國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
1
1. Introduction
From 2004, the global financial markets have entered a relatively tranquil situation, and the market volatility measured by the volatility index derived from the S&P 500 index has been a lower level for a long time until 2007. But the S&P 500 index drops about 48% from September, 2008 to March, 2009. During the same period, the Chicago Board Options Exchange (CBOE) Volatility Index performs well and increases more than 125%. The negative correlation between the S&P 500 index and VIX index leads investors to explore the VIX as a way to protect their portfolios from market crash, and even invest in the derivatives from VIX index to earn excess return during the crisis periods.
VIX is known as the CBOE Volatility Index. It measures the implied volatility that is being priced based on the S&P 500 index options, and often mentioned as
“investor fear gauge”. The VIX offers an indication of the next 30-day implied volatility priced by a variety of options from the S&P 500 index option market. Thus, VIX is an important sign of market expectations for near future volatility, and it is commonly used to measure investor sentiment. It is important to understand that VIX is forward-looking as it measures the volatility that investors expect to see in the market. Therefore, VIX is a successful market timing indicator (Hill and Rattray, 2004) and a useful tool for risk management because it is the benchmark for implied volatility of U.S. stock market.
VIX is a successful signal for entering into or out of stocks. High value of VIX is interpreted to correspond to a more volatile market in the near future. When the macro-driven environment is not running well, investors expect the future returns will be low and the sentiment of investors become pessimistic. As a result, they start to sell off their stocks so that raising the market volatility and the VIX index will go high.
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
2
VIX index can respond the atmosphere of the financial markets and show investors’
confidence level which implies both rational and irrational parts of their thinking. We should consider how the investors’ emotional aspect influences the volatility of financial markets so that we can make a better investment decision. Any trends or changes in the VIX index may help us evaluate the current and future situation of the market. For example, When VIX goes below 10 points, investors start selling stocks for short because they worry that the markets are being over-confident, and this kind of tranquil situation will change in near future. When the market trend is downward, but the VIX has not gone up, investors interpret that the downturn will be predominate until the VIX leaps higher. It would be the time to start buying stocks.
Figure 1. VIX index from 1990/1/2 to 2013/3/29
Financial time series such as stock price or VIX index change dramatically especially in recent years. Figure 1 displays the daily VIX index from January, 1990 to March, 2013. Obviously, the VIX index is very volatile and sensitive to global financial market disturbances such as the Asian currency crisis in 1997, the Long-Term Capital Management (LTCM) crisis following the Russian financial crisis
0 10 20 30 40 50 60 70 80 90
1990/1/2 1991/1/2 1992/1/2 1993/1/2 1994/1/2 1995/1/2 1996/1/2 1997/1/2 1998/1/2 1999/1/2 2000/1/2 2001/1/2 2002/1/2 2003/1/2 2004/1/2 2005/1/2 2006/1/2 2007/1/2 2008/1/2 2009/1/2 2010/1/2 2011/1/2 2012/1/2 2013/1/2
VIX index
VIX
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
3
in 1998, the 911 attacks in America, the 2002 Internet Bubble and the accounting scandals conducted by some U.S. large corporations, which made an enormous increase in VIX by 25% versus a huge decline in S&P 500 index about 36% (Fabozzi et al., 2006). In 2008, the Sub-prime crisis even caused the VIX reaching its highest level, 80.86, which is about 240% increase since January 2, 1990, and the S&P 500 index faced a substantial fall of about 48%. The European Sovereign debt crisis in 2010 made the VIX surge to 173% only in eight months and S&P 500 index decrease 12% at the same time. We can observe from the graph that generally VIX can be viewed as two states (or regimes), one is relatively smoothed and in lower levels, while the other is much fluctuated and have higher values. In this paper, I name the former one as “tranquility” state and the other as “crisis” state. This is consistent with Connors (2002). For most investors, they are eager to identify the timing when the two states occur, and especially, the state switching points between the two states. If investors know the switching moment, they can infer the future states and update their investment decision.
Identifying the trend of a stock market in advance can help investors to gain excess return and avoid losses. Of course, identifying the trend of VIX index can also achieve the same purpose. The most common classification of stock market regime is bull or bear market in the past literatures. The term bull market is associated with periods of upward trend in share prices and strong investment sentiment. On the contrary, the bear regime is the situation with downward trend in stock prices. In general, a bull regime is characterized with high returns and low volatility, and a bear regime is with low returns and very high volatility. We know that VIX index indicates the volatility of markets, thus, when the stock market is in the bull regime, the VIX index will stay in low levels and move smoothly. But when the bear market is coming, VIX will also respond to the dramatic change through the higher level of index and
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
4
intense volatility.
Such structural break is regime shift or state switching. Regime shifts usually occur due to economic and financial crises. Once the crises happen, the single linear time series model commonly used before cannot identify the breaks in structure very well, the change in property of the financial time series motivate the use of regime switching models instead. Many studies have attempted to improve the predictability for financial market crises with macroeconomic and other variables. However, little research has explored the relationship between market turbulences and state switching showed up in the VIX index through regime switching model.
To sum up, VIX index is very useful to show the financial market situation, especially during the periods of crisis or bear market. In other words, VIX can be viewed as a downside risk indicator because it always obviously strongly responds to the negative market sentiment when crises happen so that we can see from Figure 1 that the level of VIX almost soars dramatically and the movement becomes very volatile during the periods of financial crises or market instability. Therefore, this paper would like to clearly identify the state switching between tranquility and crisis state in the VIX index to help investors understand the current and future market condition and adjust their investment decision in advance so that they can increase their return and avoid suffering severe losses when the crises occur.
This paper attempts to construct a model to understand the dynamics of VIX index and identify its state switching considering the influence of exogenous financial variables. The time-varying transition probability (TVTP) Markov state switching model which characterizes the unobservable tranquility or crisis states in VIX index and dynamics between them is applied. In addition to detect state shifts in the VIX index from the structural changes itself, most importantly, this paper investigates the role of U.S. financial market variables as leading indicators of state shifts in the VIX
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
5
index, and check whether these exogenous variables added into the model, such as interest rates or exchange rates, can better help us identify the state switching and the turning point between two states in the VIX index. Therefore, proving the effect of models with extra variables is better than the model without variables added, and generalizing what variables are beneficial for the model estimation and help observing VIX are very important purposes in this paper. The TVTP model is used to achieve above purposes, and this study also applies the likelihood ratio test (LR test) to check the statistically significance of the use of time-varying transition probability Markov switching model compared with the fixed transition probability Markov switching model which is without the exogenous variables added. This paper also investigates the practical performance of each model to double examine the TVTP models’ effect.
This paper is structured as follows. After the introduction in section 1, in section 2 this paper reviews some literatures about basic idea of VIX and variables used to predict financial crisis, and learns how the past literatures apply the Markov state switching model to financial time series data. Section 3 explains the methodology about two-state Markov switching model. Section 4 describes the preparation for the time series data using in model and presents the empirical results and discussion on the results. Finally, Section 5 contains summary, findings, research limitations and future research suggestions.
The framework of research is below. First, this paper describes the background of the VIX index applied in U.S. financial markets and understands the features of VIX when crisis occurs. Thus, this paper would like to explore further that whether the VIX index is really effective to detect the occurrence of crisis state, and which triggers motivation to study this issue. Then, through literature reviews, this paper generalizes some financial indicators which may be helpful to identify state switching in VIX index, and understand how the past literatures apply the methodology used in
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
6
this paper. Time-varying transition probability Markov regime switching model is the main methodology. This paper will incorporate the selected variables to construct TVTP models and test their significance statistically. And this paper will also compare their practical performance to examine their effectiveness when applying practically. Finally, conclusion and some findings in this paper will be summarized.
Figure 2. Framework of research
Introduction
Motivation Purposes
Literature review
Characteristics of VIX
Cases of model application
Methodology
Empirical results
Conclusion
Model selection: statistical view Model comparison: practical view
Summary Findings TVTP MS model Variable generalization
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
7