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25705 Financial Modelling And Analysis

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  • Course Code: 25705
  • University: University Of Technology Sydney
  • Country: Australia

Question:

The All Ordinaries (AllOrd) contains the 500 largest listed companies on the ASX. Its volatility represents the broad market risk in the Australian stock market. In this case study, students will analyse the characteristics of the All Ordinaries Index and forecast its monthly volatility. Several variables related to the All Ordinaries Index are contained in the file “CaseData.xlsx” which can be downloaded from the subject website under “Case Study”. Variable definitions are provided in the data file. Students are encouraged to seek additional data to facilitate their analyses. The total mark for the case study is 100 and accounts for 20% of the overall subject mark.
 
Calculate the monthly stock returns (AOret) as the percentage changes in AllOrd. Plot AOSD (vertical axis) against AOret (horizontal axis). Summarize three key characteristics of the relation between AOSD and AOret.
 
Use the “CORREL” function in Excel to calculate the correlation between AOret and AOSD. Based on the plot of AOSD against AOret, discuss what the correlation measures and fails to measure. Give one potential explanation for the sign of the correlation between AOSD and AOret.
 
 

Answer:

Introduction:

The main objective for question 5 is to determine the first-order autocorrelation of   AOret and AOSD for the full sample of the dataset provided.  The main causes of autocorrelation are sluggishness in the business cycle, and the omitting variables form the model. To detect autocorrelation, simple regression is run using the data set. In this case, Return on All order will be used as the dependent variable and AOSD as the dependent variable.

The figure below shows the diagrammatic results for the autocorrelation of the two variables:

The value of R-squared which is given by 0.2086 does not give a clear explanation about autocorrelation. Autocorrelation is determined by the linear diagram. The diagram below shows a weak negative autocorrelation if AoRet and AOSD. The difference in autocorrelation is caused by the sluggishness of the economic time series and persistence of the observational errors.

The two main statistical properties that make market volatility predictable are autoregressive and autocorrelation. Autoregression is a statistical technique that involves regression of lagged data. It shows that previous values can be used to predict future values. Autocorrelation is used to compare changes of return. A negative return result in a larger change in vitality and a positive return results to a smaller change in vitality (Marra, 2015).

There are so many positive return values meaning the presence of volatility is low.

We need to conduct both SES and Holt's model to focus monthly vitality for the hold-out sample period. Below is the graphical result from the SES model

It can be noticed that both the actual and focus data are almost similar (Nazim and Afthanorhan, 2014).  Holt's model is almost similar. Below is the Holt's graphical representation of the AOSD forecast

Comparing the two models, SES has an MSE value of 3.01703E-05 and Holt's model has an MSE value of 3.64831E-05 (Maia and Carvalho, 2011). Therefore, it is evident that SES has the lowest MSE value and thus it can be deduced that it is more accurate than Holt’s model.

This section, regression analysis will be conducted to show the regression model. The sample from Q4 will be used because it contains a variety of variables to be tested in conducting the regression analysis. AOSD will be used as the dependent variable. Interest Rate, Market Value, Trading Volume, and Price-Earnings Ratio will be used as the explanatory variables.  These variables of interest are significant in determining the daily return. This is the main reason that they are included in the regression model to show their effect on detail return. Before the regression analysis was conducted, the assumption was formulated. This assumption is to be tested using the regression output that is obtained after the analysis.

 

The formulated assumption

  1. The independent variables (MV, TV, PE, IR) and the dependent variable have a linear relationship (autocorrelation)

To test the results, the regression output is used. Below is the regression output to be used,

Table 1: Regression Results

Sample Period

Coefficient

t Stat

p-Value

TV (m)

3.74357E-07

2.12E-07

1.767178

IR (%)

-0.000534412

0.000732

-0.73007

MV

-1.65442E-08

3.61E-09

-4.57972

PE

-0.002539628

0.000512

-4.95686

Constant

0.09157118

0.013368

6.849924

R2

0.2748

 

 

Adjusted R2

0.2616

 

 

Model F stat

20.74828934

 

 

DW

1.62781E-14

 

 

Testing the hypothesis

To test the hypothesis, the focus will be on the DW (Durbin Watson Statistic) value. If the DW is less than 0.05, then we reject the initial assumption, and if the DW value is greater than 0.05, then the initial null hypothesis is accepted. In this case, the value of DW is 1.678E-14 which is less than 0.05 and therefore, the assumption is rejected. Therefore, it can be concluded that there is the presence of autocorrelation in the relationship between the dependent and independent variable. Comparing the linear model with SES and Holt's model, it is clear that SES is the most accurate model. It predicts that the AOSD for December 2018 will be 0.018247.

This part aims at using the average returns from 2018/6 to 2018/11 as the return forecast for 2018/12. The volatility focus for Q8 will be used to conduct this. Using the regression analysis with AOSD as the independent variable we obtain the AOSD for2018/12 to be slightly higher than that of 2018/11. The value obtained is 0.044453583.

 

References

Marra, M., 2015. The impact of liquidity on senior credit index spreads during the subprime crisis. International Review of Financial Analysis, 37, pp.148-167.

Nazim, A. and Afthanorhan, A., 2014. A comparison between single exponential smoothing (SES), double exponential smoothing (DES), holt’s (brown) and adaptive response rate exponential smoothing (ARRES) techniques in forecasting Malaysia population. Global Journal of Mathematical Analysis, 2(4), pp.276-280.

Maia, A.L.S. and de Carvalho, F.D.A., 2011. Holt’s exponential smoothing and neural network models for forecasting interval-valued time series. International Journal of Forecasting, 27(3), pp.740-759.

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