Influences of leverage and short-selling on the performance of
mutual funds, measured by using Sharpe style analysis.
Li Li
10702032
Bachelor Thesis
Specialization: Economics and Finance
Supervisor: Dr. Pepijn Trietsch
Statement of Originality
This document is written by student Li Li who declares to take full responsibility for
the contents of this document.
I declare that the text and the work presented in this document is original and that no
sources other than those mentioned in the text and its references have been used in
creating it.
The Faculty of Economics and Business is responsible solely for the supervision of
completion of the work, not for the contents.
Abstract
This paper examines the effects of leverage and short selling on the performance of
mutual funds. With the implementation of Sharpe style analysis, and using monthly
returns from 2005 to 2015 of 24 U.S-based index funds and eight asset classes as inputs,
the results show that sample funds with leverage and short selling obtain on average 0.1%
higher alpha value in contrast to without leverage and short selling which implying a
slightly superior managerial skill. Moreover, through the differences in the beta values
which representing the changes in investment styles, the result suggests on an average
basis a lower risk of the overall portfolio (1.37% compared to 4.44%) if leverage and
short selling are allowed. Throughout the study, the results exhibit a positive effect of
leverage and short selling on the performance of mutual funds.
Table of content
1. Introduction
5
1.1 Mutual fund and legislation regarding leverage and short selling 1.2 Reconsideration of leverage and short selling in mutual funds 1.3 Central question and research design
2. Literature Review
7
2.1 Types and styles of mutual funds 2.2 Mutual funds performance 2.3 Prior studies
3. Methodology
11
3.1 Sharpe return-based style analysis
3.2 Style analysis and mutual funds performance
3.2.1 Manager Skill 3.2.2 Investment Style
4. Data Description
14
4.1 Data composition
4.2 Summary and description of data
4.2.1 Description of mutual funds 4.2.2 Asset classes
5. Empirical Results
17
5.1 Results and discussion
5.1.1 Manager skill 5.1.2 Investment style 5.2 Limitation of results
6. Conclusion
24
7. Preferences
25
8.Appendix
27
1. Introduction
1.1 Mutual fund and legislation regarding leverage and short selling
Ever since mutual funds gained popularity among public in the 1990s when mutual fund investments hit record, they have become one of the most important intermediary between households and financial market in the U.S(Engen and Lehnert, 2000). A mutual fund is an SEC-registered open-end investment company that pools money from many investors and invests the money in stocks, bonds, short-term money-market instruments, other securities or assets, or some combination of these investments(SEC,2016). Investing in mutual funds would provide investors several benefits such as professional management, diversification, liquidity and trading convenience. On the other hand, there are also disadvantages that investors need to concern, for instance, costs despite negative returns, lack of control, and potential price uncertainty(SEC, 2016). Due to these concerns, mutual funds are typically among the most strictly regulated financial products and they are subjected to a number of constraints.
For instance, shortly after the stock market crash in 1929, the SEC of United States introduced the Investment Company Act of 1940 to regulate mutual funds companies from using leverage and short selling in order to stabilize the financial market(Jaretzki, 1941). Leverage and short selling can be considered as a double-edged sword in the investments. On one side, leverage enables investment companies to achieve additional gains through taking on debt to increase the amount of holding securities that are predicted to appreciate in the future. By using short selling, investment companies are able to sell borrowed securities and return them in a later time. Short selling works on the belief that the prices of those borrowed securities will decline in the future and investment companies could purchase those securities back with lower prices and return to creditors. In such a way, investment companies can make some profits through the price difference.
However, on the other side, leverage and short selling come along with risks for investors. This is because leverage and short selling require borrowing funds in the investments, and thus, are obligated to return the borrowed funds to creditors. In case of failures in the investments, the losses will be magnified since not only the principal, but also the associated interests are required to be repaid. As a result, using leverage and short selling might cause insolvency problem due to the uncertainty of market movements. Ultimately, the risks from leverage and short selling as well as potential losses will be borne by investors. Therefore, for the sake of investors, the SEC of United States had to regulate the mutual funds industry in terms of taking leverage and short selling to avoid investment companies to take excessive risks and insure they operate in the best interests of investors.
1.2 Reconsideration of leverage and short selling in mutual fund
In the past decades, the investment industry had experienced a series of significant changes in regulatory environment and the restrictions on leverage and short selling have been steadily relaxed in the U.S financial market(Chen, Desai, and Krishmurthy, 2012). In addition, investment companies have been facing an increasingly competitive market. In order to survive in such environment, mutual funds investment companies were forced to design new financial products to attract investors through improving their returns or hedging their investment risks away. For example, there is an increasingly popular product 130/30 equity mutual fund that allows managers to lever up to 130 percent of the portfolio, and simultaneously short sell 30 percent of the portfolio(Johnson et al, 2007). The product is designed to increase the potential of gaining in the up-market and losing less in the down-market by using leverage and short selling.
It is argued that using leverage and short selling is a way of improving managers’ abilities to distinguish securities that outperform and under-perform the market and thus, it is helpful for constructing optimal portfolios since the adoption of leverage and short selling increases investment opportunities for managers(Armfelt and Somos, 2008). Using leverage and short selling as dynamic trading strategies have became an increasingly prevalent phenomenon in the mutual funds industry. According to Chen, Desai, and Krishmurthy (2012), they found out that the proportion of US domestic equity mutual funds that allow short selling has increased from 24% in 1994 to 63% in 2009 and the proportion of mutual funds that actually take short positions in a given year has also increased from 2% in 1994 to 7% in 2009. Also, Almazan et al(2003) claimed that in 1994 73.3% of the 679 funds that reported their investment policies formally restricted from selling short. By 2000, the proportion has decreased to 66.1%.
1.3 Central question and research design
Given the fact that using leverage and short sells become increasingly prevalent, it is in the interest of this paper to examine how does the use of leverage and short selling influence the performance of mutual funds. In order to achieve a valuable answer to this question, this paper is going examine the differences between the performances of mutual funds that use leverage and short selling and that of not using leverage and short selling. This paper collects 24 US-based international mutual funds that share similar characteristics in terms of investment policy, investing regions and they are index-based mutual funds. The monthly returns of these mutual funds are collected from MorningStar through a time frame from the end of 2005 to the end of 2015.
Moreover, this paper is going to examine the performance with return-based style analysis. The return-based style analysis is a widely used instrument for evaluating mutual funds performance nowadays. The analysis is based on an asset class factor model in which the factors are usually taken to be broad market indexes such as S&P 500, Dow Jones Index or Russell Index(Sharpe,
1992). Using monthly returns of mutual funds as the dependent variable and monthly returns of asset classes as independent variables in the style analysis, this paper will evaluate the differences in the performance of mutual funds that use leverage and short selling and in the case that leverage and short selling are absent .
The remainder of this paper is organized as follows. In section 2, an introduction to mutual funds performance with prior studies about the evaluation of performance, as well as the use of leverage and short selling will be given. Section 3 provides the methodology of this paper, in particular, an elaborate description of the return-based style analysis and how the performance are examined will be given. Section 4 gives a detailed data description in terms sample composition, funds characteristics, and return data of the dependent and independent variables. Section 5 gives the empirical results and corresponding discussion, and section 6 concludes this paper.
2. Literature Review
This chapter is composed of three parts and starts with a introduction to the types and investment styles of mutual funds in order to construct the basic perspectives from which mutual funds will be evaluated. Subsequently, part two provides a description of evaluating mutual funds performance with Jensen alpha and Fama-French three-factor methods. In the third part, several prior studies correspond with Jensen alpha and Fama-French three-factor methods are represented.
2.1 Types and styles of mutual funds
The analysis of mutual funds performance is motivated by investors’ investment objectives that are determined by the types and investment styles of mutual funds. There are various types of mutual funds available to investors such as bond funds which primarily invest in bonds or other types of debt securities, stock funds also known as equity funds which mainly invest in stocks. In general, when investors make decisions about investing in mutual funds, they would like to consider their financial goals and risk tolerance. Typically, investors are likely to invest in mutual funds that fit their goals and risk tolerance. For example, an investor whose financial goal is earning fixed income and dislike risks, she/he would rather to invest in bond funds instead of equity funds since equity market is more volatile.
Furthermore, investors would also like to consider the investment styles of mutual funds. Investment styles represent the investment philosophies and can be distinguished from passively managed funds and actively managed funds. Passively managed mutual funds, also known as index-based funds, are designed to track particular securities indexes to achieve the same returns as of the indexes. Passive investing is implemented through replicating, namely the money invested into the index-based funds will be automatically invested proportionally into individual
stocks or bonds according to the percentage of their market capitalization in the index(SEC,2016). Alternatively, investors could invest in actively managed funds which involves managers to use their skills to construct portfolios in order to outperform an investment benchmark or index. These professional skills are revealed through securities selection and market-timing abilities(Fung and Hsieh, 1998). Investors usually pay attention to these abilities through managers’ past performance when they make decisions about whether to invest in actively managed funds.
2.2 Mutual funds performance
There are different evaluation techniques to assess the performance of mutual funds, for instance, Jensen alpha, Fama-French factor models and Sharpe style analysis. Jensen’s alpha method has been widely used to evaluate the performance of actively managed funds. Technically, alpha is measured as the intercept from a regression with excess return of the actively managed portfolio relative to the risk-free interest rate being independent variable and excess return of a benchmark portfolio relative to the risk-free interest rate being the dependent variable(Jensen, 1968). This regression is based on the well-known Capital Asset Pricing Model which describes the relationship between systematic risks and expected returns of assets(Berk&Demazo, 2014). The model can be specified as follow:
f p( b f ) p R R R R
where R is the expected return of portfolio,p Rf is the risk-free interest rate, α is the Jensen alpha, p is the beta of portfolio and it reflects how risky the portfolio is compared to the benchmark portfolio risk and is a function of the volatility of the portfolio and the benchmark portfolio as well as the correlation between the two, and Rbis the return of benchmark portfolio. By implementing this model, if a positive alpha was obtained, then it implies that the fund manager outperforms the benchmark portfolio and thus, the manager is skilled. Conversely, a negative alpha means the fund manager underperforms the benchmark portfolio and thus, the manager is not skilled. With this method, Jensen(1968) conducted a research on 115 mutual funds and obtained on average a negative alpha at that time which indicating those funds managers had underperformed the benchmark portfolios.
Later on, in contrast to Jensen’s research, Grinblatt and Titman(1989) argued that if mutual funds managers have investment talent and are able to outperform the market, they might also be able to capture the rents from their talent in the form of higher fees, and therefore, they claimed that Jensen’s result was negative because managers turned those excess returns for investors into their rents through higher fees. As a result, using excess returns by Jensen might not be able to reveal the true skill of managers. Therefore, they evaluated the performance of mutual funds by
examining gross returns instead of excess returns, and they concluded that mutual funds in their research on average could outperform the market on the gross return basis. This finding suggests that fund managers are skilled and negative returns for investors are due to the transaction costs, fees, and other expenses that are subtracted from them.
Although these empirical researches have provided valuable arguments about evaluation of mutual funds. It is still worthy to mention that these studies could only evaluate the mutual funds in a limited extent. This is due to that Capital Asset Pricing Model uses only one variable to explain the returns of assets, namely the benchmark portfolio and often it is taken to be the whole market portfolio. However, in practice, this is often not the case since it requires to assume that the market portfolio includes all assets in the industry. As a result, using Capital Asset Pricing model might not be an accurate framework of explaining the returns of the portfolio which also makes it not an appropriate tool for evaluating the performance of mutual funds.
Due to this concern, Fama and French(1992) expanded the Capital Asset Pricing Model by adding size and value factors on top of market risks. Specifically, the Fama-French three-factor model can be described as:
R
R
R
SMB
HML
R
p f p*
(
b f)
s*
v*
where SMB(small minus big) represents the difference between the return on the portfolio of small stocks and the return on the portfolio of large stocks, and HML(high minus low) is the difference between the return on the portfolio of high-book-to-market stocks and the return on the portfolio of low-book-to-market stocks. Throughout their research, Fama and French(1992) found out that the average absolute value of α of the CAPM are large (25 to 30 basis points per month), and they are significantly higher than those of the three-factor model (5 to 10 basis points per month) and they claimed that this result is due to the three-factor model captures much of the variation in the cross-section of average stock returns, and it absorbs most of the anomalies that have plagued the Capital Asset Pricing Model. Therefore, three-factor model works in a better way at explaining the returns of portfolios since it adjusts outperformance tendency caused by anomalies, and this makes the three-factor model a better instrument of evaluating the performance of mutual funds.
Shortly after the introduction of three-factor model, it became widely used in academic researches and financial companies to manage their portfolios. This is due to that three-factor model also provides a good framework to evaluate mutual funds with leverage and short selling. Researchers often construct two groups of mutual funds, one of them contains all the mutual funds that do not use leverage and short selling, and the other group contains mutual funds that use leverage and short selling. By using three-factor model to track the past performance of these two groups, the
effects of leverage and short selling on the performance of mutual funds can be evaluated through comparing returns, alpha values as well as beta values.
2.3 Prior Studies
For instance, Chen, Desai, and Krishmurthy(2012) have examined a sample of 323 US-based mutual funds that reported using short sales during the period 1994-2006. On the one hand, they found that mutual funds that are engaged in short sales outperform size-matched control funds by a risk-adjusted 1.5% per year, therefore, they concluded that mutual funds that use short sales generate abnormal performance from both their short(4.1% per year) and long(1.5% per year) positions. Also, fund managers who used short sales exhibit superior performance in other funds they manage that do not use short sales.
Almazan et al(2003), they have examined the investment restrictions adopted by a large sample of US domestic equity funds over the period from 1994 to 2000. In their research, several constraints such as leverage, short sales, derivatives, and the holding of illiquid assets were taken into account. They claimed that even though leverage and short sales are legalized in recent years, other factors rather than the impacts on performance of mutual funds could also influence the use of leverage and short sales. In addition, they also proved that after controlling for factors such as fund size, investment style, and portfolio turnover, the variations in the level of policy restriction do not produce economically or statistically significant return differentials. Overall, they concluded that adopting those constraints like leverage and short sales is only useful for producing the optimal investment contract between investors and managers.
These studies have provided meaningful insight into the evaluation of mutual funds performance. However, there are certain limitations for these findings and this can be due to the characteristics of the Fama-French three-factor model itself. For instance, Griffin(2002) argued that Fama-French model is a country-specific model which implies that this model is not appropriate to evaluate funds that invest in foreign countries. As a result, the model is not capable of evaluating funds that invest internationally. Moreover, the Fama-French constructed the model on the basis of Capital Asset Pricing model and it uses the whole US equity market as benchmark portfolio. Bender et al(2013) documented that Fama-French include all listed equities in the US market and investors are not necessarily interested in all equities. In turn, this will not provide any transparent information about the investment styles of mutual funds.
Due to these limitations, Fama-French model is often not used in evaluating the performance of index-based funds, especially for those investing internationally. This is because index-based funds are diversified through investing in different sectors of the market such as bonds market, equity market, and mortgage market. Moreover, index-based funds can also invest in foreign markets, for instance, an index-fund could simultaneously invest in US equity market and Dutch bonds market. In contrast, Sharpe style analysis is frequently used by financial companies to
evaluate the performance of such funds. Sharpe style analysis extends the CAPM and Fama-French model by adding multiple relevant market benchmarks in the model. These benchmarks are taken with reference to common investment styles and they are not restricted to regional or sector limitations. In line with the goal of this paper, the performance of the chosen funds will be evaluated with Sharpe style analysis since they are index-based funds and invest internationally, using Sharpe style analysis can effectively avoid country-specific bias and sector bias. In next section, an elaborate description of Sharpe style analysis will be given as the methodology of this paper.
3. Methodology
3.1 Sharpe return-based style analysis
Style analysis is an asset class factor model which aims at determining an effective asset allocation for investors. Sharpe(1992) argued that the variability in the return of an investor is largely depend on his asset allocation and an effective asset allocation can be achieved through determining the exposures of each component within the investor’s portfolio to the movements in their returns. A generic representation of the asset class model can be specified as in the following:
e F b F b F b F b Rp [ 1 1 2 2 3 3 n n]
where
R
p represents the return of investor’s portfolio, α is the intercept, F represents the values of factors, b represents the sensitivities of return to the factors, and e is the error term and it is assumed to be uncorrelated with F. The mechanism of style analysis is based on the mean-variance theory which claimed that risky assets can be combined in a portfolio in an attempt to minimize the total portfolio risk at any desired level of expected return(Markowitz, 1952). This is due to that portfolio standard deviation depends on both the standard deviations of all the individual assets in the portfolio and the co-variance between the rates of return for all the assets in the portfolio. The style analysis provides a convenient process to identify the best combination of assets that can minimize the portfolio risk for a given return.Moreover, the style analysis model imposes two constraints which are: 1. The factor sensitivities need to be non-negative,
b
0
; 2. The sum of factor sensitivities is equal to 1,
b
1
. The first non-negative constraint requires that each component of the portfolio needs to be positively held, and it implies that there is no short selling involved in the implementation of this model. The second constraint implies that other than investor’s original asset, the funds managers cannot use leverage in the investments. Technically, when implementing style analysis, these two constraintscan be relaxed in order to examine the influence of leverage and short selling on the performance of mutual funds(Shape, 1992 ). The analysis in this paper is based on the theoretical framework that comparing the results obtained from style analysis with and without the constraints for the same given returns. The differences in the results will be indicated by the alpha values, beta values, and the combination of asset classes. By comparing these values, the group that results in a lower standard deviation will be considered superior and through which the effects of leverage and short selling on mutual funds performance can be achieved.
3.2 Style analysis and mutual funds performance.
According to Sharpe(1992), the key contribution of style analysis make in the performance measurement of mutual funds is that it distinguishes the performance into two terms, namely manager skill and investment style.
3.2.1 Manager Skill
The manager skill can be represented by the α+e term in the above Sharpe style model which describes how well the fund managers are able to achieve returns beyond the strategic allocation of assets. Within the style analysis, this can be shown as:
e
R
p
[
b
1F
1
b
nF
n]
. The term α has the similar implication with the traditional Jensen alpha which implies that if a positive α was obtained, the fund manager outperforms the benchmark portfolio and thus, the manager is skilled. Conversely, a negative α means the fund manager underperforms the benchmark portfolio and thus, the manager is not skilled.Nevertheless, using α as the sole resource to interpret the skill of funds managers has limitations. First of all, the style analysis is implemented on the basis of the selected asset classes, namely the F factors, however, it is often difficult to define these asset classes or there is misspecification of asset classes. As a result, it might be the case that the chosen asset classes do not reveal all the investment styles of fund managers. It is possible that α value be resulted from other asset classes that are not included in the style analysis. Secondly, α value could possibly be influenced by statistical errors. This is due to the style analysis requires the two constraints which implies that the correlations between error term and asset classes may not be zero (Deroon, Nijman, Terhorst 2000), this could potentially distort the regression results. In the case of leverage and short selling are allowed, the constraints will be dropped, and it will improve the interpretation power of α value for skill since the statistical error will be minimized.
Apart from α, the term e is an essential factor in the technical sense. The basic idea of style analysis is to determine the best combination of asset classes through which the lowest tracking error variance of e can be obtained. This lowest tracking error variance of e guarantees that the mimicking portfolio gives the minimum variance of underlying hedge position for the
funds(Wooldrige, 2009). As in the technical sense, it conforms with the ordinary least square method which can be expressed as follows:
]
)
[(
min
2 1 1 n n p bR
b
F
b
F
Applying this method to analyze the whole data set, one can achieve the the total tracking errors e and total variance of returns of the portfolio which can be used to determine the R-squared value of the model through the formula
p e
SS
SS
R
2
1
. The R-squared is also termed as the coefficientof determination which indicates the proportion of the variance in the dependent variable that is explained by the variance of dependent variables(Wooldrige,2009). It is often used to measure how well the observed outcomes can be replicated by the model. Throughout this paper, the R-squared values of the model with and without constraints will be compared. A higher R-squared value can be a good indication of the model’s efficiency at explaining the data and thus, the power of the results will be higher.
3.2.2 Investment styles
The term ∑bF is used to represent the investment styles. The investment style is reflected through two components. Firstly, F represents the asset classes. Within the asset class, the securities share similar characteristics in terms of investment vehicles and market places. For instance, all the securities from one asset class may be invest in US equity market, and specifically they invest in the equities of large-value companies. Or, all the securities from the other asset class invest in the bonds of Dutch medium-value companies. These investment styles play important role to measure the performance of mutual funds.
Firstly, these choices of investments inform investors where are their assets invest in. Meanwhile, through investing in different asset classes could ensure a certain degree of diversity of investor’s portfolio. Not only could the fund managers select asset classes across industries within the economy, but also possible to select across regions. Such diversity makes it possible for investors to reduce their investment risks. As an important concern of investor, the diversification of asset classes gives the idea about funds manager’s skill to reduce risks. Secondly, investment styles also reveal the fund managers’ ability to capture profits through the changes in the weights of each asset class by altering b values. The changes in the weights of each asset classes in the overall portfolio could be an indication of funds managers capturing profits. For instance, by dropping asset classes or reduce their weights in the portfolio that do not perform well or increase the holdings of asset classes that perform well would increase the possibility of gaining returns for investors. Through these changes, investors are able to assess the fund managers’ selection ability and form their opinions about the performance of the funds.
It is important to recognize that the identification of asset classes is the key of the utility of the analysis. In this paper, there are eight asset classes identified according to the investing regions and investment vehicles of the mutual funds. The sample of asset classes is comparable to that of Sharpe’s 12-class model in the original research which the classes are chosen with respect to the investment styles and investment regions(Sharpe, 1992). The return of each asset class is represented by a market capitalization weighted index returns on a number of securities that can be categorized with similar characteristics. Furthermore, the composition of such index is often specified in details in the market to help investors to track the performance of their investments. These indexes as the asset classes are carefully chosen according to the actual portfolio holdings of these funds, in fact, they are mainly investing in the equity market of large value companies in the US, Canada, Europe, the UK, Japan and other regions (see Appendix table 1). Therefore, using these indexes to explain the returns of investment portfolios have the potential to lower the tracking errors caused by mismatching of asset classes.
In the following sections, the analysis will be using the style regression model with constraints b≥0 and ∑b=1 as the backbone for measuring the mutual funds without using leverage and short selling, whereas the same model without the constraints will be used to measure the performance of mutual funds with leverage and short selling.
4. Data Description
4.1 Sample Composition
The sample used in this paper is retrieved from MorningStar mutual funds database which is a leading provider of independent investment research worldwide. The mutual funds in the samples are chosen based on several criteria(see Appendix table 2). Firstly, they are all index-based funds and typically passively managed. This criterion is helpful for the analysis to only focus on the influence of leverage and short selling on the performance of mutual funds by using style analysis. Other types of mutual funds often involve active management that are beyond using leverage and short selling in asset allocation, therefore, the effects of leverage and short selling on these mutual funds may be distorted. Secondly, as mentioned above, these mutual funds are investing in the same regions and have the same investment styles and vehicles. The purpose of this criteria is to eliminate the possibility that the returns of the mutual funds are influenced by different macroeconomic factors such as country-specific factors and it also guarantees that these funds are in the same risk class. Moreover, the third criterion is that the chosen funds must have long enough history to be analyzed. These funds need to provide the past performance from the end of 2005 to the end of 2015 on a monthly basis to enable the analysis provides convincing results.
4.2 Summary and description of data
4.2.1 Description of mutual fundsTable 3 below gives the summarized information about the chosen funds in terms of return and standard deviation. There are 120 observations of monthly returns throughout the end of 2005 to the end of 2015 of each mutual fund in the sample. The highest monthly return from the 24 mutual funds amounts to 20.38% and a minimum at -27.89%. The average monthly returns of these mutual funds lies in a range between 0.36% to 0.78%. Moreover, a range between 3.42% to 6.03% for the standard deviation. These numbers are similar for each mutual fund in the analysis is due to the sample selection criteria mentioned above. These mutual funds have the same investment regions and styles, as a result, the risk classes and returns of these mutual funds are quite similar. The differences could be explained by the differences in their actual holdings of assets and each company has its specific risks.
Table 3: Summary of the sample
Funds Name* Observations Average monthly returns Maximum Minimum Std.Dev
TEMWX 120 0.47% 11.73% -17.97% 4.95% DGFAX 120 0.66% 17.11% -27.02% 5.76% ALTFX 120 0.51% 14.13% -18.64% 6.03% MDEGX 120 0.59% 13.93% -18.47% 4.61% JAWWX 120 0.74% 15.94% -26.09% 5.43% EADIX 120 0.46% 11.64% -17.15% 4.12% TWEBX 120 0.49% 10.19% -15.01% 3.78% JGVAX 120 0.49% 11.15% -20.75% 4.12% OAKGX 120 0.67% 15.61% -20.38% 5.42% OPGIX 120 0.78% 20.38% -23.25% 5.96% MWEFX 120 0.71% 15.77% -20.28% 4.95% USAWX 120 0.71% 15.81% -20.26% 4.93% CWGIX 120 0.60% 12.87% -23.27% 4.87% IGMIX 120 0.66% 16.06% -24.53% 5.39% VHGEX 120 0.57% 13.91% -26.15% 5.44% OPPAX 120 0.62% 16.18% -24.79% 5.41% HLMVX 120 0.66% 13.88% -22.38% 4.91% TEPLX 120 0.40% 16.19% -23.87% 5.43% MDISX 120 0.61% 11.17% -12.45% 3.42% NWWOX 120 0.53% 11.13% -25.27% 4.69% SMCWX 120 0.72% 12.75% -27.89% 5.49% ANWPX 120 0.72% 13.42% -21.82% 4.76% DEGIX 120 0.61% 15.76% -24.53% 5.34% TAVFX 120 0.36% 15.52% -23.74% 5.74%
4.2.1 Asset classes
Table 4 gives the summarized information about the asset classes in terms of return and standard deviation. There are also 120 observations of monthly returns of those asset classes. The maximum monthly return occurs at 19.65% and the minimum at -29.65%. The average monthly returns for these asset classes fluctuate between 0.32% to 0.66%. The standard deviation ranges from 4.19% to 6.59%.
Table 4: Summary of asset classes
Index Observations Average monthly returns Maximum Minimum Std.Dev
F1 120 0.54% 14.04% -20.16% 4.69% F2 120 0.66% 14.55% -20.75% 4.79% F3 120 0.32% 11.21% -14.44% 4.50% F4 120 0.48% 11.29% -13.82% 4.19% F5 120 0.33% 15.56% -27.88% 6.09% F6 120 0.45% 9.03% -19.23% 4.20% F7 120 0.52% 19.09% -25.23% 6.21% F8 120 0.49% 19.65% -29.65% 6.59%
In addition, a correlation table of these asset classes is also given. Among these asset classes, there is no perfect multicollinearity shown, and the highest correlation amounts to 0.91 between the U.S. Large Value stocks and the U.S Large Growth stocks which indicating these two asset classes tend to co-move in the same direction to a relatively strong extend. The lowest correlation is 0.52 between British large value stocks and Japanese large value stocks which implying that they also co-move to the same direction but to a lesser extend. The correlations of these asset classes play an important role in describing the features of the asset allocation. According to Sharpe(1992), it is desirable to have mutually exclusive asset classes but not strictly necessary as long as perfect multicollinearity problem does not exist. Thus, high correlations among these asset classes will not reduce the predictive power or reliability of the style analysis in this paper.
Table 5: Correlation F1 F2 F3 F4 F5 F6 F7 F8 F1 1 F2 0.95 1 F3 0.86 0.84 1 F4 0.87 0.87 0.91 1 F5 0.69 0.69 0.65 0.61 1 F6 0.80 0.82 0.75 0.78 0.52 1 F7 0.72 0.75 0.71 0.72 0.61 0.67 1 F8 0.83 0.85 0.74 0.79 0.63 0.81 0.89 1
Using monthly returns of the mutual funds in the sample as the dependent variable and the monthly returns of the eight asset classes as the independent variables, the effects of leverage and short selling on the performance of mutual funds will be measured by the style analysis through the changes in the constraints subject to the model. In the following section, the analysis and the discussion will be given.
5. Empirical Results
5.1 Results and Discussion
In this chapter, the results are provided and discussed in two sections. The first section starts with showing the regression results of the style analysis with constraints and without constraints in table 6 and 7 respectively, and followed with the discussion of the the difference in performance in terms of manager skill and investment styles. In section two, the limitations of the analysis with regarding to omitted variable bias and further discussion of multicollinearity are represented.
Table 6: Regression results with constraints
Funds alpha B1 B2 B3 B4 B5 B6 B7 B8 TEMWX 0 0 0.1008 (1.28%)* 0 0 0 0.8992 (3.81%) 0 0 DGFAX 0 0 0.9929 (4.58%) 0 0 0 0.0071 (0.39%) 0 0 ALTFX 0 0 0.2904 (2.24%) 0 0 0 0.7096 (3.49%) 0 0 MDEGX 0 0 0.6805 (3.63%) 0 0 0 0.3195 (2.49%) 0 0 JAWWX 0.0096 0 1 (4.60%) 0 0 0 0 0 0 EADIX 0 0 0.0740 (1.09%) 0 0 0 0.9260 (3.85%) 0 0 TWEBX 0 0 0.1705 (1.68%) 0 0 0 0.8295 (3.70%) 0 0 JGVAX 0 0 0.1784 (1.72%) 0 0 0 0.8216 (3.69%) 0 0 OAKGX 0 0 1.0142 (4.67%) 0 0 0 0 0 0 OPGIX 0.015 0 1 (4.60%) 0 0 0 0 0 0 MWEFX 0 0 1.0706 (4.93%) 0 0 0 0 0 0
USAWX 0.0068 0 1 (4.60%) 0 0 0 0 0 0 CWGIX 0 0 0.6940 (3.68%) 0 0 0 0.3060 (2.44%) 0 0 IGMIX 0 0 0.9867 (4.56%) 0 0 0 0.0133 (0.53%) 0 0 VHGEX 0 0 0.5594 (3.24%) 0 0 0 0.4406 (2.87%) 0 0 OPPAX 0 0 0.7924 (3.98%) 0 0 0 0.2076 (2.04%) 0 0 HLMVX 0 0 0.9974 (4.59%) 0 0 0 0.0026 (0.23%) 0 0 TEPLX 0 0 0 0.3767 (2.49%) 0 0 0.6233 (3.20%) 0 0 MDISX 0 0 0.7425 (3.83%) 0 0 0 0.2575 (2.25%) 0 0 NWWOX 0 0 0.3947 (2.65%) 0 0 0 0.6053 (3.28%) 0 0 SMCWX 0 0 1.098 (4.60%) 0 0 0 0 0 0 ANWPX 0 0 1.0917 (5.02%) 0 0 0 0 0 0 DEGIX 0 0 0.7596 (3.88%) 0 0 0 0.2404 (2.18%) 0 0 TAVFX 0 0 0 0.6939 (3.45%) 0 0 0.3076 (2.29%) 0 0
*standard deviation is given in the parenthesis
Table 7: Regression results without constraints
Funds alpha B1 B2 B3 B4 B5 B6 B7 B8 ∑B TEMW X -0.0001 (0.002) 0.47 (0.15) 0.09 (0.13) -0.14 (0.11) 0.28 (0.12) 0.01 (0.04) -0.22 (0.09) 0.01 (0.06) 0.34 (0.09) 0.84 DGFAX 0.001 (0.001) 0.33 (0.11) 0.22 (0.10) 0.09 (0.08) -0.05 (0.10) 0.001 (0.03) -0.04 (0.08) 0.12 (0.05) 0.38 (0.07) 1.05 ALTFX -0.001 (0.003) -0.36 (0.20) 1.05 (0.17) -0.22 (0.17) 0.16 (0.18) 0.03 (0.06) -0.18 (0.13) -0.01 (0.10) 0.45 (0.12) 0.92 MDEG X 0.001 (0.001) 0.25 (0.08) 0.28 (0.08) -0.04 (0.06) 0.11 (0.08) 0.04 (0.03) -0.04 (0.05) -0.01 (0.04) 0.29 (0.05) 0.88 JAWW X 0.001 (0.001) 0.06 (0.06) 0.67 (0.07) -0.01 (0.06) 0.04 (0.07) 0.01 (0.02) -0.0001 (0.06) 0.02 (0.04) 0.28 (0.05) 1.07 EADIX 0.0001 (0.001) 0.49 (0.07) 0.07 (0.07) 0.04 (0.05) 0.13 (0.06) -0.004 (0.02) -0.001 (0.04) -0.02 (0.04) 0.15 (0.05) 0.86 TWEBX 0.001 0.70 -0.08 0.19 0.08 -0.03 -0.11 0.05 -0.13 0.82
(0.001) (0.08) (0.07) (0.05) (0.07) (0.03) (0.04) (0.35) (0.04) JGVAX 0.001 (0.002) 0.51 (0.13) 0.03 (0.13) 0.19 (0.10) -0.13 (0.10) 0.02 (0.04) -0.07 (0.11) -0.03 (0.05) 0.22 (0.07) 0.74 OAKG X 0.001 (0.001) 0.64 (0.12) 0.14 (0.11) 0.20 (0.11) -0.0006 (0.10) 0.06 (0.04) -0.06 (0.06) -0.08 (0.05) 0.20 (0.06) 1.10 OPGIX 0.001 (0.002) 0.06 (0.17) 0.75 (0.22) 0.02 (0.14) -0.04 (0.16) 0.07 (0.05) 0.001 (0.11) -0.14 (0.09) 0.33 (0.12) 1.05 MWEF X 0.002 (0.001) 0.57 (0.08) 0.30 (0.07) 0.07 (0.05) 0.05 (0.07) -0.02 (0.02) -0.25 (0.05) -0.005 (0.04) 0.22 (0.05) 0.935 USAW X 0.002 (0.001) 0.56 (0.08) 0.31 (0.07) 0.06 (0.05) 0.05 (0.07) -0.02 (0.02) -0.25 (0.05) -0.01 (0.04) 0.22 (0.05) 0.92 CWGIX 0.001 (0.04) 0.40 (0.07) 0.17 (0.07) 0.09 (0.06) 0.08 (0.07) -0.005 (0.03) -0.21 (0.05) 0.02 (0.03) 0.35 (0.04) 0.895 IGMIX 0.0007 (0.001) 0.38 (0.08) 0.44 (0.07) 0.13 (0.06) 0.02 (0.07) 0.03 (0.03) -0.20 (0.05) -0.01 (0.04) 0.25 (0.05) 1.04 VHGEX 0** (0.0007) 0.47 (0.07) 0.19 (0.05) 0.03 (0.05) 0.07 (0.06) 0.06 (0.02) -0.06 (0.04) -0.03 (0.03) 0.34 (0.04) 1.07 OPPAX 0.0003 (0.001) 0.37 (0.08) 0.46 (0.07) 0.13 (0.06) 0.03 (0.07) 0.03 (0.03) -0.21 (0.05) -0.01 (0.04) 0.25 (0.05) 1.05 HLMV X 0.001 (0.001) 0.27 (0.06) 0.46 (0.06) 0.07 (0.05) -0.08 (0.05) 0.03 (0.02) -0.14 (0.04) -0.01 (0.04) 0.31 (0.04) 0.91 TEPLX -0.0002 (0.001) 0.68 (0.07) 0.11 (0.08) 0.11 (0.06) 0.08 (0.07) 0.01 (0.03) -0.20 (0.05) 0.04 (0.04) 0.23 (0.06) 1.06 MDISX 0.002 (0.001) 0.23 (0.12) 0.13 (0.08) 0.12 (0.07) 0.20 (0.08) 0.02 (0.03) -0.04 (0.05) 0.004 (0.04) 0.06 (0.05) 0.724 NWWO X 0.0002 (0.002) 0.03 (0.15) 0.48 (0.12) -0.08 (0.10) 0.25 (0.13) 0.04 (0.04) -0.14 (0.09) -0.04 (0.05) 0.31 (0.07) 0.85 SMCW X 0.001 (0.001) -0.01 (0.10) 0.59 (0.09) -0.06 (0.08) 0.05 (0.10) 0.07 (0.03) 0.02 (0.07) -0.05 (0.04) 0.41 (0.06) 1.02 ANWP X 0.002 (0.001) 0.25 (0.07) 0.43 (0.07) 0.04 (0.05) 0.05 (0.07) 0.01 (0.02) -0.16 (0.04) 0.01 (0.02) 0.28 (0.04) 0.91 DEGIX 0.0002 (0.001) 0.68 (0.07) 0.17 (0.06) -0.01 (0.05) 0.05 (0.04) 0.04 (0.02) -0.02 (0.03) -0.01 (0.03) 0.20 (0.03) 1.10 TAVFX -0.002 (0.002) 0.56 (0.14) 0.004 (0.15) 0.08 (0.12) 0.01 (0.14) 0.03 (0.04) 0.03 (0.09) 0.14 (0.07) 0.24 (0.09) 1.094 Average 0.001 0.36 0.31 0.05 0.06 0.02 -0.11 -0.05 0.26 0.95 5.1.1 Manager skill
The intercepts of regression results are found to be close or equal to zero in both groups. In the case of constrained regression, the alpha values of the 18 valuable observations funds equal to 0 and three have positive alpha values that are not significant from 0. In the case without constraints, the average alpha value is around 0.001 with four funds have negative alpha values.
The intercepts reveal the managers’ skill to generate returns apart from the static mix of asset classes. According to the results, when leverage and short selling are not allowed to use, most fund managers obtain a alpha value that is zero and only three fund managers have positive alpha values but significantly close to zero, suggesting that fund managers on average are not able to generate returns in excess of the asset classes if they are restricted to leverage and short selling. The result is not surprising since in this case fund managers could only follow a “ buy and hold” strategy and do not possess any instruments to adjust the composition of their portfolios. As a result, the returns of their investment portfolios are highly depend upon the returns from those asset classes.
In the case of leverage and short selling are open to fund managers, they are able to achieve a slightly higher alpha value which amounts to 0.001, indicating they are capable of making excess returns relative to asset classes but to a quite small extent. There are two reasons could be addressed to explain this situation. Firstly, from a financial point of view, inappropriate usage of leverage and short selling could result in losses. Using leverage and short selling does not guarantee that managers could earn excess returns. Leverage is beneficial when stock prices are rising through which managers could arbitrage the difference between the returns and costs from using the debts. Short selling is profitable through the same mechanism when the stock prices are declining.
In fact, the direction of the movement of stock prices is often difficult to predict, therefore the timing and degree of leverage and short selling are difficult to measure since there are also other market factors such as macroeconomic environment and legal regime that are beyond managers’ control could influence the market movements. Therefore, it is possible that managers produce little returns by using leverage and short selling. Secondly, the outcome could also be explained from a statistical point of view. The alpha is automatically generated by regression to ensure a zero-mean of error term is obtained. Thus, the range of the data is a key ingredient to determine the alpha value. Outside the data range used in the analysis, the relationship between variables in the regression model might change, and as a result, the alpha will also change correspondingly.
5.1.2 Investment styles
For all 24 mutual funds in the sample, style method with constraints suggests that they should not hold any weights of US large value stocks, British stocks, Japanese stocks, Hong Kong stocks, and stocks from emerging markets in the overall portfolio. 18 mutual funds are suggested to hold positive weights of US large growth stocks in a range between 7.40% and 100%. Among these 18 mutual funds, three have the weights of US large growth stocks that amount to 100% which implies that these mutual funds should only hold US large growth stocks in their investment portfolios. Two mutual funds in the sample are suggested to hold positive weights of European stocks which account for 37.67% and 69.39% of their portfolios respectively. Moreover, 17 funds
show positive weights in holding Canadian stocks in their investments in a range from 1.33% to 92.60%. There are four funds in the sample exhibit abnormal results, these abnormal values are above one which violate the constraint of the style regression. One possible reason is due to the statistical error that occurs when constraints are set in running the regression which could distort the regression results. As a result, these abnormal outcomes cannot be used as valid arguments for further discussion and thus will be extracted. Overall, this scenario generate an average R-Squared value of 75.01%, indicating that the constrained model could well explain the data.
In the case of constraints are absent, an average of 36% holdings of US large value stocks is represented, and within the sample, 22 funds show positive weights between 3% to 70%. The rest two funds are required to short selling 1% and 36% of US large values stocks in their portfolio. Furthermore, an average of 31% positive weight for US large growth stocks, 5% for European stocks, 6% for British stocks, 2% for Japanese stocks, and 26 % for emerging markets are shown in the results. Canadian stocks and Hong Kong stocks on average have -11% and -5% holdings respectively, which implying funds should shorting stocks from these two indexes as a strategy to construct their optimal portfolios. In addition, 11 funds are found requiring leverage in the investment which including a maximum at 110% and a minimum at 102%, and an average of 106.4%. This scenario provides an average R-squared value 92.39%, suggesting that the model without constraints has a higher efficiency at explaining the data compared to the constrained group.
Through the comparison of investment styles in the two groups, investors are given access to conveniently assess investment professionals’ managerial skill at making strategic shifts in portfolio composition. The changes in asset classes enable investors to evaluate their fund managers at selecting asset classes. Managers who possess superior selection skill are able to construct a portfolio that has low risk for a given level of return. The results from style analysis suggest only using the US large growth stocks and Canadian stocks can successfully replicate the returns of the funds in absence of leverage and short selling, whereas with leverage and short selling, all asset classes are required to replicate the returns. The changes in the asset classes verify the intuition that if fund managers are given flexibility of using leverage and short selling, they are able to construct a diversified portfolio for investors.
The main advantage of such diversification is to reduce the risk of overall portfolio. Table 8 below illustrates the difference in risk levels between the two groups. Given the same return levels, the unconstrained group has a risk level fluctuates between 0.77% to 2.87% and has an average of 1.37% which is significantly lower than the constrained group that is in the range between 4.00% to 5.14% with an average 4.44%. This result is not surprising, in the constrained situation, the risks in the return of the portfolio are largely explained by the risks in the U.S large growth and Canadian stocks which have a strong correlation in between and standard deviations of 4.79% and 4.20% respectively. It is reasonable to believe that with the flexibility to diversify the portfolio
into different markets, managers are able to construct portfolio by collecting the classes that have lower correlations to achieve the same return as if they are restricted to leverage and short selling, through which the overall risk of portfolio can be reduced.
Table 8: R-squared and portfolio standard deviation
Funds
R
2 Standard DeviationWith Constraints Without Constraints With Constraints Without Constraints
TEMWX 65.24% 84.15% 4.02% 2.04% DGFAX 63.40% 93.57% 4.60% 1.51% ALTFX 46.68% 78.97% 4.15% 2.87% MDEGX 89.36% 94.29% 4.40% 1.14% JAWWX 88.25% 96.93% 5.14% 0.98% EADIX 94.46% 95.07% 4.00% 0.95% TWEBX 118.98% 93.69% 4.07% 0.98% JGVAX 100.37% 85.31% 4.07% 1.63% OAKGX 74.95% 92.27% 4.67% 1.56% OPGIX 59.21% 81.46% 4.60% 2.66% MWEFX 98.11% 95.21% 4.93% 1.12% USAWX 86.53% 95.08% 4.60% 1.13% CWGIX 80.15% 96.15% 4.41% 0.99% IGMIX 72.28% 95.85% 4.59% 1.14% VHGEX 64.10% 97.96% 4.33% 0.81% OPPAX 68.44% 95.82% 4.47% 1.14% HLMVX 87.11% 96.37% 4.60% 0.97% TEPLX 54.24% 95.00% 4.06% 1.26% MDISX 170.73% 89.54% 4.44% 1.15% NWWOX 81.88% 86.81% 4.22% 1.76% SMCWX 86.39% 93.85% 5.05% 1.41% ANWPX 92.55% 96.75% 4.60% 0.89% DEGIX 70.15% 98.04% 4.45% 0.77% TAVFX 51.67% 89.16% 4.15% 1.96% Average 75.01% 92.39% 4.44% 1.37%
The overall effects of leverage and short selling on the performance of mutual funds thus can be reflected through the changes in manager skill and investment styles. For the group of managers are constrained to use leverage and short selling, the result shows they are on average not able to generate excess returns. For the group of managers are allowed to use leverage and short selling, on average they generate 0.1% excess returns. In the investment style analysis, approximately half of funds are involve in using leverage and all funds are involved in using short selling. To generate the same returns as in the constrained group, managers use leverage and short selling as trading strategies are able to reduce the risks for the portfolio. Therefore, using leverage and short selling
has the positive effect on the mutual funds in terms of improving managers’ skill to produce excess returns and to lower the risks for the portfolio.
5.2 Limitations of results
There are two issues regarding the validity of the results that need to be addressed. First of all, there might be omitted variable bias that could influence the application of the results. The usefulness of the style analysis model depends on the asset classes chosen for its implementation. This paper has chosen eight asset classes to explain the returns for the funds according to the actual investment types and regions of the sample funds. However, there are no such rules or criteria that can precisely identify the asset classes and it is possible that omitted asset classes exist. For instance, this paper assumes that all the funds are only investing in the equity markets and thus excludes other investment vehicles such as bond and cash equivalents. This often does not apply in practice,thus only using equity market index cannot sufficiently explain the returns of the funds. As a result, this would cause distortion between the theoretical results and actual situation and thus impacts the application of the results. One possible solution could be including more relevant explanatory variables, for example, indexes for those bonds and cash equivalents into the model to reduce the possibility of omitted variable bias.
The second drawback is the multicollinearity among the asset classes. As represented in the correlation table, there are high correlation between U.S large value and growth stocks (0.95) as well as between European and British stocks(0.91). Although, it does not affect the predictive power and reliability of the analysis. However, one consequence of this situation is that a small change in the data might cause an erratic change in coefficient estimations of regression(Wooldrige,2009). For instance, there are four abnormal results achieved from regressing the constrained group and the high correlation is likely to be one cause. Another consequence could be that the model suffers from redundancy due to the mis-specification of asset classes. It is likely that the returns from U.S large value and large growth stocks contain very similar or even the same information about the returns of the funds. Adding them into the model could potentially generate high noise which lead to inaccurate estimates of the coefficients. The possible way to resolve the problem is to drop one of the explanatory variables that are highly correlated, in such a way, the redundancy can be avoided.
6.
Conclusion
This research examines the effects of leverage and short selling on the performance of mutual funds. In order to obtain a convincing result, this paper implements Sharpe style analysis as framework, and using monthly return data for a ten-year time horizon of 24 U.S index-based international funds as the dependent variable with the same data range for eight asset classes as the independent variable. By comparing the difference in the alpha values, beta values, and the changes in asset classes, the leverage and short selling effects are revealed in terms of manager skill and investment styles.
The results show a positive impact of leverage and short selling. The alpha value of the unconstrained group is 0.1% higher than the alpha value of constrained group, suggesting managers that are allowed to use leverage and short selling can generate on average 0.1% excess return relative to the asset classes than the constrained managers. Moreover, the unconstrained managers need all eight asset classes combined with leverage and short selling to construct the portfolio and it generates a standard deviation range from 0.77% to 2.87%. As of the constrained group, the figure fluctuates between 4.00% to 5.14% which is significantly higher than the unconstrained group. Overall, the results suggest that leverage and short selling have positive effects on the performance in terms of generating excess return and lower portfolio risk.
Finally, this paper has addressed two possible limitations of the results, namely the omitted variable bias and multicollinearity. These problems come from the choices of asset classes. The omitted variable bias is due to the assumption that all the funds invest only in equity funds and they invest in the same region. The multicollinearity occurs because of the high correlation between the asset classes within the portfolio. These two limitations could potentially distort the results of the research and thus influence the validity. The possible solution to overcome these problems for further studies could be including more relevant asset classes according to the actual holdings of those funds, and replace or drop asset class that are highly correlated with others.
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8. Appendix
Table 1: Asset Classes
Asset Classes Description Indexes US large-value stocks(F1) Stocks traded in S&P500 with high
book-to-price ratios
MorningStar U.S large value Index
US large-growth stocks(F2) Stocks traded in S&P500 with low book-to-price ratios
MorningStar U.S large growth Index
European large-value stocks(F3) European stocks traded in Dow Jones with high book-to-price ratios
DJ Stoxx 50 TR EUR Index
British large value stocks(F4) British stocks traded in London Exchange with high book-to-price ratios
FTSE 100 TR Index
Japanese large value stocks(F5) Japanese stocks traded in Nikkei with high book-to-price ratios
Nikkei 225 PR Index
Canadian large-value stocks(F6) Canadian stocks traded in S&P 500 with high book-to-price ratios
S&P/TSX Composite TR Index
HK large value stocks(F7) Stocks in Hong Kong with high book-to-price ratios
Hang Seng HIS PR Index
Emerging market stocks(F8) An aggregated market for equities from more than 20 emerging nations
MornigStar Diversified Emerging Mkts Index
*resource from MorningStar
Table 2: Sample of mutual funds
Fund Name Category Investment Style Investment Regions
Templeton World A (TEMWX) World Stock Large Value North America,Europe,Asia
Davis Global A (DGFAX) World Stock Large Growth North America,Europe,Asia
AB Sustainable Global Thematic A (ALTFX) World Stock Large Growth North America,Europe,Asia
BlackRock Long-Horizon Equity Inv A (MDEGX) World Stock Large Growth North America,Europe,Asia
Janus Global Research T (JAWWX) World Stock Large Growth North America,Europe,Asia
Eaton Vance Tax-Managed Global Div Inc A (EADIX) World Stock Large Growth North America,Europe,Asia
Perkins Global Value T (JGVAX) World Stock Large Value North America,Europe,Asia
Oakmark Global Investor (OAKGX) World Stock Large Value North America,Europe,Asia
Oppenheimer Global Opportunities A (OPGIX) World Stock Large Growth North America,Europe,Asia
MFS Global Equity A (MWEFX) World Stock Large Growth North America,Europe,Asia
USAA World Growth (USAWX) World Stock Large Growth North America,Europe,Asia
American Funds Capital World Gr&Inc A (CWGIX) World Stock Large Blend North America,Europe,Asia
VY Oppenheimer Global I(IGMIX) World Stock Large Growth North America,Europe,Asia
Vanguard Global Equity Inv (VHGEX) World Stock Large Blend North America,Europe,Asia
Oppenheimer Global A (OPPAX) World Stock Large Growth North America,Europe,Asia
Harding Loevner Global Equity Inst (HLMVX) World Stock Large Growth North America,Europe,Asia
Templeton Growth A (TEPLX) World Stock Large Value North America,Europe,Asia
Franklin Mutual Global Discovery Z (MDISX) World Stock Large Value North America,Europe,Asia
Virtus Global Opportunities A (NWWOX) World Stock Large Growth North America,Europe,Asia
American Funds SMALLCAP World A (SMCWX) World Stock Mid Value North America,Europe,Asia
American Funds New Perspective A (ANWPX) World Stock Large Growth North America,Europe,Asia
DFA Global Equity I (DGEIX) World Stock Large Blend North America,Europe,Asia
