t-Test for Tracking Error Volatility

[neptunhiker]

Hi everyone,

I would like to conduct a simple two sided t-test whether Tracking Error Volatility (TEvol)is different from 0.

TEvol is defined as the standard deviation of the return differences between a stock series and an index series. This is how one could compute the TEvol in eViews:

Code: Select all

' create workfile create a 1901 2000 1 ' create stock data series stock=100 for !i=1 to 100 series stock(!i)=stock(!i-1)+rnd-0.5 next ' compute return series of stock data series stock_return=stock/stock(-1)-1 ' create index data series index=100 for !i=1 to 100 series index(!i)=index(!i-1)*(1+stock_return(!i))+rnd-0.5 next ' compute return series of index data series index_return=index/index(-1)-1 ' compute return differences series series return_diff=stock_return-index_return ' calculate TE Volatility scalar TE_vol=@stdev(return_diff)

My problem is, how to test the null hypothesis that TE_vol=0.

If I wanted to conduct a test of the mean of return differences, I would simply compute the sample standard deviation of return differences, the mean of return differences and the number of observations (nobs). Using these data I could compute the t-statistic via sqrt(nobs)*(mean-0)/(sample stdev). But how do I conduct a test of a measure that is already a standard deviation? Just to clarify, this is not an eViews issue, but an econometric issue. I just inserted the program to clarify my problem.

Thanks a lot for suggestions.