I want to understand how robo advisor make cross asset selection. We have a history of asset returns and it's standard deviation so we know sharpe ratios for most asset classes or even individual securities. Now I want to construct the portfolio going forward with a specific target in mind as to how much risk and return I want. Would robo advisor take in consideration an attractiveness of one asset class vs another. Say small caps and REITs(random example) have exactly same sharpe ratio but I know one is cheaper relatively to another and I should choose the cheaper one. Do they use the metrics that are beyond history? I am trying to understand how are they different from mutual funds where human makes choices on asset allocation.
The algorithms behind most "robo-advisers" are as proprietary, and idiosyncratic, as those of a human advisor.
Index funds, however, are relatively transparent. Since they have the goal of tracking the performance of a specific index, they will try to hold stocks in the index, or equivalent stocks if they can't get enough of one in the index, in the same proportion as the index, and they publish their holdings periodically. There may be some subtleties as they use a small cash reserve or a small amount of optioning, but basically they're doing exactly what the name suggests.
There are many statistics. There is no hard evidence that any of them will reliably let you do better than a diversified spread of index funds, and some evidence they won't --websearch "Buffet bet".
If you're going to bet on individual stocks, do so because you have studied that sector and company and believe its shares will gain value, rather than expecting a magic formula to do it for you.