Risk Warning Indicators - Department of Mathematics, HKUST



Risk Early Warning Indicators

Name Student ID

Hon Wai Cheong 99334042

Yu Chun Tung 08812095

Lai Chi Kwong 05816454

12th May, 2010

MAFS Quantitative Analysis of Financial Time Series

Department of Mathematics

The Hong Kong University of Science and Technology

Content

1 Background 3

2 Data Analysis 4

2.1 VIX index 4

2.2 MOVE index 5

2.3 TED spread 6

3 Modeling 7

3.1 ARMA-GARCH Model of VIX Index 7

3.2 ARMA-GARCH Model of MOVE Index 12

3.3 ARMA-GARCH Model of TED spread 21

4 Performance of the Risk Indicators 25

5 Conclusion 30

Appendix A - FARMA Model of VIX Index 31

Appendix B - VAR model of S&P and VIX Index 32

Appendix C – Source Data and SAS Program Codes 34

Background

The collapse of Lehman Brothers has slashed an unprecedented financial shock across the globe. It initiated a deactivating wave over all major markets. In the wake of this Tsunami, stock markets plunged, money markets dried up, some other banks were overwhelmed.

Since then, attitude towards financial risk management has changed dramatically in an international scale. Regulatory bodies have imposed stricter and stricter rules onto banks. Banks are also more willing to devote resource into the research and development of risk management systems.

However, there are still many technical difficulties concerning risk manager. One of them is the early detection of financial crisis. If the early signs of trouble can be detected, further losses can be contained.

On 4th May, 2010, “Soaring VIX Index May Signal More Trouble Ahead for Stocks” was headlined in CNBC. It is market wisdom to believe that VIX index is one of the early warning indicators for a downturn of a market.

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In this project, we try to model three commonly used financial risk indicators with time series techniques. These indicators include 1) the VIX index, 2) the MOVE index and 3) the TED spread.

First of all, the VIX index is a weighted blend of prices for a range of options on the S&P 500 index. In the market, it is often referred to as the fear index, it represents one measure of the market's expectation of volatility over the next 30 day period.

MOVE stands for Merrill Option Volatility Estimate. It is a yield curve weighted index of the normalized implied volatility on 1-month Treasury options. This index serves similar purpose with the VIX but it focus on Fixed-income market.

TED spread is the difference between 3-months USD LIBOR and the 3-months government notes. It measures the liquidity among the inter-bank money market.

Data Analysis

In this paper, we extracted the daily closing prices of VIX index, MOVE index and TED spread from 2nd January 1995 to 31st December 2009 from Bloomberg. There are 3914 observations in total. The TED spread is calculated based on 3M LIBOR minus the Yield of 3M US Treasury bill.

1 VIX index

In the market, the VIX index is called “fear index”. Practitioners believe that the index level represents the cost to purchase an insurance to protect against the downturn of the market. Generally, the VIX index level will be high during crises or volatile markets. We would consider the VIX index as a reflection of the fear of the equity investors.

Based on the graph above, it is observed that the VIX index would soar sharply during the financial crises in the last decades. Crises were nearby when there were sharp jumps in the index level and the index level would maintain in a high level, say over 25, which is the 3rd Quartile of the dataset, over a certain period.

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2 MOVE index

MOVE index is similar to VIX index. As it is a volatility of treasury option, we consider the MOVE index as a reflection of the fear of the fixed income investors.

Based on the graph above, similar to VIX index, it is observed that the MOVE index would soar sharply during the financial crises in the last decades. Crises were nearby when there were sharp jumps in the index level and the index level would maintain in a high level, say over 117, which is the 3rd Quartile of the dataset, over a certain period.

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3 TED spread

The TED spread represents the average credit spread of financial institutions against US government yield. This figure reflects how financial institutions are eager to lend to each others. A high level represents the banking liquidity is dry.

Based on the graph above, similar to VIX index, it is observed that the TED spread would soar sharply during the financial crises in the last decades. Crises were nearby when there were sharp jumps in the spread level and the spread level would maintain in a high level, say over 0.6, which is the 3rd Quartile of the dataset, over a certain period.

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Modeling

1 ARMA-GARCH Model of VIX Index

The daily log return is calculated as rt = log(VIXt) – log(VIXt-1) with the plot shown below. It is a stationary process with a cluster pattern and we will study it with the ARIMA analysis first.

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Autocorrelation Function: LogReturn(VIX)

Lag ACF T LBQ

1 -0.092406 -5.78 33.44

2 -0.117801 -7.31 87.79

3 -0.003279 -0.20 87.84

4 -0.072026 -4.41 108.17

5 0.038737 2.36 114.05

6 -0.038809 -2.36 119.96

7 -0.053609 -3.26 131.23

8 0.019738 1.20 132.76

9 -0.011597 -0.70 133.28

10 0.082778 5.01 160.18

11 -0.010308 -0.62 160.60

12 -0.056022 -3.37 172.92

13 0.016043 0.96 173.93

14 -0.000656 -0.04 173.93

15 0.032237 1.93 178.02

16 -0.013176 -0.79 178.70

17 0.003996 0.24 178.76

18 0.006208 0.37 178.91

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Partial Autocorrelation Function: LogReturn(VIX)

Lag PACF T

1 -0.092406 -5.78

2 -0.127428 -7.97

3 -0.028017 -1.75

4 -0.092677 -5.80

5 0.017886 1.12

6 -0.055861 -3.49

7 -0.061160 -3.83

8 -0.010916 -0.68

9 -0.024385 -1.53

10 0.072267 4.52

11 -0.005077 -0.32

12 -0.037347 -2.34

13 -0.000381 -0.02

14 -0.000858 -0.05

15 0.028777 1.80

16 -0.008474 -0.53

17 0.021917 1.37

18 0.000571 0.04

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The Lijung-Box Q Statistics of the ρ12 is 109.78 with p-value ................
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