Yes, you are basically optimizing on sampling errors. Sjfan is right about Black-Litterman. Here are other suggestions: 1) Google Bayesian shrinkage and geek out. Fully define your beliefs and assumed uncertainties and solve away. 2) Skip the theory and take a shortcut. Get weights from your optimization. Make your actual portfolio weights w=(a)*optimized weight + (1-a)*(1/n). n is number of strategies. a is up to you. Cap the weight at something reasonable. This gets you most of what you would get with a more formal method with a lot less work. 3) Make conditional forecasts for your strategies instead of using most recent historical data. IOW, a model that says something like strat 1 will return 4% next month based on current market conditions. Use these as optimization inputs. 4) Forget all this and use 1/n as the weights. Spend your time adding more strategies to the list. Higher n and suboptimal weights is better than low n and optimal weights. Why do I feel like I responded to this already?
I like this one! I am not current on the more complicated methods, but I think the uncertainties in my strategies are almost certainly too high for such methods to provide much value anyways.
Good advice all of them. What to do depends on how much work you want to put into this. Regarding sampling errors you may try to use a longer sampling interval to improve the "signal-to-noise" ratio. Or use VWAP prices, depending on what you're trading. This could remove some of the noise. For optimization to work it is required that the algorithm can identify your edge in the noisy returns information. Otherwise the results from your optimization will be based on noisy data and therefore be very uncertain.
You neglect transaction cost. In an efficient, cost free market, this may make sense but as soon as transaction cost is introduced, the problem has some very sharp local optimum values and small perturbations around them are highly non-optimal. Think fo them as almost impulses. I have to admit I used in the past the 1/n approach because of inability to solve the non-linear optimization problem in a way that made sense but such ad-hoc solution is terrible. Then I used a simpler optimization approach based on LP. That worked well.
Yes, you should always consider how transaction costs affect the overall result. But, the total impact will depend on your rebalancing interval. Also, depending on the type of strategies involved, the average holding time for a position may affect how you implement the rebalancing.
I don't understand why this is a problem. Why should a system that switches between 10 strats and periodically rebalances system 1 back to 10% of trading capital all the time have higher costs that one that rebalances to 13.78% one time and 4.62% another time? Am I missing something? We are also talking about component strategies in the abstract, but with some systems it is not an issue at all. If the 10 systems are day trading and are in cash at the end of the day rebalancing is costless. Or you can implement the re-balancing over time by re-allocating capital as the trades close according to the component system rules. Obviously if the systems buy and hold illiquid assets it would be a different story. Also I am curious how you measure how well this works. How do you define "terrible" and "doing well"?
Yes, you are missing something because you did not read my reply carefully, it is a common thing around here, I mean impulsive responses. I replied to the following comment: I say that higher n and sub-optimal weights neglects the impact of transaction cost. That is all. You have to take it into account. As n becomes very large, any assumed convergence to a local optimum due to 1/n becomeing small is cancelled by increasing transaction cost.
only if the various n's trade the same products at the same times... otherwise, n can scale well without additional cost modeling. i don't think bd meant that as a far reaching robust solution... more as a general principle. which, of course, he was correct in asserting... while i'm sure, inferring a bit of common sense.
In that case 1/n does not do the job. His idea was to increase n for the same targets so that as n becomes large, 1/n tends to a small number and the objective function manifold in a way "flattens out". Besides, in the case of stocks and other assets or securities what you suggect increases unsystemic risk. In finance, and especially in portfolio management, you cannot have your cake and eat it too because of transaction cost. There is a trade-off between frequency of rebalancing and tracking error. Theoretically, you can track an index with zero error by rebalancing frequently but in practice it will cost you a good chunk of your performance because of commissions. This is the well-known problem of transaction cost in finance.
bill, In that case 1/n does not do the job. His idea was to increase n for the same targets so that as n becomes large, 1/n tends to a small number and the objective function manifold in a way "flattens out". Besides, in the case of stocks and other assets or securities what you suggect increases unsystemic risk. i understand what he was trying to do, you missed my point, i'll explain it more below. also, increase of unsystemic risk has nothing to do with specific asset classes in and of themselves. unless you know the makeup of my n's, your assumption is based on conjecture, not fact. In finance, and especially in portfolio management, you cannot have your cake and eat it too because of transaction cost. There is a trade-off between frequency of rebalancing and tracking error. Theoretically, you can track an index with zero error by rebalancing frequently but in practice it will cost you a good chunk of your performance because of commissions. This is the well-known problem of transaction cost in finance. i see what you're saying, but you're making assumptions about strategy trade frequency. if you're balancing a portfolio of static positions, what you're saying makes sense, but the discussion is about risk models and allocation for a portfolio of _strategies_ in the abstract, of which nothing is known a priori. if i have a portfolio of hft strategies, rebalancing is trivial as positions are dynamic and turnover at the strategy level occurs with high enough frequency that transaction costs need not be extrapolated outside of the strategy level. in this scenario 1/n can be dynamically adjusted at will with no overhead at the portfolio level and serves it's purpose well.