portfolio must be adjusted to the level of risk in benchmark, or unmanaged market. This process is based on the market opportunity cost of risk. Modigliani & Modigliani (1997) inspired from the Sharpe Ratio with an idea of need for adjustment. In M 2 Measure, excess return of keeping investment in hand instead of market index (benchmark) is calculated. In addition, the excess return is multiplied with the standard deviation of the market index in order to clarify the basis. By doing clarification, there would be a base to compare the performances of the portfolios (mutual funds). The formula of M 2 is: M 2 = (Sharpe p Sharpe m ) * σ m (6) where Sharpe p : Sharpe Ratio of the portfolio Sharpe m : Sharpe Ratio of the market index (or benchmark) σ m : Standard Deviation of the market index (or benchmark) In this paper, M 2 measure is calculated for 5-years data and is used in order to make a comparison between Danish mutual funds and Turkish mutual funds. M 2 measure has the same logic with Sharpe Ratio. The larger the M 2, the better the performance of the managed portfolio Jensen s Alpha Single-Factor Model Derived from CAPM, Michael C. Jensen (1968) generated a model in which the purpose is to calculate the certain performance of a mutual fund instead of calculating the relative performance. Jensen (1968) claims that the measurement is linear but the difference of the model comes from the model s willingness to calculate the forecasting capability of the manager s of a mutual fund. Jensen believes that in the environment of risky investments, a mutual fund should have higher returns than another mutual fund which has a management with weak predictions of the upcoming performance. 15

16 Haslem (2003, pg. 250) says that Jensen s alpha is used to evaluate the ability of the management of a mutual fund for historical time periods. While, significantly positive alphas indicate a superior skill of management of portfolio, significantly negative results are indicators of weak performances of the management of portfolio. The alphas which are significantly not different than zero, the performance is equal to market, index. In other words, management of portfolio has no noticeable impact on the performance of a mutual fund. Jensen (1968, p. 1) demonstrates the aspects of the concept of portfolio performance as in the followings: 1) The ability of the portfolio manager or security analyst to increase on the portfolio through successful prediction of future security prices, and 2) The ability of the portfolio manager to minimize (through efficient diversification) the amount of insurable risk born by the holders of the portfolio. In contrast to Sharpe (1964) and Lintner (1965), Jensen (1968) only deals with the management s performance on the prediction of mutual fund s future performance (predictive ability). As stated in CAPM, all assumptions are also valid for Jensen s Alpha model. In equation (1), CAPM gives the expectation of earning with the help of systematic (nondiversified) risk. Therefore, if the manager of the mutual fund can forecast the future performance of the mutual fund, he may earn higher earnings than expected. In this model, the only factor that has to be considered is market factor which is unobservable. Jensen (1968) assumes that random error of the asset pricing model is zero. Hence, the formula of CAPM is: E(R i ) R f = β im [E(R m ) R f ] + e im (7) where e im : random error (expected to be zero) In next step, on the left hand side of the formula, Jensen (1968) left the risk premium (the difference between expected return of the fund and risk-free rate of return) alone. In unmanaged portfolios, β im would be an efficient estimate. However, in managed portfolios, e im would be positive which means that a mutual fund may earn higher than the given risk-premium for given level of risk. 16

17 Jensen (1968) assumed that the funds are non-stationary meaning that the management has not changed the level of risk of the portfolio via changing the structure of the portfolio. In addition, Jensen (1968) demonstrates a linear regression model in which the intercept indicates the average incremental rate of return on the portfolio per unit time. In other words, the manager s ability to forecast future prices of the mutual fund is found via the intercept (α) of the Jensen s asset pricing model. The model is as follows: R im R Ft = α i + β i * (R Mt R Ft ) + u it (8) where R im R Ft : risk premium of the portfolio i in time t α i : the intercept point β i : the sensitivity of the return of portfolio i to the market return u it : the new error term which should be serially independent. According to the equation (8), if a manager has the ability to predict the future performance of a mutual fund, the α should be positive (α >0); if the manager has no effect on the prediction of the mutual fund, the interception (α) would be zero; if the manager wrongly predicts and cause to a decrease in the performance of the mutual fund, α would be negative (α<0). Because of the assumption of non-stationary, in this paper, Augmented Dickey-Fuller Test will be applied in order to support Jensen s Alpha Single Factor Model 3.4. Risk Evaluation Methods The return of a portfolio has a strong relationship with the risk of the portfolio. In other words, risk has to be estimated properly in order to make predictions of a portfolio s future performance. In this paper, log-normally distributed and analytical value-at-risk (VAR) models, risk-adjusted performance (based on VAR), Cornish-Fisher model (Modified VAR), equally moving average, root mean squared deviation and log-likelihood ratio have been used as risk evaluation techniques. 17

18 Log-Normally Distributed and Analytical Value-at-Risks (VARs) Meng-Lan & Wong (2010) defines value-at-risk (VAR) as a technique which is used to estimate the possibility of losses in a portfolio. The underlying reason is portfolio risk is seen as a single statistic. Linsmeier & Pearson (1996) defines value-at-risk as method to measure a company s market risk exposure. In addition, they depict three techniques in order to compute VAR amount: Historical simulation, delta-normal method and Monte Carlo Simulation. In this paper, calculation of log-normally distributed and analytical value-at-risks are chosen due to their non-complexity and explanatory aspects. Historical data of mutual funds have been used in the analysis. Benninga (2008, p. 402) shows the path of calculating value-at-risk amounts of mutual funds via cutoff amounts that indicate the maximum expected losses in a given confidence level and financial circumstances (Johansson, Seiler & Tjarnberg, 1999). In order to make comparison between funds, a basis point has been decided which is 100. In other words, cutoff amounts are calculated over 100 basis points. Therefore, expected risk of loss in a given confidence level is calculated. The most important point in log-normally distributed value-at-risk calculation is it is assumed that that prices of the funds are log-normally distributed which means that end-of period (5-years in our case) log of the portfolio of mutual fund is normally distributed. The formulas of parameters (mean and standard deviation) of normal distribution in log-normally distributed VAR are given below. Mean of the portfolio for normal distribution; ln (V 0 ) + (µ-(σ 2 /2))*T (9) And Standard deviation of the portfolio for normal distribution; σ (10) which, ln(v 0 ): lognormal value of the portfolio in the beginning µ: mean of the portfolio for lognormal distribution 18

19 σ 2 : variance of the portfolio for lognormal distribution T: time period (in years) The excel formula of normal is: ln(v T ) = loginv[ci, ln(v 0 ) + (µ-(σ 2 /2))*T, σ ] (11) which, ln(v T ): lognormal value of the portfolio in the end of period T (Cutoff Amount) CI: Confidence Interval As a result, the amount of value-at-risk in % is equal to 1-cutoff amount which means the lowest expected loss of the mutual fund in a given time horizon. The other method of estimating the risk of a portfolio is analytical value-at-risk model which is relatively simple and non-complex with respect to log-normally distributed value-at-risk model. The main assumption in this model is data in portfolio is normally distributed. Ural (2009) defines the formula of parametric VAR as the following: VAR = -σ*z (12) where σ: standard deviation of the portfolio z: critical value of given confidence interval level (e.g. 95%) The simplicity of the formula comes from the acceptation of normally distribution so z-value and the value of standard deviation are enough to forecast the risk of the portfolio. In risk-adjusted performance model and Cornish-Fisher model (modified VAR), a analytical VAR calculation is going to be taken as basis. 19

20 Cornish-Fisher Model (Modified VAR) Until now, it is assumed that a portfolio has normal distribution. What if a portfolio has non-normal distributed data? Cornish & Fisher (1937) generate a model called Cornish-Fisher Expansion Model. This model takes financial time series in a portfolio into consideration and has widely been used especially in value-at-risk modeling due to its explanatory power in non-normally distributed portfolios (Ural, 2009). In value-at-risk modeling, Cornish-Fisher expansion is used to calculate critical z-value. By doing this, more accurate critical z-values have been calculated with consideration of financial time series by including skewness and curtosis values of the portfolio in the formula. The formula is (Ural, 2009): z cf = z c (13) Where z c : critical value in normally-distributed portfolio with given confidence level S: Skewness of the portfolio K: Kurtosis of the portfolio z cf : critical value in cornish-fisher expansion model Then, a formula which is derived from eq. (12) is used in order to calculate value-at-risk in Cornish- Fisher expansion called modified value-at-risk (mvar). mvar = -σ*z cf (14) In this paper, modified VAR is going to be used for each mutual fund. The model is useful for riskaversive investors because it gives higher risk expectations than traditional VAR calculation (eq.12). Higher risk expectation is coming from highly negative kurtosis values. On the other hand, if kurtosis and skewness values are close to the zero, modified VAR (mvar) comes closer to the VAR in the assumption of normal distribution. 20

21 Risk-Adjusted Performance (Based on mvar) Gregoriou & Gueiye (2003) define a modified Sharpe ratio model due to several limitations on the original Sharpe ratio model. Unlike performance measurement of Sharpe Ratio, modified value-atrisk value is used as denominator instead of standard deviation of the portfolio. Hence, the name of the ratio becomes modified Sharpe ratio (S VAR ). In order to overcome the problem of nonnormality, the mean, standard deviation, skewness and kurtosis of the portfolio are taken into account (Favre & Galeano, 2002). The formula of modified Sharpe Ratio as the following: S VAR = (R P R f ) / mvar (15) where S VAR : Modified Sharpe Ratio R P R f : Excess Return of the Portfolio mvar: Modified Value-at-Risk To conclude, Gregoriou & Gueiye (2003) conclude that modified Sharpe ratio (S VAR ) gives lower results than Sharpe ratio because of taking into account of tail risk of the portfolio. In other words, the risk of the portfolio is considered in the prediction of future performance of a portfolio Equally Weighted Moving Average (EWMA) in Rolling Basis VAR Unlike traditional VAR model, Johansson, Seiler & Tjarnberg (1999), claim that different variables in a market may have different effects on certain kinds of portfolio. Therefore, in order to release managements of the portfolios from the idea of a single VAR statistics for all funds, estimating VAR models in terms of how different assumptions affect and which assumptions are proper to a portfolio. Different characteristics of portfolios result in different exposure to downside market risk and different VARs (Johansson, Seiler & Tjarnberg, 1999). In rolling basis, volatility is seen as an independent variable which means it moves upside or downside according to the sample size. There is no constant volatility for the all data in our total sample size in the portfolio. 21

22 In EWMA, it is assumed that each sample in the portfolio has the same weight as the others have and fluctuations in historical data may change the volatility of the portfolio drastically. The expected return in the model is assumed to be zero. The reason is deviations from the mean of the portfolio will be estimated so in overall perspective, the expected return is assumed to be zero. The deviation from the mean of the portfolio (r t ). Also, the volatility of the portfolio (σ 2 ) fluctuates in time horizon due to the assumption of non-stable mean and variance in a portfolio in rolling basis VAR estimation. In the light of those assumptions and information above, the formula for equally weighted moving average (EWMA) as the following: = (16) in which, r t = R t E(R t ) (17) : Estimated volatility (variance) of the portfolio r t : Deviation from the mean of the portfolio R t : Return of the portfolio N: number of observations E (R t ): expected return of the portfolio (assumed to be zero) Via equation (16), the volatility of a portfolio varies from the other portfolios volatility values Root Mean Squared Deviation (RMSD) Root Mean Squared Deviation (RMSD) is a statistical model in order to calculate the fitness of a model and its estimation. RMSD is used to find how many samples should be used in statistical analysis. A large amount of samples may cause involvement of too old samples and the analysis may not give up-to-date results. In the same way, using small number of samples may result in overlook important information which affects the overall analysis dramatically. Montez-Rath et.al (2006) formulates RMSD as the following: RMSD = (18) 22

23 where n: The number of samples planned to be used in the analysis : Observed Cost in Period i Predicted (Estimated) Cost in Period i However in this paper, instead of cost prediction as Montez-Rath et.al did in their study, actual values and estimated volatility values is going to be used. The reason is I need to decide how many samples I should use in volatility estimate of mutual funds. Therefore, the formula is, RMSD = (19) Where n: The number of samples planned to be used in the analysis : Deviation from the mean of a mutual fund in time : Estimated Volatility of a mutual fund in time t 8 The smaller the RMSD value, the better amount of samples to select Log-Likelihood Ratio The use of financial models to estimate VARs of mutual funds may involve some risk related to the parameters in the model. The name of this type of risk is model risk. In order to question the validity of the model, some kind of tests has to be applied. A concept called back-testing can be executed. In back-testing, the actual returns of a mutual fund and VAR amounts are going to be compared (Jing, Zong-Fei & Kai, 2006). 8 Look at eq. (16) 23

24 According to Jing, Zong-Fei & Kai (2006), Kupiec s Log-Likelihood Ratio is a good way to measure the model risk of a portfolio as back-testing procedure. The modified formula of Kupiec s Log Likelihood Ratio in our case is: LR = -2ln [ ] +2ln [ ] (20) Where p: p-value (significance level, 1-confidence interval) p : (the fraction of number of failure and total number of observations in a portfolio) T: Total number of observations in a portfolio f: Number of failures (if an actual return value of a portfolio exceeds parametric VAR amount of a portfolio, it fails) 9 in a portfolio Theoretically, an actual return value cannot be more than VAR amount in a given significance level. When return exceeds number, it means that there is a failure and a certain level of risk in our financial model we applied. Therefore, a null hypothesis has to be generated in order to test it. Because p-value gives significance level means the tolerated amount of failure in a portfolio, the failure rate should be equal to p-value ( = p). Therefore, H 0 : = p AND H 1: p 4. EMPIRICAL EVIDENCE 4.1. Data The empirical study in this paper involves mutual funds of Denmark and Turkey. All mutual funds in the study are equity-based. The study contains data of 5-years time span which is Jing et.al, (2006, p.505) 24

25 Moreover, each datum is a daily price of a fund in its market and prices are in Danish Kroner (DKK) and Turkish Lira (TL). In order to suppress confusion in the study, continuously compounded return (logarithmic return, r log ) is used. The formula of r log is as the following 10 : Where P t : Price of a mutual fund in day t P t-1 : Price of a mutual fund previous day of t r log = (21) Then, the performance and risk-based comparison between Danish and Turkish funds will be objective. In addition, mutual funds in the study are not categorized according to the industry they involve. The reason is all Turkish mutual funds are in the sectors of banking and finance. However, Danish mutual funds are in several categories such as IT, health care. In order to provide the accuracy of the comparison, funds will be treated as a whole. In other words, the common point of trading in the stock market will be taken as basis. As a result, only one benchmark will be taken intoconsideration for each country s mutual funds. Because the use of risk-free rate of return is needed, the rate of return of treasury bills (T-Bills) for 6-months of central banks in Denmark and Turkey utilized Data of Danish Mutual Funds As seen in Table 1 below, there are 18 companies in this paper with 60 mutual funds in total. The main criterion is the existence of a mutual fund in between the dates of and The data have been obtained from the mutual funds section of Yahoo Finance 11. Then, mutual funds that have been traded in Copenhagen Stock Exchange are chosen and the lists of historical prices of mutual funds have been gathered. 10 Hull J.C., Fundamentals of Futures and Options Markets, 5 th international edition, Prentice Hall,

26 As risk-free rate, fixed rate of government bonds in central government domestic debt of Denmark with 150 days of maturity as of December 31th, 2010 is used (Arslan & Arslan, 2010, p. 1). The rate is 6% per annum 12. Log-normal return of the fixed rate is calculated in order to use it as riskfree rate in order to calculate Jensen s Alpha ratio in the analysis. The formula is: Risk-free rate of return = r: 6% per annum days of maturity: 150 days. = = Table 1 List of Danish Fund Suppliers and Number of Mutual Funds in the Study Names of Fund Suppliers # of Mutual Funds Names of Fund Suppliers # of Mutual Funds Alm Brand 1 Gudme 2 Atrium 1 Handels Invest 2 Bank Invest 2 Jyske Invest 9 Carnegie Worldwide 1 LD Invest 4 Danske Invest 7 Nordea 2 Dexia Invest 1 Nykredit 1 Dexia 2 Spar Index 8 EGNS 2 Spar Invest 4 EGNS Invest 8 Syd Invest 3 TOTAL 60 Source: Own Work While measuring the performances of Danish funds, a benchmark must be used as basis. The selection of a benchmark is the key point in the analysis. Therefore, the decision has to be made accurately and precisely. There are two choices for a benchmark for Danish funds which are OMXC and OMXC20. OMXC is the overall price index of Copenhagen Stock Exchange and OMXC20 is the price index of top 20 most-traded stocks in Copenhagen Stock Exchange. OMXC has been selected as the benchmark because of its scope. Because Danish funds are not classified according to their industries but treated as a whole, the decision is made for use of OMXC index. The values for OMXC index are taken from DataStream software. Detailed list of companies can be seen in 12 on/$file/tab07.htm 26

27 appendix Data of Turkish Mutual Funds There are 38 companies and 65 Turkish mutual funds in this paper. In Turkey, mutual funds are based on securities and as seen in Table 2 below, are mainly provided to investors by banks and financial institutions. Hence, there are lots of mutual fund suppliers. Each bank or financial institution usually owns not more than 2-3 funds (except Denizbank A.S. and T. Is Bankasi A.S.). The difference between number of funds in Denmark and Turkey comes from the availability of data between List of the Turkish fund suppliers and number of funds is as the following: Table 2 List of Turkish Fund Suppliers and Number of Mutual Funds in the Study Number of Mutual Funds Number of Mutual Funds Names of the Companies Names of the Companies Acar Yatirim 2 Strateji Menkul A.S. 1 Akbank T.A.S. 2 T.C. Ziraat Bankasi A.S. 3 Alternatifbank A.S. 2 T. Garanti Bankasi A.S. 2 Anadolubank A.S. 1 T. Halk Bankasi A.S. 2 Ata Yatirim A.S. 1 T. Is Bankasi A.S. 7 Baskent Menkul A.S. 1 Tacirler Menkul A.S. 2 Bizim Menkul A.S. 2 Taib Yatirim A.S. 1 Denizbank A.S. 4 TEB A.S. 1 Eczacibasi Menkul A.S. 1 Teb Yatirim Menkul A.S. 2 Evgin Yatirim Menkul A.S. 1 Tekstil Bankasi A.S. 1 Finans Yatirim Menkul 1 Tekstil Menkul A.S. 1 Finansbank A.S. 2 TSKB A.S. 1 Gedik Yatirim Menkul A.S. 2 Turkish Yatirim A.S. 1 Global Menkul A.S. Turkiye Kalk. Bankasi 3 A.S. 1 HSBC Bank A.S. 1 Vakiflar Bankasi A.S. 2 HSBC Yatirim Menkul A.S. 1 Yapi Kredi Bankasi A.S. 2 Is Yatirim Menkul A.S. 1 YK Yatirim Menkul A.S. 3 Meksa Yatirim Menkul A.S. 1 Yatirim Finansman A.S. 1 Sanko Menkul Degerler A.S. 1 Ziraat Bankasi Menkul A.S. 1 TOTAL 65 Source: Own Work 27