Active fund management: The case of global asset allocation funds

Transcription

1 Active fund management: The case of global asset allocation funds Norris L. Larrymore a,*, Javier Rodriguez b,1 adepartment of Finance, School of Business, SB-DNF, Quinnipiac University, 275 Mount Carmel Avenue, Hamden, CT 06518, USA bgraduate School of Business Administration, University of Puerto Rico, P.O. Box 23332, San Juan, Puerto Rico * Corresponding author. Tel.: ; fax: addresses:norris.larrymore@quinnipiac.edu (N. Larrymore), and jarodrig@upracd.upr.clu.edu (J. Rodriguez). 1 Tel.: ext

2 Active Fund Management: The Case of Global Asset Allocation Funds Abstract Using a unique daily data set and a modified Sharpe (1992) Return-based Style Analysis methodology to create a three and a nine index model, this paper examines the value of active fund management of global asset allocation funds over the period Prior studies fail to consider the dynamic reapportioning of assets in measuring asset management performance. We introduce an alternative methodology derived from Sharpe (1992) Return-based Style Analysis to calculate attribution returns that serve to measure active fund management performance. We define an attribution return as the difference between the actual monthly fund return and the return that would have been generated by the apportionment of assets in the previous month. Consistent with prior studies, our results suggest that a sample of global asset allocation funds add value to their investors, as evidenced by a positive and statistically significant attribution return for fund survivors. Not surprisingly, the subgroup of surviving funds outperforms subset of non-survivors. JEL classification: F21, G11, G15 Keywords: Style analysis; Global asset allocation funds; Active fund management 1

3 1. Introduction Global asset allocation funds have not attracted the attention of academic researchers. However, the attractiveness of these funds is gaining traction among investors seeking alternative paths to diversification of their portfolios. This paper seeks to inform the debate on whether those who rebalance their portfolios with global asset allocation funds are correct. Global asset allocation funds are part of the family of hybrid mutual funds, which also includes domestic asset allocation funds, balanced mutual funds, and flexible portfolio funds. These funds differ from traditional global or international mutual funds in that they face fewer investment restrictions, 2 which along with information costs have discouraged investments abroad. They are known to actively shift assets across asset classes within a global framework. Due to the investment philosophy of these funds to dynamically rebalance, traditional performance measures may fail to correctly calculate the value they provide to their investors because conventional measures assume that allocation is fixed. The difficulty faced by researchers is that fund managers rarely report their allocation with a frequency higher than quarterly, but rebalancing actually occurs more frequently. This study addresses that problem by introducing a measure of the previous month s portfolio allocation and applying it in the current month s return calculations. In doing so, fund managers are being evaluated each month by their own dynamic benchmark. In order to implement our chosen methodology, we need a monthly time series of each fund s portfolio allocations among stocks, bonds, and cash. 2 An international fund is a mutual fund that invests outside the country in which it is based. Global funds invest at least 25% of its resources in foreign investments. 2

4 Turning to the Return-based Style Analysis methodology presented in Sharpe (1992) and Ibbotson (1996), we offset the absence of more frequent portfolio allocation information, resulting from quarterly reporting. A modified version of Sharpe s style methodology allows us to dynamically mimic fund allocations as conditions change in an integrated market. With daily fund and index data, we estimate a monthly time series of each fund s portfolio allocations and calculate attribution returns. To our knowledge, no other study uses daily data to examine global asset allocation funds. The rest of the paper is organized as follows. The literature review discusses other related work. Next, the data and method used to examine our research question are described. The empirical results expand the analysis with findings from tests. Then, we present the summary and conclusion. Lastly, future research directions are discussed. 2. Literature Review There is sufficient evidence to show that it is advantageous to internationally diversify an investment portfolio. Researchers have found that severe market conditions have generally produced high correlations between domestic assets. Along these lines, Levy and Sarnat (1970) show that international diversification lowers correlation between portfolio assets. De Santis and Gerard (1997) argue for the long term benefits of holding a diversified portfolio. Despite evidence favoring diversification gains, French and Poterba (1991) show that investors have been slow to adopt this practice and explore the reasons for incomplete diversification. Direct investment abroad has to overcome the perspectives of U.S. investors, holding perceptions and the optimism that domestic 3

5 markets are better, safer, and cost effective. However, direct investment abroad is not the only way to accomplish low correlation and funds that invest abroad have dispelled some of these misconceptions. Through international and global funds, U.S. investors might have achieved a more diversified holding than they would have otherwise through direct investment. Errunza, Hogan, and Hung (1999) find that by investing in foreign assets that trade in the U.S., investors can achieve the diversification benefits of assets that strictly trade outside the U.S. Investing in global allocation funds is another indirect method of investing in international markets. Previous studies of international and global funds use Jensen (1968) security line measure to evaluate performance. Many studies report that the performance of international mutual funds is no better than that of world indices. For example, see Cumby and Glen (1990), Eun, Kolodny and Resnick (1991) and Droms and Walker (1994). Global asset allocation funds and global (or world funds) funds have received little attention from academia. Studies of international mutual funds include global funds as part of their overall sample. Bhargava, Gallo, and Swanson (2001) studied 20 global mutual funds as part of their overall sample. In their study, global funds outperformed the Morgan Stanley Capital International Index (MSCI). Shukla and Singh (1997) is one of the few papers that only study global funds, they provide evidence of superior performance by world equity mutual funds when compared with the MSCI world index. Also, global funds did better during the months when the S & P 500 did poorly. Because this methodology is not based on a security market line framework, we avoid the problems presented in the companion papers Dybvig and Ross (1985a and 1985b), which evaluate performance measurement when portfolios deviate from the security market line (SML) and expose the 4

6 information issues with the SML analyses. Dybvig and Ross (1985a) analyze performance measurement when portfolios deviate from the security market due to superior performance based on superior information. Dybvig and Ross (1985b) examine performance measurement when portfolios deviate from the security market due to choice of inefficient markets or reference portfolios. In Dybvig and Ross (1985a) the question is posed, What should we require of a new performance measurement technique? The study goes on to answer that first the measurement technique should accurately measure performance. Next, that the measure should be immune to gaming by managers who understand the technique being used to measure their performance. Finally, it should find practical usefulness. The method suggested in this study meets those criteria and addresses the finding in Dybvig and Ross (1985b) that ranking of portfolios based on SML analysis depends on the choice of index. Prior studies fail to consider the dynamic reapportioning of assets in measuring asset management performance. We introduce an alternative methodology derived from Sharpe (1992) style analysis to calculate attribution returns that serve to measure active fund management performance. Ibbotson (1996), Dor, Jagannathan, and Meier (2003), and Myers, Poterba, Shackelford, and Shoven (2001) also estimate attribution returns. Sharpe estimated attribution returns as a way to show the applicability of the style analysis. Ibbotson classified his sample of 205 equity mutual funds based on their attribution returns in order to test whether winning funds repeat. Myers, Poterba, Shackelford, and Shoven (2001) used attribution returns to compare an actual mutual fund with a copycat portfolio based on semiannual portfolio allocations. We adopt the methodology of Comer, Larrymore, and Rodriguez (2005), which uses 5

7 attribution returns to evaluate hybrid mutual fund managers, from 1997 to They find that hybrid mutual fund managers did not appear to show forecasting skill as evidenced by negative attribution returns. However, in the figure 2 results of our simulation in Appendix A, we show that negative attribution returns may not necessarily convey poor management skill and may be better explained by transaction costs and expenses. Since the fund returns are net of expenses and the equity, debt, and cash returns are a gross figure, including expenses, 1.0% in fees can be added back to the attribution returns, which then may become positive. Grinblatt and Titman (1994) suggest that benchmarks that are meanvariance inefficient lead to incorrect inferences. Our primary reason for not using Grinblatt and Titman (1993) is that the study makes use of the fund s prior portfolio holdings to risk-adjust a fund s average return. For our unique daily data set, we do not have that information because these funds report quarterly and even then, allocation information is incomplete. For that reason, we turned to using a modified Sharpe (1992) Return-based Style Analysis methodology to generate the prior period s apportionment of assets. Here, we study the value of active fund management by focusing on global asset allocation funds and find that our sample of funds adds value to investors as evidenced by a positive and significant, attribution return for fund survivors. We also find that the subgroup of surviving funds performs better than the group of funds that disappear during the time interval of the study. Our results are consistent with previous works on global mutual funds. As earlier noted, see Bhargava, Gallo, and Swanson (2001) and Shukla and Singh (1997). 6

8 3. Data and Method 3.1 Data We collected daily net asset values and distributions of global allocation funds from Bloomberg. Funds disclose information to the National Association of Security Dealers, which in turn provides the data to Bloomberg. We calculate daily fund return series starting on January 1999, and we follow all funds through the timeframe of the study or until they cease to exist, which makes this sample free from survivorship bias. Table 1 shows the descriptive statistics of our fund sample. 3.2 Sample Characteristics Our three-index sample of 27 funds and nine-index sample of 26 funds consist of all mutual funds classified as global asset allocation funds as of December 31, 1998 in the Morningstar Principia CD. We excluded funds that reported greater than 10% of assets invested in asset classes different from equities, fixed income and cash. We also deleted funds that clearly state in their prospectus the use of derivatives. This is important because the style analysis is not well suited for portfolios heavily invested in derivatives. For fund groups with multiple classes of shares, we keep only one fund. We keep the share class with the longest history. This is the standard in the mutual fund literature. Many funds have different share classes, but are claims on the same portfolio. The only difference is the load structure. 7

9 With regard to our nine index model, three of these 26 funds lasted for less than a year, so we have less than twelve monthly attribution returns. The daily data for this analysis starts on February 2001 and ends in December The reason for selecting this time period is that daily global bond indices only became available on the 17 of January For the surviving funds we have 34 monthly attributions returns, from March 2001 until December For the equity portion of the model, we used the Global MSCI indices on value stock, growth, and small cap. For the bond segment, we used the Global Bond Lehman indices on high and low quality, long and short maturity, and cash. 3.3 Research Design In order to implement the style methodology we need daily return series on both the fund sample and the index benchmarks. For each fund, we used daily data to estimate monthly portfolio allocations. We use a model that includes an index for each major asset class. Our three index model is defined as follows: rf i bi, MSCIrMSCI bi, globalbondrglobalbond bi, cashrcash, (1) where r f i : is the fund daily return r MSCI : is the daily return on the MSCI World Index r globalbond : is the daily return on the Lehman Global Aggregate Index r cash : is the daily return on 90 day Treasury Bill Index. 8

10 The simplicity of this model ensures that we have enough degrees of freedom for the estimation process. Also, it would be easy for an individual investor to implement this methodology. The methodology proposed here calls for a monthly time series of each fund s portfolio allocation. The difficulty is that the highest frequency of reporting fund portfolio allocations is quarterly. In order to mitigate this issue, we turn to the Return-based Style Analysis methodology first proposed by Sharpe (1992) and later by Ibbotson (1996). Style analysis allows us to estimate each fund s portfolio allocation from their daily return series. This is dynamically accomplished through a quadratic programming problem, which renders, as a solution, a set of weights on publicly available indices as the estimates for the true portfolio allocations. After estimating each fund portfolio allocation s series, we calculate a time series of attribution returns. We define a fund s attribution return as the difference between the actual monthly fund return and the return that would have been generated by the previous month portfolio allocation and actual returns of the asset class. In essence, fund managers are evaluated based on their own dynamic benchmark. Each month the manager must improve the portfolio allocation in order to generate a positive attribution return. Over time, however, the benchmark of a superior manager optimizes the estimated return and the attribution return asymptotically approaches zero. In order to implement this methodology, we assumed that the daily return for each fund can be represented by an index model: rf i k bijr j 1 j e i, (2) 9

11 where r f i : is the daily total return of fund i b ij : is the exposure of fund i to asset class j r j : is the daily total return of asset class j e i : is the unexplained component of the fund return Following the guidance of Dor, Jaganathan, and Meier (2003), the objective is to select a set of coefficients that minimize the unexplained component of the fund return, ei. Because standard regression equations do not allow the imposing of restrictions, fund portfolio allocations ( b ij ) are estimated as the solutions for the following quadratic program: min k bijr rf i j 1 j var, (3) where the weights are confined to the unit interval, and b ij [ 0,1], j 1,..., k, 1 bi 1 bi 2... bik. The weights are positive because the fund manager does not take short positions. These portfolio weights are the best estimates of the fund portfolio allocations, replicating the return of the fund for a given period. Market risk is captured in these weights. We estimate these portfolio weights at a monthly frequency from the fund s daily return series. Given each fund monthly series of portfolio allocations, we calculate the attribution return for month t as follows: 10

12 r r k b r atti, t f i, t ij, t 1 j, t (4) j 1 where r, : att i t is fund i attribution return for month t r, : f i t is fund i total return for month t b : is the average monthly exposure of fund i to asset class j ij, t 1 during month t-1 r j, t : is the total return of asset class j during month t A positive attribution return implies that the fund manager, by changing his/her asset mix, beat a benchmark he/she created the previous month. Also, a manager can attain a positive attribution return through market timing ability, security selection ability, or both. Our second model is a nine index model defined as follows: rf i bi, sprsp bi, smrsm bi, grrgr bi, varva bi,lgrlg bi, shrsh bi, hqrhq bi, lqrlq bi, tbrtb (5) where r f i = total return for fund i rsp rsm rgr rva rlg = total return on the World Index = total return on a small stock portfolio = total return on a growth stock portfolio = total return on a value stock portfolio = total return on a long maturity bond portfolio 11

13 rsh rhq rlq rtb = total return on a short maturity bond portfolio = total return on a high quality bond portfolio = total return on a low quality bond portfolio = total return on a Treasury bill portfolio This second model is developed to perform a comparative analysis. We compare the attribution returns of the global asset allocation funds for the, more parsimonious, three index model with those of the more inclusive nine index model that includes indices that better reflect the investments choices the fund managers have. The equity portion of the 9 index model includes indices that represent an aggregate equity index, small capitalization stocks, value stocks, and growth stocks as used by Sharpe (1992), Elton, Gruber, Das, and Hlavka (1993), Fama and French (1993), and Elton, Gruber, and Blake (1996). The aggregate equity index is represented by the MSCI World Equity Index. The small, growth, and value indices are also from MSCI. For the fixed income and cash portion of the model, both Fama and French (1993) and Blake, Elton, and Gruber (1993) identify the common risk factors in returns on bonds as related to maturity and default risk. Following these works, we include indices that represent high quality bonds, low quality bonds, long maturity bonds, and short maturity bonds. The model is similar to the nine index model used by Comer (2003) to examine the market timing performance of hybrid funds. Although, when using this model, there are a limited number of degrees of freedom in the estimation process, the advantage of this model is that it will likely result in a better approximation of a fund s portfolio allocation during any given month. Morningstar reports a wide variation in the equity and 12

14 fixed income investment styles of the hybrid funds included in our sample. The additional indices included in the nine index model may better equip the model to capture this variation. However, as noted in Dor, Jaganathan, and Meier (2003), the use of a larger number of benchmarks may introduce considerably more noise into the analysis. Throughout the remainder of the paper, we report results for both the three and nine index models. 4. Empirical Results We calculated the monthly attribution returns for all 27 global asset allocation funds in our sample. Table 2 presents the distribution of the average attribution returns for both models. To obtain the average attribution return, we first averaged the monthly time series of attribution returns for each fund and then average across funds. For the three index model, we computed attribution returns for the February 1999 to December 2003 time period. Consistent with the previous literature on global mutual funds, we find that, as a group, our sample of global asset allocation funds provide value to their investors as evidenced by a positive and statistically significant average attribution return of 0.205%. Further inspection of the distribution of attribution returns for the three index models presents more evidence of out-performance. There are 20 funds out of a total of 27 (or 74%) with positive mean attribution returns. Of these, 8 mean attribution returns are statistically significant at the ten percent level or below. In contrast, only 7 funds (or 26%) attained a negative attribution return and none of these are statistically significant. 13

15 Next, we consider the results from the nine index model. For this model, we calculate attribution returns for the March 2001 to December 2003 time period and the sample is comprised of 26 instead of 27 mutual funds. The results from this model are quite different from what we report for the three index model. The mean attribution return is % and statistically insignificant. A group of 10 funds out of the 26 funds in the sample (or 38%) achieve a positive mean attribution return with only one of these being statistically significant. Finally, 16 funds (or 62%) attain a negative mean attribution return with two of these being significant. Next, we look into the issue of surviving and non-surviving funds to further explore the disparity between the results from the two models we consider. In other studies that look at the performance of mutual funds, nonsurviving funds often disappear due to lack of performance. Table 3 presents the results of a comparison of average attribution returns between survivors and non-surviving funds. Not surprisingly, for both models, we find that surviving funds outperformed non-survivors. For the three index model, the average attribution return for surviving funds is %, and it is statistically significant at the one percent level. For the non-survivors, the average attribution return is %, and not statistically significant. The difference between the average attribution return for survivors and nonsurvivors is %. For the nine index model the difference in performance between surviving and non-survivors is more striking. This is a possible explanation for the difference in the results between the two models. The average attribution return for the surviving funds is % while that figure for the nonsurviving funds is %, both of these number are statistically insignificant. The difference between the average attribution return for 14

16 survivors and non-survivors is.3578%, which represents a statistically significant difference at the five percent level. A closer inspection of these results reveals that there is a stronger evidence of underperformance by nonsurviving funds. A subset of the non-surviving funds attained an unusually high and negative mean attribution return pushing the overall mean attribution return for the nine index model into the negative territory. Next, we estimate Jensen s alpha for the group of 27 Global Asset Allocation funds for the period February 1999 until December This period covers the same interval over which we calculated the attribution returns for the three index model, so these two measures are directly comparable. Consistent with the literature on global funds, we find that our sample of Global Asset Allocation funds out-perform the MSCI World Index. The mean alpha is % (mean attribution return is %) and this value is statistically significant at the one percent level (p-value is and t-value is: 3.08). A more detailed inspection of the results shows that there are 22 positives and only 5 negative alphas. All the negative alphas are nonsignificant, but there are 11 positive alphas that are statistically significant 1%, 5%, and 10%). Generally, this sample of Global Asset Allocation funds show more over-performance when it is measured using a more traditional measure (alpha) than our alternative measure (attribution returns). When the correlation between alpha and the attribution return is calculated, we find a statistically significant value for the Pearson correlation of with a p-value of The R 2, a goodness of fit measure, is the percent of variation in the fund return that can be explained. For our purposes, it is calculated as follows: 15

17 R 2 var( ep ) 1 var( r ) (6) p where the var(ep) is the variance of the attribution return and var(rp) is the variance of the actual fund returns. R 2 will equal one if the model fits perfectly. That is, it will equal one when there is no attribution return variance. The allocations to the style benchmarks, b ij, are dynamically generated to minimize the variance of the attribution return. In minimizing the variance of the attribution return, the R 2 measure is maximized. Dor, Jagannathan, and Meier (2003) note that passively managed funds have high R-squares. As illustrated below, such is seen in our three-index model, indicating that the fund employs a low level of active management. However, increasing the number of indexes from three to nine weakens the R 2 from 77.88% to 37.46%. Because the nine-index model has a low R 2 does not necessarily imply that it has a high level of active management. It could mean that the model benchmark is improperly specified. Three Index Model Nine Index Model R % 37.46% Note that the R 2 is calculated after imposing constraints, so it may not equal the standard R 2, which is represented by the variance of the weighted factors, k var j 1 b ij r j return, var( e i )., divided by the variance of the residual or in this case the attribution 16

18 6. Summary and Conclusions Focusing on global asset allocation funds, this study applies the Returnbased Style Analysis methodology of Sharpe (1992) to the measurement of active fund management performance. These global funds differ from traditional global or international mutual funds in the way that they actively rebalance their portfolio across asset classes within a global framework. This paper addresses concerns of those investors who believe that traditional performance measures may fail to correctly assess asset value and subsequently managerial performance. Based on this style methodology, we define a fund s attribution return as the difference between the actual monthly fund return and the return that would have been generated by the previous month portfolio allocation, which is dynamically generated. Attribution returns for the 27 funds that comprise our sample were calculated during the time period. We consider two models, a parsimonious three index model and a broader nine index model. Confirming the findings of earlier global fund studies, we find that our sample of global asset allocation funds adds value to their investor portfolios. When the three index model is employed we find a positive and statistically significant, average attribution return. When the nine index model is used, the surviving group of funds attains a positive mean attribution return. For both formulations, the subgroup of surviving funds performs better than the non-surviving funds. Further evidence of out-performance is evident when the more traditional performance measure alpha is used. These funds outperformed a global benchmark during the sample of the study as evidenced by a positive and statistically significant mean alpha. Finally, the 17

19 two performance measures used here, attribution returns and alpha, are positively correlated and this correlation is statistically significant. Acknowledgements The authors gratefully acknowledge the help of George Comer who provided extensive comments and some of the index data. We also thank John R. Aulerich, Michael Boldin, Martin Cherkes, and seminar participants of the 2005 Midwest Finance Association Meeting and Paul Rivera and seminar participants of the the 2005 Global Conference on Business & Economics. Rodriguez we would like to thank Mary C. Ferreira and Vivian Acosta (both from the University of Puerto Rico) for their excellent research assistance. Rodriguez acknowledges financial support from the Graduate Business School at the University of Puerto Rico. Larrymore acknowledges financial support provided by the Quinnipiac University School of Business. 18

20 APPENDIX A To show that the attribution return can be used as an indicator of hybrid fund performance, using SAS, we have constructed a simulation of the three index model. The simulation addresses the effects of return variation in an integrated market. The results of an attribution return simulation are shown in figures 1, 2, and 3. Base Ranges of Data The actual range of average monthly returns from our sample is shown below. Base Ranges of Actual Monthly Rates of Return Asset Low High Equity Index Debt Index Cash Fund When converted to daily returns, the ranges for average actual daily returns 20 appear as follows. DailyRates ( 1 MonthlyRates) 1 Base Ranges of Actual Daily Rates of Return Asset Low High Equity Index Debt Index Cash Fund For our simulation, the 20 daily returns were randomly generated each month over a thirteen month period within the base ranges described in the following table, which closely match actually observed figures. We also constrain the random fund return to match the actual correlation between the fund return and the equity index, 84.5% and between the fund return and the debt index, 13%, resulting in R-squares (See figures 1, 2, and 3.) that closely match the three index model. 19

21 Fundreturn. 45( Equityreturn).18( debtreturn).37( randomreturn), where the returns vary randomly within the preset ranges shown below. Base Ranges of Randomly Generated Daily Rates of Return Asset Low High Equity Index Debt Index Cash Fund These ranges were used each month to generate the stationary set of figures. There were also two additional sets of figures for the equity index, the debt index, and the fund, representing growth and decline. To arrive at growth set, the range of the base set was shifted higher at a monthly compounded rate of return of 1%. For example, the range of the growing equity index in the next month would be from to and the month following that from to , and so forth. Similarly, to arrive at the declining set, the range of the base set was shifted lower at a monthly compounded rate of return of 1%. For example, the range of the declining equity index in the next month would be from to and the month following that from to , and so forth. Following the attribution return method described in the paper, the allocations were calculated from the prior month returns. The attached figures 1, 2, and 3 show the 12-month average allocations and monthly attribution return for each scenario. If a sponsor or individual investor sought to use attribution returns to evaluate an active manager s performance, they could run a style analysis with no change in the current level of fund return, as seen in figure 1. The attribution returns found under the various conditions would become the 20

22 guideline for performance. As market conditions vary, the standard changes, but in the attribution return, the Return-based Style Analysis finds a separation between superior and inferior managers. For instance, in figure 1, where fund performance is constant, under a growing equity market, a declining debt market, an average manager should generate an attribution return of approximately basis points. A superior manager, such as the one found in figure 2, with growing fund returns, should achieve an attribution of basis points under similar market conditions. Under the same conditions, an inferior manager, such as the one described in figure 3, with declining fund returns, should achieve a lower attribution of basis points. In figure 2, where the fund outperforms the indices, the attribution return is least negative under every scenario when contrasted with figures 1 and 2. If the rate of return of the fund is growing, the attribution return is least negative. Clearly, supporting common wisdom, the attribution return is better when the fund is growing and outperforming the market indices. In figure 3, understandably, we find the worst attribution returns. Note that the average attribution return is negative under all scenarios. Since the fund returns are net of expenses and the equity, debt, and cash returns include expenses, 1.0% in fees can be added back to the attribution returns, which may yield positive returns in figure 2. The allocation to the equity should be in the 55-60% range. 21

23 SCENARIO EQUITY INDEX Figure 1 AVERAGE MONTHLY ATTRIBUTION RETURN RATE OF RETURN AVERAGE ALLOCATION DEBT INDEX CASH FUND EQUITY DEBT CASH ATTRIBUTION R 2 A Growing Growing Stationary Stationary B Growing Declining Stationary Stationary C Growing Stationary Stationary Stationary D Declining Growing Stationary Stationary E Declining Declining Stationary Stationary F Declining Stationary Stationary Stationary G Stationary Growing Stationary Stationary H Stationary Declining Stationary Stationary I Stationary Stationary Stationary Stationary

24 SCENARIO EQUITY INDEX Figure 2 AVERAGE MONTHLY ATTRIBUTION RETURN RATE OF RETURN AVERAGE ALLOCATION DEBT INDEX CASH FUND EQUITY DEBT CASH ATTRIBUTION R 2 AA Growing Growing Stationary Growing BB Growing Declining Stationary Growing CC Growing Stationary Stationary Growing DD Declining Growing Stationary Growing EE Declining Declining Stationary Growing FF Declining Stationary Stationary Growing GG Stationary Growing Stationary Growing HH Stationary Declining Stationary Growing II Stationary Stationary Stationary Growing

25 SCENARIO EQUITY INDEX Figure 3 AVERAGE MONTHLY ATTRIBUTION RETURN RATE OF RETURN AVERAGE ALLOCATION DEBT INDEX CASH FUND EQUITY DEBT CASH ATTRIBUTION R 2 AAA Growing Growing Stationary Declining BBB Growing Declining Stationary Declining CCC Growing Stationary Stationary Declining DDD Declining Growing Stationary Declining EEE Declining Declining Stationary Declining FFF Declining Stationary Stationary Declining GGG Stationary Growing Stationary Declining HHH Stationary Declining Stationary Declining III Stationary Stationary Stationary Declining

26 Appendix B Funds in the Study Advantus Intl Balanced A Bailard, Biehl Diversified Brinson Global Carillon Capital Delaware Global Assets A Fidelity Asset Manager Fidelity Asset Manager: Growth Fidelity Global Balanced Fremont Global IDS Global Balanced A Invesco Adv MultiFlex C Invesco Multi-Asset Allocation Kemper Worldwide 2004 MAS Multi-Asset-Class Institutional Merrill Lynch Global Allocation A MFS World Asset Allocation A MFS World Total Return A Oppenheimer Multiple Strategic A Permanent Port Putnam Asset Allocation: Bal A Putnam Asset Allocation: Cons A Putnam Asset Allocation Growth A Smith Barney Intl Balanced A SoGen International Stellar Investment USAA Cornerstone Strategy Vanguard Horizon Glob Asset 25

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29 Table 1 Overview of Data Number of funds 27 Average total net assets 555 Median total net assets 205 Average stock allocation (%) Average bond allocation (%) Average cash allocation (%) Average range of stock allocations (%) Average range of bond allocations (%) 9.06 Average range of cash allocations (%) 10.5 Annual portfolio turnover (%) 93.5 Annual expense ratio (%) 1.25 The table presents descriptive statistics for the sample of global allocation funds over the sample period All values are averages across all funds in the sample. Averages are calculated by first calculating the average value for each individual fund over the time period and then calculating the cross section mean. Return data is from Bloomberg. The range of stock, bond, and cash allocations are based on the minimum and maximum annual portfolio weights provided by CRSP. 28

30 Table 2 Attribution Returns Three Index Nine Index Number of funds Average Attribution Return 0.205%** % Standard Deviation % % Maximum Value % % Minimum Value % -1.46% Number of Positive Values Number of Negative Values 7 16 Positive and Significant Values 8 1 (at 10 percent or below) Negative and Significant Values 0 2 (at ten percent or below) *, **, *** Significant at the 10, 5, and 1 percent levels, respectively, for a two-tailed test. Table 2 shows the distribution of attribution returns for the 27 global asset allocation funds in our sample. Attribution returns are calculated as the difference between the actual monthly fund return and the return that would have been generated by the previous month portfolio allocation. 29

31 Table 3 Survivorship Panel A: Three Index Number of funds Average Attribution Return Survivors %*** Nonsurvivors % Difference % Panel B: Nine Index Number of funds Average Attribution Return Survivors % Nonsurvivors % Difference % *, **, *** Significant at the 10, 5, and 1 percent levels, respectively, for a two-tailed test. Table 3 shows a comparison of average attribution returns between surviving and nonsurviving funds. 30

32 Table 4 Attribution Returns and Alphas Three Index Alpha Number of funds Average Attribution 0.205% %*** Return/Jensen s Standard Deviation % % Maximum Value % 1.39% Minimum Value % % Number of Positive Values Number of Negative Values 7 5 Positive and Significant Values 8 11 (at 10 percent or below) Negative and Significant Values 0 0 (at 10 percent or below) *, **, *** Significant at the 10, 5, and 1 percent levels, respectively, for a two-tailed test. Table 4 shows the distribution of attribution returns for the 27 global asset allocation funds in our sample for the 3 index model and the distribution of the results for the Jensen s alpha. The time period is from February 1999 until December