Эконометрика финансовых рынков (стр. 1 )

Забирник Алексей

Зенкова Елена

Эконометрика финансовых рынков

ДЗ №3

№ 1

We chose a Russian equity fund “Ermak FKI” with data interval 12/15/00-10/14/05. Weekly frequency. As a risk free rate YTM of 1y GKOs were used. Market index is RTS. As instruments we used lagged market index, EMBI, RUB/USD-exchange rate, oil price, LIBOR3m and MIBOR1d. All data were set as returns.

(i) First, run a simple regression of excess fund return on constant and market premium for the all sample period. Results are quite predictable, positive beta=0.96 significantly differ from 1. Alpha is small and negative, but significant and equal to -0.0035. Investment style is rather mild. At first sight, selection ability seems to be poor, as alpha is negative. But it could be explained by a plethora of reasons, mainly transaction costs, inability to invest in indexes directly.

Variable	Coefficient	Std. Error	t-Statistic	Prob.
C	-0.003538	0.001253	-2.823821	0.0051
LEXRTS	0.946235	0.012199	77.56769	0.0000
R-squared	0.966612	Log likelihood	623.7851

Now, consider an estimation if model over subperiods of 1 year. We use dummy for years to capture the necessary period in order to estimate all submodels in a one regression. As for alpha, it’s significant only in year 2001 and negative. In other periods it’s equal to zero, but in general there is a negative tendency in signs. We can state that alpha=0 as any combination of different independent instruments. Selection style is rather good; fund’s portfolio is at the SML in .

Variable	Coefficient	Std. Error	t-Statistic	Prob.
Y01	-0.004949	0.001768	-2.800054	0.0055
Y02	-0.003238	0.002877	-1.125347	0.2616
Y03	-0.003241	0.003912	-0.828475	0.4082
Y04	0.000470	0.001619	0.290138	0.7720
Y05	-0.001163	0.002095	-0.554953	0.5794
Y01*LEXRTS	0.766279	0.032945	23.25899	0.0000
Y02*LEXRTS	0.732857	0.047469	15.43869	0.0000
Y03*LEXRTS	0.929300	0.028285	32.85522	0.0000
Y04*LEXRTS	0.974227	0.009689	100.5462	0.0000
Y05*LEXRTS	0.993324	0.013132	75.63871	0.0000
R-squared	0.972236	Log likelihood	646.9365

Beta is varied in time and reflects systematic risk and investment style of fund. As we can notice from estimation output beta grows in time. Wald test proves this hypothesis. Betas are not equal pairwise. Roughly, we may conclude that ‘Ermak FKI’ fund’s performance is not good enough. Their alpha is negative in 2001 and then they increase beta (risks). For further research, we may check the dependence of beta on market premium and conclude about alpha underestimation.

Variable	Coefficient	Std. Error	t-Statistic	Prob.
C	-0.002745	0.001361	-2.016635	0.0449
LEXRTS(-1)	-0.005280	0.009411	-0.561076	0.5753
LEMBIRU(-1)	0.018337	0.026374	0.695260	0.4876
LLIBOR3M(-1)	0.021373	0.040025	0.534000	0.5938
LMIBOR1D(-1)	-0.000863	0.002292	-0.376394	0.7070
LOIL(-1)	-0.002061	0.025899	-0.079589	0.9366
LRUBUSD(-1)	-0.583816	0.421290	-1.385781	0.1671
LEXRTS	0.936632	0.012781	73.28094	0.0000
LEMBIRU(-1)*LEXRTS	0.015114	0.170291	0.088757	0.9294
LLIBOR3M(-1)*LEXRTS	1.393929	0.511980	2.722624	0.0070
LMIBOR1D(-1)*LEXRTS	0.024257	0.016011	1.515038	0.1311
LOIL(-1)*LEXRTS	-0.013139	0.218237	-0.060205	0.9520
LRUBUSD(-1)*LEXRTS	0.052773	2.920671	0.018069	0.9856
R-squared	0.969089	Log likelihood	630.4703

Lagged instruments’ coefficients are insignificant jointly. Alpha doesn’t depend on instruments. Wald test gives p-value =0.88%. Throw it out from the regression. The same is true for some coefficients in regression of β on instruments. Especially for EMBI, oil price, MIBOR (significant at 6%) and exchange rate.