Step 6
In order to have a better understanding of the influence of the collapse on our fund, we compared the sample mean and validity of the return before(Data 1) and after(Data 2) the collapse. We think the data serious of returns in two periods are unpaired. So we first checked whether they have the same validity.
We assume they have same validity, in other words:
H0：S1-S2=1
We use a F-distribution to check the assumption under a significant level of 5%. In order to check the hypothesis, we performed following calculation(Refer to Excel):
S1^2 S2^2 D.O.F 1 D.O.F 2 F=S1/S2 Sig. Level Upper Lower
7.56 25.86 49 68 3.42 5% 1.71 0.59
As we can tell, the F-Value goes far beyond the critical range, we can reject the assumption that the validity stays the same after the collapse under strict condition.
So, when we have to verify whether the sample mean return remain unchanged before and after the collapse, we chose to use unpaired statistics with different sample standard diviation. Let’s assume that the mean has not been changed, in other words:
H0: X bar 1- X bar 2=0.
We use a T-distribution with a degree of freedom of 117 to check the hypothesis. The significant level we used is still 5%. We performed following calculations(Refer to Excel):
X1 bar X2 bar Std. Error t-value D.O.F Upper Lower
0.66 1.07 0.73 -0.56 117 1.98 -1.98
As the t-value belongs to the range, we can not reject the hypnoses that the mean stays the same under a significant level of 5%.