Your intuition is good. If you are trading completely uncorrelated markets with uncorrelated signals, then one still gets a diversification benefit which bumps the portfolio Sharpe. In real life, the markets are correlated and your signals are correlated. This can help or hurt the portfolio depending upon whether you consider this in your trading. R is a column vector of returns w is a column vector of your portfolio weighting (w>=0) (sum w = 1) V = covariance matrix. R0 is Risk-free rate = 0% these days Sharpe_port = Expected excess return / expected volatility = R * w -R0/ sqrt( w * V * w) If no correlation, then V is diagonal. If all N markets have equal volatility v, and an equal weighting Sharpe_port = R/N / sqrt( v * v * 1/N) = Sharpe_each /sqrt(N) If all of your systems on all of your markets perform equally, then the portfolio Sharpe is 1/sqrt(Number of traded market system pairs) Adding one degree of realism, your system-market pairs are not expected to perform identically so one needs to weight intelligently. If almost all of your money is in one stock, then the portfolio is really just the one stock, and the Sharpe Ratio will follow accordingly. Adding another degree of realism, your system-market pairs are not uncorrelated. This is especially true when major adverse affect occur. If you want to buy stocks that all fit the same mold, then bad news affects several trades so w * V * w is closer to N*N*v*v/N/N = v*v so you expect the average return with no diversification benefit. One can keep at this, and do some really sophisticated money-management/portfolio allocation math to look at your current positions and your current opportunities to find your smartest moves. For example, if you already have a long Euro trade, and have a signal for a short Swiss Franc trade, should you resize your Euro trade? Good traders know how their markets are related, and take this kind of thing into account. Objectively doing this has a bad name. Real-life rebalancing costs are substantial, and too often these models are unrealistic. I have my own way of doing this. One easy way to get some diversification benefit without going huge on analysis is to use pair-trading/spread trading. If you want to bet on the general market, then one can just bet an index. If you have an opinion on a particular stock or future, then find a correlated/cointegrated reference point. For example, maybe you like a particular gold mining stock relative to an index of gold mining stocks. If you are right, then buying one and selling the other should net a positive return, but if balanced, a low volatility. This makes for a good Sharpe Ratio. By making a portfolio of pair-trades, one can lower volatility through diversification. (How correlated is a gold stock vs a gold index trade when compared with an Internet stock vs a technology index?) By minimizing the volatility, one can trade larger for the same risk, and make more money off of the same trading opportunities.
What are your thoughts on the following formula for âallocationsâ? Capital to be employed for instrument ABC = (average capital available daily for the strategy across all instruments / average # of Nasdaq 100 strategy positions expected to be outstanding on any given day) X (ATR of instrument ABC / average ATR of Nasdaq 100 instruments) Advantages, as I see them, are: Exposure will be greatest to the instruments that move the most Easy to calculate, and to code into the strategy Disdavantages: Iâm sure there will be many, and that I am about to be told what they are â¦
To the various thread contributors, thanks for your helpful and insightful suggestions! As a result of the above, I've determined that the NASDAQ 100 stocks less 24 of them (Biotech, 10; Healthcare, 8; Media, 4; and Transportation, 2) would have performed better than trading the strategy over all 100 of the NASDAQ 100. But if I decide to trade just the 76 "good" stocks (rather than the full 100) aren't I just "curve fitting"? Or does the fact that I would be taking out whole sectors (*) (rather than individual companies) redeem me - at least to some extent - from this cardinal sin? _________ (*) The sector assignments are my own; I decided on the categories Industrial, Technology, Retail, Telecomms, Biotech, Healthcare, Transportation, Media, and Services (see "History" under http://en.wikipedia.org/wiki/NASDAQ-100); and then made my own assignment judgement for each company, only allowing it to reside in one category (i.e. not in multiple categories). Not a perfect method, and also subjective ...
Curve fitting, IMHO. Especially since the sector assignments are your own. One of the "gurus", Zweig I'm thinking but I can't find it in a quick google search, excludes the real estate sector. Ridiculous, I say. The only "sector" to exclude might be ADR's since foreign companies might be operating under different financial regulations. OTOH, you might convince me that you're right if in backtesting the performance improves significantly *and* in blind forward testing for 1-2 years the performance difference persists.
Good question...I'm not sure about that. Can you elaborate how to apply this idea? I think it is more of selection bias issue. Most people do not realize that the performance of stock indices in the long term is chosen purposly to be positive by constantly eliminating worse performers and inluding best ones.
Stoxtrader and intradaybill, many thanks. So it would be "curve fitting". Fair enough ... No, the improvement in backtest performance is not earth-shattering ...
Selection bias is the same as censored/truncated data. Search for Heckman algorithm, Heckman solution, Heckman selection model, Heckman two-step procedure, Heckman correction. One implementation is in the R package sampleSelection. http://cran.r-project.org/web/packages/sampleSelection/vignettes/selection.pdf