Question

XYZ Investment company invests clients’ money across 200 different investment portfolios, each of which has been structured and managed by a specialist portfolio manager. Mr Jack Nelsen, the Director of XYZ Investment suspects that a significant difference exists between the returns on portfolios managed by male portfolio managers and those managed by female portfolio managers.

Mr Jack Nelsen decided to conduct an empirical study to determine whether the returns on portfolios differ significantly according to the gender on the portfolio manager. 120 portfolio managers were chosen for this study and they completed a questionnaire which included a demographic information sheet on gender, age, educational level and job tenure. The average annual returns of the portfolio managed by each of the 120 portfolio managers were objectively measured using data from the database of XYZ Investment.

The SPSS output after data analysis is provided below:

Table 1:		Group	Statistics
	Gender	N	Mean	Std. Deviation	Std. Error Mean
Portfolio_return	Male	65	11.23%	2.79%	0.34%
	Female	55	15.56%	3.93%	0.53%
Table 2:			Rank
	Gender	N	Mean Rank	Sum of Ranks
Portfolio_return	Male	65	43.53	2873
	Female	55	81.24	4387
	Total	120
Table 3:	Test	Statistics
	Portfolio_	Return
Mann-Whitney	662
Wilcoxon W	2873
Z	-5.929
Asymp. Sig (2-tailed)	0.000

Required:

Provide an interpretation of the output in Tables 1-3.                           [20 marks]

Answer 1

Table1:

The average of male of portfolio return is 11.23% and standard deviation is 2.79%.

The average of female of portfolio return is 15.56% and standard deviation is 3.93%.

Table2:

There we change the orindal or numerical data into ranks and then take the mean of the ranks and sum of ranks.

There mean rank of males of portfolio return is 43.53 and sum of ranks is 2873.

There mean rank of females of portfolio return is 81.24 and sum of ranks is 4387.

Table3:

There used two test first is Mann Whitney and Wilcoxon both are non-parametric test.

Mann whitney test used for two independent sample whereas Wilcoxon test used for two dependent sample.

Table 2 data used in table 3 to calculate test statistics of Mann Whitney and Wilcoxon.

Test statistics: Mann Whitney = 662 and Wilcoxon = 2873

Where p-value is 0.000 which is less than 0.05(level of significance), it is means there is a significant difference between the male portfolio return and female portfolio return.