Mutual Funds

1. Introduction

Mutual funds are increasingly common investment vehicles throughout the world. Theoretically, mutual funds have many advantages, including the following (DeFond et al., 2011):

• Diversification

• Regulation

• Professional management

• Information reporting requirements

• Liquidity

In exchange for these advantages, mutual funds charge fees to investors. The four most commonly recognized types of mutual funds are equity funds, balanced funds, fixed income funds, and money market funds. 

Of these types of funds, equity funds have the highest return potential as well as the highest risk potential, because equity funds invest in stocks that are subject to significant volatility. Money market funds have the lowest risk potential as well as the lowest return potential, as these types of mutual funds invest in fixed income securities of high quality and short-term duration, including Treasury bills and certificates of deposit.  Fixed income funds are riskier than money market funds but also have a higher return potential. This type of mutual fund is focused on bonds, mortgages, and debentures. Balanced funds are riskier than fixed income funds, but not as risky as equity funds. This type of mutual fund invests in different asset classes depending on opportunities detected by the mutual fund manager. Investors are warned about engaging with fraudulent managers.

The great recession of 2008, also known as the global financial crisis, affected mutual funds along with all other classes of investments. The great recession was the worst global financial crisis since the great depression of 1929 and saw the erosion of a great deal of wealth invested in mutual funds as well as other vehicles (Mankiw, 2011). The recession of 2008 was the first global financial crisis to have taken place during the widespread existence of mutual funds, which, in their current form, did not proliferate until after the great depression. In 1929, there were fewer than 800 mutual funds in existence while, by 2008, there were roughly 12,000 mutual funds dispersed throughout the world. Clearly, then, the recession of 2008 provides an opportunity to understand how financial crises affect mutual funds.

The focus of this empirical analysis is on the following research questions:

RQ1: To what extent did the great recession impact the returns of U.K. mutual funds?

RQ2: To what extent did the great recession impact the Sharpe ratios of U.K. mutual funds?

RQ1 offers the opportunity for inferential statistical analysis, especially regression. Regression can be used to model the impact of time changes on mutual fund returns. The second research question will draw upon the same inferential methods as the first, but with a different dependent variable. The Sharpe ratio is a highly informative datum; however, for purposes of robustness, the Sortino ratio and Treynor ratio were also utilized as dependent variables for RQ2. Data were collected on Alpha and Beta as well.  

In terms of descriptive statistics, mean, standard deviation, skewness, and kurtosis data were collected for U.K. mutual funds. In order to understand mutual fund performance in context, comparisons were made to different asset classes, with fuller details provided under the discussion of methodology. The window for analysis was chosen based on the observation that the U.K. entered recession in Q3 2008. Hence, the pre-recession period was 6/30/2003 to 6/30/2008. The U.K. officially came out of recession in Q4 2009, so the post-recession period was designated as 10/1/2009 to 10/1/2014.

This study has both an academic and a practical component. Academics have displayed a high level of interest in the performance of mutual funds, and this study represents a contribution to that body of literature, not merely in duplicating the results of past findings but also in applying some new statistical techniques (such as different forms of time series analysis in addition to the traditional ordinary least squares approach) to the measurement of mutual fund performance before and after the great recession. However, perhaps more importantly, the study’s results have practical implications for investors considering how to allocate their investment funds during a recession. The global recession of 2008, while not widely anticipated, certainly followed the template of past bubbles, with several financial authorities having called attention to the unsustainability of collateralized debt obligations (CDOs) and other securities attached to a booming subprime market (Laux and Leuz, 2010). Canny investors, reading the signs of recession—or even deciding to respond in the early days of what is presumed to be a recession—will want to know how to rebalance their portfolios in such times. The analysis performed in this study is likely to be of use to such investors in deciding what kind of role mutual funds ought to play in times of financial crisis.    

The main findings in the study were that there were time-dependent effects in the data—in other words, that the recession did seem to exert some causal impact on both the returns of U.K. mutual funds and on their Sharpe ratios. The positive autocorrelation and other time-dependent effects in the data mean that the use of OLS regression models to examine the impact of the recession on U.K. mutual funds is not likely to be an effective approach. The ARIMA model used in this study, accompanied by other forms of time-series analysis, is more likely to be appropriate for the U.K. mutual fund data. 

2. Characteristics of the Sample Data

The sample data were drawn from the Bloomberg database. An important problem to be considered in gathering the sample was survivorship bias. Because several mutual funds closed over the course of the study period, excluding these mutual funds would have resulted in the artificial inflation of mutual fund performance. However, because the smallest unit of analysis in the study consisted of mutual fund class (choosing from among equity funds, money market funds, fixed income funds, and balanced funds), average each quarter’s (a) returns and (b) Sharpe ratios for each existing mutual fund in the sample allowed the problem of survivorship bias to be successfully addressed. In other words, the calculations of the dependent variables reflected contributions from every listed U.K. mutual fund that was active during a given quarter, providing a more accurate estimation of returns and Sharpe ratio than if specific mutual funds had been tracked over a given time period, which would necessarily have imposed a survivorship bias by excluding short-lived mutual funds. Because there were different numbers of mutual funds active in each quarter, the sample size varied from quarter to quarter.    

In addition to the mutual fund data, data were collected from the FTSE All-Share, FTSE 100, the S&P GSCI, the FC Tremont Hedge Fund Index, and the U.K. Government Bond Index. Hence, stocks, bonds, commodities, and hedge funds were all compared to the performance of the mutual funds in the sample. The longitudinal model of the study appears in Table 1 below. Note that there are 46 quarters in the dataset, with data from Q3 2003 to Q1 2009 representing the pre-recessionary period and data from Q2 2009 to Q4 2014 representing the post-recessionary period. The actual data categories collected for each asset type are presented in Table 2. The schemas in Tables 1 and 2 guided both data collection and data analysis for the study.   

(Table 1 omitted for preview. Available via download).

(Table 2 omitted for preview. Available via download).

3. Presentation of Results

The results will be presented in the following order. First, the results pertaining to mutual fund performance (as returns) will be presented. Second, the results pertaining to mutual fund Sharpe ratio will be presented. Third, the mutual fund performance characteristics will be examined in light of the performance of the other asset classes.

3.1 Mutual Fund Performance (Returns): Entire Sample

During the entire period of the sample, the mean mutual fund return was -0.09% (SD = 2.62), that is, fairly close to 0, with a small standard deviation. The smallest observed return was -7.67%, while the larger observed return was 6.2%. The variance was 6.90, skewness was -0.47, and kurtosis was 4.28. The distribution was clearly leptokurtotic, which was to be expected; mutual fund performance theory suggests that extreme outliers are unlikely, which implies leptokurtosis. The time series trend in mutual fund performance is presented in Figure 2 below:  

(Figure 2 omitted for preview. Available via download).

The data presented in Figure 2 are of interest. Note that there are clear linear effects leading up to the recession of 2008 (see in particular performance between quarters 190 and 200, which were coded in that manner because Stata codes q = 1 as 1960q1). Afterward, there is a period of heterogeneity of returns followed by what looks to be an asymptotic convergence back to just above 0. In the post-recession period, there are bouts of high returns that were not apparent in the pre-recessionary period. While the descriptive statistics inform us that the mean performance of U.K. mutual funds over this time period was essentially flat, the time series dynamics clearly tell another story, one that requires further statistical analysis.

The first step in exploring these dynamics was to fit an ARIMA model with two AR terms, first-differencing, and no moving-average terms—hence, an ARIMA(2,1,0). At an α of 0.10, both the coefficients were significant:

• L1 coefficient = -0.28, p = 0.02

• L2 coefficient = -0.22, p = 0.07

There, therefore, seemed to be some temporal dependence in the mutual fund performance data. Next, the stationarity of the ARMA process was checked by determining whether the inverse roots of the AR polynomial lay inside the unit circle, which they did:  

(Figure 3 omitted for preview. Available via download).

The stability of the VAR allows valid inferential results to be obtained from the ARIMA. Next, the dependence structure of mutual fund performance was analyzed using a plot of parametric autocorrelations of mutual fund performance: 

(Figure 4 omitted for preview. Available via download).

The autocorrelations display a clear exponential decay towards 0, which tends to occur with stationary AR processes. Finally, because of the exogenous shock represented by the recession, an impulse-response function (IRF) was created for the ARIMA model. The IRF suggests that there is actually an increase in mutual fund performance as the result of the recession, but an increase that rapidly converges back to 0 by quarter 8 after the recession. The results of the IRF graph add some context to the time-series graph (see Figure 2), in which mutual funds appeared to do well after the recession. The 95% confidence band in Figure 5 is thick, further solidifying the impression that there were winners and losers during this time rather than the entire mutual fund class shifting.  

(Figure 5 omitted for preview. Available via download).

Having confirmed that the mutual fund returns process was stationary (see Figure 3), it was of particular interest to try to decompose mutual fund performance into random components through the measurement of spectral density. To some extent, Figure 2 supports the use of some kind of spectral density calculation, because there were numerous results above and below the mean. The mutual fund return data were fitted to a first-order autoregressive process, and the statistically significant (p < 0.001) coefficient for the autoregressive coefficient was 0.54. Therefore, there was positive autocorrelation in the series, confirming intuitive responses to Figure 2. Next, the spectral density of the process was measured, yielding Figure 6.  

(Figure 6 omitted for preview. Available via download).

Because the curve is highest at 0, and then tapers off asymptotically close to 0, we can infer that there was a low-frequency random component—namely, the recession itself—that was the most important random component of the AR process. In other words, the recession has some causal power in explaining time-dependent variations in U.K. mutual fund performance. In fact, because of the causal power of the regression, the use of an ordinary least squares (OLS) regression is not appropriate for the data. Based on the data collected for this study, the adjusted R2 for mutual fund returns was -0.0037, indicating that linear approaches are a bad fit for the data. This adjusted R2 is different from that reported in some previous results, which could be because (a) the time period for this study was somewhat wide (5 years before and 5 years after the recession) and (b) any U.K. mutual fund that was active in any of the quarters of the study contributed to the data. There might be survivorship bias in studies that have pooled results from mutual funds based on their length of existence.  

Another means of establishing the causal power of the recession is to perform a cumulative periodogram white-noise test, accompanied by Bartlett’s statistic and a p value. This periodogram appears in Figure 7 below: 

(Figure 7 omitted for preview. Available via download).

Having performed these various time series analyses, it has been established that (a) there are significant temporally dependent effects in U.K. mutual fund return data and (b) these effects appear to be related to the recession. To further explore this finding, the sample was divided into pre- and post-recession years and some of the time series analyses conducted on the entire sample were then conducted on the pre- and post-recession data in isolation The results are presented below. 

3.2 Mutual Fund Performance (Returns): Pre- and Post-Recession Samples

Time dependence was measured separately for the 23 pre- and the 23 post-recession U.K. mutual fund performance data. For each of the sub-datasets, an ARIMA model was fit with two AR terms, first-differencing, and no moving-average terms, that is, ARIMA(2,1,0). At an α of 0.10, neither of the coefficients was significant for the pre-recession period:

• L1 coefficient = -0.18, p = 0.59

• L2 coefficient = 0.17, p = 0.82

There, therefore, did not appear to be some temporal dependence in the mutual fund performance data in the pre-recessionary period, so no further time series analysis of this period was carried out. In fact, an OLS regression is a good fit for mutual fund performance in the pre-recession era, with an adjusted R2 of 0.70 and a β coefficient per quarter of -0.32, at p < 0.001. The OLS regression equation was as follows:

U.K. Mutual Fund Returns in Pre-Recession Period = (Quarter)(-0.32) + 2.54 

The time-dependent effects begin to appear after the recession. An ARIMA(2,1,0) was run on the post-recession performance of U.K. mutual funds. At an α of 0.01, both of the coefficients were significant for the pre-recession period:

• L1 coefficient = -0.63, p = 0.005

• L2 coefficient = -0.54, p = 0.001

Next, the stationarity of the ARMA process for the post-recession values of U.K. mutual fund performance was checked by determining whether the inverse roots of the AR polynomial lay inside the unit circle, which they did:

(Figure 8 omitted for preview. Available via download).

The process of U.K. mutual fund performance after the recession was, therefore, both time-dependent and stationary. The next step in the time-series analysis was to compare the IRF graph for the post-recession values only with the IRF graph for the entire dataset. This comparison, provided in Figure 9 below, confirms that there are stronger exogenous shock-related effects in the post-recessionary period. Note that the initial increase after step 1 is much stronger for the post-recessionary mutual fund performance data than for the entire dataset, which seems to suggest that a number of U.K. mutual funds were able to find significant opportunities for return in the wake of the recession. However, this effect seems to have peaked in the two quarters after the recession, after which a return to 0 can be been in the IRF graph of the post-recessionary return data. These graphs add further validity to the claim that the great recession constituted a meaning shock for U.K. mutual funds, and that the shock provided a narrow window of opportunity in the quarters after the recession.  

(Figure 9 omitted for preview. Available via download).

There is another factor that deserves discussion in terms of the pre- versus post-recession performance of U.K. mutual funds, namely the identification of a structural break. Given the time-dependent effects identified in the model, it is likely that there is such a break in the data. A modified Chow test was conducted on the data, with the results presented in Table 3 below. The estimated break date was found to be Q1 2007, significantly earlier than the beginning of the recession. The identification of this breakpoint suggests that factors ultimately resulting in the great recession were already beginning to drive down the performance of U.K. mutual funds at the beginning of 2007.   

(Table 3 omitted for preview. Available via download).

It is not clear why the breakpoint is so much earlier than the recession itself. The breakpoint was identified with a modification of the Chow test that was recently made available in Stata 14, and that might, therefore, yield different results than those obtained in previous studies. 

3.3 Mutual Fund Performance (Sharpe Ratio): Entire Sample

Mutual funds’ Sharpe ratios for the entire period of the sample are presented in a histogram in Figure 10 below, followed by a longitudinal presentation in Figure 11. There does not appear to be linearity in the data, but there is a possible time-dependent effect visible around the time of the recession. The lowest observed Sharpe ratio for mutual funds was -3.9, while the highest observed value was 0.207. The mean Sharpe ratio for mutual funds was -1.13 (SD = 1.05). The variance was 1.11, skewness was -1.15, and kurtosis was 3.57. The distribution was thus leptokurtotic, but not as much as the distribution for returns, indicating that risk-adjusted returns were more evenly distributed across the years considered in the sample.  

(Figure 10 and 11 and omitted for preview. Available via download).

An OLS regression confirmed that the Sharpe ratio was not a good candidate for linear fitting, p = 0.85, adjusted R2 = -0.02.

Next, an ARIMA(2,1,0) was run on the Sharpe ratios. At an α of 0.01, only one of the coefficients was significant for the pre-recession period:

• L1 coefficient = -0.43, p = 0.003

• L2 coefficient = -0.09, p = 0.52

Because this ARIMA was not significant, a much simpler ARIMA, a differenced first-order autoregressive model—ARIMA (1,1,0) was attempted, with the following result:

• L1 coefficient = -0.47, p < 0.001 

Next, the stationarity of the ARMA process for the Sharpe ratios was checked by determining whether the inverse root of the AR polynomial lay inside the unit circle, which it did:

(Figure 12 omitted for preview. Available via download).

Finally, an IRF graph was generated for mutual funds’ Sharpe ratios. This graph is presented in Figure 13 below, in conjunction with the IRF graphs for mutual fund returns over the entire sample (top left) and mutual fund returns over the post-recession period.  

(Figure 13 omitted for preview. Available via download).

The IRF indicates a sudden decline in Sharpe ratios after the recession, but, by the second quarter after the recession, the effect is close to 0 again. The time-dependent effects on the Sharpe ratio faded out much more quickly than did the post-recession effects of mutual fund returns. A cumulative periodogram white-noise test whose results are presented in Figure 14 further confirmed that the changes in Sharpe ratio over time were not a white-noise process, Bartlett’s statistic = 3.01, p < 0.001.     

(Figure 14 omitted for preview. Available via download).

Next, a modified Chow test was conducted on the data, with the results presented in Table 4 below. The estimated break date was found to be Q3 2008, right at the beginning of the recession. It was at around this time that Sharpe ratios began to decline, indicating that risk-free investments became better alternatives to mutual funds. Note, however, that the break date for returns was Q1 2007. An investor who had been looking to exit mutual funds on the basis of returns would, therefore, have diversified away from this asset class around one a half years earlier than if Sharpe ratios had been the criterion.  

(Table 4 omitted for preview. Available via download).

3.4 Mutual Fund Performance (Sharpe Ratio): Pre- and Post-Recession Samples

In order to study mutual funds’ Sharpe ratios before and after the recession, two separate OLS regressions were conducted. The regression of the pre-recession data was significant at an α of 0.10 (p = 0.08), but adjusted R2 was only 0.0944. The OLS regression equation was as follows: Sharpe ratio = (Quarter)(-0.05) + 7.39 

Thus, in every quarter before the recession, Sharpe ratio declined by 0.05, indicating the steadily waning attractiveness of mutual funds in relation to risk-free investment vehicles. This finding was as expected. The regression of the post-recession data was significant at an α of 0.001 (p = 0.0003), and the adjusted R2 was 0.44. The OLS regression equation was as follows: Sharpe ratio = (Quarter)(0.12) – 24.22 

(Figure 15 and 16 omitted for preview. Available via download).

An ARIMA of 1,0,0 was conducted on the pre-recession Sharpe ratios, with the coefficient being -0.44 (p = 0.017).  The negative value of the coefficient predicted mean-reverting behavior with an alternation of signs, which seems consistent with a random walk around the mean. The suspicion of a random walk was confirmed by a cumulative periodogram white-noise test in which Bartlett’s statistic (1.19) was not significant (p = 0.12).  

(Figure 17 omitted for preview. Available via download).

Given the suspicion of a random walk / white noise, no further time series analysis was conducted on the pre-recession Sharpe ratio data.  Next, an ARIMA of 1,0,0 was conducted on the post-recession Sharpe ratios, with the coefficient being -0.54 (p = 0.007).  The negative value of the coefficient predicted mean-reverting behavior with an alternation of signs, which seems consistent with a random walk around the mean. However, the suspicion of a random walk was not confirmed by a cumulative periodogram white-noise test in which Bartlett’s statistic (1.89) was significant (p = 0.0016).  

(Figure 18 omitted for preview. Available via download). 

These findings suggest that, after the recession, there was a more systematic return to higher Sharpe ratios, probably explained by investors returning to mutual funds that had increasing returns over their investment solely in the stock market (as also demonstrated in Figure 2). 

Interestingly, there did not appear to be a linear relationship between the Sharpe ratio and the return of U.K.. mutual funds, p = 0.70. Theoretically, there should have been more flight away from mutual funds at lower returns, but this effect was not seen in the data, for reasons that deserve to be examined further.

(Figure 19 and 20 omitted for preview. Available via download).

3.5 Comparative Performance Overview

Table 5 contains an overview of the pre-recession data of interest for the FTSE All-Share, FTSE 100, the S&P GSCI, the FC Tremont Hedge Fund Index, the U.K. Government Bond Index, and the U.K. mutual fund portfolio constructed for this study.

(Table 5 omitted for preview. Available via download).

(Table 6 omitted for preview. Available via download).

Mutual funds underperformed the other asset classes during the recession and outperformed after the recession. It is therefore not clear why mutual funds had lower Sharpe ratios. One possibility is that the method used to calculate relevant figures for mutual funds (in which any mutual fund active in at least quarter contributed data to the study) was different from the methods used for the other asset classes, accounting for some of the possible disparities. In other words, there might be survivorship bias in some of the aggregate figures for the other asset classes obtained from the Bloomberg database. 

4. Raw Data (Mutual Funds Only)

(Raw data omitted for preview. Available via download).

References

Defond, M., Hu, X., Hung, M. & Li, S. 2011. The impact of mandatory IFRS adoption on foreign mutual fund ownership: the role of comparability. Journal of accounting & economics, 51, 240-258.

Laux, C. & Leuz, C. 2010. Did fair-value accounting contribute to the financial crisis? The journal of economic perspectives, 24, 93-118.

Mankiw, N. G. 2011. Principles of economics, New York, NY, Cengage.