Quantitative Finance and Financial Market - Desklib

Running Head: QUANTITATIVE FINANCE AND FINANCIAL MARKET
Quantitative Finance and Financial Market
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1QUANTITATIVE FINANCE AND FINANCIAL MARKET
Table of Contents
Answer 1..........................................................................................................................................2
Answer 2..........................................................................................................................................3
Answer 3..........................................................................................................................................5
Answer 4..........................................................................................................................................7
Answer 5..........................................................................................................................................9
Answer 6........................................................................................................................................11
Answer 7........................................................................................................................................14
References:....................................................................................................................................19

2QUANTITATIVE FINANCE AND FINANCIAL MARKET
Answer 1.
We are applying Two-sample t-test with unequal variances to verify the hypothetical
proposition about median incomes of men and women.
1. a)
The hypotheses:
Null hypothesis (H0): The difference of median incomes for men and women who are buying
homes is less than or equal to $10000.
Alternative hypothesis (HA): The difference of median incomes for men and women who are
buying homes is greater than $10000.
Level of significance: 0.05.
Calculated t-statistic: 0.006039.
Critical t-statistic: t (395, 0.05) = 1.966003.

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Decision-making: 0.006039<1.966003. Hence, there is an absence of significance of the test of
equality of means (De Winter 2013). The null hypothesis cannot be rejected with 5% level of
significance. Similarly, the alternative hypothesis could be rejected.
Interpretation: The difference of median incomes for men and women who are buying homes is
not greater than $10000. Therefore, it is 95% obvious that the ‘median salary’ for men is just
$10000 higher than ‘median salary’ for women.
Conclusion: The median income of males to buy homes is more than $10000 larger than that of
females.
1. b)
The additional assumptions required to validate the results of the hypothesis test are-
 The two variables are continuous or non-discrete.
 The two samples follow normal distributions.
 Both samples are ‘independent’ in nature.
 The two samples are simple random samples from their respective populations. Every
data in the population has an equal probability to be selected in the sample.
Answer 2.
The Chi-square test is applied to test the association between two categorical variables
that are ‘Employment sector’ and ‘Investment preference’. Failing to establish the association of
two categorical variables, Chi-square test proves the independence between these two variables.

4QUANTITATIVE FINANCE AND FINANCIAL MARKET
2. a)
The hypotheses:
Null hypothesis (H0): ‘Employment sector’ and ‘Investing preference’ are independent (no
associated) to each other.
Alternative hypothesis (HA): ‘Employment sector’ and ‘Investment preference’ are associated to
and dependent to each other (McHugh 2013).
2. b)
The Chi-square statistic with 1 degrees of freedom is calculated to be 8.36. It creates the
p-value 0.0038. The calculated p-value is less than assumed ‘Level of significance’ (5%).

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Therefore, null hypothesis could be rejected (Sharpe 2015). Correspondingly, alternative
hypothesis is accepted with 95% probability.
It could be interpreted that ‘Employment sector’ and ‘Investing preference’ are
independent to each other. That is, the types of preferences of investment depend upon the types
of employment sector.
2.c)
The p-value for the hypothesis testing of the Chi-square statistic ( χ2 ( 0.05 , 1 )) is found to
be =0.003838762.
Answer 3.