I am a little confused. I have calculated the tracking difference of an Index and a n ETF using the return getting 0,4% tracking difference per year. I have then leveraged both, the Index and the ETF to a lever of 2 getting 0.63% tracking difference per year. I have then done some testing with hypothecical value and got 10% unleveraged and 20% levaraged with an lever of 2. So, $$ leveraged\ tracking\ difference = lever*(unleveraged\ tracking\ difference) $$ in the hypothetical case. In the real case, I am not getting an equality.
However the real case used a 5-year period and I calculated the annual return using the geometric mean. In the hypothetical case, I only simulated one year of return.
My question is. Should the tracking difference always be equal to my formula when leverage? if that is the case, I might have done some mistake in the real case. Else, it differs when a 5-period is used along with the geomtric mean.