Hi all, Let's say we have N assets, for each asset we have M strategies, how do we form an "optimal" portfolio? I am thinking of the following: 1. Treating each of the N*M assets as a seperate and individual strategy, and run optimization for each of them, (need to be careful not to do over-fitting, but I don't know what's the best way to do optimization without overfitting; let's discuss about this also). 2. For each of the optimized strategies (there are N*M in total), (optimized in the sense of highest possible Sharpe ratio for each one), obtain the returns time series. 3. Run the correlation on the returns time series and obtain the covariance matrix of size N*M x N*M. And do a mean-variance analysis with a target expected return and an arbitrary number of risk aversion parameter. Solve for the optimal weights. The data are daily data; but somehow I do monthly rebalancing. So the optimal weights are sought for each month. The above procedure is again optimized in a robust way (but not sure how to do it robustly without getting into overfitting), to get the highest possible robust Sharpe ratio. -------------------\ Any thoughts on the above procedure? Thanks a lot!
http://www.castrader.com/2006/11/universal_portf.html I'm pretty sure its impossible except in a perfect world... You would need a switching algorithm that would detect the best position size, entry / exit, position, stops, scalability and the appropriate hedge for the position given market slippage, liquidity risks, etc.. You'd also need a set of above strategies and a method for determining their expectancy and deviation from, along with adequate risk management for a specific return characteristic i.e drawdown. to provide for the desired return for a given level of risk... etc Switching algorithms would be likely different for different timeframes - i.e mean reverting in short timeframes, and trend following in longer.. as well the portfolio would have to deal with propagation effects as the Market corrects or rises as a whole.
I would wonder about calculating the risk (I just asked about that in another thread). Anyways I have wondered about this too. I had thought that portfolio theory, and the newer post-modern portfolio theory would have something to say about this if you were able to at least statistically represent the mean and standard deviation for projected returns on a particular choice. The example I saw when first reading about this talked about choosing between various instruments like stocks, bonds, notes, ... what have you. I couldn't see why it similarly couldn't be applied to trading strategies. Well, I suppose I could; you'd have to be able to calculate risk with some tolerance. I would expect it to be computationally intensive unless you limit the amount of items you carry simultaneously. There very well might be some badass portfolios where you only hold a handful of a ton of shares--despite brokerage fees--but your computer will still be thinking about it when the sun comes up.
This approach is correct in theory but the big problem is that you don't have the true mean, vol, and correlations, you only have estimates from your sample. Then when you optimize, you end up optimizing on the errors more than the true properties. There are strategies used by quant funds to correct for this, google bayesian shrinkage or the Black-Litterman model. I discussed this in another thread, maybe with more details, but the bottom line is I don't think it is worth the effort to follow these methods precisely. The basic idea is you use the information from your optimization but consider it suspect and end up with something between the optimized weights and neutral weights. The other big issue - you have to decide if you assume the inidividual strategies are stationary or if you think you can time them. The basic approach you mentioned assumes they are slowly time varying, so you are timing them in the sense that you assume recent history is your best estimate of the next-period characteristics. The other approaches that come to mind: (1) you assume they are really stationary and use all the data you can (an expanding estimation window instead of the rolling window) or (2) try to time them by building a model that generates predicted means,vols, and correlations based on some variables that capture the market state or strategy specific stuff. I think unless you strategies are easy to time, you are probably best off equal weighting and spending your time on something else.
Would you rather spend time optimizing individual asset+strategy w.r.t sharpe ratio, or you would spend time constructing a better portfolio, w.r.t to sharpe ratio?
Whichever I thought was more achievable. Of course it is the portfolio performance you care most about. But with all the uncertainty around your inputs you can do a lot of work for little or no gain. Whether optimizing the individual strategies much is worthwhile I don't have a strong opinion on. Depends on the strategy and your personal views on the tradeoff between overfitting and leaving low hanging fruit on the table. Early on, probably the most bang for the buck would be adding another strategy. Most of the benefit comes from adding strategies with less than perfect correlation to the existing portfolio, not from calculating the optimal weight on every strategy to several decimal places.
Any practical way of constructing a good portfolio striking a good balance of "optimality" and "practicality"? Any pointers? I just don't know a realistic (non-simplistic) portfolio is constructed... Thanks!