The VIX is said to be a “fear” index. Can it forecast the direction of the market? Can it forecast the volatility of the market?

The VIX is said to be a “fear” index. Can it forecast the direction of the market? Can it forecast the volatility of the market?

Given the monthly data in the attached EXCEL spreadsheet do the following steps.

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1) Convert each series into returns using the following formula.
Returnt =LN(Pt/Pt-1)

2) Run the following two regressions
i) Return of SP500t = a + b*(Return of VIXt-1)
ii) (Return of SP500t)^2 = a + b*(Return of VIXt-1)

[NOTE: (Return of SP500t)^2 is a measure of volatility)

3) Based on the results, answer the two questions.
a) Can the VIX forecast the direction of the market?
b) Can the VIX forecast the volatility of the market?
You should review your statistics concerning tests of significance.

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