Models of evaluation of the effectiveness of hedge funds

Hedge fund research. Multifactor asset-pricing models. Hedge funds factor models. Data on asset pricing factors and descriptive statistics. Carhart four-factor model. Betting against beta. Quality minus junk. Analysis of regional focuses, asset pricing.

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Applying correlation condition in addition to Alpha and R-squared constraints, we say that correlations should be below average (-1.65%) and Alpha should be above average of strategy-model for corresponding fund group.

The results of this condition follow (Table 16).

Table 16

Outcomes after application of correlation criteria for efficiency

MKTRF

MKTRF SMB HML

MKTRF SMB HML BAB

MKTRF SMB HML MOM

MKTRF SMB HML RMW CMA

MKTRF SMB HML RMW CMA QMJ

CTA

1

0

0

0

0

0

ED

0

0

0

0

0

0

EH

0

0

0

0

0

0

FID

0

0

0

0

0

0

FIRV

1

1

0

1

1

1

M

1

0

0

0

0

0

MS

0

0

0

0

0

0

NA

0

0

0

0

0

0

With the correlation constraint applied, it can be seen that CTA strategy have been eliminated from efficient for most of the models. FI Relative Value though remains efficient nevertheless, as well as Macro strategy according to CAPM model. The constraint significance is questionable since due to its negative value (-1.65%), so that it eliminates even hedge funds with close to zero positive correlations. It is not our case though since the funds eliminated were CTA, which had correlation value of almost 1 previously.

4.3 Analysis of regional focuses and asset pricing models

Then we perform similar analysis for different regional focuses by various models. Below are the Alphas (Table 17) and R-squares (Table 18).

Table 17

Average annual Alpha for different regional focuses and models

Alpha

E

G

P

NA

US

Average

MKTRF

-0.71%

0.16%

3.49%

1.41%

2.71%

1.41%

MKTRF SMB HML

-1.17%

0.19%

3.18%

1.19%

2.79%

1.24%

MKTRF SMB HML BAB

-1.28%

-0.31%

3.70%

0.76%

2.58%

1.09%

MKTRF SMB HML MOM

-0.78%

-0.08%

2.62%

0.88%

2.71%

1.07%

MKTRF SMB HML RMW CMA

0.47%

1.25%

3.70%

0.82%

3.14%

1.87%

MKTRF SMB HML RMW CMA QMJ

0.90%

1.28%

4.39%

3.37%

3.46%

2.68%

Average

-0.43%

0.42%

3.51%

1.41%

2.90%

1.56%

Table 18

R-squared

E

G

P

NA

US

Aver R-sq

Alpha 1-yr

MKTRF

12.66%

5.36%

14.99%

17.35%

8.26%

11.72%

1.41%

MKTRF SMB HML

14.46%

6.01%

17.07%

18.78%

9.57%

13.18%

1.24%

MKTRF SMB HML BAB

14.66%

6.10%

17.14%

19.53%

13.09%

14.10%

1.09%

MKTRF SMB HML MOM

14.90%

6.30%

15.03%

19.00%

10.01%

13.05%

1.07%

MKTRF SMB HML RMW CMA

15.47%

6.44%

17.70%

20.02%

10.46%

14.02%

1.87%

MKTRF SMB HML RMW CMA QMJ

15.89%

6.45%

18.02%

22.44%

10.73%

14.71%

2.68%

Aver R-sq

14.67%

6.11%

16.66%

19.52%

10.35%

13.46%

x

Alpha 1-yr

-0.43%

0.42%

3.51%

1.41%

2.90%

x

1.56%

Exposure of hedge funds' to asset pricing models across regions

It is observable that even though Alpha and R-squared value differ slightly across models, there is significant difference between them for regions. That said, it can be seen that in terms of R-squared North American and Pacific finds show greatest exposure of 16-19%, with the latter being among the most profitable locations for investing. Globally oriented funds tend to have lowest exposure, and at the same time smallest average Alpha.

We then apply the same constraints as before regarding Alpha and R-squared values. Efficient funds' Alphas should be above 1.56% and R-squares below 13.46% (Table 19).

Table 19

Outcomes after application of efficiency criteria for Alpha and R-squared

E

G

P

NA

US

MKTRF

0

0

0

0

1

MKTRF SMB HML

0

0

0

0

1

MKTRF SMB HML BAB

0

0

0

0

1

MKTRF SMB HML MOM

0

0

0

0

1

MKTRF SMB HML RMW CMA

0

0

0

0

1

MKTRF SMB HML RMW CMA QMJ

0

0

0

0

1

There is no argument that hedge funds investing within United States are efficient according to the table above. American hedge fund industry proved not only to be among the most developed, but is efficient after all as it turned out.

We also try to find the differences in Alpha - R-squared relationship for different regions (Table 20).

Table 20

Correlation of funds' Alphas and R-squared for different regions and models

Correlation

E

G

P

NA

US

Average correlation

MKTRF

38.94%

-45.31%

-25.98%

-7.25%

-69.08%

-9.08%

MKTRF SMB HML

35.66%

-50.84%

-30.14%

-1.82%

-70.50%

-10.54%

MKTRF SMB HML BAB

36.17%

-48.85%

-29.89%

-0.27%

-68.90%

-11.14%

MKTRF SMB HML MOM

41.99%

-31.89%

-31.37%

13.17%

-64.91%

-8.27%

MKTRF SMB HML RMW CMA

23.24%

-24.25%

-36.18%

17.13%

-61.91%

-13.60%

MKTRF SMB HML RMW CMA QMJ

45.54%

-13.94%

-24.00%

25.33%

-55.38%

5.87%

Average correlation

37.76%

-32.56%

-26.34%

9.58%

-64.16%

-11.47%

For different regionally-focused funds we can say that on average, funds aimed at Europe tend to be more positively-correlated with the models under analysis, particularly to Momentum and Quality factors, which can be a sign for more conservatism among European investors and asset-managers. The U.S.-oriented funds, on the other hand, are showing significant negative correlation, which combined with a positive Alpha shows that these funds managed to capture inefficiencies in the stated models and profited on them. Funds focused on other parts of North America proved to be the most creative - the highest correlation is 25.33% and with positive Alpha we can say that North America-focused funds (most of which are actually offshore-based) tend to imply not typical investment strategies. However, since its Alpha is lower than our outlined benchmark (1.78%), we cannot name these funds to be entirely efficient. Considering that the average Alpha - R-squared correlation tends to be around -11%, we can also confirm our Hypothesis 2.1 about negative relationship between hedge funds' Alpha and exposure. Application of correlation constraint does not change the outcome - U.S. hedge funds remain efficient regardless of the model applied.

4.4 Analysis of time-related dependencies

Finally, of a much interest to us is how past exposure relates to future performance. We try to expand the findings of Titman, Tiu (2008) on a pool of different strategies and geographical focuses of hedge funds. We separated our sample on 132 months into two 66-months subsamples (breaking point is June 2010).

Table 21

Correlation of funds' future Alphas and past R-squared for two time-samples

E

G

P

NA

US

Alpha <66

Alpha >66

Alpha-R-sq correlation

CTA

-81.43%

-16.34%

-59.92%

-

-

10.40%

-0.41%

65.80%

ED

-32.91%

75.71%

-36.38%

98.60%

-

-1.53%

-1.83%

94.58%

EH

35.74%

57.63%

39.34%

93.53%

57.15%

4.26%

-3.28%

41.64%

FID

38.24%

4.60%

60.66%

-

25.36%

7.21%

2.55%

12.63%

FIRV

-

3.83%

5.52%

-

45.86%

1.15%

4.25%

-35.92%

M

15.13%

-26.18%

21.76%

-

-1.79%

11.85%

-10.66%

51.56%

MS

53.55%

0.41%

-17.15%

61.42%

-32.09%

2.05%

5.10%

-63.36%

NA

95.12%

60.89%

68.87%

-

7.65%

-1.85%

-16.70%

-15.01%

Alpha <66

6.18%

2.41%

4.48%

3.25%

2.99%

x

x

x

Alpha >66

-8.42%

-3.16%

2.80%

-4.58%

-2.66%

x

xx

x

Alpha-R-sq correlation

18.06%

28.24%

11.62%

1.21%

-1.16%

x

x

12.37%

In Table 21 the correlations of first sample R-squares and second sample Alphas are presented. We can see that for some hedge funds, such as Event driven, Equity hedge North American funds, N.A. European funds or CTA European funds the correlations can be quite significant. Event driven funds tend to be the most correlated in terms of past exposure and future performance, which, given its low Alpha on both subsamples and high exposure, tells us poor performance will most likely persist in the future of these funds. For Macro and CTA funds, which we named efficient above, the correlation also tends to be quite significant, although lower especially for Macro funds. It can warn us since the increase of exposure for these funds has to lead to the Alpha increase, but given overall correlations to be low enough, Alphas can become lower in the future. The conclusion though should be addressed with caution though, since not much performance can be predicted for these funds via correlations and exposure. Multi-strategy and FI Relative Value funds show negative past R-squared - future Alpha correlations, and increase in Alpha with time. For these funds there is still room for exposures to drop lower and therefore for Alphas to increase even more.

There is also enough evidence to state that the industry of hedge funds experiences tough times now as compared to the years 2005-2010. The Alphas have dropped from around 4% annually to -3% for the second sample. Alphas have dropped across all regions of hedge funds interest, leaving only Asian and Pacific funds to add value nowadays.

From the two-sample analysis we can distinguish funds that provide positive return across time and eliminate funds that we previously named as efficient. This can be applied to CTA funds, which turned out to have positive Alpha solely due to the success of the strategy of earlier years. Since Alpha for CTA strategy dropped from 10.4% to -0.4% it is obvious there is no reason to name this funds group as efficient. Same can be applied to the Macro strategy, which we would call efficient 5 or 10 years ago, but not anymore. Fixed Income Relative Value funds and Multi-strategy funds though have shown an increase in Alphas ever since. FIRV funds have justified their investment strategy statement, proven able to find and exploit market inefficiencies and arbitrage opportunities, for which there were enough room during unstable recent years on financial markets. Multi-strategy funds bear their name for a reason as well, given close to zero Alpha - R-squared correlations. Multi-strategy Global funds also turned out to be efficient previously. Combined with positive growing Alpha funds of these type can be distinguished by us to be the most efficient. We can also say that even though some fund categories can experience low past exposure - high future Alpha relationship, the average correlation of about 12.37% makes us reject our Hypothesis 2.2 about negative relationship between these two factors.

5. Contribution, limitations and opportunities for further research

This paper adds value for the hedge funds research by producing the comparative analysis of hedge funds' profitability and exposure to the commonly used models for calculating required returns. Having divided our initial sample into groups of funds varied by investment strategy and regional focus, we applied asset pricing models to them and found out that there is no reason to invest in some categories of hedge funds given that the excess returns they provide from typical investment strategies rarely cover high management fees. Moreover, our findings allowed to distinguish hedge funds that have persistently high Alphas and low exposure to standard asset pricing models. Thereafter we adjusted the results in order to see if a fund group derives its profits from a particular return factor, which influenced the outcomes concerning truly efficient hedge funds. We created a framework, using which an investor can understand whether the commission a fund takes is justified or not. The research resulted in statement that nowadays only a few strategies can outperform a benchmark more demanding than S&P 500.

There are some problems that we face during the research. First, it is obvious that hedge fund databases lack information that would be vital for the research of any other investment vehicle. These problems were mentioned as drawbacks of any hedge fund research to date. Obtaining additional information would make the research much more representative and complete. Second, it is possible that we will not be able to find return factors for some hedge funds' strategies due to their specifics. The more complex analysis of hedge funds' returns decomposition is required in order to derive actual drivers of funds' returns.

There is still plenty of room for continuing this research. The opportunities vary from the usage of more and more complex asset pricing models and factors to dividing the sample into more specified strategy and precise location focus areas. One of the most promising frameworks of research would be a year-to-year comparison of hedge funds' performance and exposure, which can lead to interesting results given availability of monthly market and return factors data. Since the industry of hedge funds is transforming into high frequency algorithmic trading, it may be also necessary to include factors associated with this new field.

Conclusion

In this paper we performed comparative analysis of hedge funds efficiency and exposure. We analyzed 6 different asset pricing model specifications for a pool of 3668 hedge funds, divided into 8 strategies and 5 geographical focuses. We addressed efficiency of hedge funds in terms of their ability to generate returns above a benchmark, which we defined as Alpha, and their exposure to the asset pricing models, which we identified as regression R-squared. We assessed Alpha - R-squared relationship between different investment strategies, regional focuses, model specifications and timeframes.

We found out that absolute returns are on average 2% higher than the Alphas derived from the models. It is therefore reasonable to question efficiency of such funds, considering that investors usually pay 2% commission on their assets. Given that there is a necessity for a framework to distinguish efficient funds, we stated than a group of funds may be called efficient if its Alpha is above average, while its R-squared of asset pricing regression models should be below average. We managed to derive hedge fund strategies that suit this criteria, as well as regions where hedge funds tend to be creative as well as profitable. The employment of multiple asset pricing models allowed us to track the exposure to some of factors used in the models. multifactor research pricing asset

However, after dividing out sample into two timeframes, it turned out that most of hedge funds' positive Alphas were created 5-10 years ago. Not only it was possible to distinguish strategies that do not bring positive Alpha anymore, we saw evidence that the whole hedge funds industry is experiencing a downturn, supporting our research in pursuit of efficient hedge funds.

References

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Appendix 1

Cumulative return of CTA/Managed futures strategy and S&P 500 index

Cumulative return of Fixed Income Relative Value strategy and S&P 500 index

Cumulative return of Event Driven strategy and S&P 500 index

Cumulative return of not-available strategy funds and S&P 500 index

Cumulative return of Multi-strategy and S&P 500 index

Cumulative return of Macro strategy and S&P 500 index

Cumulative return of Equity Hedge strategy and S&P 500 index

Cumulative return of Fixed Income Directional strategy and S&P 500 index

Appendix 2

Descriptive statistics for CTA/Managed futures strategy returns for different regions

CTAG

CTANA

CTAUS

CTAE

CTAP

Average

0.35%

0.51%

0.52%

0.23%

0.55%

Min

-4.43%

-40.93%

-10.48%

-5.05%

-18.54%

Max

7.30%

32.37%

3.29%

6.68%

21.14%

Std dev

2.30%

11.67%

2.55%

2.24%

5.67%

Descriptive statistics for Equity Hedge strategy returns for different regions

EHG

EHNA

EHUS

EHE

EHP

Average

0.53%

0.49%

0.39%

0.54%

0.52%

Min

-10.09%

-10.93%

-12.94%

-9.88%

-12.04%

Max

8.61%

13.82%

9.39%

8.02%

9.66%

Std dev

2.99%

4.01%

3.23%

2.86%

3.14%

Descriptive statistics for Event Driven strategy returns for different regions

EDG

EDNA

EDUS

EDE

EDP

Average

0.17%

0.13%

0.35%

0.62%

0.13%

Min

-8.89%

-37.19%

-14.48%

-8.55%

-11.71%

Max

4.38%

13.53%

23.77%

5.52%

7.27%

Std dev

1.95%

5.93%

3.74%

2.14%

2.52%

Descriptive statistics for FI Directional strategy returns for different regions

FIDG

FIDNA

FIDUS

FIDE

FIDP

Average

0.37%

-0.29%

0.32%

0.32%

0.41%

Min

-8.44%

-2.41%

-8.89%

-7.40%

-8.92%

Max

3.59%

2.80%

5.95%

4.44%

4.13%

Std dev

1.55%

1.52%

1.76%

1.66%

1.58%

Descriptive statistics for FI Relative Value strategy returns for different regions

FIRVG

FIRVNA

FIRVUS

FIRVE

FIRVP

Average

0.35%

0.84%

0.50%

0.00%

0.50%

Min

-10.86%

-21.44%

-8.79%

0.00%

-5.68%

Max

7.08%

22.19%

12.32%

0.00%

3.68%

Std dev

1.85%

7.03%

1.96%

0.00%

1.22%

Descriptive statistics for Macro strategy returns for different regions

MG

MNA

MUS

ME

MP

Average

0.42%

0.55%

0.33%

0.16%

0.51%

Min

-3.91%

-8.02%

-7.12%

-16.96%

-8.29%

Max

5.09%

7.72%

8.83%

13.28%

5.81%

Std dev

1.70%

5.07%

3.08%

3.33%

2.33%

Descriptive statistics for Multi-strategy returns for different regions

MSG

MSNA

MSUS

MSE

MSP

Average

0.42%

1.17%

-0.10%

0.47%

0.40%

Min

-6.32%

-9.96%

-22.34%

-10.29%

-4.73%

Max

9.45%

9.96%

44.89%

6.70%

5.53%

Std dev

1.93%

2.85%

8.31%

2.30%

1.58%

Descriptive statistics for not-available strategy funds' returns for different regions

NAG

NANA

NAUS

NAE

NAP

Average

-0.48%

1.44%

0.04%

-0.15%

0.19%

Min

-22.36%

-7.37%

-9.60%

-9.11%

-20.43%

Max

13.87%

59.21%

11.14%

5.79%

7.93%

Std dev

4.41%

7.45%

3.24%

2.49%

3.04%

Appendix 3

Descriptive statistics for asset pricing models factors (Europe)

E

MKT-RF

SMB

HML

RMW

CMA

RF

MOM

BAB

QMJ

Average

0.47%

0.14%

-0.13%

0.40%

0.07%

0.11%

0.88%

0.52%

0.63%

Min

-22.14%

-4.65%

-4.60%

-5.25%

-3.66%

0.00%

-25.96%

-10.89%

-10.75%

Max

13.78%

4.85%

7.45%

3.77%

5.54%

0.44%

9.87%

7.90%

8.79%

Std dev

5.68%

1.93%

2.23%

1.40%

1.39%

0.15%

3.90%

2.82%

2.46%

Descriptive statistics for asset pricing models factors (Global)

G

MKT-RF

SMB

HML

RMW

CMA

RF

MOM

BAB

QMJ

Average

0.42%

0.03%

0.08%

0.29%

0.15%

0.11%

0.74%

0.70%

0.49%

Min

-21.14%

-4.67%

-4.01%

-2.84%

-5.59%

0.00%

-22.48%

-6.95%

-7.71%

Max

13.70%

4.54%

4.41%

2.88%

6.88%

0.44%

8.57%

7.08%

8.49%

Std dev

5.13%

1.79%

1.62%

1.05%

1.50%

0.15%

3.39%

2.15%

2.23%

Descriptive statistics for asset pricing models factors (North America)

NA

MKT-RF

SMB

HML

RMW

CMA

RF

MOM

BAB

QMJ

Average

0.57%

0.01%

-0.08%

0.31%

0.03%

0.11%

0.28%

0.57%

0.38%

Min

-18.23%

-4.33%

-7.47%

-3.48%

-3.49%

0.00%

-24.83%

-8.51%

-6.77%

Max

11.49%

5.64%

5.25%

5.58%

4.79%

0.44%

11.30%

11.40%

9.10%

Std dev

4.38%

2.14%

2.11%

1.49%

1.48%

0.15%

3.97%

2.69%

2.61%

Descriptive statistics for asset pricing models factors (United States)

US

MKT-RF

SMB

HML

RMW

CMA

RF

MOM

BAB

QMJ

Average

0.58%

0.08%

-0.04%

0.23%

0.03%

0.11%

0.19%

0.44%

0.32%

Min

-17.23%

-4.78%

-9.67%

-4.50%

-3.16%

0.00%

-34.58%

-9.25%

-7.44%

Max

11.35%

6.75%

7.65%

4.39%

3.44%

0.44%

12.45%

11.56%

8.86%

Std dev

4.31%

2.37%

2.35%

1.48%

1.31%

0.15%

4.78%

2.79%

2.65%

Descriptive statistics for asset pricing models factors (Asia and Pacific)

P

MKT-RF

SMB

HML

RMW

CMA

RF

MOM

BAB

QMJ

Average

0.71%

-0.05%

0.24%

0.02%

0.35%

0.11%

0.89%

1.20%

0.50%

Min

-26.06%

-10.91%

-6.51%

-9.31%

-7.77%

0.00%

-19.15%

-7.46%

-6.54%

Max

18.58%

10.42%

6.92%

6.62%

8.57%

0.44%

7.65%

7.94%

6.29%

Std dev

6.27%

3.01%

2.38%

2.42%

2.44%

0.15%

3.92%

2.59%

2.37%

Appendix 4

Regression results for CTA/Managed futures strategy funds

Asset pricing model specification

Regional focus

Strategy

Alpha (constant)

R-squared (overall)

MKTRF

E

CTA

0.001995

0.0071

MKTRF SMB HML

E

CTA

0.001904

0.0118

MKTRF SMB HML MOM

E

CTA

0.001892

0.0118

MKTRF SMB HML BAB

E

CTA

0.001824

0.0132

MKTRF SMB HML RMW CMA

E

CTA

0.003375

0.0148

MKTRF SMB HML RMW CMA QMJ

E

CTA

0.002155

0.0217

MKTRF

G

CTA

-4.8E-05

0.0049

MKTRF SMB HML

G

CTA

-0.00013

0.0103

MKTRF SMB HML MOM

G

CTA

-0.00186

0.0217

MKTRF SMB HML BAB

G

CTA

-0.00033

0.0103

MKTRF SMB HML RMW CMA

G

CTA

-0.00052

0.0139

MKTRF SMB HML RMW CMA QMJ

G

CTA

-0.00133

0.0146

MKTRF

P

CTA

0.009935

0.0039

MKTRF SMB HML

P

CTA

0.010714

0.0199

MKTRF SMB HML MOM

P

CTA

0.010632

0.02

MKTRF SMB HML BAB

P

CTA

0.011434

0.0218

MKTRF SMB HML RMW CMA

P

CTA

0.010991

0.0468

MKTRF SMB HML RMW CMA QMJ

P

CTA

0.011369

0.0471

Regression results for Event Driven strategy funds

Asset pricing model specification

Regional focus

Strategy

Alpha (constant)

R-squared (overall)

MKTRF

E

ED

-0.00938

0.0399

MKTRF SMB HML

E

ED

-0.01029

0.0721

MKTRF SMB HML MOM

E

ED

-0.01242

0.0825

MKTRF SMB HML BAB

E

ED

-0.0107

0.075

MKTRF SMB HML RMW CMA

E

ED

-0.00587

0.0837

MKTRF SMB HML RMW CMA QMJ

E

ED

-0.01

0.0956

MKTRF

G

ED

-0.00151

0.1062

MKTRF SMB HML

G

ED

-0.00153

0.1195

MKTRF SMB HML MOM

G

ED

-0.00194

0.1204

MKTRF SMB HML BAB

G

ED

-0.00255

0.1229

MKTRF SMB HML RMW CMA

G

ED

-0.00018

0.1244

MKTRF SMB HML RMW CMA QMJ

G

ED

-5.91E-06

0.1245

MKTRF

P

ED

0.004342

0.2598

MKTRF SMB HML

P

ED

0.00355

0.2961

MKTRF SMB HML MOM

P

ED

0.003115

0.3048

MKTRF SMB HML BAB

P

ED

0.002551

0.2965

MKTRF SMB HML RMW CMA

P

ED

0.002906

0.2991

MKTRF SMB HML RMW CMA QMJ

P

ED

0.002957

0.2992

MKTRF

NA

ED

-0.00178

0.1125

MKTRF SMB HML

NA

ED

-0.0015

0.1174

MKTRF SMB HML MOM

NA

ED

-0.00146

0.1175

MKTRF SMB HML BAB

NA

ED

-0.00194

0.1201

MKTRF SMB HML RMW CMA

NA

ED

-0.00152

0.1263

MKTRF SMB HML RMW CMA QMJ

NA

ED

-2.7E-05

0.1456

MKTRF

US

ED

0.000821

0.2019

MKTRF SMB HML

US

ED

0.00044

0.2299

MKTRF SMB HML MOM

US

ED

0.000146

0.2339

MKTRF SMB HML BAB

US

ED

-0.00115

0.4423

MKTRF SMB HML RMW CMA

US

ED

0.001404

0.2598

MKTRF SMB HML RMW CMA QMJ

US

ED

0.001836

0.2642

Regression results for Equity Hedge strategy funds

Asset pricing model specification

Regional focus

Strategy

Alpha (constant)

R-squared (overall)

MKTRF

E

EH

-0.0003176

0.1422

MKTRF SMB HML

E

EH

-0.0008963

0.1598

MKTRF SMB HML MOM

E

EH

-0.001071

0.1599

MKTRF SMB HML BAB

E

EH

-0.0008555

0.1598

MKTRF SMB HML RMW CMA

E

EH

-0.0003811

0.166

MKTRF SMB HML RMW CMA QMJ

E

EH

0.0006633

0.1671

MKTRF

G

EH

0.000466

0.0998

MKTRF SMB HML

G

EH

0.000458

0.1046

MKTRF SMB HML MOM

G

EH

0.0006263

0.1047

MKTRF SMB HML BAB

G

EH

0.0006273

0.1046

MKTRF SMB HML RMW CMA

G

EH

0.0018538

0.1072

MKTRF SMB HML RMW CMA QMJ

G

EH

0.0021829

0.1072

MKTRF

P

EH

0.0021063

0.2343

MKTRF SMB HML

P

EH

0.0017603

0.2592

MKTRF SMB HML MOM

P

EH

0.0012234

0.2605

MKTRF SMB HML BAB

P

EH

0.0033406

0.2615

MKTRF SMB HML RMW CMA

P

EH

0.0021296

0.2606

MKTRF SMB HML RMW CMA QMJ

P

EH

0.0039929

0.2652

MKTRF

NA

EH

-0.001917

0.1428

MKTRF SMB HML

NA

EH

-0.0023408

0.1558

MKTRF SMB HML MOM

NA

EH

-0.002327

0.1573

MKTRF SMB HML BAB

NA

EH

-0.0029135

0.1697

MKTRF SMB HML RMW CMA

NA

EH

-0.0019898

0.18

MKTRF SMB HML RMW CMA QMJ

NA

EH

0.000118

0.2019

MKTRF

US

EH

-0.0018443

0.2548

MKTRF SMB HML

US

EH

-0.0014958

0.2633

MKTRF SMB HML MOM

US

EH

-0.0014091

0.2644

MKTRF SMB HML BAB

US

EH

-0.0017376

0.2659

MKTRF SMB HML RMW CMA

US

EH

-0.0008328

0.2664

MKTRF SMB HML RMW CMA QMJ

US

EH

-0.0002982

0.27

Regression results for Fixed Income Directional strategy funds0

Asset pricing model specification

Regional focus

Strategy

Alpha (constant)

R-squared (overall)

MKTRF

E

FID

0.003983

0.1757

MKTRF SMB HML

E

FID

0.003444

0.2232

MKTRF SMB HML MOM

E

FID

0.0037914

0.2255

MKTRF SMB HML BAB

E

FID

0.0030867

0.2291

MKTRF SMB HML RMW CMA

E

FID

0.00376

0.2372

MKTRF SMB HML RMW CMA QMJ

E

FID

0.0038853

0.2373

MKTRF

G

FID

0.0011987

0.0742

MKTRF SMB HML

G

FID

0.0006559

0.0867

MKTRF SMB HML MOM

G

FID

0.000712

0.0867

MKTRF SMB HML BAB

G

FID

0.0004604

0.088

MKTRF SMB HML RMW CMA

G

FID

0.0013985

0.0907

MKTRF SMB HML RMW CMA QMJ

G

FID

0.0013003

0.0908

MKTRF

P

FID

0.0027031

0.2046

MKTRF SMB HML

P

FID

0.0020611

0.2143

MKTRF SMB HML MOM

P

FID

0.0029684

0.02177

MKTRF SMB HML BAB

P

FID

0.0020417

0.2143

MKTRF SMB HML RMW CMA

P

FID

0.002689

0.2165

MKTRF SMB HML RMW CMA QMJ

P

FID

0.0027879

0.2166

MKTRF

US

FID

0.0011629

0.0013

MKTRF SMB HML

US

FID

0.0019709

0.0018

MKTRF SMB HML MOM

US

FID

0.0020259

0.0039

MKTRF SMB HML BAB

US

FID

0.0020988

0.008

MKTRF SMB HML RMW CMA

US

FID

0.0028244

0.0063

MKTRF SMB HML RMW CMA QMJ

US

FID

0.0026745

0.0073

Regression results for Fixed Income Relative Value strategy funds0

Asset pricing model specification

Regional focus

Strategy

Alpha (constant)

R-squared (overall)

MKTRF

G

FIRV

0.0018747

0.0284

MKTRF SMB HML

G

FIRV

0.0020869

0.0338

MKTRF SMB HML MOM

G

FIRV

0.003735

0.0429

MKTRF SMB HML BAB

G

FIRV

0.001343

0.0351

MKTRF SMB HML RMW CMA

G

FIRV

0.0037434

0.0506

MKTRF SMB HML RMW CMA QMJ

G

FIRV

0.0039428

0.0506

MKTRF

P

FIRV

-0.0014194

0.0511

MKTRF SMB HML

P

FIRV

-0.0014949

0.0617

MKTRF SMB HML MOM

P

FIRV

-0.0018386

0.062

MKTRF SMB HML BAB

P

FIRV

-0.0018239

0.0618

MKTRF SMB HML RMW CMA

P

FIRV

0.0004182

0.0692

MKTRF SMB HML RMW CMA QMJ

P

FIRV

-0.0017387

0.0737

MKTRF

US

FIRV

0.0045554

0.0107

MKTRF SMB HML

US

FIRV

0.0043741

0.0309

MKTRF SMB HML MOM

US

FIRV

0.0043559

0.0315

MKTRF SMB HML BAB

US

FIRV

0.0043904

0.031

MKTRF SMB HML RMW CMA

US

FIRV

0.0039911

0.0341

MKTRF SMB HML RMW CMA QMJ

US

FIRV

0.0042391

0.0388

Regression results for Macro strategy funds

Asset pricing model specification

Regional focus

Strategy

Alpha (constant)

R-squared (overall)

MKTRF

E

M

0.003379

0.2031

MKTRF SMB HML

E

M

0.0028314

0.2134

MKTRF SMB HML MOM

E

M

0.0064218

0.2272

MKTRF SMB HML BAB

E

M

0.0034912

0.2157

MKTRF SMB HML RMW CMA

E

M

0.0039401

0.2186

MKTRF SMB HML RMW CMA QMJ

E

M

0.0087921

0.2267

MKTRF

G

M

0.0013919

0.029

MKTRF SMB HML

G

M

0.0013666

0.0309

MKTRF SMB HML MOM

G

M

0.0009492

0.0316

MKTRF SMB HML BAB

G

M

0.0014694

0.0309

MKTRF SMB HML RMW CMA

G

M

0.0018538

0.0314

MKTRF SMB HML RMW CMA QMJ

G

M

0.0019868

0.0314

MKTRF

P

M

0.0002501

0.1861

MKTRF SMB HML

P

M

3.72E-06

0.218

MKTRF SMB HML MOM

P

M

-0.0010336

0.2278

MKTRF SMB HML BAB

P

M

0.0011246

0.2201

MKTRF SMB HML RMW CMA

P

M

0.0007706

0.224

MKTRF SMB HML RMW CMA QMJ

P

M

0.0020931

0.2287

MKTRF

US

M

0.0071685

0.0051

MKTRF SMB HML

US

M

0.0071256

0.0111

MKTRF SMB HML MOM

US

M

0.0076324

0.0235

MKTRF SMB HML BAB

US

M

0.0071234

0.0118

MKTRF SMB HML RMW CMA

US

M

0.0074982

0.0217

MKTRF SMB HML RMW CMA QMJ

US

M

0.0079981

0.0253

Regression results for Multi-strategy funds

Asset pricing model specification

Regional focus

Strategy

Alpha (constant)

R-squared (overall)

MKTRF

E

MS

-0.000185

0.1471

MKTRF SMB HML

E

MS

-0.0005466

0.151

MKTRF SMB HML MOM

E

MS

0.0000693

0.1556

MKTRF SMB HML BAB

E

MS

-0.0006209

0.152

MKTRF SMB HML RMW CMA

E

MS

0.0010891

0.1797

MKTRF SMB HML RMW CMA QMJ

E

MS

0.0014244

0.1799

MKTRF

G

MS

0.0019575

0.015

MKTRF SMB HML

G

MS

0.0016691

0.017

MKTRF SMB HML MOM

G

MS

0.0012429

0.0175

MKTRF SMB HML BAB

G

MS

0.0011134

0.0174

MKTRF SMB HML RMW CMA

G

MS

0.0025471

0.0172

MKTRF SMB HML RMW CMA QMJ

G

MS

0.0025648

0.0172

MKTRF

P

MS

0.0063317

0.1272

MKTRF SMB HML

P

MS

0.0053884

0.1579

MKTRF SMB HML MOM

P

MS

0.0041273

0.1642

MKTRF SMB HML BAB

P

MS

0.006227

0.1566

MKTRF SMB HML RMW CMA

P

MS

0.0054533

0.1585

MKTRF SMB HML RMW CMA QMJ

P

MS

0.0066711

0.162

MKTRF

NA

MS

0.0018519

0.3625

MKTRF SMB HML

NA

MS

0.0019451

0.3964

MKTRF SMB HML MOM

NA

MS

0.0021769

0.3979

MKTRF SMB HML BAB

NA

MS

0.0017039

0.398

MKTRF SMB HML RMW CMA

NA

MS

0.0023224

0.404

MKTRF SMB HML RMW CMA QMJ

NA

MS

0.0048687

0.4441

MKTRF

US

MS

0.0045647

0.0272

MKTRF SMB HML

US

MS

0.004253

0.0532

MKTRF SMB HML MOM

US

MS

0.0044435

0.0587

MKTRF SMB HML BAB

US

MS

0.0047791

0.0745

MKTRF SMB HML RMW CMA

US

MS

0.0038049

0.063

MKTRF SMB HML RMW CMA QMJ

US

MS

0.003966

0.0648

Regression results for not-available strategy funds

Asset pricing model specification

Regional focus

Strategy

Alpha (constant)

R-squared (overall)

MKTRF

E

NA

-0.0043715

0.1711

MKTRF SMB HML

E

NA

-0.0040767

0.1807

MKTRF SMB HML MOM

E

NA

-0.0045177

0.1808

MKTRF SMB HML BAB

E

NA

-0.004532

0.1816

MKTRF SMB HML RMW CMA

E

NA

-0.0036408

0.1827

MKTRF SMB HML RMW CMA QMJ

E

NA

-0.002791

0.1839

MKTRF

G

NA

-0.0044743

0.0716

MKTRF SMB HML

G

NA

-0.0034488

0.0779

MKTRF SMB HML MOM

G

NA

-0.0042087

0.0781

MKTRF SMB HML BAB

G

NA

-0.0043614

0.0786

MKTRF SMB HML RMW CMA

G

NA

-0.0025806

0.08

MKTRF SMB HML RMW CMA QMJ

G

NA

-0.002304

0.08

MKTRF

P

NA

-0.0019868

0.1321

MKTRF SMB HML

P

NA

-0.001733

0.1382

MKTRF SMB HML MOM

P

NA

-0.0026162

0.141

MKTRF SMB HML BAB

P

NA

-0.0013493

0.1384

MKTRF SMB HML RMW CMA

P

NA

-0.0017048

0.141

MKTRF SMB HML RMW CMA QMJ

P

NA

-0.0000914

0.1491

MKTRF

NA

NA

0.006255

0.0762

MKTRF SMB HML

NA

NA

0.0056331

0.0815

MKTRF SMB HML MOM

NA

NA

0.0043827

0.0874

MKTRF SMB HML BAB

NA

NA

0.005435

0.0934

MKTRF SMB HML RMW CMA

NA

NA

0.0037786

0.0906

MKTRF SMB HML RMW CMA QMJ

NA

NA

0.0059353

0.1058

MKTRF

US

NA

-0.0012063

0.077

MKTRF SMB HML

US

NA

-0.0009054

0.0799

MKTRF SMB HML MOM

US

NA

-0.0019639

0.0848

MKTRF SMB HML BAB

US

NA

-0.0010048

0.083

MKTRF SMB HML RMW CMA

US

NA

-0.0009512

0.0807

MKTRF SMB HML RMW CMA QMJ

US

NA

-0.0008532

0.0807

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