## Why choose us?

We understand the dilemma that you are currently in of whether or not to place your trust on us. Allow us to show you how we can offer you the best and cheap essay writing service and essay review service.

# Quantitative Techniques

Quantitative Techniques

1. The plot

In the late 2008 during the financial crisis, the exchange rate of the Australian dollar against the Japanese Yen was very low and was very high against the UK pound.

The US Treasury bill of rate during this was on downward trend and it was approaching zero.

• The returns for each asset have been calculated in the excel  using the formulae

where Pt is the rate at time t

• The histogram for each of the returns is shown below
• The histograms on the returns from the exchange rate for the Australian dollar against the Japanese Yen

The mean=0.00237694

Median=0

Variance=1.09710006

Standard deviation=1.04742544

Skewness=0.37218026

Kurtosis=7.21318797

Looking at the coefficient of kurtosis for these data, the curve is more peaked than the normal curve, what is called leptokurtic.

• The histograms on the returns from the exchange rate for the Australian dollar against the UKP

The mean= -0.0107221

Median=0

Variance= 0.53947729

Standard deviation= 0.73449118

Skewness= 0.05875106

Kurtosis= 4.49591754

Looking the coefficient of kurtosis for these data the curve is more peaked than the normal curve, what is called leptokurtic.

• the returns from the exchange rate for the Australian dollar against the USD

Looking the coefficient of kurtosis for these data the curve is more peaked than the normal curve, what is called leptokurtic.

• The hypothesis is stated us

The test statistics is given by

reject the  null hypothesis when

For the means of the returns for the Australian dollar against other currencies, since the t-value is less than the critical value, we reject the null hypothesis at 5% level of significance and conclude that the means are statistically significance from zero.

• The hypothesis is stated as :

The test statistics is given by

reject the  null hypothesis when

Since the t- values are less than the critical values, we reject the null hypothesis at 5% level of significance and conclude that the means for the returns are significantly different from each other.

• The correlation matrix  for the returns is given by
• The assumption for independence is not realistic because the returns are highly correlated.

The appropriate test statistic is a chi square test, which is used to test for independence.

1. If were to choose a maximum of two portfolio,  I will choose the ones with the highest expected returns. That is  Australian dollar against the USD, and  Australian dollar against the Japanese Yen.

The covariance matrix is given by

The inverse of covariance matrix is

Now we multiply the c and the excess expected return

*

The weights are

W1=-0.0593

W2=1.063

The optimum expected return will be

=0.002014