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Say I want to do Portfolio Optimization using the mean-variance approach (i.e Markowitz model), but that some of my assets are new with no returns history.
I can use a judgmental (expert knowledge, not statistic based) forecast to come up with mean expected return values from my new assets, but how can we estimate variances and coefficients of correlation for the new assets?
If we accept that there is no really accurate way to do this (barring time travel, which introduces multiple paradoxes), one possible way to at least get something vaguely plausible would be to look for older assets with known variances that are "similar" to a new asset (same industry, comparable capitalization, being investigated by the same government agencies, ...) and then take a possibly weighted average of their variances and covariances. Now how you define similarity will be a whole new can of worms.
I assume that "new" means "newly on the market", not just "new in my portfolio", since in the latter case the variances and covariances are out there somewhere waiting to be looked up. So, if "new" means "recent IPO", you would want to look for older assets that were similar to the new ones around the time of the older ones' IPOs.
You can try the Black-Litterman model, which allows to rate the relative expectations on the returns of assets. Because this evaluation does not necessarily rely on historical data it allows the incorporation of new assets.
