Active fund management: Global asset allocation funds

J. of Multi. Fin. Manag. 17 (2007) 244–256

Active fund management: Global asset allocation funds Norris L. Larrymore a,∗ , Javier Rodriguez b,1 a

b

Department of Finance, School of Business, SB-DNF, Quinnipiac University, 275 Mount Carmel Avenue, Hamden, CT 06518, USA Graduate School of Business Administration, University of Puerto Rico, P.O. Box 23332, San Juan, PR 00931, USA Received 16 January 2006; accepted 3 December 2006 Available online 25 January 2007

Abstract We examine the value of active fund management of global asset allocation funds. We use unique daily data and a modified Sharpe’s [Sharpe, W., 1992. Asset allocation: management style and performance measurement. Journal of Portfolio Management 18, 7–19] Return-Based Style Analysis method to create a three-index model. We introduce an alternative method derived from Sharpe to calculate attribution returns that measure active fund management performance. Our results suggest that a sample of global asset allocation funds add value for investors. To determine the estimation ability of our model and the implications for estimated asset allocation decisions, we report historical and cross-sectional root mean square errors, which give positive indications of reliability. © 2006 Elsevier B.V. All rights reserved. JEL classification: F21; G11; G15 Keywords: Style analysis; Global asset allocation funds; Active fund management

1. Introduction Global asset allocation funds, which are part of the family of hybrid mutual funds, differ from traditional global or international mutual funds in that they face fewer investment restrictions. Previously, investment restrictions, along with the information costs associated with investment ∗ 1

Corresponding author. Tel.: +1 203 582 8913; fax: +1 203 582 8664. E-mail addresses: [email protected] (N.L. Larrymore), [email protected] (J. Rodriguez). Tel.: +1 787 764 0000x2043.

1042-444X/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mulfin.2006.12.001

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outside the United States, discouraged investments abroad, but fewer investment restrictions allow a fund manager to trade more frequently and move funds more freely among asset classes. Recently, the popular press has touted hybrid mutual funds as a less risky alternative to hedge funds. Global asset allocation funds are specifically chartered to invest overseas and adopt an asset allocation strategy that takes advantage of changing global market conditions and asset classes. For example, the Fidelity Global Balanced Fund states in its prospectus that the fund invests in equity and debt securities, including lower-quality debt securities, issued anywhere in the world. The MFS Global Total Return Fund states that it primarily invests in a balanced combination of global and fixed-income securities. These investment strategies involve a high degree of diversification across global geographical markets. Investors find it advantageous to invest abroad when the global asset allocation fund is referenced in U.S. dollars (throughout the paper, all references to dollars mean U.S. dollars), the non-U.S. investment is denominated in a foreign currency, and that foreign currency advances against the dollar. Active asset allocation managers can also benefit from favorable fundamentals in foreign stock and bond markets, such as low inflation, falling interest rates, and economic growth. However, there are risks in holding global asset allocation funds. If the foreign currency declines against the dollar, then the foreign portfolio’s value will be lowered after translation to dollars. Adverse fundamentals in foreign stock and bond markets may appear. Inflation and/or interest rates may rise. Or the economy may contract. Additionally, these funds invest in both stocks and bonds worldwide, including U.S. securities. When short-term interest rates creep upward, when stock prices are relatively high, or when dividend yields are low compared to bond yields, fund managers can reposition toward bonds, which can include both corporate and sovereign debt in U.S. and non-U.S. markets. Money that the fund does not deploy in stocks and bonds remains in the form of cash or cash equivalents. Global asset allocation funds have not attracted the attention of academic researchers, primarily because fund managers rarely report their allocation with a frequency higher than quarterly, but rebalancing actually occurs more frequently. Traditional performance measures may fail to correctly calculate the value that fund managers provide to their investors, because conventional measures assume that allocation is fixed. Our study, which to our knowledge is the first to examine global asset allocation funds, is motivated by the information gap on these funds. Amid international and global fund studies, this one is the first to use daily data and to recognize the impact of fixed-income exposure. The paper is organized as follows. Section 2 discusses other related work. In Section 3, we describe the data and method we use to examine our research question. In Section 4, we present our empirical test results and report both the historical and cross-sectional root mean squares to give some insight into the performance of the Return-Based style model. Section 5 summarizes and concludes. 2. Literature review Most previous research focuses on international funds and many studies report that the performance of international mutual funds is no better than that of world indices. Using the security market line measure of Jensen (1968, 1969) and the positive period weighting measure of Grinblatt and Titman (1989), Cumby and Glen (1990) find no superior performance against a selected international equity index benchmark. In their test, covering the period January 1982 through June

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1988, they compare the mean-variance efficiency of a sample of 15 U.S.-based internationally diversified mutual funds with the Morgan Stanley Capital International Perspective world index. Eun et al. (1991) show that most of the 19 U.S.-based international mutual funds in their study fail to outperform the Morgan Stanley Capital International (MSCI) World Index. Although global asset allocation funds and global (or world funds) funds have received little attention from academia, some studies of international mutual funds have included global funds as part of their overall sample. The Eun et al. (1991) paper noted earlier is one. Bhargava et al. (2001) study 20 global mutual funds as part of their overall sample and find that global funds outperformed the MSCI World Index. Shukla and Singh (1997) is one of the few papers that study global equity mutual funds, which hold both U.S. and foreign equities. These authors provide evidence of superior performance by global funds when compared with the MSCI World Index in total and risk-adjusted measures. Since prior studies fail to consider the dynamic reapportioning of assets in measuring asset management performance, we introduce an alternative method derived from Sharpe’s (1992) style analysis to calculate attribution returns that serve to measure active fund management performance. Sharpe (1992) estimates attribution returns as a way to show the applicability of the style analysis. Blake et al. (1993), Brown and Goetzmann (1997), Dor et al. (2003), Fung and Hsieh (1997), Ibbotson (1996), and Myers et al. (2001) also estimate attribution returns. Blake et al. (1993) design a model called QPS-6, a replicating portfolio with all index weights greater than zero. Ibbotson (1996) classified his sample of 205 equity mutual funds based on their attribution returns in order to test whether winning funds repeat. Myers et al. (2001) used attribution returns to compare an actual mutual fund with a copycat portfolio based on semiannual portfolio allocations. Through selection of this Return-Based Style Analysis, we address a concern in analyzing balanced funds raised by Blake et al. (1993) that may produce upward-biased estimates of alphas. Blake et al. (1993) noted that “Most studies of mutual fund performance ignore in their analyses the part of a fund’s portfolio invested in bonds.” They conclude that “studies that include balanced funds and do not include indexes that pick up the bond component produce upward-biased estimates of alphas.” Our multi-index model includes a bond index for the purpose of avoiding that bias. We have considered the significance of Grinblatt and Titman (1993, 1994), which suggests that benchmarks that are mean-variance 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 found in Morningstar is incomplete. For that reason, we turned to using a modified Sharpe (1992) ReturnBased Style Analysis method to generate the prior period’s apportionment of assets. We adopt the methodology of Comer et al. (2006), which uses attribution returns to evaluate hybrid mutual fund managers, from 1997 to 2003. They find that hybrid mutual fund managers did not appear to show forecasting skill as evidenced by negative attribution returns. Our primary reason for using this method of portfolio development follows the standpoint taken in Blake et al. (1993) for mutual funds. Since global asset allocation funds do not take short positions, the allocations to their various asset categories cannot have negative sensitivities. Thus, a replicating portfolio of indices must exhibit positive portfolio weights. Ordinary least squares regressions, which are typically used for linear index models, can sometime produce negative weights. Positive weighting can be achieved through the quadratic programming solutions of Sharpe (1992), which are described in the next section.

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3. Data and method 3.1. Data We obtain daily net asset values (NAVS) and daily dividend distributions from Bloomberg for mutual funds classified as global asset allocation funds as of December 31, 1998 in the Morningstar Principia CD. We begin our study in 1999 because this is the first year in which daily data on global bond indexes are available. From this information, we constructed the daily fund return series for each fund, as shown by: rfi ,t =

navfi ,t + divfi ,t − 1, navfi ,t−1

(1)

where rfi ,t is the total return of fund i at the end of day t, navfi ,t the net asset value of fund i at the end of day t, navfi ,t−1 the net asset value of fund i at the end of the prior day, and divfi ,t are the dividend or other distributions of fund i on day t. The study covers the period from the beginning of 1999 through the end of 2003, or until the funds ceased to exist. Thus, our sample is free from survivorship bias. Table 1 shows the descriptive statistics of our fund sample. Our sample comprises 27 mutual funds, all of which are classified as global asset allocation funds. We exclude funds that report more than 10% of assets invested in asset classes other than equities, fixed income, and cash. We also delete funds that state in their prospectus that they use of derivatives. This exclusion is important because the style analysis is not suitable for portfolios that are heavily invested in derivatives. For fund groups with multiple classes of shares, we keep only the share class with the longest history. 3.2. Method To implement our style method, we construct daily return series on both the fund sample and the index benchmarks. For each fund, we use daily data to estimate monthly portfolio allocations. Our model includes an index for each of the three major asset classes. Eq. (2) defines the resulting Table 1 Descriptive statistics Number of funds Average total net assets in millions of dollars Median total net assets in millions of dollars Average stock allocation (%) Average bond allocation (%) Average cash allocation (%) Average range of stock allocations (%) Average range of bond allocations (%) Average range of cash allocations (%) Annual portfolio turnover (%) Annual expense ratio (%)

27 555 205 52.23 29.92 10.26 19.43 9.06 10.5 93.5 1.25

The table presents descriptive statistics for the sample of global asset allocation funds over the sample period 1999–2003. All values are averages across all funds in the sample. We calculate averages by first calculating the average value for each individual fund over 1999–2003 and then calculating the cross-section mean.

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three-index model: rfi = bi,MSCI rMSCI + bi,globalbond rglobalbond + bi,cash rcash ,

(2)

where rfi is the fund daily return, rMSCI the daily return on the MSCI World Index, a U.S. dollar denominated index, consisting of U.S. and international equities, rglobalbond the daily return on the Lehman Global Aggregate Bond Index, and rcash is the daily return on the Lehman Short Treasury Index. We use the U.S. dollar denominated MSCI World Index to represent the world equity market. For the global bond index, we use the Lehman Global Aggregate Bond Index. For the cash index, we use the Lehman Short Treasury Index, which is a weighted average of the returns of all bills with less than 90 days to maturity. We obtain this information from the Lehman Brothers fixedincome database. Given our small sample size, the simplicity of this model ensures that we have enough degrees of freedom for the estimation process. This technique requires a monthly time series of each fund’s portfolio allocation, which is not publicly available. The highest frequency of reporting fund portfolio allocations is quarterly, and even that is incomplete. To mitigate this issue, we turn to the Return-Based Style Analysis method first proposed by Sharpe (1992) and later by Ibbotson (1996). Because we use a style analysis, we can estimate each fund’s portfolio allocation from their daily return series. We perform this estimation by using a quadratic programming method that gives us a set of weights on publicly available indexes as estimates for the true portfolio allocations. After estimating each fund’s portfolio allocation 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 if we had used the prior month’s portfolio allocation and current month’s actual returns of the index representing each 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. Eq. (3) uses the index model to represent the daily return for each fund: rfi =

k 

bij rj + ei ,

(3)

j=1

where rfi is the daily total return of fund i, bij the exposure of fund i to asset class j, rj the daily total return of asset class j, and ei is the unexplained component of the fund return. Following Dor et al. (2003), our 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 us to impose restrictions, we estimate fund portfolio allocations (bij ) as the solutions for the quadratic program described in Eq. (4): ⎡ ⎛ ⎞⎤ k  min ⎣var ⎝rfi − (4) bij rj ⎠⎦ , j=1

where the weights are confined to the unit interval. The weights are positive because fund managers do not take the short positions, bij ∈ [0, 1],

j = 1, . . . , k,

(5)

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and 1 = bi1 + bi2 + · · · + bik .

(6)

These portfolio weights, which capture market risk, are the best monthly estimates of the fund portfolio asset allocations. The R2 , which is our goodness-of-fit measure, is the percent of variation in the fund return that can be explained. For our purposes, we calculate it as described in Eq. (7): R2 = 1 −

var(ei ) , var(rfi )

(7)

where var(ei ) is the variance of the unexplained component of the fund return and var(rfi ) is the variance of the actual daily total return of fund i. Eq. (4) shows that we dynamically generate the allocations to the style benchmarks, bij to minimize the difference between the actual fund return and the return generated by the allocation benchmarks. Given each fund’s monthly series of portfolio allocations, we use Eq. (8) to calculate the attribution return for month t: ratti ,t = rfi ,t −

k 

bij,t−1 rj,t ,

(8)

j=1

where ratti ,t is fund i attribution return for month t, rfi ,t the fund i total return for month t, bij,t−1 the average monthly exposure of fund i to asset class j during month t − 1, and rj,t is the total return of asset class j during month t. A positive attribution return indicates that the fund manager beats a benchmark based on the prior month’s estimated allocation. Although a manager can attain a positive attribution return through his market-timing ability, security selection ability, or both, it is difficult to determine the proportion of each. The majority of the mutual fund performance studies base their evidence on the alpha measure of Jensen (1968), or some variation of it. As a robustness check, we compute the Jensen’s alpha as the intercept from the regression, as described in Eq. (9): (ri − r f ) = α + β(r b − r f ) + ε,

(9)

where ri is the total return of the individual fund i, rf the total return of the 90-day Treasury Bill Index, and rb is the total return of the MSCI World Index, which includes U.S. and foreign equities, representing Jensen’s (1968) market benchmark. To further evaluate the effectiveness of the dynamic program in the generation of asset allocations, we calculate the root mean square error (RMSE) between the dynamically generated estimated asset allocations and the actual asset allocations reported in Morningstar. One benefit of using the RMSE is that it has the same dimension as the dynamically generated estimated asset allocations and the actual asset allocations reported in Morningstar. We screen funds for completeness of information. Of the 27 funds in the study, 11 have no sector weights reported in Morningstar, and three were partially complete. We select the remaining 13 funds for RMSE calculations. Of these 13 funds selected, 2 are missing 2 observations and 1 is missing 1. We fill in the missing items by averaging the last reported item prior to, and the next reported item following, the omission.

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Using the actual and estimated asset allocation, we calculate and analyze the RMSE in two ways. First, we generate and then examine the time series RMSE for the selected funds as described in Eq. (10):  n 2 t=1 (Ati − Eti ) (10) RMSEi = n where RMSEi is the average root mean square error for asset allocations in fund i over the 20 quarters of the study, n the number of observations (20 quarters), Ati the actual asset allocation as reported in Morningstar in quarter t for fund i, and Eti is the dynamically generated asset allocation in quarter t for fund i. We generate and then examine the cross-sectional RMSE for the selected funds as described in Eq. (11):  n 2 i=1 (Ait − Eit ) RMSEt = (11) n where RMSEt is the average root mean square error for asset allocations in quarter t across the 13 selected funds, n is the number of observations (13 funds), Ait the actual asset allocation as reported in Morningstar for fund i in period t, and Eit is the dynamically generated asset allocation for fund i in period t. 4. Empirical results Our attribution return method requires that we estimate each fund’s monthly portfolio allocations. Thus, the model’s goodness of fit becomes an important issue. As noted, we use Sharpe (1992) style analysis to infer each fund’s asset allocation from the daily return series. To demonstrate how well the procedure estimates, we run a style analysis on an equally weighted portfolio of all the funds that exist on any given day during the sample period. Table 3 displays the results of this estimation. In Table 2, our primary finding is that the model does well at explaining fund returns. Panel A shows the results for the entire sample period and Panel B does so by year. For the entire sample period the adjusted R2 is 0.871, and for the individual yearly estimation the adjusted R2 ranges from a low of 0.803 to a high of 0.934. Also, in all the estimations, the estimated portfolios, weights are significant at least at the 5% level. These results provide evidence in favor of the use of the style analysis method. The three-index model seems to do well in explaining fund return variability. 4.1. Attribution returns We calculate the monthly attribution returns for the 27 global asset allocation funds in our sample. Table 3 presents the distribution of the average attribution returns. To determine the average attribution return, we first average the monthly time series of attribution returns for each fund and then average across funds. We compute attribution returns for the full sample period from February 1999 to December 2003. We find that as a group our sample of global asset allocation funds outperforms the benchmarks. This finding is evidenced by a positive, statistically significant average attribution return of 0.205% over the entire period.

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Table 2 Estimation of the portfolio weights for an equally weighted portfolio Panel A: Estimated portfolio weights for the complete sample period Asset class

Weight

t-Value

Stocks Bonds Cash Adjusted R2

0.483*** 0.131*** 0.385***

91.92 8.32 22.22 0.8714

Panel B: Yearly estimated portfolio weights Year

1999

2000

2001

2002

2003

Stocks Bonds Cash Adjusted R2

0.473***

0.489***

0.499***

0.462***

0.080** 0.447*** 0.866

0.076** 0.435*** 0.883

0.146*** 0.355*** 0.922

0.125** 0.413*** 0.803

0.514*** 0.186*** 0.300*** 0.934

The table shows the results from a style analysis that we perform on an equally weighted portfolio comprising all the existing funds in any given day during the estimation period from January 1999 to December 2003. Panel A presents the estimated portfolio weight and corresponding t-value for the complete sample period. Panel B shows the yearly average exposure. *** , ** , and * denote statistical significance at the 1%, 5%, and 10% level, respectively.

Further inspection of the distribution of attribution returns for the three-index model presents more evidence of outperformance. In Table 3, we show that there are 20 funds out of 27 (or 74%) with positive mean attribution returns. Of these, eight mean attribution returns are statistically significant at the 10% level or below. In contrast, only 7 funds (or 26%) attained a negative attribution return and none of these are statistically significant. Our fund returns are post-expenses and management fees, while the index returns are pre-expenses, so the pre-cost performance may be even better.

Table 3 Attribution returns and alphas

Number of funds Average attribution return/Jensen’s (%) Standard deviation (%) Maximum value (%) Minimum value (%) Number of positive values Number of negative values Positive and significant values (at 10% or below) Negative and significant values (at 10% or below) Pearson correlation (with p-value 0.004)

Three index

Alpha

27 0.205** 0.442 1.542 −0.837 20 7 8 0 0.533

27 0.268*** 0.452 1.39 −0.724 22 5 11 0

The table shows the distribution of attribution returns for the 27 global asset allocation funds in our sample for the threeindex model and for the distribution of the results for the Jensen’s alpha. The time period is from February 1999 until December 2003. We calculate attribution returns as the difference between the actual monthly fund return and the return that would have been generated by the previous month’s portfolio allocation. *** , ** , and * denote statistical significance at the 1%, 5%, and 10% level, respectively.

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4.1.1. Attribution returns and alpha Table 3 shows our estimations of the more conventional alpha measure of Jensen (1968) for the group of 27 global asset allocation funds. We estimate the alpha over the period February 1999 to December 2003, which is the same interval for our three-index model calculation, so these two measures are directly comparable. We find that our sample of global asset allocation funds outperform the MSCI World Index, with a mean alpha of 0.268%. This value is statistically significant at the 1% level with a p-value of 0.005 and t-statistic of 3.08. This result is similar to the attribution return (the mean attribution return is 0.205%). A more detailed inspection of the results shows that there are 22 positives and only 5 negative alphas. All the negative alphas are non-significant, but there are 11 positive alphas that are statistically significant at the 10% level or better. Of these 11, six are significant at a level of 5% or better, and two of these are significant at the 1% level. Finally, Table 3 shows that when we calculate the correlation between alpha and the attribution return, we find a statistically significant value for the Pearson correlation of 0.533 with a p-value of 0.004. The Pearson correlation adds evidence that the attribution return and the Jensen alphas measure have similar capabilities. We find additional support in the number of positive alphas and attribution returns. We find that 19 of the 27 funds that comprise the sample have both positive alpha and mean attribution return. Moreover, of the 27 funds in the sample, 20 have positive attribution returns, meaning that 95% of these funds also have a positive alpha. Generally, under the more traditional Jensen (1968) alpha measure, this sample of global asset allocation funds shows more over performance than when we use our alternative attribution returns measure. We expect this result because, as discussed in Section 3.2, we expected the alpha to be biased upward. 4.1.2. Attribution returns and survivorship A feature in many mutual funds studies is the comparison between the performance of surviving and non-surviving funds with evidence that surviving funds outperform funds that cease to exist. In our study, 12 of the funds in the sample (or 44.44%) disappear at some time during the sample period. This percentage is significant and indicates that we should make a more detailed inspection of the empirical results. Table 4 presents the results of comparing average attribution returns of subsets of surviving and non-surviving funds. Not surprisingly, we find that the subgroup of surviving funds outperforms the group of funds that ceased to exist during the 1999–2003 study period, as evidenced by a positive and significant average attribution return of 0.301%. For the exiting funds, the average attribution return is 0.085%, and not statistically significant. The difference between the average attribution return for survivors and non-survivors is 0.216%.

Table 4 Attribution returns and survivorship

Survivors Non-survivors Difference

Number of funds

Average attribution return (%)

15 12

0.301*** 0.085 0.216

The table shows a comparison of average attribution returns between surviving and non-surviving funds. *** , denote statistical significance at the 1%, 5%, and 10% level, respectively.

** ,

and

*

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4.2. Predictive performance of the dynamic apportionment model In Table 5, we show the results of our calculation of RMSE between the dynamically generated asset allocations and the actual asset allocations reported in Morningstar. Panel A shows the time series RMSE for 13 funds selected on the basis of completeness of information reported to Morningstar. Panel B presents the cross-sectional RMSE for the selected funds over the 20 quarters of the study. We find similarities in both panels. The RMSE for all three asset classes is significantly different from zero. We see that the RMSE for bonds and cash are observed to be statistically indistinguishable, but that the RMSE for stocks is significantly lower than the other two asset classes. The lower RMSE for the stocks relative to bonds and cash may be explained by the broader investment base. There are notable differences between Panels A and B. When we compare the RMSE in Panels A and B of Table 5, we see that the means of each sector are statistically indistinguishable. The lower standard deviation in RMSE for the cross-sectional calculations suggests that the RMSE variation between funds is greater than the variation between quarterly periods. In Panel A, the correlation between the RMSE of bonds and cash is 78.3%, which suggests that there is some correlation between the returns of the indexes that drive the dynamic asset allocations to cash and bonds over time. In Panel B, over the study period 1999–2003, the model maintains a relatively stable RMSE with no discernible time trend. There are several reasons why the Morningstar sector weights may not be a rigorous standard against which to compare the dynamic apportionment, but we use it absent a more stringent metric. First, the frequency of the Morningstar reported sector weights is quarterly, rather than

Table 5 Root mean square error (RMSE) Panel A: Time series (RMSE by fund) Stocks

Bonds

Cash

Brinson Global Fidelity Global Balanced Fremont Global IDS Global Balanced A Kemper Worldwide 2004 Merrill Lynch Global Alloc A MFS World Total Return A Oppenheimer Multiple Strat A Permanent Port Putnam Asset Alloc: Bal A Putnam Asset Alloc: Growth A SoGen International USAA Cornerstone Strategy

0.2261082 0.1044383 0.1038185 0.1185468 0.1152511 0.1485702 0.1285682 0.1621185 0.2788983 0.2126453 0.2630972 0.3506668 0.1775656

0.2202681 0.1204307 0.2039161 0.1313176 0.519518 0.1205423 0.1355842 0.3098282 0.2175073 0.2055864 0.1379597 0.1917593 0.2471364

0.2361714 0.1040821 0.1717723 0.1195699 0.5017881 0.2491629 0.1905403 0.1956419 0.2113433 0.1575888 0.1775644 0.336597 0.2367706

Mean

0.183869

0.212412

0.222199

Standard deviation

0.077595

0.10823

0.103042

Minimum Median Maximum

0.1038185 0.1621185 0.3506668

0.1204307 0.2039161 0.519518

0.1040821 0.1956419 0.5017881

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Table 5 (Continued ) Panel B: Cross-sectional (RMSE by quarter) Quarter ending

Stocks

Bonds

Cash

January 1999 April 1999 July 1999 October 1999 January 2000 April 2000 July 2000 October 2000 January 2001 April 2001 July 2001 October 2001 January 2002 April 2002 July 2002 October 2002 January 2003 April 2003 July 2003 October 2003

0.2218289 0.2853059 0.232733 0.1951795 0.2354385 0.2275532 0.2133986 0.1918942 0.2179665 0.1923676 0.1676351 0.1721078 0.1710999 0.1708026 0.1828977 0.1878035 0.1527857 0.1676056 0.1720419 0.1562914

0.222015 0.1663328 0.1839482 0.1706238 0.2015119 0.2284148 0.2562481 0.3013281 0.2434618 0.2539324 0.2638052 0.2255789 0.219546 0.2276868 0.254633 0.2620486 0.256472 0.239909 0.2531062 0.2535767

0.2678113 0.3575702 0.2121953 0.2459752 0.2615945 0.2866241 0.1879451 0.2712864 0.1835406 0.1994518 0.2253943 0.187094 0.1960749 0.197379 0.2651612 0.230749 0.2889981 0.2605099 0.2269071 0.2361093

Mean

0.1957368

0.234209

0.2394186

Standard deviation

0.033286

0.0336808

0.0441551

Minimum Median Maximum

0.1527857 0.1898489 0.2853059

0.1663328 0.2416854 0.3013281

0.1835406 0.2334291 0.3575702

Panel A of the table shows the results from the root mean square error calculation of the times

series RMSE for 13 funds selected based on completeness of data as described by the following equation: RMSEi =

 n



t=1

(Ati − Eti )2 /n,

where RMSEi is the average root mean square error for asset allocations in fund i over the 20 quarters of the study, n the number of observations (20 quarters), Ati the actual asset allocation as reported in Morningstar in quarter t for fund i, and Eti is the dynamically generated asset allocation in quarter t for fund i. Panel B shows the results from the root mean square error calculation of the cross-sectional RMSE for 13 selected funds selected on the basis

of completeness of asset allocation data reported by Morningstar as described by the following equation: RMSEt =

 n

i=1



(Ait − Eit )2 /n,

where RMSEt is the average root mean square error for asset allocations in quarter t across the 13 selected funds, n the number of observations (13 funds), Ait the actual asset allocation as reported in Morningstar for fund i in period t, and Eit is the dynamically generated asset allocation for fund i in period t.

monthly, which is the frequency of the dynamically apportioned assets in our study. However, we compensate for this difference by averaging the monthly allocations over quarterly periods. Second, our dynamic apportionment model uses three indexes to represent asset classes, while Morningstar reports sector weights in five categories: cash, U.S. stocks, non-U.S. stocks, bonds, and other. Our model has only one equity index, the MSCI World Index, which includes both domestic and foreign equities. Thus, for comparative purposes, we aggregate the two Morningstar stock categories: U.S. stocks and non-U.S. stocks. It was not necessary to match the Morningstar category described as “other,” which includes derivatives, because our initial sample excluded funds with more than 10% of derivatives. Next, over the first 16 periods of the 20 periods of

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the study, the Morningstar sector weights change only once. Since these are actively managed funds, there is invariability over 16 quarters and this suggests that the sector weights are not being reported as often as they should be. 5. Conclusion In this paper, we address the concerns of those investors who believe that traditional performance measures fail to correctly assess asset value and subsequently managerial performance of global asset allocation funds. We believe ours is the first study to examine global asset allocation funds and the first among global and international fund studies to use daily data and to recognize the effect of fixed-income exposure. We find that our sample of global asset allocation funds adds value to their investor portfolios, thus confirming the findings of earlier global fund studies. Based on a three-index model, we find a positive and statistically significant average attribution return. We find further evidence that funds outperform when we use the more traditional performance measure alpha as evidenced by a positive, statistically significant mean alpha during the study sample period. Also, the two performance measures we use here, attribution returns and alpha, are positively correlated; this correlation is statistically significant. Finally, when we partition the fund sample between the surviving funds and non-surviving funds, we find that surviving funds outperform their counterparts. This is also consistent with previous studies. Next, we examine the effectiveness for valuing global allocation fund management performance because estimating sector weights plays a central role in the model. To determine the estimation ability of the Return-Based Style Analysis model and the implications of estimated allocation decisions, we compare the sector weights reported in Morningstar Principia and with the sector weights that we estimate using style regression. To make this comparison, we use both historical and cross-sectional root mean square error calculations. Our analysis shows that the estimation is relatively consistent across funds and over the period of study. This finding suggests that our estimates are reliable. We note especially that the standard deviation of cross-sectional RMSE calculations is close to zero, which implies a relative time insensitivity of the fit of sector weight estimations. This feature has important positive implications for valuation when we apply the model over longer periods with dramatically changing market conditions. We also report the lowest RMSEs in equity sector weights. The results suggest greater estimation effectiveness with the size of equity holdings. The higher capability of our three-index model to describe stock sector weights can have important favorable implications for applying this model because in most global allocation funds, the stock asset class overshadows the bond and cash asset classes. Acknowledgements The authors thank Ike Mathur (the editor) and an anonymous referee for their many helpful suggestions, and we gratefully acknowledge the extensive contributions of George Comer. We also thank John R. Aulerich, Michael Boldin, Martin Cherkes, seminar participants of the 2005 Midwest Finance Association Meeting, and Paul Rivera and seminar participants of the 2005 Global Conference on Business & Economics. We appreciate suggestions from Mitchell Ratner and seminar participants of the 2006 Eastern Finance Association Conference. The comments of Sandeep Singh were particularly helpful, as were the suggestions of the Mutual Fund Management session attendees of the 2006 Financial Management Association European Conference. We owe a special debt to Mila Getmansky Sherman and participants at the 2006 European Financial Man-

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agement Association Conference, to Bin Wei, and participants at the 2006 Financial Management Association Conference, and to Hendrik Scholz and participants at the 2006 Southern Finance Association Conference. The many insights of Wayne Lee, Anna Martin, and Ann Marie Whyte were invaluable. Rodriguez would like to thank Mary C. Ferreira and Vivian Acosta from the University of Puerto Rico for their excellent research assistance and 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. References Bhargava, R., Gallo, J.G., Swanson, P.E., 2001. The performance, asset allocation, and investment style of international equity managers. Review of Quantitative Finance and Accounting 17, 377–395. Blake, C.R., Elton, E.J., Gruber, M.J., 1993. The performance of bond mutual funds. Journal of Business 66, 371–403. Brown, S., Goetzmann, W., 1997. Mutual fund styles. Journal of Financial Economics 43, 373–399. Comer, G., Larrymore, N., Rodriguez, J., 2006. Measuring the value of active fund management: the case of hybrid mutual funds. Working Paper. Cumby, R.E., Glen, J.D., 1990. Evaluating the performance of international mutual funds. Journal of Finance 45, 497–521. Dor, A.B., Jagannathan, R., Meier, I., 2003. Understanding mutual fund and hedge fund styles using return based style analysis. Journal of Investment Management 1, 97–137. Eun, C.S., Kolodny, R., Resnick, B.G., 1991. U.S.-based international mutual funds: a performance evaluation. Journal of Portfolio Management 17, 88–94. Fung, W., Hsieh, D., 1997. Empirical characteristics of dynamic trading strategies: the case of hedge funds. Review of Financial Studies 10, 275–302. Grinblatt, M., Titman, S., 1989. Portfolio performance evaluation: old issues and new insights. Review of Financial Studies 2, 393–421. Grinblatt, M., Titman, S., 1993. Performance measurements without benchmarks: an examination of mutual fund returns. Journal of Business 66, 47–68. Grinblatt, M., Titman, S., 1994. A study of monthly mutual fund returns and performance evaluation techniques. Journal of Financial and Quantitative Analysis 29, 419–444. Ibbotson, R., 1996. Do winning mutual funds repeat? TMA Journal 16, 50–53. Jensen, M., 1968. The Performance of mutual funds in the period 1945–1964. Journal of Finance 23, 389–416. Jensen, M., 1969. Risk, the pricing of capital assets, and the evaluation of investment portfolios. Journal of Business 42, 167–247. Myers, M., Poterba, J., Shackleford, D., Shoven, J., 2001. Copycat funds: information disclosure regulation and the returns to active management in the mutual fund industry. Working Paper, MIT. Sharpe, W., 1992. Asset allocation: management style and performance measurement. Journal of Portfolio Management 18, 7–19. Shukla, R., Singh, S., 1997. A performance evaluation of global equity mutual funds: evidence from 1988–1995. Global Finance Journal 8, 279–293.