How do you decide how many investments to own, how risky they are, how long to hold, and how much to invest in each? Please provide a concrete hypothetical example explained in a dumbed down way so I can understand.
How do I decide? It is the outcome of a quadratic optimisation which takes my views about the expected returns on assets or clusters of assets and builds portfolios subject to tracking error or total volatility limits. These volatility estimates are estimated generally via principal components analysis, and either GARCH processed or Bayesian shrunk to a diagonal matrix, after front weighting, depending on the purpose. The reasonableness of this is tested against the implied volatility of the market itself and my knowledge of events that might make this inaccurate. Then, there are hard limits put in to place to prevent corner solutions from dominating outcomes. These hard limits are often aware of what the stock or the cluster of assets actually does for a living. Where the return outcomes are still subject to strong tail events, I hedge or insure them in some way. When all of this is done, the stock number and portfolio composition pops out and I put it in to the market.
I own lots of different things, not just stocks. I would represent the other extreme on the issue of portfolio diversification, but what I do is not normally found outside of multi-strat hedge funds which makes it uncommon from the outset. I have certain skills and this is how I apply them.
Although I use lots of maths, I also take the radical step of....actually checking if the output makes any sense. Why might the training window not be reasonably representative of the forecast window?
In general, my thinking is strongly influenced by risk parity and risk budgeting concepts, though adapted for my circumstances.
At present, I have no idea about how to explain this simply and don't feel particularly motivated right this minute. Howard has some ideas for estimating risk for single assets or, otherwise, strategies for trading them. Perhaps that's a good place to start.