Elation Between R2 And Uk Equity

Published Date: 02 Nov 2017

Abstract

Understanding and forecasting the performance of funds, regardless of their country of origin or investment type has undoubtedly been one of the core subjects of financial research in the modern world. This dissertation uses a large sample of 376 UK mutual funds and compares their published returns between 1990 and 2012, against their style benchmarks by measure of Jensen’s (1968) alpha. These are divided into four core categories to control for style: equity, equity and bonds, small companies and all companies. Additionally, a regression analysis will allow to compare and correlate the portfolio holdings to style benchmarks as well as to their performance.

In this dissertation, we found that for all four categories, there is a statistically significant negative relation between the regressional R² and alpha. This means that for the study period, a large number of UK mutual funds which have applied stock picking strategies have indeed added value above and beyond replicating passive indexes. This assertion remains true, even after applying control variables. These findings are in line with the study from Goyenko and Amihud (2008). It is interesting to note that on average, these funds only deviated by about 15% from these benchmarks.

These findings also have a significant repercussion on the forecasting potential of R². If research in other financial markets outside the UK had similar findings, this would mean that a mutual fund with a low R² could be used as a potential indicator of long term superior performance rather than simply a measure of manager intervention in portfolio holdings. However it is important to note that some funds within the boundaries of the sample distribution did not behave as expected. Using a holding-based style analysis as well as setting limits to R²’s variance could improve its forecasting performance.

Declaration

This dissertation is submitted in partial fulfilment of the requirements for the Degree Bachelor of Arts in the University of Strathclyde, and accords with the University regulations for the programme as detailed in the University Calendar.

I declare that this document embodies the results of my own work and that it has been composed by myself. Following normal academic conventions, I have made due acknowledgement of the work of others.

Date

Acknowledgement

I would like to thank my family, as well as my partner Ruth Watson, for their continuous support throughout the year in achieving this dissertation. Furthermore, I would like thank Professor Jonathan Fletcher who though was unable to see this dissertation develop until the end, was of tremendous support and inspiration. Finally, I wish to thank Dr Lei Lei Tang whose support, constant availability and advice in completing this dissertation were invaluable.

Table of Contents

i. Introduction

Investment fund performance has not only been a topic of great research but also of great debate. Because these funds sell the potential for future superior performance, some at a high price, they are scrutinized as the industry tries to find ways to separate unkept promises to real portfolio manager talent.

Mutual funds in particular have experienced explosive growth in the last decade of the twentieth century. In Europe alone, total assets under management rose from 1 trillion dollars to 2.6 trillion between 1992 to 1998 which represents a 17.7 percent annual growth rate. One of the factors explaining this dramatic increase is the popularisation of mutual funds within traditional households. According to the Investment Company Institute (2002), in the United States alone 6 percent of households invested in mutual funds, whereas that number grew to 44 percent during the same 1992-1998 period.

The increase in mutual fund accessibility has pushed for new attempts to try and filter the noise of poor performing funds against those who did manage to persist in their superior performance against their benchmark. Since Sharpe (1966), mutual fund performance measures of all sorts have emerged, in an attempt to find better ways to gauge how much return can be attributed to the replicating features of funds, and to the stock-picking skills of their managers. Most of them use a similar approach, where they compare returns from an actively managed portfolio over a set period of time, against an equivalent passive portfolio (typically an index such as the S&P500 or FTSE250) used as a benchmark. Ferson & Aragon (2006) describe these "Otherwise Equivalent" (OE) benchmark portfolios as being nearly identical in terms of explaining movements in expected returns. Many of the measures used to compare portfolios to each other are based on the early Capital Asset Pricing Model (CAPM) developed by William Sharp in 1964. However this model assumes that all investors hold the "market portfolio", consisting of the weighted sum of all assets in the investment universe. Many research papers have criticized this aspect of the CAPM as it does not hold in the real world. Another issue with benchmarking money managers is that many of the previous academic papers have used similar size and book-to-market portfolios which restricts the variety of findings, especially as most studies are conducted in the United States.

The 1980s saw the development of more formal models on estimating the ability of active fund managers to balance their portfolios in perfect timing with the market. This regression approach to fund performance analysis allowed a stronger focus on fund holdings and how they performed compared to their Otherwise Equivalent benchmarks. Over time, this gave birth to two different approaches with both their advantages and drawbacks: weight-based style analysis and return-based style analysis. Weight-based style analysis is used when the actual portfolio holdings are known and examines the covariance of these weighted holdings against the return of the assets. On the other hand return-based style analysis only uses the returns of the fund as a whole which makes it more approachable when studying a sample which covers a large time period. Overall, though style analysis is considered a powerful tool in fund performance research, it raises several key core issues. If an investor decided to divide his capital into several funds which all had unique investment style, monitoring that the stated style is maintained over time becomes quite complex. Return-based style analysis does provide a partial solution to this problem by comparing the mix of assets as a whole to a selected style benchmark. This also means that appropriate choice in benchmark is key to produce significant findings.

Gauging portfolios against each other becomes problematic to the extent that the mutual fund sphere is very secretive as to how it generates extra revenue. Therefore when analysing funds on an individual basis, it can become complex to get a realistic picture of portfolio holdings and weights in order to compare it to popular benchmarks such as large stock indices. According to Cuthbertson et al. (2007), the two key issues associated with this are to identify whether risk-adjusted abnormal performance is positive, negative or zero, as well as its persistence over time if it does exist.

Prior studies in the United States tend to suggest that there is actually very little to no proof of better-than-average performance by fund managers. In many cases, the inverse is actually usually true. Fama & French (2010) found that the portfolios of most U.S. equity portfolio managers are very close to the market portfolio. This means that after accounting for fund costs and charges, negative returns tend to be what investors perceive if they compare this to investing in a passive equivalent such as an Exchange Traded Fund.

UK studies in the late 1990s have corroborated these findings, though Teo and Woo (2001) have found signs of persistence for up to six years in style adjusted returns. Cuthbertson et al. (2007) also argues that portfolio rebalancing should occur at least once a year, and that the time period studied should not exceed a year. Previous US studies advocate that this one-year potential persistence in better-than-average returns could be explained by stocks being carried over passively from one period to another, rather than the actual purchase or selling of new stocks. In the UK, there is actually very few evidence of any kind of persistence in superior performance by top performing mutual funds at all. The opposite is actually usually true, where "looser" funds tend to keep on underperforming over time.

A popular tool used by investors to actually differentiate funds that have a lot of manager input compared to their OE benchmark is R². It is a factor resulting from a regression analysis which gives a percentage of replication of a dependent variable compared to one or several independent variables. Typically Treasury bill or a stock index data is used as an independent variable which can sometimes be a poor choice of style comparison. Indeed, mutual funds hold increasingly complex products, and using such straightforward benchmarks could potentially hinder the statistical significance of findings. This is why over time, different factor models have been developed ranging from one, all the way up to five factors.

Cremers and Petajisto (2009) is an example of a one factor model as it uses an index which reflects most the fund’s investment style. Fama-French (1993) have developed a popular three factor model, using the excess market return, and both the performance of value/growth and small/large stocks against each other. Later they extended this model to a more global context using a World High Minus Low (WHML) factor which could better explain returns in funds who invest across the globe. The model came under criticism when Lakonishok et al (1994) found that the factors used were due to overreaction rather than investors trying to compensate for risk. They believe that corporate as well as macro-economic news tends to make investors overreact particularly impacting the HML factor. On the other hand, Liew & Vassalou (2000) find that the Fama French factors accurately predict economic growth in several international markets. Other models add a group factor which benchmarks a mutual fund against the average returns of an entire group of funds.

Using such multi-factor models, the purpose of this study is to find evidence of above or below average performance from mutual fund portfolio managers in the UK. More importantly, this will add to the existing research on indexing versus selectivity, i.e. the true value behind more stock picking instead of passive replication. This will be accomplished by considering a large sample of funds which primarily focuses on UK based equity investments. Furthermore, a correlation analysis between these returns and portfolio holdings should help determine if active management over the study period was worth the premium for investors compared to passive macroeconomic factors. This would allow to complement previous research from Amihud and Goyenko (2012) in allowing for new statistical tools to evaluate fund performance ex-ante in the UK. Future research from these findings could include the use of these tools as prediction of possible future superior performance.

In section 2, we will review existing literature on fund performance and persistence as a whole, with a particular focus on UK evidence. This will allow a better understanding of previous evidence in mutual fund persistence as well as well as the return-based analysis approach. More importantly, section 2 will review previous findings in the relationship between performance measures, namely Jensen’s (1968) alpha and the R² from a multi-factor regressional analysis. Finally, potential biases in data will be examined as they have the power to affect the results statistical significance.

Section 3 will describe the data sample used in this study, as well as the methodology used to compare funds against each other. For a time period spanning from January 1990 to December 2011, we will focus on UK-based equity mutual funds listed in the Investment Management Association database, using associated control variables. In order to generate fund performance measures we will use an ordinary least squares generalized method of moments approach which will also allow to regress the fund returns against economic factors. Ultimately, this will generate data that will either prove or disprove the existence of a correlation between superior performance by UK fund managers and the amount of stock-picking they use to construct their portfolios (alpha and R²).

Section 4 will analyse in detail the findings from section 3 and will be divided into three core subsections for each fund style: data analysis, correlation analysis as well as control variables. The latter enables to verify that the findings from the first sub-section remain true after controlling for investment style.

ii. Literature Review

ii.i Fund performance

It is impossible to start a review of previous literature on fund performance without first mentioning Jensen’s (1968) research. Jensen’s (1968) early paper is a strong advocate against any realistic added value from fund managers’ stock picking abilities. Jensen names this skill "predictability" and defines it as the capacity of a manager to correctly anticipate the future value of risky assets in order to gain above normal returns. His research was a cornerstone in fund performance analysis, as his paper gave birth to the widely used "alpha" measure. Jensen’s alpha is defined by:

Where is the expected portfolio return, is the risk free rate, is the portfolio Beta based on the Capital Asset Pricing Model, and represents the expected market return.

Using alpha, Jensen showed that through an analysis of 115 mutual funds between 1955-1964, US mutual fund managers were on average incapable of using their predictability skills to outperform any "buy-the-market-and-hold" strategy. Henriksson (1984) found similar results investigating the market timing performance of 116 mutual funds between 1968 and 1980. He used both parametric and non-parametric testing to analyse monthly return data which was inclusive of dividends and fund management fees. Ultimately, both tests showed that fund managers failed to follow a consistent successful strategy, and that they were not able to predict accurately small or large movements of the market portfolio.

However, one of the arguable shortcomings of Henriksson (1984)’s study was the way he considered fund returns as a whole, rather than look at the specifics. This is why Grinblatt and Titman (1993) took a different approach, and instead of analysing the returns that investors make from holding the fund looked at the performance of individual stocks within the funds’ portfolios. Doing so has several advantages, namely that being specific at an individual stock level allows them to create custom benchmarks that better capture the fund manager’s individual investment style. This also means that the actual returns found do not include any fees, trading costs, or expenses which would otherwise alter their findings. Though it could be argued that doing so would actually overestimate the true value of managers’ predictability skills, it would still remain a meaningful result since the benchmarks created also do not include any fees or expense. Their paper actually found that between 1975 and 1984, aggressive-growth funds did outperform their custom benchmarks by 2 to 3 percent (before expenses). It is important to note that Grinblatt and Titman’s finding swere somewhat criticized, as the sample of mutual funds they used was relatively small (around 275). Furthermore, they had only done research on a 10 year period. Finally, some question the fact that their paper did not take into account anomaly factors such as book-to-market, size or momentum.

Yet another approach to fund performance was developed a bit further down the line by Daniel, Grinblatt, Titman and Wermers (1997) who use "Characteristic timing" and "Characteristic Selectivity" in order to measure portfolios’ performances in 2500 equity funds between 1975 and 1994. Characteristic timing is defined by the ability of the fund manager to alter portfolio weights accordingly in time of potential abnormal return. On the other hand, characteristic selectivity is the manager’s aptitude to stock-pick specific assets to bring superior performance. Their research showed that though some aggressive-growth funds exhibited partial selectivity benefits, most funds failed to convert characteristic timing into above-normal returns. It is interesting to note that though their approach and measures were different from Grinblatt and Titman (1993)’s paper, their findings did partially match. However as a whole, Daniel et al. found that mutual funds do on average tend to beat their passive benchmarks, though this is usually by less than 100 basis points, which would then be engulfed by management fees. This seems to corroborate what Grinblatt and Titman found in 1993.

Brands, Brown & Gallagher (2005) discuss the common perception that increased portfolio concentration on specific asset classes or sectors is usually a valid way of trying to outperform the market. The magnitude to which the fund manager’s asset allocation strategy deviates from passive benchmarks should therefore be a valid measure of skill, as well as the value of active management. Their paper proved the existence of a positive relation between higher manager input (i.e. portfolio concentration as well additional stock picking) and superior performance in Australian equity funds. This seems particularly the case for portfolios that are both overweight and hold stocks outside popular benchmarks such as the S&P500. Wermers (2003) support this research, by finding a similar relation in a sample of US mutual funds.

More recently, Petajisto (2010) studies US domestic all-equity mutual funds and divides them into several categories of style using "Active Share" and "Tracking Error". Tracking error would be defined as the volatility of the difference between the returns of a fund against its assigned benchmark, typically a market index. Active share simply is the amount of portfolio manager input into building the portfolio so that it differs from the passive indexes. Petajisto particularly focuses on "closet indexing", a phenomenon that is increasingly present in the mutual fund sphere. This occurs when funds sell active management at a premium, when actually their portfolio holdings are nearly identical to any low cost index fund. He finds that there a significant increase of closet indexing between 2007 and 2009, which now encompasses about a third of all mutual funds. Petajisto believes that this can in part be attributed to above-normal market volatility from the credit crisis, as similar growth was found between 1999 and 2002 which corresponds to the "dot com" bubble. Overall, Petajisto (2010) finds an average mutual fund performance of -0.41% compared to low cost index fund benchmarks. As a number of them secretly just replicated their benchmarks, after taking into account fees and expenses, their performance lagged behind by exactly that amount. Interestingly, funds who were most active in stock picking added the most value to investor capital. On average they exceed their benchmark performance by 1.26% net of all fees and expenses. By using a multivariate regression, Petajisto (2010) found similar results in each fund category, also finding that active share has most predictive powers in finding alpha in small-cap funds though it still has statistical and economic significance in large-cap investment pools.

In the same year, Fama & French (2010) studied a sample of 3,156 funds which focus on U.S equity investments. They used a perspective they call "equilibrium accounting" which implies that the aggregate alpha value is equal to zero before taking into account fund costs. They found that between 1984 and 2006, most mutual funds underperformed both three and four factor model benchmarks as well as the CAPM which was mainly due to fund fees and expenses. This means that if some portfolio managers within the sample were actually able to produce similar returns to their benchmarks, these were hidden by the weight of fund costs. At a more individual level, they found it difficult to provide any meaningful evidence of managerial skill versus luck in excess returns. However Fama & French (2010) do find that very few funds actually have enough active management skill to cover their costs using a distribution of Jensen’s alpha estimates using net returns. When using gross returns, the opposite becomes true, where the evidence for skill in winner funds or lack of it in loser funds becomes much clearer. But again, for the majority of funds within the $5 million Assets Under Management (AUM) sample, few had enough skill to beat their benchmarks.

ii.ii UK Evidence

The main limiting factor in previous research on fund performance is that most of it emanated from the United States, or at least studied funds based in the U.S. Luckily, Fletcher (1997) looks at the performance of 85 UK mutual funds that invest in North American securities between 1985 and 1996. Fund excess returns were calculated on the basis of the Jensen (1968) measure as follows:

"where rit is the excess return on trust i in period t, rjt is the excess return on the jth benchmark portfolio in period t for j 5 1, . . . , K, bij is the beta of asset i relative to factor j, K is the number of portfolios in the benchmark, and eit is a random error term with E(eit) 5 0 and E(eitrjt) 5 0 for j 5 1, . . . , K.". p456. These excess returns are then benchmarked against two sets of portfolios: one constructed as the excess return from the S&P 500 index, the second as a three index model. In order to appropriately capture each fund’s investment style, they were then divided into four categories: Growth, Income, Special Situations/Smaller Companies, and General. The study revealed that there was no evidence of superior performance by the funds compared to their benchmark, and that no significant predictability in performance was possible. Quigley and Sinquefield (1998) use a similar methodology, though they consider 752 UK equity unit trusts between 1978 and 1997. In order to complete their analysis, they complete their testing before and after adjusting for risk using Jensen’s alpha, as well as three factor model based on market risk, value and size. Quigley and Sinquefield find that after trading costs are paid, top earning fund returns are not significantly higher than the sample average, however low earning funds appeared markedly worst.

Blake and Timmermann (1998) also studied UK Mutual fund performance through a large sample of 2300 UK open-ended funds over the period 1972-1995. Using multiple regressions, they did find signs of persistence in performance (positive and negative) in both best and worst performing funds. Black and Timmermann argue that these findings are surprising as the spread for UK mutual funds are typically higher than those found in the United States which would make it more costly for investors to transfer their capital from a poorly performing fund to a top-performing one. Allen and Tan (1999) also found partial evidence of positive performance persistence within a sample of 131 UK equity mutual funds between 1989 and 1995. They used an alternative approach to performance analysis of previous studies, by comparing the relative performance of a fund against the sample itself rather than to an index benchmark (FTSE100 or S&P500). To complete this comparison, Allen and Tan used four separate empirical tests including and Ordinary Least Squares (OLS) regression of excess returns, a table analysis of winners and losers as well as a Pearson’s Chi squared tests on these tables, and Spearman Rank Correlation Coefficient analysis. These tests are executed on two groups of funds divided by low and high variance. Ultimately, this outlined that superior performance does persist on long time horizons however it doesn’t in the very short term. Furthermore, both low and high variance groups exhibited persistent "winners" which indicates that risk-taking is not a necessity for superior performance. Heffernan (2001) finds similar results examining 288 UK investment trusts divided into eight categories between 1994 and 1999. Similarly to Allen & Tan, Heffernan benchmarked the average annual performance of each fund against its respective category. He found that there were no relation between higher fees and better fund performance, and that there was some evidence of persistent success over the longer term both in terms of performance and variance.

Finally, Cuthbertson, Nitzsche, & O’Sullivan (2008) apply a cross-sectional bootstrap approach to UK equity mutual funds to distinguish if the persistence in returns they display is actually due to above-normal stock picking abilities, or if there are simply a consequence of luck. They found that only 5 to 10% of top performing funds actually do display superior performance due to stock picking abilities, whereas smaller stock funds did not perform well at all. There also seems to be an opposite relation between on and off-shore funds, as the former’s performance is due to skill, and the latter to luck.

ii.iii. R² and style analysis

Sharpe’s (1992) Return-style based analysis provides a solid framework that enables investors to compare the fund manager’s asset allocation strategy to that of its benchmark. He justifies this methodology by asserting that "if it acts like a duck, assume it’s a duck". Essentially, this approach consists of a regression analysis of historical returns against the identified benchmarks’ performances. These returns are calculated using the Capital Asset Pricing Model (CAPM).

Furthermore the benchmark portfolio needs to represent a realistic passively managed alternative. By using this approach, an individual investor can evaluate how much return is due to the diversification skills of the portfolio manager, and how much is simply due to the replicating features of the fund. It is important to note that appropriate choice in the style benchmark is vital to ensure proper analysis. For example, if the mutual fund focuses on a particular asset class (i.e. equity, money market, etc.) or sector (technology, retail, healthcare etc.), the style benchmark should include these specific limitations. Because of the wide spectrum of mutual funds in the UK, it is impossible to match exactly each asset allocation strategy, creating a necessity for custom-made benchmarks. This is achieved by blending a combination that will generate the highest R² possible, R² being the fund returns’ variance explained by the benchmarks’ variance.

Ben Dor & Jannagathan (2002) define R² as:

with being the amount of return attributable to the portfolio manager’s stock picking ability, also called "selection" and the amount of return associated with the replicating features of the fund to its benchmark, also called "style". In their study, Ben Dor & Jannagathan estimate the fund’s style by using returns in a 36 month timeframe. This is mainly to reduce potential "noise" from shorter time horizons, but also to increase the accuracy of the fund’s style exposure description. By computing the fund’s return and subtracting to it the benchmark’s return for that period, they can calculate the "selection" return.

Goyenko & Amihud (2008) argue that R² is a strong predictor of Mutual fund performance. They achieve this by regressing fund returns on those of multi-factor benchmark models, mainly by Fama and French (1993). The Carhart (1997) multifactor model is also widely use to analysis persistence in mutual fund performance. Essentially, it is based on similar parameters as the Fama-French model except Carhart adds a momentum factor which is defined as the difference in return between the 30% best performing stocks within an equally weighted portfolio over a 12-month period, and the 30% worst performing stock over a 12-month period. In their research, Goyenko & Amihud proved that a negative relation exists between R² and the mutual funds’ performance measure by the CAPM’s alpha. Ultimately, this means that a low R² indicates a large input into the asset allocation strategy by the portfolio manager compared to the passive benchmark. They believe that this relation supresses the need to use benchmarking as per Return Based Style Analysis (RBSA). Though many researchers in Finance make no reserve of the use of multi-factor models such as Fama French (1993) or Carhart (1997), it is important to note that the use of such models have been criticized as being too fitting in the broad context of the such research. For instance, Daniel and Titman (2012) believe that using a wider range than the "traditional" 25 size and book-to-market portfolios would make these Fama French (1993) a much more powerful testing tool. This is seconded by Lewellen et al (2010) who finds that expending the set of benchmark portfolios to also include industry portfolios has a positive effect on the validity of findings through a regressional analysis using those factors. After controlling for style using control variables, Amihud & Goyenko (2012) firstly found that funds within their sample which had the lowest R² produced the highest excess returns, with a maximum associated alpha value of 3.8%. Secondly, they found that some of their control variables such as fund size, or fund manager tenure, were actually quite closely correlated to R² to an extent that they can explain approximately 40% of the variation between funds. This helps them ascertain that indeed R² is a predictor of persistence in fund performance. Finally, the relation held true for mutual funds that invested in other products than equity, such as corporate bonds. These findings have quite a deep meaning for financial research. If their findings were tested in a varied range of markets and were proven to be consistently correct, then investors would have an approachable new tool to forecast the future performance of a selection of mutual funds.

ii.iv. Biases

Because the choice of style benchmark is so crucial in a successful style analysis, further research was done on the actual categorization that funds give themselves, and their accuracy.

Dibartolomeo and Witowski (1997) found that 9% of equity mutual funds were highly misclassified, while 31% were somewhat out-of-category. According to their research this could be due to the fact that existing classification systems are ambiguous, but also that competitive nature of the open-end fund industry pressures managers in rebalancing their portfolios outside their original mission statement. Kim, Shukla and Thomas (2000) support Dibartolomeo and Witowski’s research by finding that 46% of 1043 funds analysed actually had investment attributes that matched their original mission statements. Over the three years of their study, 57% of the funds changed their investment approach at least once.

For the above reasons, Dibartolomeo and Witowski (1997) also argue that that return-based style analysis should prevail over similar approaches such as Holding-Based Style Analysis (HBSA) which solely rely on the fund manager’s stated objectives and the investment style he declares. In order to achieve their style analysis, they used quadratic programming in order to measure the influence of different investment styles on each fund within their sample.

Elton & Gruber (2012) also pointed out biases that might negatively impact any return-based analysis. In their paper, they explain that at their inception many mutual fund families enter an "incubation" period. In this period, funds are opened with different style and limited capital. When the incubation phase is over, the underperforming funds are either merged or closed completely, leaving only the successful ones to be opened to the public. Because only the funds that make the cut will have historical data available, this creates an upwards bias in the information available. Evans (2010) supports this by applying the Fama-French four factor model on US equity mutual funds which ultimately outlined a 3.5% risk-adjusted outperformance compared to nonincubated funds. Though this means that they attract higher flows at their opening, any outperformance seems to disappear over time. Evans finds that using a Fund age control variable is a suitable way of suppressing this bias.

Survivorship in mutual fund performance is another bias discussed by Elton, Gruber & Blake (1996). When funds perform poorly over a certain period of time, or if their total market value is not large enough to be deemed worthy of the managements’ efforts, then they are usually closed completely. In some cases they can also be merged to another fund within the same family. Elton, Gruber & Blake make the assertion that this is done in order for the fund managers to keep receiving their fees on the investors’ capital, but also erase any poor performance from both hard copy and digital databases. Ultimately, their paper finds that when α is examined on the largest and smallest funds within their sample, smaller funds have much worse performance, with a negative α twice as large as the larger funds. This seems to be consistent with the fact that a large number of smaller mutual funds fail to survive compare to the larger ones, and that in turn, those who fail have poorer performance than those who do. Brown, Goetzmann, & Ibbotson (1992) find similar adverse effects of the survivorship bias. According to their research, surviving funds have an apparent persistence in positive performance solely due to the dilution of risk among different fund managers. Moreover, they find that it would have a negative effect on the volatility and return relationship (namely CAPM’s β) on risk-adjusted historical data.

Interim trading can also have a negative impact on any fund performance analysis. This was first described by Fama (1972), when portfolio managers trade in or out of the fund in a way that would affect perceived stock picking ability over several periods of time. For example, a study considers two separate time periods of a fund’s performance. If a significant macroeconomic event occurs between the two time periods, this would increase market volatility, but also imply that expected risk-return ratios are readjusted to be less favourable. Because the data calculated would be an average of both time periods and does not cover the specific market-shifting event, then it would appear as if the fund manager anticipated in part the increase in risk. If a return-based style analysis approach is used, then this would be perceived as superior performance. On the other hand, weigh-based style analysis would considering the difference in weighting between the two time periods and would therefore not create a bias. For this reason, a conditional weight-based approach would be more suitable.

Finally, Ferson & Aragon (2006) describe costs as playing a major role in creating biases. These can include initial joining fees, transaction fees, portfolio managers’ fees, income tax, marketing, and more. When considering mutual fund performance, returns are always net of all these expenses. Additional costs at an individual investor level can be incurred such as load fees, or redemption costs when buying or selling the fund’s units. This means that comparing these fund returns against a passive benchmark’s cost structure can become quickly out of hand. Most previous studies in fund performance consider the benchmark portfolio to be free of any costs, while funds returns are net of all costs and expenses. Most investors would consider that any portfolio managers should be able to earn back trading costs, and therefore would only be considered to add value to the fund past that threshold. Therefore treatment of costs and how they should be accounted for is crucial to get a true perspective on fund performance.

ii.v Conclusion

At both a US and UK level, previous evidence of superior performance which is sustainable in mutual funds is not clear cut. However, style analysis and the correlation between R² and Jensen’s alpha as found by Amihud and Goyenko (2008) are significant tools which can help filter the noise in an attempt to distinguish portfolio managers that bring true added value to their funds, to consistent underperformers. Moreover, careful consideration should be taken into factors that could create negative biases in analysing the data set.

iii. Data

The sample consists of 376 UK unit trusts collected from the Investment Management Association (IMA) database. These are subdivided into four sectors: "UK Equity Income", "UK Smaller Companies", "UK All Companies", and "UK Equity and Bond Income".

"UK equity income" funds aim to build portfolios of equity investments that yield high dividend payments. Therefore their goal is to have a steady growth of capital, with a typical target of at least matching the Retail Price Index [1] . In some cases, they may invest in low or no-dividend equity products as long as they believe that they will contribute to the long-term growth of future earnings. They are usually good alternatives for investors seeking slow growing but high yielding portfolios. "UK smaller company" funds invest in UK based companies which have low to mid-size levels of capitalisation. Normally, they are not restricted to any specific economic sector, and can sometimes invest in transferable securities, or money market instruments. "UK All Companies" funds are less restrictive and can invest in any company that has a registered main office in the United Kingdom. It is important to note however that in most cases this does not constitute the entire portfolio, though a minimum of 65% is usually expected. Finally, "UK Equities & Bonds" will invest in a mix of UK equity and fixed income products with the aim of creating a sustainable income growth over a long time horizon.

The purpose of selecting these four categories is to encompass a large and varied sample of UK unit trusts. Though they all focus on UK based products, they will invest trough different strategies and offer different types of investment solutions for investors. For "UK Equity Income", the sample includes 91 funds. For smaller companies, all companies and Equity & Bond income, the sample includes respectively 49, 216, and 20 funds.

Monthly fund index return data was then collected through the Thomson Reuters Datastream service for the period of 1st January 1990 to 30 December 2011. After filtering for funds which were not listed, or had missing or no data available, the total sample was reduced to 67 funds in the Equity income category, 34 in smaller companies, 159 in all companies, and 11 in equity & bond income, bringing the total to 271. This includes an additional layer of filtering for funds that had less than 24 months of observations .In order to calculate monthly excess returns, equation (1) was applied to each entry:

With the excess fund return at moment t+1, and the fund index returns at moments t+1 and t.

Carhart (1997) factors data was kindly provided by Professor Jonathan Fletcher of the University of Strathclyde.

Control variables were gathered through TrustNet and Morningstar on an individual basis. These are Total Net Assets, the expense ratio, 12-month turnover, fund age, annual and initial charge, and manager tenure. These variables are fixed through the time period.

TABLE 1 – Summary Statistics of control variables

Initial charge

Expense Ratio

Annual Charge

TNA (m£)

Turnover (%)

Fund Age (years)

Tenure

Mean

4.30

1.58

1.44

375.75

15.44

18.48

7.03

Median

5.00

1.65

1.50

147.83

13.26

17.63

6.25

Min

0.88

0.55

0.51

3.67

-1.18

1.50

1.00

Max

5.44

2.09

2.51

5312.43

178.15

46.75

25.25

iv. Methodology

The analysis in this study is two-fold: the individual performance of funds through Jensen’s (1968) alpha, as well as a correlation analysis between R² and alpha.

In order to calculate alpha as well as R², we will use a time-series regression following the Carhart (1997) four-factor model. It uses return vectors Rm-Rf (with Rm being the market return, and Rf the return on a risk-free asset), Small Minus Big stocks (SMB), and High Minus Low (HML) book-to-market ratio stocks. This multi-factor model is defined as:

(1)

Where is the excess return of fund i at time t, is the Jensen (1968) measure of fund i, is the excess return of the market at time t, is a factor mimicking portfolio for size, alongside HML and MOM which are for book-to-market value and Momentum. is the residual for fund i at time t. In in order to control for overestimates within the sample, all future reference to R² will actually be from its adjusted value. This allows to improve the significance of the results by returning a figure that decreases the likelihood of a better fitting model by chance. By default, adjusted R²s have a lower value than the raw R². The null hypothesis is defined as: "Jensen’s (1968) alpha is not related to a regressional R²". Furthermore, we will calculate t-statistics at a 95% confidence level which will allow to control for both type I and type II errors. Having a confidence level of 95% means that the associated t-statistics must be greater than 1.96 for the determinant to be statistically significant.

This regression will be achieved using an Ordinary Least Squares Generalized Method of Moments (GMM) approach.

The GMM approach can be expressed as:

Where is a vector of sample moments, corresponds to the data series, and the parameters. From this, we derive the following, developed by Cochrane (2005) as an OLS GMM framework:

(2)

Using such an approach allows us to create an asymptotic distribution which corrects heteroskedasticity, serial correlation, as well as non-normality.

When fund i has zero abnormal performance.

As the purpose of this paper is to determine if there is a level of R² at which there is a significant correlation with alpha, we name this relationship "selectivity" and define it as:

1-R² =

Goyenko and Amihud (2008) explain that the selectivity measure is higher if the set of portfolios is not as driven by systematic risk than its factors. This is in line with expected findings, as we expect actively managed portfolio returns to be driven by the individual risk associated with stock picking, rather than market risk. Furthermore, if fund managers rebalance their portfolios more actively than the frequency at which betas are calculated (based on monthly returns), then this could drive R² lower.

In an effort to potentially identify the determinants of selectivity, we will apply:

(3)

With being the amount of selectivity from fund j at time t, and R² the estimate from the Carhart (1997) regression. Equation (3) is derived from the Fama-Macbeth (1973) model used by Amihud & Goyenko (2008).

In their model, Amihud and Goyenko (2008) use both a transformed and untransformed R². The transformed R² has a more symmetric distribution, however by using the untransformed approach, they find determinants with greater statistical significance. Therefore we will restrict this analysis using an untransformed R².

We will not use style dummy variables as each fund style has been pre-divided into their respective style. Studying the determinants of selectivity is a very important aspect of this analysis as different factors can significantly impact the findings in section 5.

v. Empirical Analysis

v.i UK Small Companies

v.i.i Results

After running an OLS GMM regression using the Carhart (1997) four-factor model, we find the results depicted in table 2 below.

TABLE 2 - Summary statistics for UK Small Companies mutual funds

Expense Ratio

Total Net Assets

Turnover

Fund Age

Tenure

R²

Alpha

Mean

1.62

196.21

18.98

19.09

7.78

0.8552

0.0059

Median

1.66

115.35

19.75

17.5

8

0.8689

0.0062

Minimum

0.86

10.7

-4.6

5

1

0.6509

-0.0061

Maximum

1.94

1037.1

33.1

49

25

0.9246

0.0121

We find a mean value for R² of 0.8552, which means that on average 14.5% of the fund returns in this category can be attributed to selectivity. The associated alpha value is 0.0059. This is in contrast of a maximum selectivity of 34.9% and a minimum of 7.5%. These results imply that for the majority of the funds in this category, around 85% of their returns can be attributed to the replication of a stock market index.

There is a large spread in Total Net Assets, which ranges from 10.7 to 196.21 million GBP. The same can be said about fund age, with a minimum value of 5 years, up to a maximum of 49 years. Because of this spread, biases described in section 2.4 could have a potential impact on these findings.

Overall, the average fund in the sample did manage to outperform its benchmarks by using stock picking, with an average value for alpha of 0.0059.

v.i.ii Correlation Analysis

TABLE 3 – Control variables, and correlation analysis

 

Expense Ratio

Total Net Assets

Turnover

Fund Age

Tenure

R²

Expense Ratio

1

TNA (£)

0.1026

1

Turnover (%)

-0.1266

0.0334

1

Fund Age

-0.0474

0.0978

0.0278

1

Tenure (years)

0.1470

0.3062

0.1188

0.180

1

R²

0.0994

0.0346

0.3402

0.2943

0.1223

1

Alpha

0.1253

0.3382

0.1130

0.1706

0.0495

-0.1446

Within the small funds sample, there is a negative correlation of -0.1446 between R² and alpha. This shows that during the time period, mutual funds with higher selectivity (lower R²) have generated higher excess return (higher alpha). Fund age also seems to have a positive effect on returns. With a 34.02% correlation with R², it appears that "UK small companies" mutual funds that have been around for longer periods of time have a better chance at giving stakeholders better results. Interestingly though, the link between manager tenure and fund age, as well as manager tenure and R² are not as high. Implications are that even if the portfolio manager has been in place for a long time, his experience does not guarantee as much above-normal returns compared to the fund’s age. This partly matches results from Chevalier and Ellison (1999) who find that young portfolio managers tend to avoid excess risk. This implies that managers with lesser experience in a specific fund will have a higher R² which in turn affects the results of the overall sample. Part of these findings could also be explained by the survivorship bias, as older funds can merge successful sub-funds into their existing portfolio offerings, but also get rid of poor performing ones, which in turn erases traces of their impact.

Within this sample, turnover has a strong impact on R². With a correlation coefficient of 0.3402, the lower the amount of selectivity in the mutual fund, the higher the turnover. This infers that greater selectivity can be associated to more frequent trading. Portfolio re-balancing is an important aspect of fund management, and for UK Small company funds, this means that they tend to target a higher benchmark replication by doing so, rather than try to time the market for abnormal excess return. This could perhaps be partly explained by the fact that smaller companies tend to have higher inherent risk due to their smaller levels of capitalisation, and therefore credit and bankruptcy risk.

v.i.iii Determinants of Selectivity

TABLE 4 – Determinants of Selectivity in UK Small Companies

 

Coefficients

Standard Error

t Stat

P-value

Expense Ratio

-0.0634

0.0646

-0.9813

0.3363

Total Net Assets

-0.0966

0.2228

-0.4334

0.6686

Turnover (%)

-0.0718

0.0742

-0.9672

0.3431

Fund Age (years)

-0.0796

0.0562

-1.4156

0.1697

Tenure

0.0092

0.0345

0.2666

0.7921

What we learn from this test is that none of the control variables have t-statistic values that have an absolute value large enough to be statistically significant in explaining the determinants of selectivity. This is not necessarily surprising as it can expected for some samples with large spreads within certain factors (TNA for example) to fail to produce particular trends that give noteworthy results.

v.ii Equity & Bonds Mutual Funds

v.ii.i Results

Below in Table 5 are the results from the OLS regression on UK Equity and Bonds mutual funds from the sample.

TABLE 5 - Summary statistics for UK Equity and Bonds mutual funds

Expense Ratio

Total Net Assets

Turnover (%)

Fund Age

Tenure

R²

Alpha

Mean

1.61

188.35

12.18

18.4

9.2

0.7703

0.0043

Median

1.63

164.7

13

17.5

9

0.8136

0.0046

Minimum

1.33

0.7

0.7

8

1

0.4411

-0.0013

Maximum

1.87

514.4

17

39

19

0.9171

0.0087

With a mean value of 0.7703 for R², on average 22.97% of returns can be attributed to selectivity which is lower than for UK small company funds. There is a large spread between both tenure and fund age with minimum values of 1 and 8, and maximum values of 19 and 39. There is a markedly large spread in total net assets within the sample, as the smallest funds hold £0.7 million and the largest £514.4 million. Expense ratios on the other hand are very similar to the previous sample, with a small spread of 1.33 to 1.87. This spread is rather typical of mutual funds in general and is not specific to an investment style.

Though the average value is quite similar to other style sample, interestingly there is a large difference between the maximum and minimum value of R² (0.9171 and 0.4411). It was originally anticipated that the R² range would be tighter than other samples because of the specificity of the products traded. Indeed this sample is the only one to incorporate bonds as well as equity instruments. As Equity and Bonds mutual funds typically have a published objective of sustainable growth, it is conceivable that a fair weight is giving to products such as high quality government bonds as well as corporate bonds. Because the time period in this paper covers two major financial crises including the "dot com" crisis in 2000 as well as the more recent global recession which started in 2008, the availability of government bonds in Western Europe was drastically reduced. This means that if managers wanted to rebalance their portfolios, the choice in fixed income products quickly became narrower. It would then impact the resemblance between their holdings and the market benchmarks as investors converged towards the same few viable investments left. It was also affected by exceptional volatility in the equity markets. In the case of equity and bonds mutual funds, it would be fair to assume that an increased focus on bonds in parallel to their lack of availability during that time would affect R² in an upward fashion. However, it is interesting to see that some funds within the sample had more of a risk taking strategy than others, and perhaps focused more strongly on high risk equity products than others.

Though some funds had a negative alpha value, the average mutual fund in the sample exceeds the performance of the benchmark with a corresponding alpha of 0.0034.

v.ii.ii Correlation analysis

TABLE 6 - Control variables, and correlation analysis

 

Expense Ratio

TNA

Turnover

Fund Age

Tenure

R²

Alpha

Expense Ratio

1

TNA (m£)

-0.0886

1

Turnover (%)

-0.2830

-0.1202

1

Fund Age

-0.1751

0.3235

0.0916

1

Tenure

-0.0784

-0.1533

-0.4122

0.4371

1

R²

0.0412

0.3553

-0.0715

0.0121

0.0077

1

Alpha

0.0807

0.0846

0.5026

-0.0581

-0.3307

0.0288

1

Table 5 shows a remarkable correlation between R² and Alpha of 0.0288. This means that there is a positive relationship where to a 2.88% correlation level, higher excess returns and portfolio replication move in unison. This figure is opposite to findings from previous research from Goyenko and Amihud (2008). However, this could be explained by the size of the sample, which after filtering for missing data only accounts for 11 funds in total. Therefore the statistical significance of such a small universe could be negatively impacted. Additionally, the specificity of the investments products which include both equity and bonds cannot explain such a drastic difference in findings compared other samples in this analysis.

Other variables within the sample have strong relationships that are noteworthy. Alpha and Total Net Assets have a positive correlation of 8.46%. This implies that the higher the fund alpha, the higher the amount of assets it holds. In short, smaller funds have produced smaller excess returns than funds with large amounts of cash. This is contradicted by a 35.61% correlation between R² and TNA which means that the larger the fund, the more it replicates its benchmarks. This is in line with Amihud & Mendelson (2010) who find that larger funds tend to hold a larger number of stocks in their portfolios than funds with low TNAs as selling them could incur serious liquidity issues. More stocks in a portfolio is typically synonymous with better diversification, hence the higher R². Berk & Green (2004) actually found that as some mutual funds are increasingly successful in their investment strategies, they increase their number of holdings which in turns damages their long term performance (higher R², lower alpha). Koijen (2008) also explains that large funds might have higher R² than smaller funds in an attempt to gain higher utility by appearing as a larger fund in terms of size in the league tables. This would also imply that this incentivises smaller funds to take more risk and therefore have more idiosyncratic risk components in their portfolios in order to grow. This means they will have lower associated R²s when successful, and when successful in their strategies, a higher alpha. With time, this would help them increases their TNA, as well as their standing in the league tables.

There is also a strong positive correlation of 43.71 % between fund age and tenure within this sample. Funds that have been trading the longest seem to have portfolio managers which have a longer experience within their respective funds. As there is also a negative correlation between Fund Age and Alpha, this slightly contradicts the expectations that more experienced managers within the equity & bonds product line will take more risks than inexperienced ones.

v.ii.iii Determinants of selectivity

TABLE 7- Determinants of selectivity for UK Equity & Bonds

 

Coefficients

Standard Error

t Stat

P-value

Expense ratio

-0.2935

0.2589

-1.1336

0.3203

TNA

-0.2484

0.0956

-2.5993

0.0601

Turnover

-0.1817

0.1244

-1.4612

0.2178

Fund Age

0.2366

0.2677

0.8837

0.4268

Tenure

-0.1203

0.1125

-1.0701

0.3448

Within this sample, the only factor with an absolute t-stat greater than 1.96 is Total Net Assets which has a negative coefficient of -0.2484. This would infer that the smaller the fund in terms of holdings, the more selectivity there is. This could be explained by the fact that larger funds have the financial ability to diversify the portfolios more efficiently, and as noted in section 5.2.2 hold a larger number of investments in order to avoid liquidity issues. This would in turn increase the similarity between their portfolios and passive benchmarks which would therefore affect selectivity.

v.iii UK All Companies

v.iii.i Results

TABLE 8 – Summary statistics for UK All Companies mutual funds

Expense Ratio

TNA (m£)

Turnover

Fund Age

Tenure

R²

Alpha

Mean

1.516

395.7

10.8

17

6

0.8907

0.0036

Median

1.62

166.6

10

14

5

0.9004

0.0033

Minimum

0.27

3.1

-4.3

1

1

0.5445

-0.0017

Maximum

2.56

3819.3

35.9

50

31

0.9952

0.0101

Within the UK All Companies category, we observe an average value of 0.8907 for R² which ranges from 0.5445 as a minimum value and 0.9952 as a maximum. This means that the average fund within the sample used 10.93% of stock-picking. This sample also generated an average alpha value of 0.0036 with a minimum of -0.0017 and a maximum of 0.0101. Therefore on average, the mutual funds within the sample did exceed their benchmarks.

The minimum and maximum values of R² are actually quite interesting as they show the difference in portfolio manager intervention in these funds. An R² of 0.9952 means that there is a near perfect replication of the fund holdings with a passive benchmark. This is what investors call "closet indexing", as described in section 2.1. This is usually done because managers feel that it is a safer strategy in uncertain markets. However, because of the large time period considered in this paper, it is reasonable to assume that this secret indexing is not a temporary strategy, but rather a long term approach. Interestingly, this fund has a corresponding alpha value of 0.0030 which is just 0.0006 shy of the mean alpha value for this sample, therefore slightly contradicting the idea that such a high R² would have a significant impact on the resulting alpha.

Yet again, there is a very large spread between funds in terms of TNA, with the smallest funds managing £3.1 million, and the largest £3.8193 billion. This is to be expected as the sample universe contains over one hundred funds.

v.iii.ii Correlation Analysis

TABLE 9 - Control variables, and correlation analysis

 

Expense Ratio

TNA

Turnover

Fund Age

Tenure

R²

Expense Ratio

1

Total Net Assets

-0.1930

1

Turnover (%)

0.1671

0.0479

1

Fund Age (years)

-0.1430

0.1659

-0.1090

1

Tenure

-0.0756

0.0137

0.0460

0.1324

1

R²

-0.2007

0.0531

-0.1873

-0.0289

0.0588

1

Alpha

-0.0971

0.0352

0.2430

-0.0465

-0.0135

-0.1783

The correlation between R² and alpha is -17.83%, therefore there is an inverse relationship between excess return and benchmark tracking within the sample.

Interestingly, there is also a negative relation between expense ratio and R² which would signify that the more investors pay to upkeep fund operations, the more the fund manager stock-picks compared to its benchmark. This would be expected from investors who would rather pay a larger fee to buy into the experience and diversification skills of a money manager, rather than opt for low cost tracker funds such as Exchange Traded Funds (ETFs). However, within the sample universe, there is a negative relation between that expense ratio and fund age which would indicate that younger funds would charge higher expenses. Because these funds invest in all UK Equity companies, portfolios would include both large and small capitalization companies. This spectrum of investments could require higher operating costs, especially for younger funds with less experience, as they require extensive investment research. Portfolio rebalancing would be a more frequent occurrence as well, which would affect trading costs as well as turnover. Interestingly, funds within the sample that have a higher turnover of assets have a higher associated alpha. Because of the negative correlation of -10.90% between turnover and fund age, we can assume that younger funds generate more excess return by having a higher turnover than older funds which tend to have lower expense ratio and less portfolio interference. This could perhaps be pinned on more experience managers being able to successfully identify "winning" strategies which they can hold longer

v.iii.iii Determinants of selectivity

TABLE 10 – Determinants of Selectivity for UK All Companies

 

Coefficients

Standard Error

t Stat

P-value

Expense Ratio

0.0426

0.0111

3.8269

0.0002

Total Net Assets (£)

-0.0177

0.0081

-2.1998

0.0295

Turnover (%)

-0.0286

0.0220

-1.2992

0.1961

Fund Age (years)

-0.0044

0.0153

-0.2856

0.7756

Tenure

-0.0054

0.0119

-0.4545

0.6502

This sample returns interesting results in terms of selectivity figures. There are two determinants that have t-statistics greater than 1.96: expense ratio, total net assets, and Alpha. With a coefficient of 0.0426, expense ratios seem to have a small effect on selectivity. This means that the higher the fund charges investors for its expensive the more selectivity is applies to its portfolios. This could perhaps be explained by the fact that these funds have larger operating costs and that investors are willing to pay the premium as they are not able to create portfolios that replicate their strategies themselves.

In this sample, TNA also plays a role in determining selectivity though it has a fairly insignificant coefficient of -0.0177. Interpretations for this can be reviewed in section 5.2.3.

It is interesting to note that though both coefficients have associated t-stats that make them significant, neither of them are quite large enough to make them particularly noteworthy. Therefore we cannot say that even within this sample that either TNA or expense ratio plays a significant role in determining higher levels of selectivity.

v.iv UK Equity Income

v.iv.i Results

TABLE 11- Summary statistics for UK Equity Income mutual funds

Expense Ratio

Total Net Assets

Turnover

Fund Age

Tenure

Alpha

R²

Mean

1.55

725.7

10.54

20.8

5.9

0.00374

0.82603

Median

1.64

171.2

10.5