### Correlation between VIX, Dow, S&P500, Yield

Recently the market becomes more and more volatile. Many people turn to VIX to see if there is any indication in the future trend of stock market. VIX is the ticker symbol for the Chicago Board Options Exchange Volatility Index, a popular measure of the implied volatility of S&P 500 index options. it represents one measure of the market's expectation of volatility over the next 30 day period. Generally, VIX is referred to as Fear Index which shows whether the market "fears" about the future. When VIX is high, the more "fears" the market is.

In order to have a more scientific view on the relationship bewteen VIX and common market indices, I have done an analysis between VIX and Dow (Dow Jones Industrial Average Index), S&P500 and 10 Year Treasury Notes Yield. The analysis is to calculate the Correlation Coefficient* of VIX to the other three to see how these more indices or figures are correlated. Five year data (daily close from 31 Oct 2003 to 31 Oct 2008) are taken in this analysis.

Below is the result of calculation :

**Correlation between VIX , dow and 10 Year Treasure Notes Yield :**

**VIX & Dow : -0.02577**

**VIX & SP500 : -0.15889**

**VIX & 10 Year Treasury Notes Yield : -0.44814**

Analysis of result :

1. All three are negatively correlated with VIX which means when VIX goes higher, Dow, S&P500 and Yield will goes lower. This is very close to our general thoughts. When the market has more "fears", the stock market will goes lower as people are more likely to sell their securities. On the other hand, more people will buy treasury notes which drives the yield lower.

2. On the level of correlation, S&P500 has a higher correlation than Dow which is also expected as VIX is the IV of S&P500 in the coming 30 days. However, it is a surprise that the correlation between Dow and VIX is close to zero which means they are almost non-correlated. Therefore, we should NOT use VIX to indicate the trend of Dow. S&P500 represents a broader market and the indication to its trend from VIX is more effective. However, the correlation for these both is rather low.

3. The correlation of 10 Year Treasury Notes Yield is the highest among the three. More people will park their money to the relatively safer Treasury Notes when they feel more fears. When VIX is higher, the Treasury Notes Yield is more likely to be lower.

Conclusion :

From the above analysis, we can see that VIX is not a very effective indicator of Stock Market but more indicative to Treasury Notes Yield. Higher VIX will drive a lower yield.

*Correlation coefficient is measure of linear association between two variables X and Y. The coefficient lies from -1 to 1. Correlation coefficient -1 means the set of data are negatively correlated and 1 means positively correlated. 0 means non-correlated.

Labels: Value Investing

## 3 Comments:

the duration of the sample is too short

Five year is an optimal sampling for this analysis as the estimated data points will be around 10000 (I use daily close figures). With a much longer period, the result can be distorted because the financial market is rapid changing. Longer period may lead to more changing factors. For example, the correlation coefficient between Hang Seng Index (HSI) and Hang Seng Chinese Enterprise Index (HSCEI) is becoming higher recently because more and more chinese enterprises are selected as components of HSI.

I think we should not correlate VIX vs DOW/SP500 index. Correlation is used to measure the relationship of two variables which relationship are linear. VIX is the implied volatility. SP500 can go up or down when VIX value rise.

If you correlate VIX with the volatility of SP500, you should get a more meaningful figure.

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