OSEC Econometrics 2014 Class assignment
Name: David Broadstock
Stock code: 600269
Student number: (XXXX-XXXX)
E-mail:
1. Estimate CAPM
The aim of the assignment is to estimate a simple capital asset pricing model (CAPM). The risk free rate is not required for this assignment. The model takes the following form:
(1)
Where R are the returns on the stock (Jianxu Expressway, a toll road company) in period t, and RM are the returns on the market. This company may have a low beta due to its market operations, and following existing CAPM literature, it is generally expected that the intercept is insignificant, whole the beta is significant and ranges between zero and one.
Figure 1: The estimation data. The black line shows the returns for the stock, while the
We can see from Figure 1 that the value of the market and the stock are similar. There is one period early in 2009 where the returns of the market fall suddenly, but the returns of the individual stock in the same period remain largely on the positive trend they have at that time period. Otherwise, the data are around the same size and sign for most periods.
Estimation is done by OLS and the results are as follows:
From the results above, we can see that the intercept is statistically equal to zero (insignificant). This is consistent with the theory of asset pricing in an efficient market. The slope coefficient beta is significant and equals 0.56 which is not too high. Since the coefficient is positive we can see that this firm is moving in the same general direction as the market, as was implied also in Figure 1.
The goodness of fit of the model (from the R-squared) is respectable, suggesting that around 30% of the variation in the data is explained using only the market returns.
2. Test for serial correlation
The test for serial correlation requires 3 lags be considered. The Breusch-Godfrey test is a natural choice, and takes the following form:
(2)
Which is to say that the residuals from the original CAPM model in equation (1) are regressed against the X-variables in equation (1) e.g. the market returns (RM), and the lagged values of the residuals. The test then checks the joint restriction that against the alternative that at least one of them is not equal to zero. The p-value for the test is 0.7614, which implies that the null hypothesis (of no serial correlation) cannot be rejected since it exceeds the required p-value of 0.05 (or 5%).
3/4. Estimation of ARDL and ECM models
Since the serial correlation test is passed, there is no need to consider either the ARDL or ECM models. The static CAPM used here does a sufficiently adequate job of modeling the data over the period 2009-2013.
5. GARCH model results
Next I consider a simple GARCH(1,1) estimation of the CAPM model. The model is estimated in STATA using the command “arch r rm, arch(1/1) garch(1/1) arima(0,0,0) technique(nr)”. The results are given in the plot below. Concentrating on the slope coefficient, the estimated value is 0.547 compared to the slightly larger value of 0.557 for the OLS estimates. The standard errors are similar for both approaches also. In this case then, the effects of modeling time based heteroskedasticity (GARCH) offer no obvious benefit.
6. Additional comments
The overall estimation results suggest that the CAPM model, used widely to study financial markets around the world, applies well to Chinese stock markets and firms. The estimated model shows that there is no significant intercept, implying no constant risk (either positive of negative for the stock. The intercept terms suggests that the firm is moving in a reasonably consistent manner with the market, taking a value of around .55, implying that a little over half the risk faced by this firm is passed through the overall risk in the market.
It was considered whether there remain any un-modelled dynamic effects, but in the present case they were not found to exist. There was therefore no need to try and model auto-regressive models, or even consider an error correction model.
As a robustness check, the original CAPM was re-estimated with allowance for GARCH errors. The results are extremely similar to OLS, implying no strong GARCH effects (an ARCH LM-test might be used to demonstrate this also). Given that the data used here were monthly frequency this is not too surprising.