FINANCIAL ECONOMETRICS AND FORECASTING

QUESTION # 1:

The objective is to make the investment strategy using international stock market indices data. In this study we choose ‘meteor shower’ effect, it is the intradaily volatility spillovers from one market to another. The information transmission mechanisms were quantified through returns and volatilities. To capture mean spillover and volatilities spillover ARMA GARCH (1, 1) model has been applied to the data set. After analyzing the descriptive statistics we prefer the market which have high return and low volatility i.e. RCACOC market, it has low volatility with high return. We check the cointegration between the markets using unrestricted cointegration Rank test which trace the cointegration between the markets at the 0.05 level of significance. To estimate the spillover effect of other markets to RCACOC, we introduced the return series of other seven markets in conditional mean equation of RCACOC return series and for volatility spillover effect the square return series of one market is introduced as regressor in the conditional variance equation of other markets which is significant it mean that there is mean and volatility spillover effect from other markets to RCACOC. If spillover is one sided its called unidirectional spillover. If it is two sided it is called bidirectional spillover.

After applying the model to overall return series, we observe that model is correctly capturing the mean and volatility spillover from other financial markets. The actual values and fitted values are very close to each other and the residual series is not too much distorted. The model fitted show that there is bidirectional mean and volatility spillover effect between RCACOC and other financial markets. There are some periods where there is high volatiles followed by low volatility periods.

QUESTION # 2:

To evaluate the models’ performance, direction quality measures were applied. The analysis was conducted by comparing the insample forecasts from the predictive ARMA GARCH (1, 1) models, computed for the whole estimation period of 1 year:01/01/2002 to 31/12/2020, with the outofsample forecasts generated from the same models in the period of the next 1 year: 01/01/200331/12/2003. The outofsample forecasts were obtained on the basis of the rolling regression procedure. Therefore, the forecasts for time 1+t are calculated based only on the values of the explanatory variables in time t with iterations rolling until the end of the sample. For the insample forecasts the measure indicates that the analyzed models explain about 0.812 – 0.12 of the RCACOC index value direction of change .The turning points, as measured, are captured at the 0.569 – 0.599 level. They prove that sum of absolute rates of return when the model successfully reflected the direction of change is about 2.18974 – 2.401551 higher than in cases when the model was missing the right direction.

The market returns exhibit nonnormality, leptokurtic, and heteroscedastic properties, such effects are clearly important and in interaction with criteria for portfolio construction may have an impact on momentum strategies and its profits. The implication that returns of financial assets exhibit a heavy tailed distribution may have a significant impact on risk management and investment. Extreme returns may occur with a much larger probability where the return distribution is heavy tailed than where it is normal. In addition, quantilebased measures of risk, such as value at risk, may also be significantly different if calculated for heavytailed distributions. This may have a significant impact on the evaluation of risk/return profiles of individual assets, their subsequent aggregation, and the impact on the investment decision in a risk/return framework. When other markets fall down there will be the negative impact on the return of RCACOC, it goes down with the rate of 2.189 and when the other global markets booms, RCACOC will increase by 2.40155. To prevent the loss we have use stop loss policy. The realized cumulative return as a selection criterion is a simple measure which does not reflect the riskreward framework. Moreover, empirical evidence shows that individual market returns exhibit nonnormality, so that it would be more reliable to use a measure that could account for these return properties.  One of the most commonly applied measures for riskreward framework is the Sharpe Ratio. This Ratio is the mean return of the trading strategy divided by its standard deviation and can be interpreted as a return/risk Ratio which is about 3.2961.

QUESTION # 3:

To estimate the optimum lag for vector ‘Yt’ using VAR model, initially we perform the causality test to check the causal effect of independent variable on S&P 500 return series. There we found the casual effect in the system. We run VAR 1 model to check whether there is any nonstationarity present in the system. We observe that inflation rate and US federal fund has unit root, to remove the unit root we take the first differential for all the variables and then run the VAR 1 again to check the stability of the model but the Pvalues of the model represents the insignificant effect of independent variables on return series of S&P 500. For the optimum lag of the model, Akike information criterion (AIC) has been used. At lag four the minimum AIC is obtained this means that at lag four the model will be stable. After applying VAR at lag 4 the pvalues shows the significance of the system. Furthermore we test the VAR 4 lag structure unit root, if there was a unit root present in the lag structure of the model it means model is not capturing all the information and it is not stable. We test the unit root for the lag structure, it is observe that all the roots are less than 1, this shows that model is capturing all the information from the system. Now residual of system has no autocorrelation.

To interpret the effect of interest rate, inflation and output growth, we apply shocks to these variables and check the impulse response of market risk premium. To do that we use impulse response function in Eviews and for impulse definition we use choleskydof adjusted degree of freedom. The impulse response shows the 1 standard deviation shock to variables with 95% confidence intervals.

1. Shock to Interest rates: A one SD shock to interest rate, initially decreases returns of S&P 500. This negative response increases till period 5 and then gradually decreases to period 7 and slowly converges to zero till period 12
2. Shock to Output growth: A one SD shock to output growth, initially increases returns of S&P 500. This positive response decreases till period 3 and then gradually increases to period 6 and then decreases to period 8 then have a less impact till period 12.
3. Shock to Inflation rate: A one SD shock to inflation rate, initially deceases returns of S&P 500. This response has no noticeable impact on S&P 500 and hits the steady state till period 12.

QUESTION # 4:

Pairs trading has existed in multiple forms for a long time. In this question we focuses on one specific form of pairs trading using cointegration of time series as method to identify suitable pairs to trade in. The core concept of pairs trading is to identify a pair of stocks where the difference between the prices of the two stocks is, for some reason, believed to have meanreverting properties. In order to make 5 pairs of stocks we select 10 companies stock from S&P 500 including JP Morgan, Honeywell int’l Inc., Johnson & Johnson, Wells Fargo, The interpublic Group of companies, Omnicom group, Exxon Mobil Corp, Chevron Corp., General Electric and Texas Instruments. Initially, correlation matrix is use to check the high correlation pairs, on the basis we select the 5 pairs of the stocks i.e. JNJ & HON, IPG & WFC, OMC & IPG, TXN & JPM and TXN & HON. We check the stationarity of all the pairs . All the pairs are nonstationary, to check the long run relation between the pairs we perform ordinary least square method on nonstationary time series data after that we perform Engle Granger Cointegration test to check the stationarity of residual series. All the residual series are stationary means that there is cointegration present between the pairs. The Pvalues are less than Alpha which is 0.05 level of significance and tstats are greater than Engel granger critical values at 0.05 level of significance.

For IPG & OCM there is positive long run relation between the IPG and OCM with 35% relation of OCM on IPG with 0.000 Pvalue. TXN & HON also has a positive long run relation with 73% impact of HON on TXN with 0.000 Pvalue. IPG & WFC has a positive long run relation with 49% impact of WFC on IPG with 0.000 Pvalue. TXN & JPM has a positive long run relation with 111% impact of WFC on IPG with 0.000 Pvalue. JNJ & HON have a positive long run relation with 67% impact of HON on JNJ with 0.000 Pvalue.

Basically, the strategy will consistently rotate around identifying periods where the inconsistency between the prices of the two stocks is bigger than it should be and expected to reduce at a later point. One would therefore have the option to make a benefit from taking a long position in the underestimated stock and a short position in the overestimated stock as of right now and closing the position when the price discrepancy as came back to some normal level. To have a long or short position we take 3 standard deviation of X offer to Y share. For instance shares are exchanged the relationship Y – 3X. That is, some numerous of one portion of Y is purchased and the equivalent various of 3 portions of X are undercuts. Accept that the standard deviation of the estimation of Y – 3X is 10 during the intest period. This would infer that a deviation of 20 from the average during the in sample period is adequate to start a trade in outsample period.

QUESTION # 5:

Error correction models are a specific type of VAR representation of the relationship between two variables that are of particular use given that the two variables exhibit certain characteristics. Generally speaking, an error correction model between two variables ?? and ?? may take the following form: 

∇?? = ? + ?∇?? + (??−1 − ? ′ − ? ′??−1 ) + ?? (1)

This representation will be of use when ?? and ?? are such that:

1. Both ?? and ?? are nonstationary. That is, neither variable is (0).
2. Both ?? and ?? are (1) the first difference of both variables is stationary.
3. There exists a cointegration relationship between ?? and ?.

If two variables exhibit these variables, then all parts of (1) will be stationary ((0)), as ??−1 − ? ′ − ? ′ ??−1 is the stationary residual from the cointegration relationship between ?? and ??. Important estimates of the parameters of the equation may consequently be evaluated under the conditions that the variables X? and Y? have these properties. Specifically compelling to the applications is the parameter ?. This parameter is a estimate of how much the variable Y? reacts to divergence from the consistent expected value of the cointegration relation among X and Y. The parameter is relied upon to be negative should such a relationship exist, as a negative parameter shows that Y? reacts to a divergence so as to decrease the distinction to the steady anticipated worth. The bigger the parameter ?, the more the time series of Y? creates so as to counterbalance a divergence.

In order to estimate Error correction model for short term relation between the pairs of stock we take the first difference of 5 pairs of stock to make them stationary then add lag 1 series of residuals in the equation and run the Ordinary least square model to estimate the Beta coefficients. If we only see the Beta function of price of stock and not considering the error correcting term, IPG & WFC has a short term positive relation, the impact of WFC on IPG is about 15% with Pvalue of 0.000. TXN & JPM has a short term positive relation, the impact of JPM on TXN is about 43% with Pvalue of 0.000. JNJ & HON has a short term positive relation, the impact of HON on JNJ is about 40% with Pvalue of 0.000. IPG & OMC has a short term positive relation, the impact of HON on JNJ is about 23% with Pvalue of 0.000 and TXN & HON has a short term positive relation, the impact of HON on JNJ is about 47% with Pvalue of 0.000. An error correction model might be definitively evaluated for all sets of stocks X? and Y? considered for trading. The advantage of undertaking this strategy is somewhat direct: Ponder that X? and Y? are cointegration time series of stock prices. Assessing error correction model of the type of (1) will in this manner give a gauge of how rapidly the cost of stock X reacts to a divergence from the consistent value of the cointegration relationship. Ceteris paribus, exchanging on a couple of stocks X and Y will be desirable over a couple of stocks P and Q if the assessed parameter ?? is bigger for the pair X and Y than it is for the pair P and Q.

Error correction term actually correct the disequilibrium of the system. The Beta function show the speed at which error correction term corrects the system. If we consider the error correcting term in the model, it shows the long term relation between the pair of stocks for all 5 pairs because the error correction term has a negative sign with significant PValues. The error correction for IPG & WFC, TXN & JPM, JNJ & HON, IPG & OMC and TXN & HON are 0.0087, 0.0087, 0.0085, 0.0124 and 0.0065 respectively. To check whether the model is spurious or not we check the Durbin Watson stats all the values are near 2, this means that all models are authentic and real.