From the above table, the CAPM model is:
Y= 29.55 -3064.82R where 29.55 (Constant) is the Risk free rate and -3064.82 is beta value.
Aggressiveness and defensiveness of a stock depends on the beta value. Here, securities that have beta >1 are very risky and thus referred to aggressive stocks while those with beta less than 1 are less risky and thus called defensive stocks.
In this case, since beta= -3064.82, then the Microsoft stocks are defensive.
The R squared value also coefficient of determination is 14.37% which is approaching 0. This is a clear indication of the weak variability between the dependent variable- Microsoft stock prices and the independent variable- Microsoft risk free rate and this implies that the regression model’s coefficients do not explain all of the variability around the mean making this model a poor model.
Ho: Microsoft stock has same volatility as the market portfolio
H1: Microsoft stock does not have the same volatility as the market portfolio
In this case, I will use a two sample t-test assuming unequal variances (two sided test) and below is the table results.
The p value of interest is one in the middle because it indicates a two sided test. The p value is 0 which is below the alpha value 0.05 and thus we reject the null hypothesis and conclude that Microsoft stock does not have the same volatility as the market portfolio.
Some of the assumptions of CLRM - Classical Linear Regression Models include:
The explanatory variable is considered non-stochastic
The line plot shows that the Microsoft prices are positively related to the market prices or volatilities as indicated by the positive line. No violation of this property.
Test for Heteroscedasticity
Used to test and determine if the residuals’ variances are constant or not.
There is no value for the Prob > F and thus we can conclude that there is no heteroscedasticity. Thus there is no violation of this property.
I will use a Durbin Watson statistic. The statistics ranges from 0 to 4. 0<2 value indicates a positive autocorrelation. >2 to 4 indicates negative autocorrelation. 2 indicates no autocorrelation. Below is the stata table result for the same
From the table, DW d-statistic is 0.36 indicating a positive autocorrelation among the residuals. Therefore, the model violates this assumption.
The Fama-French 3-factor model is a CAPM which expands on capital asset pricing model by adding size risk and value risk factors to the market risk factor. The three factors used are SMB- Small Minus Big, HML-High Minus Low and the portfolio’s return less risk free rate return.
Therefore, the two factors that I will add to my CAPM model will be HML and SMB and the following is the STATA output for the same
The new CAPM model will be:
Y= 29.55 – 3069.442R + 0.23SMB+ 0.34HML
From the model, the addition of SMB and HML do not affect the risk free rate of the model but it does slightly affect the beta value by reducing it compared to the original model.
I will select the Fama-French model, Y= 29.55 – 3069.442R + 0.23SMB+ 0.34HML. This is because first, the inclusion of the two extra variables does not affect the risk free rate. HML is used to indicate the value premium or it shows the spread in returns between value stocks and growth stocks. A positive HML value of + 0.34 indicates that Microsoft have high value stocks which shows a good performance and shows the excess returns of Microsoft due to its high book-to-market equity value. The positive SMB value shows that Microsoft stocks are weighted towards small-cap stocks.
Therefore, these variables help in determining the size of the Microsoft stocks’ risk as well as the value of the risk.
For the goodness of fit, let use the value of R squared and the F statistic. For the new model, R ^2 is 14.74. This shows a weak variability between the independent and dependent variables indicating that the coefficients of the model do not explain all of the variability around the mean making this model a poor model. The F statistic is 57.75 which is greater than 1 and this shows that the model generally is a good fit.
Comparing this model to the CAPM one, R squared value is the same and thus no improvement here. The F value was 168.48 which is greater than the new second model. Thus the CAPM model is more a good fit compared to the Fama-French model by considering the F statistic value.
Time series data is a historical data in a given time period. This data is helpful in forecasting future values and mostly used in financial analysis. In this section, I chose Alibaba historical stock prices data from Oct 06, 2014 to Dec 11, 2019. This historical data can be used in determining a suitable model that can be employed and used in forecasting future Alibaba stock prices. Some of the well-known forecasting models are ARMA, ARIMA, ARIMA-GARCH.
One cannot fit ARMA model to the daily close prices series. First, the series data have to be converted into time series version before any STATA analysis the series by running the code:
gen time = _n
tsset time
In determining the ARIMA (p, d, q) model, the coefficients p, d, q have to be determined first. To determine the value of p, I plotted Partial Correlogram (pac) graph and determined the first lag or lags outside the confidence bound as shown below. As my order, I chose the first lag hence p=1.
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