I would most appreciate any insight into the following problem ~I need to calculate ex ante tracking error for a portfolio of asset classes vs. a benchmark mix of the same asset classes, with differing asset class weights.My definition of tracking error is the standard deviation of the return difference between the portfolio and the benchmark:where a' and b' are the vectors of portfolio and benchmark weights, respectively, with each summing to 1.I have all of the necessary variance/covariance/return assumptionsMy problem is that we are now leveraging the portfolio, so that the notional value of the portfolio is 125% of the actual underlying assets.Should the vector of portfolio weights now sum to 1.25 while the benchmark still sums to 1? - or will this not work?TIA for any help you can give me!

If the leverage is by means of borrowing at some reference rate (T-bill etc) then i think you should include it in your portfolio.Which implies that the sum of weights would again be 1.The return on your investment can be higher, obviously, with leverage.

it is not that complicated...always ask yourself: what is my exposure? if you own security A with 150% leverage, your exposure is 150%. so your weights vector will be 150%.

Gmike2000,Thank you very much for your reply. I was on vacation last week, so I am just getting to this now. As you can see in my original post, I did hypothesis that the portfolio weights should sum to 100% + Leverage%. I am sorry to be dense and make you repeat yourself, but I am questioning what to do with the benchmark weights. Should they still sum to 100% (This is what I am guessing, because if they were also sum to (100%+ Leverage%), then the vector of differences, which is used to calculate the tracking error, would remain unchanged from the unlevered situation, and thus, wouldn't the tracking error will be the same as in the unlevered situation?I was not sure if this will work: (portfolio weights sum to 100% + Leverage%, benchmark weights sum to 100%) however, because I was not sure if there was a constraint that the weights must sum to 100%, or if the sum of weights in the portfolio can be different than the sum of weights for the benchmark when using this formula.I very much appreciate any more insight you can provide me on this!