Question

Suppose that you would like to examine the way in which the volatility of index returns is related to the magnitude of index returns of different signs. To this end, you have estimated the following time-series regression

?ol? =?+?1 ×?et_t +?2 ×?_{t_}ret_tt +?_t

where ?ol?  is the volatility of the S&P500 index returns at time t, ?et_t  is the level of the S&P500 index return at t, and??_? is a dummy variable that takes the value of 1 if the index return at t is negative, and the value of zero otherwise. The term ?? is a

random error term.

Estimating the above model across a sample of 250 daily observations has resulted in slopes equal to ?₁ = -1.54 (p-value = 0.005) and ?₂ = -0.45 (p-value = 0.008).12

i) Briefly discuss the intuition behind the coefficients ??1 and ??2 in the above model.

ii) Perform the appropriate hypothesis test to determine if the estimated slopes are statistically significant. Assume a significance level of 5%. Based on these results, what would you conclude about the impact of returns of different sign to volatility?

iii) BrieflydescribetheassumptionsunderpinningOLSregression.

Answer 1

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