I would like to know if there is a way (or theory) to manage a multi-strategy, multi-instruments portfolio that would calculate the optimal weight to allocate capital for each combination of strategy and instrument (sometimes we may find one strategy works for many instrument or vice versa).
My first idea is that we can treat each combination of strategy and instrument as a imaginary instrument and introduce Markowitz's portfolio theory to find the optimal weight.
However, I also learned that the estimated return and covariance is very noisy in practice and deduce very different results from CAPM. May not be a ideal way. Another problem is that my strategies could be various across types and timeframe (from intra-day to month holding times). Estimating average return on daily basis could be misleading and underestimate return of strategies that works infrequently (for instance, strategies that take advantage on annual earning announcement or monthly FOMC meeting).
I checked Kelly formula and found the answer from it is exactly as Markowitz's theory. Thus, most issues on mean-variance theory (e.g. noise of estimation for mean and variance) applies here.
I wonder if anyone can share some thoughts on this issue. Any idea/example?