I have a portfolio of assets. For each asset I have a back-tested time series of daily profits. I'm tying to optimize, using the correlation of daily returns, to minimize the total draw-down of the portfolio. My problem is that I have 5 years of data for 6 of my assets, and 10 years of data for 4 of my assets. I've taken two approaches so far, neither of which I'm satisfied with.
First - simply optimize using the 5 years where I have data for all assets.
Second - optimize the 4 assets for 10 years independently to create 1 asset, then optimize with remaining 6 assets for the 5 year period with complete data.
My major issue with this is if one of the assets with a longer data-set contains large draw-down 6 years ago, my optimization is ignoring this and likely over-weighting that asset moving forward. On the flip side, if that asset's returns are slightly negative the past 5 years, but strongly positive the years prior, the optimization will under-weight this moving forward.
I understand this is probably a classic issue with trivial solutions, but I'm not well versed in portfolio theory when it comes to optimizing using daily returns. I appreciate any thoughts on this.