Summary order to estimate conditional variance and portfolio

Summary of the Research ProposalThe study undertakes a semi-parametric approach to investigate the risk dependence among the most liquid assets from different markets. A combination of linear and non-linear models are employed in order to estimate conditional variance and portfolio risk between Stock, Gold and foreign exchange markets firstly in Pakistan by using daily prices from 2011(M1) to 2018(M4). This kind of investigation has not been engaged for the combination of high frequency investment alternatives. The study incorporates guassian and non-guassian Copula models and the results are compared in order to capture the best dependence structure among various asset combinations and Portfolio VaR is estimated based on the parameters obtained from the selected model.

Copula model provides a more robust estimate of dependence by looking into the joint distribution possessed by the variables where marginal distributions are obtained by ARMA-GARCH (1,1) model. This approach is consistent with the fact that many financial time series variables exhibit some specific non-guassian distributional properties. The study also compares the efficiency of linear and non-linear dependence measures. The study has implications for investors and policy makers to best understand the interaction among financial and commodity markets.Significance of research on the topic.The study provides a semi-parametric distributional approach to capture the dependency and risk contagion among highly liquid asset combinations.

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The analysis aids in investment decisions concerning financial assets, real assets and portfolio diversification. Also the study gives insights about the interaction of financial and commodity markets of Pakistan.Research GapTo the best of author’s knowledge such kind of comparative investigation has not been engaged for the combination of most liquid investment alternatives. This study is also first in assessing the risk dependence of most liquid assets together in Pakistan. Previous studies are focused mostly on unidirectional analysis by undertaking parametric approaches to model the dependencies among various financial and macroeconomic time series variables (see for example Gobind 2016; Rafiq and Hasan 2016; Khan, Aziz and Herani 2016; Badshah, Shoaib, Alvi and Sayilir 2016; Najaf, Yousaf and Ashraf 2016).

The study contributes to literature by incorporating various guassian and non-guassian copula models to capture the best dependence structure and Portfolio Risk among commodity, stock and exchange markets.Scope of StudyThe study provides insight about the interaction of financial and commodity markets of Pakistan. Also the analysis has implications for researchers, policy makers and investors regarding investment decisions and risk management.Methodology used Dynamic Copula model has been used on daily returns data to investigate the risk dependence and Portfolio VaR estimationVariablesStock, Forex and Gold.

Study TypeApplied StudyDataDaily Prices for the time span of 2011 (M1) to 2018 (M4) are used in the study..Key words (4-5)Dependence Structure, Risk Contagion, Co-integration, GARCH, Copula, VaRIntroduction Stock, forex and gold prices represent the three important macro finance variables that are intrinsically linked (Jain ; Biswal, 2016). Analyzing the interaction between various asset markets is of great concern among portfolio investors and risk managers. Three assets are among the most liquid investment alternatives having less turnover period as compared to other assets like real estate and bonds.

Hence the stock, forex and commodity markets provide a great venue for short term as well as long term investments and portfolio diversification. Exchange rate movements have impact on stock prices such that fluctuations in the domestic currency affects international competitiveness of domestic firms and their cash flows, thereby affecting domestic stock prices (Reboredo, Rivera-Castro, ; Ugolini, 2016). Similarly, stock price changes impact exchange rates, since an increase in domestic stock prices triggers currency adjustments to accommodate variations in demand and supply for domestic and foreign assets included in internationally diversified portfolios. Hence determining the interaction of foreign exchange with stock market is a great concern for both domestic and foreign investors in evaluating their investment risk (Mishra, 2016). Gold is not only an industrial commodity but also an investment asset which is commonly known as a “safe haven” to avoid the increasing risk in the financial markets (Akgül, Bildirici, ; Özdemir, 2015). Investors also invest in gold to hedge against inflation, to offset stock market declines and counteract against declining domestic currency (see Bilal, Noraini Bt., Haq, Khan, ; Naveed, 2013; Bildirici and Turkmen, 2015; Raza, Jawad Hussain Shahzad, Tiwari, ; Shahbaz, 2016).

This is because higher inflation causes the decline in both stock and foreign asset markets and investors tend to secure their investment especially in the developing countries when the economy of country is not doing well (Johansson, 2014; Kal, Arslaner, ; Arslaner, 2015). The study is conducted in Pakistan to show the interaction among financial and commodity markets in the developing economy. Moreover financial markets of Pakistan have shown a significant potential for foreign investment in recent years. In 2002 Karachi Stock Exchange, the biggest stock market in Pakistan was the best performing market in terms of the local market index. In 2013 it was declared as the world’s second best performing stock market recording a 37% rate of return in US dollars and 49% in local currency (Azher & Iqbal, 2016). This makes the Stock Market of Pakistan an important venue for both domestic and foreign investment. Due to globalization, investors are interested in portfolio diversification and they look for alternative baskets for their portfolio selection (Badshah, Shoaib, Alvi, & Sayilir, 2016). However, foreign portfolio investment comes with additional sources of risk and uncertainty.

This study provides a much deeper investigation of risk dependence among stock and its alternative investment markets by incorporating a semi-parametric copula model and portfolio VaR estimation in order to minimize the uncertainty about future. Findings of the study help investors in deciding about financial investment, real assets investment and portfolio diversification. Traditionally, the interdependence between the assets is measured by linear methodologies using Pearson’s correlation coefficient, which works with the assumptions that financial assets are normally distributed and that the relationships between financial assets are linear ( see Rafiq and Hasan, 2016; Gobind, 2016; Reddy, 2016). However, empirical studies have shown that correlations between assets returns are both non-linear and time- varying. This is due to the fact that mostly financial asset returns follow some specific non-guassian and fat tailed distributional properties which the linear dependence measures are unable to explain (Rachev, Menn, ;Fabozzi, 2005; Cont, 2001). Nawaz (2014) proved that non-parametric models outperform in order investigate the risk dependence and portfolio VaR estimation for mostly financial time series variables. This gives us the motivation to look into the distributions possessed by financial variables in order to obtain best insights about the interaction and risk contagion among assets from different markets.

Therefore a semi-parametric copula model is applied in the study where the dependence parameters are obtained from joint distribution among the variables. Results from several classes of copula models are compared to capture the best association among the variables.Problem Statement”Interaction among the most liquid assets is concerned for short term investment solutions where Copula provides an adequate measure of Risk Dependence.”Since Embrechts, Mcneil, and Straumann (2002) identified the limitations of correlation-based models and noted the relative advantages of copula model, many researchers have started using copula to directly model the dependence structure across financial markets. Works along this line include Chollete et al.

(2006), Hu (2006), and Mashal and Zeevi (2002), who reported asymmetric extreme dependence between equity returns, i.e., the stock markets tend to crash together but do not boom together.

Hotta, Lucas, and Palaro (2008) used a mixed model with the conditional copula and multivariate GARCH to estimate the VaR of a portfolio composed of NASDAQ and S;P500 indices. Huang, Lee, Liang, and Lin (2009) use the GARCH-Copula model in the estimation of VaR for a portfolio comprising NASDAQ and TAIEX and the results are compared with traditional models, the copula model captured the VaR more successfully. However, these studies are focused on the equity portfolio risk using the copula model. Recently, Han, Gong and Zhou (2016) did a dynamic VaR-copula measurement analysis on several combinations of stock, gold and real estate portfolios firstly in China. Incidentally, all of the above studies have been conducted for different assets using financial data taken from various developed and developing countries other than Pakistan.

Also the risk dependence among stock, gold and forex need to be explored which are the main focus of attention among portfolio investors especially for short term investment preferences. Hence the paper tries to fill this gap while using financial data from Pakistan which has a huge potential to attract investors to diversify their portfolios.Research Questions • What is the dependence structure of assets (Gold, Stock and Forex) from different markets in Pakistan?• Are Stock, Gold and Forex Markets Co-integrated?• Does Gold provides a safe hedge against Currency and Stock Market?• What is the estimated VaR of given portfolio?• Which asset combination has minimum Risk?• Which class of Copula performs better?Research Objectives• To know the dependence structure among Stock, Gold and Forex in Pakistan.• To make an efficient Portfolio.• To assess the performance of linear and non-linear approach.• To minimize future uncertainty.• To explore diversification opportunities for investors.

Literature Review Nowadays stock, forex and gold are gaining more attention among portfolio investors and risk managers. These assets belong to the most liquid investment markets and allow investors to meet their long term as well short term investment objectives. The volatility of returns, risk dependence between stock, forex and gold assets and mixed-asset portfolio optimization in Pakistan are the focus of this study.

Several researchers have investigated the interaction between various investment assets using different econometric techniques in different economies and sample periods. The studies on associations among assets gained more attention after the US crisis, but in the area of risk estimation across assets of different markets, the studies are not that much. Chan Treepongkaruna, Brooks and Gray (2011) examined the relationship between US financial, commodity and real estate returns and found flight to quality between asset returns indicating that investors tend to shift their capital from riskier towards safe investment market. Miyazaki and Hamori (2013) investigated the causality between gold and S;P 500 index returns, and argued that gold is not considered as a safe hedge for stocks in the long run. However Dee, Li, and Zheng (2013) concluded that gold serves as a good hedge tool for stock and inflation in China by holding it for a longer period of time. To test gold hedging ability against exchange rate, Wang (2013) conducted a non-linear panel data investigation about the hedging property of gold against a collection of major currencies (Australian dollar, Euro, Canadian dollar, Japanese yen, Indian rupee, British pound and South African rand) and reported that gold can hedge exchange rate risks. However, in the case of the excessive depreciation of the US dollar (by –7.

5% or lower), the safe haven effect of gold disappears. Financial Markets of different countries respond differently to other financial and macroeconomic variables depending on the economic and political environment where they operate. Raza et al. (2016) examined the asymmetric relationship between stock and commodity markets from different emerging economies (Brazil, Russia, India, China, South Africa, Mexico, Malaysia, Thailand, Chile and Indonesia) and argued that the interaction is mostly shaped by domestic factors including currency market situations, inflation, interest rate and level of economic growth.

Reddy (2016), Patel (2013) and Mishra et al. (2010) found significant long-run association between gold and stock markets in India. These findings are also consistent with Jain and Biswal (2016) who found short-term negative correlations between gold and forex and between forex and stock market which shows that gold is considered as a safe investment alternative in indian economy. Contrary to this, Khan et al. (2016), Najaf et al.

(2016) and Baig et al. (2013) applied several co-integration and correlation techniques and found no significant long run relationship among stock and gold markets in Pakistan. Different methodologies used in the literature create ambiguity for the readers when they show different relationships among the same variables.

This generally happens when improper techniques are applied or when insufficient assumptions are held about the variable(s) under study. For example Qayyum ; Kemal (2006) applied a multivariate EGARCH-VAR model and found a significant relationship among forex and stock market of Pakistan, where Rafiq and Hasan (2016) and Barakat et al. (2016) used co-integration and OLS techniques and reported insignificant association between the same markets. Previous studies are also focused more on parametric approaches with normality assumptions to model the dependence among different macro finance variables (see for example Khan et al., 2016; Bilal et al., 2013; Shahzadi ; Chohan, 2013). However, a number of contributions to financial risk management have shown that mostly financial variables follow non-normal distribution (Rachev et al., 2005; Cont, 2001), where semi-parametric models are shown to produce more accurate measures as compared to other parameric approaches (Nawaz, 2014).

Moreover, Angelidis and Degiannakis (2005), Giot and Laurent (2003a) and Lambert and Laurent (2001) among others, proposed the use of Student t-distribution, so as to take into account the fat tails of varibales in financial risk analysis. After a comprehensive review of existing literature a gap was found to exist in the exploration of interaction and risk contagion among stock, gold and foreign exchange market. The study incorporates ARMA, GARCH and Copula models to obtain the dependence parameters and portfolio VaR is estimation. A number of studies on risk modeling have indicated the superiority of Copula methodology over other parametric models. Embrechts, Mcneil, and Straumann (2002) identified the limitations of correlation-based models and noted the relative advantages of copula model. Huang, Lee, Liang, and Lin (2009) observed that conditional copula-GARCH models are better than other normal models on measuring the risk of portfolios. Research MethodologyEstimation of portfolio VaR requires the knowledge of multivariate distribution of assets. However, it is a strong requirement which can be relaxed using copulas.

The estimation of VaR under dynamic copula models is implemented as follows:I. Fit an appropriate ARMA-GARCH model to the return data. Obtain model parameters and compute standardized residuals to check the adequacy of the models.II. Construct three portfolios by different two asset combinations.III.

Fit the most appropriate copula on the standardized residual series to obtain the dependence parameters and bivariate distribution for different asset combinations. If the appropriate copula is not known, several copula are estimated and the appropriate copula is chosen based on model selection criteria.IV. Simulate Q Monte Carlo Scenarios over the time horizon ( t+1 ) using the conditional bivariate distribution modeled by the estimated copula model and obtain Q two-dimension vector future returns.V.

Calculate VaRt+1 for each portfolio and compare the results to find the efficient portfolio.


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