The confidence level (VaR) is considered as prediction interval as this is one of the suitable methods of testing. For example, in case there is any random sample which is required in the distribution given by Bernoulli has been selected with the probability which has a nominal value , in that case these tests are done in order to validate whether the sequences of losses is smaller in comparison to the value of VaR.
Let rt1≤t≤T = Realization of series of returns of any financial asset
Lpt|t-1,Up)t|t-1 = sequence of interval forecast outside the given random sample
Lpt|t-1= Lower limit of forecast interval at any point of time ‘t’ and confidence level ‘p’, given the information until time ‘t-1’
Up)t|t-1= Upper limit of forecast interval at any point of time ‘t’ and confidence level ‘p’, given the information during the unit time ‘t-1’
Let consider further that the null hypothesis is that It1≤t≤Tis independent and EIt|∅t-1=p. The test statistics is given as below:
In the above case, if there is a rejection in case of the null hypothesis than the above model which is constructed is not good for hypothesis.
Based on all above modelling, the leverage affect is given as in form of simple regression as well:
Whereas, ∆σ=overall change which may be observed in the value of the volatility range R= logarithmic return on the underlying stock.
Whenever there is a fall in the market price of the stock, there will be an increase in the value of subsequent volatility and there is rise in the price of the same magnitude. This leads to the reduction in the value of volatility by a comparable amount.
Where Down = 1, if R – negative and 0 otherwise. Now based on above equation the leverage affect is measured with the help ofa1 in up market and a1+a2 in down market. On the other side, if the value of a2 is significantly negative then the effect will be more strong because the price falling more (Gao & Kling, 2008).
The leverage effect which may be related to the price change on the value of the underlying stock is permanent and it also dies over time. This can be examined with the help of the equation of the regression:
Where, t is time given for 3 months. Similarly, for next months the volatility can be calculated (Firth et al., 2008). Therefore, the volatility for up and down market can be calculated from the given regression equation
The above constructed model including the hypothesis with various factors indicate that if the model results in negative or any other way then that means the hypothesis for financial leverage and leverage affect does not meet with its initial objective (Lin et al., 2009). Hence, in this case the hypothesis as mentioned above is not good for testing the financial leverage effect for the given data. On the other side, it is assumed that refined model will test the hypothesis as expected and will lead to the analysis of the financial leverage and the overall leverage effect which may be there on the 50 listed companies of China.
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