Hello,Naive question, kindly help.I have a set of 200 stock names, I would like to create a weighted portfolioof stock names that would give me highest sharpe ratio. I would like this analysisto be based on the returns of the stocks for the past 3 months or 6months.I would like to add a few more constraints, but I am new to this whole are ofportfolio construction. any ideas/materials really appreciated.Regards

1. Estimate growth rates and vols for each stock, and then the correlations of stock returns.2. Calculate growth rate and standard deviation for an arbitrary portfolio (arbitrary weights for each stock, but adding up to one). The formulae are simple (linear in growth rates and weights for the portfolio growth and the obvious expression for the standard deviation of the portfolio, sameexpression as appears in basic VaR. Some assumptions in here about the distribution of returns.3. Optimize over the weights to get the highest Sharpe ratio = (pfolio growth - risk free) / s.d. pfolio.4. In your optimizer add any constraints.Problems:1. Stability of correlations. They won't be stable!2. Optimization time with 200 stocks.Mike Staunton's book (of course!) has plenty on this topic.P

There is a discussion in the Bouchaud's book (the chapter on random matrices) as to why what you're trying to do (200 stocks, data over 6 months or less) basically makes no statistical sense.

Historical price/return data is next to useless for portfolio/strategy selection because of sample error. Portfolios/strategies with a very broad range of historical performances are statistically indistinguishable.Consider the following eye-opener: Imagine you have a Sharpe ratio 2.0 money-machine strategy or portfolio which generates returns according tod Equity = Equity * ( mu dt + sig dZ) with mu = 16 % per annum and sig = 8% per annum. Note that mu and sig are static -- there is none of the time variation that might come a changing world, other investors jumping into a previously profitable strategy, etc.If I generate 100 different 10y histories for this process (i.e. 100 realizations of 2500 steps with timestep = 1/250) I get a distribution of realized Sharpe ratios ranging from 1.24 to 3.0 (standard deviation among the 100 Sharpes is .33) and maximum drawdowns ranging from 6% to 21%!In fact, my experience is that best-fit strategies/portfolios almost always trade worse out-of-sample (i.e. in the future!) than do strategies/portfolios defined by parameters that are chosen with robustness in mind...Hope this helps.

drona, Alex is perfectly correct...but I would recommend you to try his experiment for yourself. P

btw, don't show this thread to fund-of-fund managers who claim a quantitative basis for their allocations. they might not appreciate it...

Hello,Thank you I will try what you have suggested. Regards

So what you're saying, Alex, is that if a local fund of funds allocates money between several different investment managers, with different styles, strategies, and philosophies, that1) there is no reason anybody should be given any more money than anybody else, and2) every new guy who shows up with some stupid beta complex or other, he should get an even cut.Or are they just pretending to have a "quantitative basis" for the same reason they call a strategy "arbitrage" - meaning purely as a sales tool?Some managers would argue that you're just being fooled by randomness no matter how you pick hedge funds, that they'll all lose money in the long run.MP

<FONT face="Times New Roman">To 1 and 2: No, what I'm saying is that it is usually the case that only crude properties of historical price action and/or strategy performance are likely to persist. If you don't have a simple and convincing reason why a strategy should have worked well in the past then it probably won't work well in the future and your simulated historical results are probably just an exercise in curve-fitting. I believe that allocators should spend their time understanding 1) what inefficiency gives a given manager "edge", 2) do their managers seem to be smart and reliable individuals with a sound infrastructure, 3) which component funds/strategies are <I>logically</I> distinct and therefore likely <I>a priori</I> to generate uncorrelated returns and 4) are they likely to <I>become</I> (anti)correlated in the extreme events most allocators fear? For example, most relative value strategies can be expected to lose money in market dislocations even if they're trading totally different risks simply because the "contagion" phenomenon can link markets and risks that are usually largely independent of one another (this is an unproved assertion, obviously). At any rate, these are all qualitiative rather than quantitative issues...As for your other points/questions: If by "quantitative basis" you mean a claim that, say, a 22% allocation to a given manager can reliably be expected to generate better results than a 25% allocation then, yes, I think that's ridiculous and likely to be a sales tool or just plain misguided. But I do think that a quantitative framework in terms of correlations, Sharpes, etc. gives an allocator a useful framework in which to organize his thoughts and make rational (if imprecise) allocations.... I don't think the author in question expects <I>everyone</I> to lose money in the long run (if he does, it's certainly not in his fund's prospectus!)-Alex</FONT><FONT face="Times New Roman" size=2></FONT>

<I>yikes!</I>

Let me underscore Alex's point from the opposite perspective.3 months of stock returns means about 65 data points. 200 stocks means 199 free parameters. That gives you 134 free parameters after you've made your Sharpe ratio infinite by setting standard deviation to zero. Six months of data still leaves you with 69 free parameters. Nine months and you're down to 4 free parameters and with a year of data you will have to live with a finite Sharpe Ratio. But even with 10 years of data, you will get the standard deviation very near zero.I know you plan to add other constraints, presumably enough to make the Sharpe ratio finite. But this is still a numerically flawed approach.