Theoretical and Applied Economics Volume XVIII (2011), No. 2(555), pp. 75-88 Portfolio Risk Analysis using ARCH and GARCH Models in the Context of the Global Financial Crisis* Oana Mădălina PREDESCU Bucharest Academy of Economic Studies predescu_oana85@yahoo.com Stelian STANCU Bucharest Academy of Economic Studies stelian_stancu@yahoo.com Abstract. This paper examines both the benefits of choosing an internationally diversified portfolio and the evolution of the portfolio risk in the context of the current global financial crisis. The portfolio is comprised of three benchmark indexes from Romania, UK and USA. Study results show that on the background of a global economic climate eroded strongly by the effects of the current financial …show more content…
According to the three researchers, a more specific form of the non-linear model is given by the following equation: (2) where g is a function of past error terms, and σ is the variance term. Campbell, Lo and MacKinlay characterize models with non-linear g as being non-linear in mean and those with non-linear σ 2 as being non-linear in variance. Models can be linear in mean and variance (the classic regression model, ARMA models) or linear in mean, but non-linear in variance (GARCH models) (Brooks, 2010, pp. 380). The most commonly used financial models to measure volatility are the non-linear ARCH and GARCH models. 2 y t = f (e t , et −1 , et − 2 ,...) y t = g (et −1 , et −2 ,...) + et σ 2 (et −1 , et − 2 ,...) 2.1. The autoregressive conditional heteroscedasticity model (ARCH) One of the fundamental hypotheses of the classical regression model is the homoscedasticity or the hypothesis of constant error variance: var(et ) = σ 2 (et ) , where et ~ N (0, σ 2 ) . The opposite case is known as heteroscedasticity. In the case of financial time series it is unlikely that the variance of the errors will be constant over time and hence it is preferred to consider a model that does not assume constant variance and which can describe how the variance of the errors evolves. As we mentioned earlier another important feature of financial series is known as volatility clustering or volatility pooling. This characteristic shows that the current level of volatility tends to
The extracted data used includes monthly returns from January 1972 to July 2011. The assets are selected so that the portfolio contains the largest, most liquid, and most tradable assets. The choice of such a variety of assets across several markets was used in order to generate a large cross sectional dispersion in average return. It helped to reveal new factor exposure and define a general framework of the correlated value and momentum effects in various asset classes.
Advisors and investors would do well to pay as much attention to the expected volatility of any portfolio or investment as they do to anticipated returns. Moreover, all things being equal, a new investment should only be added to a portfolio when it either reduces the expected risk for a targeted level of returns, or when it boosts expected portfolio returns without adding additional risk, as measured by the expected standard deviation of those returns. Lesson 2: Don’t assume bonds or international stocks offer adequate portfolio diversification. As the world’s financial markets become more closely correlated, bonds and foreign stocks may not provide adequate portfolio diversification. Instead, advisors may want to recommend that suitable investors add modest exposure to nontraditional investments such as hedge funds, private equity and real assets. Such exposure may bolster portfolio returns, while reducing overall risk, depending on how it is structured. Lesson 3: Be disciplined in adhering to asset allocation targets. The long-term benefits of portfolio diversification will only be realized if investors are disciplined in adhering to asset allocation guidelines. For this reason, it is recommended that advisors regularly revisit portfolio allocations and rebalance
“The Benefits of diversification are clear. Portfolio theory has played a crucial role in explaining the relationship between risk and return where more than one investment is held. It also enables us to identify optimal and efficient portfolios.”
the network parameters associated with xt and ht−1 respectively. φ is a nonlinear function which we can choose from
X- C. The composition of the optimal international portfolio is identical for all investors of a particular country, whether or not they hedge their risk with currency futures
White H. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica. 1980;48:817-830.
After considering the limitation of linear function and graph, I have discovered applying any model of equation that has an infinite increase range, such as quadratic or exponential, is unrealistic, since the
Just after ten years of Asian financial crisis, another major financial crisis now concern for all developed and some developing countries is “Global Financial Crisis 2008.” It is beginning with the bankruptcy of Lehman Brothers on Sunday, September 14, 2008 and spread like a flood. At first U.S banking sector fall in a great liquidity crisis and simultaneously around the world stock markets have fallen, large financial institutions have collapsed or been bought out, and governments in even the wealthiest nations have had to come up with rescue packages to bail out their financial systems. (Global issue)
The success of the model is attributed to Yale’s ability to combine both quantitative analysis (mean-variance analysis) with market judgments to structure its portfolio. In addition, Yale also uses statistical analysis to actively test their models with factors affecting the market, therefore understanding the sensitivity of their portfolio in response to various market changes. Yale also follows and forecasts the cash flow of private equity and real assets in its portfolio to decide the need for hedging.
Second, research on Flash Crash stated that HFT has the impact to create irregular volatility because HFTs sold the S&P 500 stocks which E-Mini was linked and reinforced the illusion of event to scared fundamental buyers out of the market. Under normal market conditions, HFT decreases a short term volatility by making it possible to buy and sell without significantly altering prices. (Prewitt, 2012). In addition, Brogaard showed HFT data from 120 US stock from the period 2008 to 2010 that high levels of HFT performance led to lower volatility, but Foucault et al. conflicted that investors provide more stock market volatility when they have faster access to news. (Manahov et al, 2014).
Traditional model presented in Figure 1 includes points (i) through (iv) of the latter list. In some cases
International portfolio diversification gives your investments a passport to added diversification benefits. The international boundaries to investing have collapsed. Fairly recently, foreign securities have become easier to trade due to improved communications and data
The different market indices that will be examined include: the Dow Jones Industrial Average, the NASDAQ Index and the 10 Year US Treasury Note Yield (10 Yr T-Note Yield). Understanding the relationship between them will offer specific insights as to various factors impacting volatility. It will also highlight potential changes and the lasting effects on everyone. (Weinstein, 1988) (Graham, 1976)
Volatility is main important variable in finance. Its appears mainly in pricing, portfolio theory ,risk management , derivatives , business finance , investment valuation and financial econometrics. Volatility cannot be directly observed. Hedging volatility risk is main for investors fluctuating from individuals to pension funds. Volatility risk followed the 1987 crash. Example: Barings Bank , Long Term Capital Management. In Hedging volatility risk there are three issue. First, a strong volatility measure has to be specified. Second, the properties of this particular measure have to be modeled. Third, the suitable instrument should be priced.
the same variance) as the moving average fllters already considered. Figs 3.2(a) and (b) can be