Occidental petroleum corp

ECON 3206 - FINANCIAL ECONOMETRICS GROUP ASSIGNMENT

NYSE | OIL AND GAS EXPLORATION | EQUITY PRICE FORECAST OCCIDENTAL PETROLEUM CORPORATION NYSE Ticker: OXY QUESTION 1 Occidental Petroleum Corporation is an international gas and oil exploration and production company. The company was established in 1987 starting as a manufacturer of basic chemicals and vinyls used in health products. Occidental is an S&P 500 listed oil&gas exploration and production company. Its operations span across the USA, Middle East and Latin America. It is a large core energy a stock with a market capitalisation of 55.7 Billion American Dollars and is currently valued at 73 Dollars and 54 cents American, per share.

QUESTION 2 LOG RETURNS OVER TIME

The compiled data shows that over the long-term, log-returns has shown a small positive increase of 0.059 as demonstrated by its mean. Extreme maximum and minimum values (16.64323 and -20.44832 respectively) as well as relatively high standard deviations show a considerable spread within the data. Hence the data does not appear to show any discernible trend. The histogram shows that results are slightly negatively skewed, which would explain why the mean value is slightly less than the median. Tests for Skewness and Kurtosis show that the log returns for Occidental Petroleum Corp cannot be attributed to a normal distribution. The relatively high Jarque-Bera value obtained reinforces this observation. Log returns over time for Occidental Petroleum Corp. shows signs of a stationary process as the observations appear to fluctuate around the mean. The only exception to this observation is the period 2008-09 where there is very high volatility in returns. The relative economic uncertainty in this period most likely caused this, giving basis to the assumption that this period should be considered an outlier in modelling long term log returns.

OCCIDENTAL PETROLEUM CORP EQUITY PRICE FORECAST

QUESTION 3 Below is our CAPM estimation for the OXY data:

When markets are in equilibrium, CAPM assumes that investors are only compensated for systematic risk. OXY is positively correlated with the market since its beta is positive (1.09). As beta is greater than one, OXY's systematic risk is higher than the market proxy S&P500. The R-squared value is very close to 0, therefore the regression does not explain the variation of the excess return of OXY's stock price. As the constant alpha does not equal zero, we reject the null that the data supports CAPM. Further, as alpha is greater than zero, this indicates that OXY beats the market. This excess return indicates the non-linearity between risk and return, possibly due to the volatile nature of the petroleum industry. To overcome this issue we could extend the CAPM model to include a variable that accounts for unexpected risky events such as a shock to oil prices, as in the case of the Arbitrage Pricing Theory.

Shown below is the replication portfolio generated with the S&P500 index and T-Bill:

The historical expected return of the above portfolio was calculated to be 2.019 with variance 1.276. Comparing this to the variance of the OXY share of 4.54, suggests that the bank should invest in the portfolio given the smaller variance, and hence smaller risk of loss.


QUESTION 4 LOG RETURNS MODEL

SQUARED RETURNS

The correlogram for log returns show strong autocorrelation in returns due to low p values. There are no obvious lags in the ACF and PACF and this implies that we should use the constant mean equation for our return series. The patterns for ACF and PACF for squared returns appear to be erratic and does not give a clear indication of what AR,MA or ARMA process should be used to minimise SIC either. Since squared returns serve as an imprecise proxy for modelling volatility in the price of returns we will instead use our log returns model to present our forecasts for the stock price of Occidental Petroleum Corp. SIC is used as our deciding factor in regards to model choice because SIC is more consistent compared to AIC across large samples. i.e.: lower probability of choosing incorrectly, a bigger model.

QUESTION 5 The following are the Schwartz BIC values for our chosen combinations (Refer Appendix for relevant Eviews commands): Process SIC

C 4.334908 MA (1) 4.335085 MA (2) 4.332899 AR (1) 4.334983 AR (2) 4.333851

ARMA (1,1) 4.333768 ARMA (1,2) 4.335041 ARMA (2,1) 4.334738 ARMA (2,2) 4.336612

ARCH (1,0,h) – c 4.244465 ARCH (2,0,h) – c 4.133129 GARCH (1,1) – c 3.979487 GARCH (2,1) – c 3.980113

EGARCH (1,1) – c 3.980538 GJR (1,1) –c 3.977466

GJR (1, 1) – c appears to be the process that achieves the lowest SIC value. Shown below is the estimate of our chosen model. A GJR model is a generalisation of the GARCH process that better addresses volatility clustering in the innovations process. Shown below are the results of our estimate of the GJR (1, 1) - c process.


QUESTION 6 Standardized residuals were obtained using the Proc/Make Residual Series tab and selecting the histogram.

To test for a dependence structure in the residuals we can use the BDS test. This test identifies if the residuals are independent and identically distributed (iid). It does so by denoting a given distance, epsilon, between a pair of points or multiple pairs of points. It tests that the null hypothesis is that the model is independent and identically distributed, that the distance is equal to or less than epsilon. i.e.: H0: The residuals are iid H1: The residuals are not iid We can reject the null hypothesis in favour of the alternate indicating some structure remains in the residuals that could include non-linearity and non-stationarity. The BDS test was calculated using the epsilon method of standard deviation with a value of 0.5 and dimensions of 5. The eviews output for the BDS test is as follows:

As the results indicate, the p-values for all dimensions of the BDS test are above 0.05. At a 95% confidence level, we would fail to reject the null for all dimensions and thus conclude that the residuals for our model are all independent and identically distributed. This indicates there is not a dependence structure in the residuals and no reason to suspect non-stationarity or non-linearity.

QUESTION 7 The conditional mean and conditional variance were obtained using a dynamic forecast command on Eviews. The dynamic forecast generated dates immediately after the estimation period, i.e. 02/09/16. Doing so generated two graphs; the first graph below featured a forecast of the mean equation, with two standard deviation bands (2 S.E.). The second graph below features the forecast of the conditional variance. These forecasts are depicted below. Conditional Mean:

Conditional Variance:


QUESTION 8 Residual distribution

The conditional Value at Risk (VAR) for one day ahead at 5% significance (95% confidence) is -3.33298.

Standardised Residuals Conditional Value at Risk using a non-parametric estimate of quantile =

Value at Risk for portfolio value of $1 million = -$23590.87 When comparing the residual and standardised residual distributions normality is rejected in both cases as demonstrated in the histograms. Both show a relatively high Jarque-Bera statistic, as well as negative skew and kurtosis. However the standardised residuals show considerably improved results in comparison to residuals. It has a much lower Jarque-Bera statistic of 183, smaller negative skew and kurtosis of 4, only 1 off a desired 3 for normality. Hence using standardised residuals will provide for a more precise model. In the case where the bank has large holdings in the share and it may take a week to sell the share without impacting the market a one-day ahead value at risk may not be sufficient. Rather considering a seven-day ahead value at risk or following the market capital risk using ten-day ahead value at risk would be more suitable. Value at Risk for portfolio value of $1 million = -$24515.5


QUESTION 9

ARMA(1,1)-GARCH(1,1) model

Residual Series from the ARMA(1,1)-GARCH(1,1) model

QUESTION 10 The in sample period is from 1 September 2000 to 20 September 2016 with a total of 4037 OXY log returns. In order to forecast the conditional mean and conditional variance for the out of sample period, dynamic forecasting option is applied as it uses the chain rule of forecasting to compute the one step ahead forecast, . Essentially each forecasted value, for instance, is estimated by inferring the lagged dependent variable on updated information set that includes the entire in sample returns as well as the prior derived one step ahead forecasts. The model we use to forecast is a simple ARMA(1,1)-GARCH(1,1) model and we have forecasted for 1 through 500 days ahead from the end of our sample 21 September 2016 ,to 2 November 2018. Our forecasting horizon has expanded by 400 days more as opposed to the horizon of 100 days because we believe that a longer horizon draws a clearer picture on the characteristics of long term forecast trend. As we see from graph 1.RF and graph 2. VF in the following page, they exhibit a nice prediction of the forecasted values. In graph 1.RF, the conditional mean is based on ARMA(1,1) model with the assumption that conditional residual is normally distributed with a zero residual mean and a time-varying residual variance. When the forecast horizon increases towards infinity, the conditional mean will eventually converge to the constant term of the ARMA(1,1) model but how fast of such convergence depends on the persistence of OXY log returns. There is a half-life time method to measure the stock’s persistence with GARCH(1,1) volatility model. Half life time for OXY stock is 72 days and it is supported by the graph 1.RF whereby at approximately 140 days (i.e: July 2017) the conditional mean stabilises. Similarly, the conditional variance is derived from GARCH(1,1) model that shows a mean-reverting feature, given the sum of the coefficients of lagged squared residual and lagged conditional variance is less than one. Our Eviews estimated coefficients for the GARCH(1,1) model have met the covariance stationary condition and thus the forecasted conditional variance will tend towards the unconditional variance in the long run.


QUESTION 11 The model used in Question 9 is the ARMA(1,1)-GARCH(1,1) model. Conditional mean for one-day-ahead forecast with the information set up to time T (ie 20 September 2016)

( | ) = ( + | + | + | ) = + + = 0.005042 + 0.935602*-0.45287 + (-0.955934)*(-0.68079) = 0.232122 Conditional variance for one-day-ahead forecast with the information set up to time T

( | ) = ( + | + | + | ) = ( | ) = ( | ) -

( | ) = ( | ) = + + = 0.035724 + 0.062245*( 0.68079) + 0.92813 * 2.070825 = 1.986568 We see from our Eviews outputs for the conditional mean and variance of the ARMA(1,1)-GARCH(1,1) model (Appendix) that the manual computation generates the same numbers as the programmatic outcomes. The conditional mean is precisely 0.232122 and the conditional variance is 1.986568.


QUESTION 12 The model used in Question 9 is the ARMA(1,1)-GARCH(1,1) model. According the rule of iterated expectations, the unconditional mean is given by:

( ) = ( + ( ) + ( )) = 0.005042 + 0.935602 * 0.057359 + -0.955934 * -0.02903 = 0.08645 Unconditional variance for model:

( ) = ( + + + ) = + + = 0.035724 + 0.062245 * 18.93349 + 0.928130 * 0.00329 = 1.21729

APPENDIX Question 2: genr Log_Return = log(adj_close/adj_close(-1))*100 plot Log_Return hist Log_Return Question 3:

(a) genr tbill_r=100*((1+tbill_annual_r/100)^(1/360)-1) genr OXY_er = Log_Return - tbill_r genr Market_r = log(m_adj_close/m_adj_close(-1))*100 genr Market_er = Market_r - tbill_r *CAPM Estimation ls oxy_er c market_er *Portfolio Replication ls oxy_er market_er tbill_r

Question 4: genr r=100*(log(oxy_adj_price)-log(oxy_adj_price(-1)))r.correl(10) genr r2=r*r r2.correl(10)

Question 5: arch(1,1,h) r c ‘change Model to EGARCH and in the Options tab, the covariance method is Bollerslev_wooldridge

Question 8: ‘Make residual series-After estimating the model, click Proc\Make Residual Series. Click for residual type - Standardized. Note the default name for the residual series is resid01. View\Descriptive Statistics\Histogram and Stats. To calculate the percentile, click View\Descriptive Statistics\Stats by Classification. Click on the Quantile box and type 0.05

Question 9: arch(1,1,h) r c r(-1) ma(1) ‘Change to Bollerslev-Wooldridge

Date Conditional Variance Conditional Mean Y(t) Residual(t)9/20/2016 2.07082533 -0.452873687 -0.45287 -0.680788829/21/2016 1.986568055 0.232121766 0.2321229/22/2016 2.003171241 0.222216115 0.2222169/23/2016 2.01961462 0.212948364 0.2129489/24/2016 2.035899729 0.204277434 0.2042779/25/2016 2.052028091 0.196164892 0.1961659/26/2016 2.068001216 0.188574777 0.1885759/27/2016 2.083820598 0.181473447 0.1814739/28/2016 2.099487716 0.174829426 0.1748299/29/2016 2.115004035 0.168613264 0.1686139/30/2016 2.130371009 0.162797408 0.162797

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Occidental petroleum corp