I choose the risk adjusted return, or alpha, from Fung-Hsieh extended 8 factor model as the measurement for hedge fund performance. Total return volatility is used as the measurement for fund risk.
While the more or less standard measurement for mutual fund performance is the excess returns from a variety of CAPM variations, measuring hedge fund performance is particularly troublesome because of its dynamic hedging and diverse strategies. Common models to estimate the hedge fund risk-adjusted return, hence the information ratio, include Fama and French (1993) 3-factor model;
Agarwal and Naik (2004) option-based model; and Fung, Hsieh, Naik, and Ramadorai (2008) 7-factor model. In this study, I use an extension of Fung-Hsieh 7 7-factor model with the addition of an eighth factor, the emerging market risk factor, as suggested by Hsieh on his data library website.
The emerging market risk factor is especially relevant for funds specialized on emerging markets, which presenting in our sample. Table 6 shows the summary statistics for all eight factors used in Fung-Hsieh model.
𝑟𝑖,𝑡 = 𝛼𝑖+ 𝛽1𝑆&𝑃𝑠+ 𝛽2𝑆𝐶𝐿𝐶 + 𝛽310𝑌 + 𝛽4𝐶𝑟𝑒𝑑𝑆𝑝𝑟 + 𝛽51𝐵𝐷𝑂𝑝𝑡 + 𝛽6𝐹𝑋𝑂𝑝𝑡 + 𝛽7𝐶𝑜𝑚𝑂𝑝𝑡 + 𝛽8𝐸𝑚𝑒 (2) Two equity-oriented risk factors: the excess return of the S&P500 index over the 3-month T-bill rate (S&P); and a small-minus-big cap factor (SCLC) constructed as the difference between the Russell 2000 index monthly return and S&P 500 month total return.
Two bond-oriented risk factors: the yield spread the monthly change in the 10-year treasury constant maturity yield over 3-month T-bill (10Y), and the change in the credit spread of Moody's BAA bond over the 10-year Treasury bond (CredSpr)
Three trend-following risk factors: the excess returns on portfolio of lookback straddle options on currency (FXOpt), commodities (ComOpt) and bonds (BDOpt).
Emerging market risk factor: the excess return of the MSCI Emerging Market index monthly total return over the 3-month T-bill rate (Eme).
Data for the risk factors are retrieved from Hsieh's Data Library.
As similar to how alpha is calculated in Fung et al. (2008) and Li et al. (2011), the alpha is estimated from model (2) using data from a rolling window of the most recent 24 month period.
Based on Li et al., the alpha estimation is repeated at the beginning of each quarter as opposed to each year in Fung et al. to obtain higher fidelity. Table 7 shows the summary statistic of each coefficient in regression model (2) over the whole period 1994-2014 for female funds and their matched male funds. The average month alpha for female funds is 0.56%, while the male funds have an average monthly alpha of 0.41%. Fung-Hsieh model is able to explain up to a maximum 71% of female fund return variation and averaging at 55%. In case of male funds, up to 76% of return variation is explained, averaging 64%. I consider the explanatory power of the model adequate for this research.
The preferable risk measurement is total return volatility, since it has the advantage of being model-free and certain hedge fund investors do care about absolute performance (Li, Zhang, and Zhao, 2011). Total return volatility is calculated quarterly based on monthly return in a 24-month period rolling window to match how the alpha is calculated. Since the regression is repeated every quarter, the risk-adjusted returns alpha and volatility are allowed to be time-varying. This allows me to analyse the variation over time of the gender effect on alpha and volatility.
Table 6: Summary statistics for Fung-Hsieh factors
This table shows the summary statistics for the independent variables in the regression model (2) 𝑟𝑖,𝑡 = 𝛼𝑖+ 𝛽1𝑆&𝑃𝑠+ 𝛽2𝑆𝐶𝐿𝐶 + 𝛽310𝑌 + 𝛽4𝐶𝑟𝑒𝑑𝑆𝑝𝑟 + 𝛽51𝐵𝐷𝑂𝑝𝑡 + 𝛽6𝐹𝑋𝑂𝑝𝑡 + 𝛽7𝐶𝑜𝑚𝑂𝑝𝑡
+ 𝛽8𝐸𝑚𝑒 S&P: the monthly excess return of the S&P500 index over the 3-month T-bill
SCL: difference between the Russell 2000 index monthly return and S&P 500 month total return
10Y: the yield spread the monthly change in the 10-year treasury constant maturity yield over 3-month T-bill CredSpr: the change in the credit spread of Moody's BAA bond over the 10-year Treasury bond
BDOpt: lookback straddle options on bonds FXOpt: lookback straddle options on commodities FXOpt: lookback straddle options on currency
Eme: the excess return of the MSCI Emerging Market index monthly total return over the 3-month T-bill rate
All measurements are in percent, per month.
The variables are retrieved from https://faculty.fuqua.duke.edu/~dah7/HFRFData.htm
Mean STD Min Max
S&P 0.57 4.31 -16.94 10.72
SC-LC 0.09 3.64 -16.38 18.41
10Y 0.37 2.21 -7.87 9.53
Cred Spr 0.26 2.12 -14.25 8.13 BD Opt -1.66 15.23 -25.63 68.86 FX Opt -0.35 19.21 -30.13 90.27 Com Opt -0.24 14.18 -24.65 64.75
Eme 0.61 7.04 -29.45 17.56
Table 7: Summary statistics for Fung-Hsieh factor loadings
This table shows the summary statistics for the factor loadings in the regression model (2), across all female funds and male fund for the whole period 1994-2014.
𝑟𝑖,𝑡 = 𝛼𝑖+ 𝛽1𝑆&𝑃𝑠+ 𝛽2𝑆𝐶𝐿𝐶 + 𝛽310𝑌 + 𝛽4𝐶𝑟𝑒𝑑𝑆𝑝𝑟 + 𝛽51𝐵𝐷𝑂𝑝𝑡 + 𝛽6𝐹𝑋𝑂𝑝𝑡 + 𝛽7𝐶𝑜𝑚𝑂𝑝𝑡 + 𝛽8𝐸𝑚𝑒
S&P: the monthly excess return of the S&P500 index over the 3-month T-bill
SCL: difference between the Russell 2000 index monthly return and S&P 500 month total return
10Y: the yield spread the monthly change in the 10-year treasury constant maturity yield over 3-month T-bill CredSpr: the change in the credit spread of Moody's BAA bond over the 10-year Treasury bond
BDOpt: lookback straddle options on bonds excess return over the 3-month T-bill FXOpt: lookback straddle options on commodities excess return over the 3-month T-bill FXOpt: lookback straddle options on currency excess return over the 3-month T-bill
Eme: the excess return of the MSCI Emerging Market index monthly total return over the 3-month T-bill rate
All measurements are in percent, per month.
female funds male funds
Mean STD Min Max Mean STD Min Max
alpha 0.56 3.47 -2.12 3.39 0.41 2.74 -3.26 3.87
S&P 0.08 1.45 -2.77 1.32 0.06 1.72 -3.21 1.69
SC-LC 0.35 0.80 -0.92 0.55 0.25 0.59 -0.61 0.71
10Y -0.07 0.79 -0.33 0.27 0.01 0.75 -0.32 0.27
Cred Spr 0.23 1.23 -1.38 0.80 0.25 0.54 -1.18 0.99
BD Opt 0.04 0.77 -0.06 0.09 -0.01 0.15 -0.33 0.18
FX Opt 0.003 0.07 -0.07 0.09 -0.04 0.06 -0.07 0.09
Com Opt 0.01 0.60 -0.29 0.07 0.05 0.69 -0.19 0.09
Eme 0.02 0.19 -0.35 0.06 0.02 0.66 -0.62 0.26
R_squared 0.55 0.28 0.18 0.71 0.64 0.47 0.09 0.76
6. Result
In each quarter, the average gender effect of the manger being female on hedge fund performance and risk is estimated as the average difference of monthly alpha and monthly volatility difference between all female fund-male fund pairs.
𝐴𝐺𝐸𝐹𝑎𝑙𝑝ℎ𝑎,𝑡 = 𝐸(𝑎𝑙𝑝ℎ𝑎𝐹𝑒𝑚𝑎𝑙𝑒 𝐹𝑢𝑛𝑑𝑖,𝑡 − 𝑎𝑙𝑝ℎ𝑎𝑀𝑎𝑙𝑒 𝐹𝑢𝑛𝑑𝑖,𝑡)
𝐴𝐺𝐸𝐹𝑎𝑙𝑝ℎ𝑎,𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑎𝑔𝑒𝑛𝑑𝑒𝑟 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑓 𝑓𝑒𝑚𝑎𝑙𝑒 𝑚𝑎𝑛𝑎𝑔𝑒𝑟 𝑜𝑛 𝑟𝑖𝑠𝑘 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 (𝑎𝑙𝑝ℎ𝑎) 𝑜𝑣𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝑎𝑙𝑝ℎ𝑎𝐹𝑒𝑚𝑎𝑙𝑒 𝐹𝑢𝑛𝑑𝑖,𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑖𝑠𝑘 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑡ℎ𝑒 𝑓𝑒𝑚𝑎𝑙𝑒 𝑓𝑢𝑛𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑎𝑖𝑟 𝑖 𝑜𝑣𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡
𝑎𝑙𝑝ℎ𝑎𝑀𝑎𝑙𝑒 𝐹𝑢𝑛𝑑𝑖,𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑖𝑠𝑘 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑡ℎ𝑒 𝑚𝑎𝑙𝑒 𝑓𝑢𝑛𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑎𝑖𝑟 𝑖 𝑜𝑣𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡
𝐴𝐺𝐸𝐹𝜎,𝑡 = 𝐸(𝜎𝐹𝑒𝑚𝑎𝑙𝑒 𝐹𝑢𝑛𝑑𝑖,𝑡 − 𝜎𝑀𝑎𝑙𝑒 𝐹𝑢𝑛𝑑𝑖,𝑡)
𝐴𝐺𝐸𝐹𝜎,𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑔𝑒𝑛𝑑𝑒𝑟 𝑒𝑓𝑓𝑒𝑐𝑡 𝑜𝑓 𝑓𝑒𝑚𝑎𝑙𝑒 𝑚𝑎𝑛𝑎𝑔𝑒𝑟 𝑜𝑛 𝑣𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦 𝑜𝑣𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝜎𝐹𝑒𝑚𝑎𝑙𝑒 𝐹𝑢𝑛𝑑𝑖,𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑣𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑒𝑚𝑎𝑙𝑒 𝑓𝑢𝑛𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑎𝑖𝑟 𝑖 𝑜𝑣𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡
𝜎𝑀𝑎𝑙𝑒 𝐹𝑢𝑛𝑑𝑖,𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑣𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑙𝑒 𝑓𝑢𝑛𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑎𝑖𝑟 𝑖 𝑜𝑣𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡
Figure 1 illustrates the time-varying average differences in alpha, while figure 2 shows the average difference on volatility. As can be seen from the graph, the gender effect of female manager on monthly risk-adjusted return is on an increasing trend. There seems to be two major periods that the gender effect on alpha is positive: from 1998 to 2005, and from 2007 to 2014. Meanwhile, the trend line of gender effect on volatility is nearly flat. The gender effect on volatility seems to be positive during the period 2000 to 2008, and negative during the rest.
Figure 1: The gender effect of female manager on risk adjusted return
This graph shows the time-varying gender effect of female manager on risk adjusted return (alpha) over the period Jan 1994-Jun 2014. The first data is calculated on Jan 1996. The gender effect on alpha is calculated each quarter, based on the return of the latest 24 months. The gender effect is displayed as monthly return.
Figure 2: The gender effect of female manager on net return volatility
This graph shows the time-varying gender effect of female manager on net return volatility over the period Jan 1994-Jun 2014. The first data on volatility is calculated on Jan 1996. The gender effect on alpha is calculated each quarter, based on the return of the latest 24 months. The gender effect is displayed as monthly volatility.
-0.20%
-0.10%
0.00%
0.10%
0.20%
0.30%
0.40%
0.50%
1996 1996 1997 1998 1999 1999 2000 2001 2002 2002 2003 2004 2005 2005 2006 2007 2008 2008 2009 2010 2011 2011 2012 2013 2014
The gender effect of female manager on risk adjusted return
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
1996 1996 1997 1998 1999 1999 2000 2001 2002 2002 2003 2004 2005 2005 2006 2007 2008 2008 2009 2010 2011 2011 2012 2013 2014
The gender effect of female manager on net
return volatility
The two first hypotheses can be tested with the gender effect of female manager and its standard deviation using t-test. The first hypothesis will be rejected if the gender effect of female manager for alpha is not significantly greater than zero. The second hypothesis will be rejected if the gender effect of female manager on volatility is not significantly smaller than zero. Estimate the standard deviation of gender effect of female manager to use in the paired-sample t-test is not straight forward because previous estimation steps have added variation beyond the normal sampling variation (Heckman, Ichimura, and Todd, 1998). Two main methods can be used to estimate the standard error, either by bootstrapping, or as the squared root of the variance approximation by Lechner (2001). I choose to use Lechner model instead of bootstrapping to avoid repeating verifying unidentified fund when resampling. In this case, because matching without replacement is used, Lechner’s variance coincides with the usual variance formula, which simplifies the calculation greatly.
Table 8 shows the gender effect of female manager on alpha and volatility, its standard deviation and the result of two-tail paired-sample t-test for zero mean difference. Panel 8A, 8B, 8C shows the results for the whole period Jan 1994-Jun 2014, the subperiod Jan 1997-Dec 1998 and the subperiod Jan 2007- Dec 2009 respectively. The two subperiods are chosen to cover two major financial distress periods in the last two decades: the 1997 Asian financial crisis and the Global financial crisis of 2007-2008.
The gender effect of female manager on alpha is found to be 0.17 percent monthly over the Jan 1994-Jun 2014 period, significant at 10 percent level. I consider this result to be a weak support for the hypothesis that funds with female managers earn superior return compared to those with male managers. However, during two financial distress period Jan 1997-Dec 1998 and Jan 2007- Dec 2009, the gender effect of female manager on alpha is 0.16 percent and 0.31 percent, both significant at 1 percent level. Therefore, I support the notion that female managers earn a significant positive return over their male counterparts at least during the time of financial turbulence.
The gender effect of female manager on monthly net return volatility is not found to be significantly different from zero during the whole period 1994-2014 and the subperiod 2007-2009. During the subperiod 1997-1998, gender effect of female manager on monthly volatility is negative 3.5 percent, significant at 1 percent level. As the difference is only found to be significant in one distress period, the result is insufficient to conclude that the net return volatility of female managed funds to be different from those of similar male managed funds.
To test whether the differences in volatility can explain the differences in risk-adjusted return, I run a simple regression model in which the gender effect of female manager on volatility is the independent variable, and the gender effect of female manager on alpha is the dependent variable for the whole period 1994-2014.
𝐴𝐺𝐸𝐹𝑎𝑙𝑝ℎ𝑎,𝑡 = 𝑎 + 𝛽 ∗ 𝐴𝐺𝐸𝐹𝜎,𝑡
𝐴𝐺𝐸𝐹𝑎𝑙𝑝ℎ𝑎,𝑡 𝑖𝑠 𝑡ℎ𝑒 𝐴𝐺𝐸𝐹 𝑜𝑛 𝑟𝑖𝑠𝑘 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑣𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 𝐴𝐺𝐸𝐹𝜎,𝑡 𝑖𝑠 𝑡ℎ𝑒 𝐴𝐺𝐸𝐹 𝑜𝑛 𝑣𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦 𝑜𝑣𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡
Table 9 show the results of the above regression model. The coefficient for 𝐴𝐺𝐸𝐹𝜎,𝑡 is not statistically significant even at 10 percent level. More importantly, the model only explains about 4 percent of the variation in the gender effect of female manager on alpha. Therefore, I conclude that the difference in volatility cannot explain a significant portion of the difference in risk adjusted returns.
To test for robustness and address the concern that female managed funds left in the unidentified group will negatively affect the matching procedures, I re-estimate the probit model (1) and repeat the PSM process but using the funds from the verified one-or-several male manager group as the potential match for female fund, instead of the unidentified group. Table 10 show the result of the probit model estimated with the verified group. The coefficient is not every different from first estimation. After a similar matching process, only 6 out of 71 female fund-male fund pairs change compared to the original matching. Tablet 11 shows the gender effect of female manager on alpha and volatility. The results are in agreement with the previous one: gender effect of female manager on alpha is positive and significant at 10 percent level throughout the period and at 5 percent level during the two financial crisis periods. The gender effect of female manager on volatility is not statistically significant on any tested periods. Therefore, the first results obtained are considered robust with regards to the matching procedure.
Table 8: The gender effect of female manager on risk-adjusted returns and volatility This table show the gender effect of female manager on risk-adjusted returns and volatility for the whole period 1994-2014 and two subperiods 1997-1998 and 2007-2009. Panel A shows the gender effect of female manager for the period 1994-2014. Panel B shows the gender effect of female manager for the period 1997-1998. Panel C shows the gender effect of female manager for the period ´2007-2009. All measurements are in percent per month.
***: the coefficient is significant at 1% level
**: the coefficient is significant at 5% level
*: the coefficient is significant at 10% level
Panel A: gender effect of female manager for the period Jan 1994- June 2014
Average std Min Max t p value
risk adjusted
return 0.174 0.103 -0.092 0.421 1.689 0.092 *
Volatility -0.781 2.715 -5.578 3.967 -0.288 0.774
N (months) 246
Panel A: gender effect of female manager for the period Jan 1997- Dec 1998
Average std Min Max t p value
risk adjusted
return 0.163 0.045 0.101 0.227 3.622 0.000 ***
Volatility -3.505 0.857 -5.204 -2.787 -4.091 0.000 ***
n (months) 24
Panel A: gender effect of female manager for the period Jan 2007- Dec 2009
Average std Min Max t p value
risk adjusted
return 0.315 0.064 0.220 0.421 4.922 0.000 ***
Volatility -1.98 2.734 -5.373 2.283 -0.438 0.664
n (months) 36
Table 9: The regression of gender effect of female manager on alpha vs gender effect of female manager on volatility
This table show the result of the regression model (3)
𝐴𝐺𝐸𝐹𝑎𝑙𝑝ℎ𝑎,𝑡 = 𝑎 + 𝛽 ∗ 𝐴𝐺𝐸𝐹𝜎,𝑡
𝐴𝐺𝐸𝐹𝑎𝑙𝑝ℎ𝑎,𝑡 is the gender effect of female manager on monthly risk adjusted return over period t 𝐴𝐺𝐸𝐹𝜎,𝑡 is the gender effect of female manager on monthly volatility over period t
***: the coefficient is significant at 1% level
**: the coefficient is significant at 5% level
*: the coefficient is significant at 10% level
cof. std t p
_cons 0.17 0.01 13.78 0.00 ***
dif in vol -0.01 0.00 -1.23 0.22
R_squared 0.041
Adj. R
squared 0.028
Table 10: The probit model for PSM, matching female and pre-verified male funds This table shows the results of the estimation for the probit model
Pr(𝐷 = 1|𝑆𝑖𝑧𝑒, 𝑀_𝑓𝑒𝑒,𝐼_𝑓𝑒𝑒, 𝐿𝑒𝑣_𝑑𝑢𝑚𝑚𝑦, 𝑃𝐶_𝑑𝑢𝑚𝑚𝑦 )
= Φ (β1𝑆𝑖𝑧𝑒 + β2𝑀_𝑓𝑒𝑒 + β3𝐼_𝑓𝑒𝑒 + β4𝐿𝑒𝑣_𝑑𝑢𝑚𝑚𝑦 + β5𝑃𝐶_𝑑𝑢𝑚𝑚𝑦 )
The dependent variable is the dummy variable which takes value of 1 if the fund is a female fund, 0 if it is a MF. The independent variables are Size (hedge fund size at its inception – calculated as total asset under management on the earliest reporting date, in million USD), M_fee (Management fee in percent), I_fee (Incentive fee in percent), Lev_dummy (leverage dummy, =1 if the fund use leverage, =0 otherwise), and PC_dummy (personal capital dummy, =1 if managers have money invested in the fund, = 0 otherwise).
***: the coefficient is significant at 1% level
**: the coefficient is significant at 5% level
*: the coefficient is significant at 10% level
coeffcient std t
_cons 0.36 0.12 2.93 ***
Size 0.57 0.10 5.59 ***
Management fee 0.00 0.00 -0.29
Incentive fee 0.03 0.02 1.17
Average dummy 0.33 0.25 1.32
Personal dummy 0.13 0.39 0.32
Pseudo R_squared 0.376
n 3936
Table 11: The gender effect of female manager on risk-adjusted returns and volatility, matching female and pre-verified male funds
This table show the gender effect of female manager on risk-adjusted returns and volatility for the whole period 1994-2014 and two subperiods 1997-1998 and 2007-2009. Panel A shows the gender effect of female manager for the period 1994-2014. Panel B shows the gender effect of female manager for the period 1997-1998. Panel C shows the gender effect of female manager for the period ´2007-2009. All measurements are in percent per month.
***: the coefficient is significant at 1% level
**: the coefficient is significant at 5% level
*: the coefficient is significant at 10% level
Panel A: gender effect of female manager for the period Jan 1994- June 2014
Average std Min Max t p value
risk adjusted return 0.184 0.110 -0.092 0.421 1.679 0.094*
Volatility -0.660 1.905 -5.578 3.967 -0.346 0.729
n (months) 246
Panel A: gender effect of female manager for the period Jan 1997- Dec 1998
Average std Min Max t p value
risk adjusted return 0.142 0.032 0.101 0.257 4.364 0.000***
Volatility -3.240 0.732 -5.104 -2.387 -4.429 0.000***
n (months) 24
Panel A: gender effect of female manager for the period Jan 2007- Dec 2009
Average std Min Max t p value
risk adjusted return 0.351 0.114 0.200 0.421 3.079 0.004***
Volatility -1.366 2.405 -5.273 2.183 -0.568 0.574
n (months) 36
7. Discussion
In section VI, the evidences suggest there is a positive increase in risk adjusted return associating with female manager, especially during the financial crises. On the other hand, the gender effect on volatility remains inclusive. The gender effect on volatility cannot explain the variation in the gender effect on risk adjusted return. In this chapter, I will offer explanations on those results as well as consider the limitation of this study.