Hey Kettle! Yes, I can't do it, so it can't be done. BTW, I agree with you, I'm definitely a smarty as you have stated. So you should definitely listen to me. It's like your post, it looks good on paper, but in reality it's just a lot of meaningless writing mixed with a heavy dose of sarcasm, and bad hearing. You should probably get a hearing aid.
...so all back to the lovely topic of "hedging". If you want to be a trend follower and value investor you maximize your risk adjusted returns by running one strategy that buys after a bottom is confirmed and after the strategy confirmed an uptrend. I fail to see how you could top this with two strategies one which buys lows, another that rides trends. Most of the time (about 70% to be pretty accurate) your trend strategy would produce losses while at other times you would not suffer performance if the market is trending up not down, clearly a combination that can mathematically not beat one strategy that applies filters and is long-only, trading after bottoms were made and a new uptrend ensued. (or run those two strategies but apply filters to each, it has exactly the same effect as combining the two with both sets of filters applied to the combined strategy). Same applies to your example of being long and short gamma. If you do not want to take exposure to gamma then you hedge it out (there are stable hedges), but you then take a clear exposure in something else otherwise you would not trade options in the first place. This is entirely different from running a strategy with negative expected returns and hoping that it may add value to risk adjusted returns (which it cannot over time). P.S.: From my many years of experience in running systematic strategies mid-to high frequency: I recommend focusing on filters and not strategy hedges. Correlations are NEVER stable, the benefits from "hedging" come and go. But if you run a collection of positive expectation strategies then the natural diversification effect kicks in with different asset classes and strategy approaches anyway. The key difference here is that filters prevent each individual strategy from taking positions in environments that are ill suited for such particular strategy. Thats the very important difference between filters and hedges. Just my 2 cents. With that bit of wisdom I am out of this thread. I made my points clear if some are still convinced that losing strategies add value then so be it, maybe such person cannot be helped...
So you would rather take volatility and massive P&L swings over something even-keeled and consistent? I was not suggesting that a losing strategy have money put behind it - only that a consistent strategy is much more superior to a random, irrational strategy that could make or break you on any given day. If a trader came up with a really good idea that was very consistent - but in the end it lost $500-$1000/day we kept them around and tried to encourage them to tweak or change. If they were consistent and lost massive amounts of money we simply changed nothing and automated the opposite side of the trade they had developed. Most often to their benefit as long as consistency was on their side.
I guess we both agree actually on the topic at hand. Obviously low-vol strategies are favored over high-vol ones at same return profiles. That's where risk-adjusted metrics come in handy. If you re-read my comment then you will notice that I said something else than what you paraphrased: I said I prefer a high-vol strategy with positive expectancy over a low-vol strategy with negative expectancy.
I was not advocating running strategies with no filters. I was simply saying that negative correlation adds value, and that there are some types of negative correlation which are stable due to their inherent properties (e.g. long gamma strategies and short gamma strategies). If the portfolio value-added (the smoothing effect) from that negative correlation is high enough, then it can improve the portfolio risk/return characteristics despite its individual negative total return.
But it's the portfolio return and risk that matters, not the individual components. For example, it is possible to improve both the returns and lower the risk of many stock/bond portfolios by adding a bit of gold, an asset with no intrinsic real return. How can that be? Because its stock/bond correlation is very low.
and again, I ONLY agree under very special circumstances. (a) if negative correlations are stable, and (b) if the risk reduction benefit outweighs the negative contribution to returns (meaning, if the risk benefit outweighs the fact that the negative return strategy makes less in times when the rest of the book loses more and that the negative return strategy loses when the rest of the book gains. You need to always look at things from a relative value standpoint: Your competitor for the negative return strategy could be (a) cash, (b) more exposure in the remaining strategies. Statistical fact, however, still remains that if you rank all strategies already in a risk adjusted return fashion then picking a sub-optimal strategy only does damage. You are getting hung up on the idea that you may reduce draw downs with negatively correlating strategies, but I am saying that you must apply the same risk-adjusted return metric to the total strategy book as you apply to each individual strategy. If you care about draw downs as your definition of risk then build a new metric and apply it to each strategy, re-rank them and again allocate capital to each with favorable risk-return profiles. Yes, portfolio diversification effects are to be had by spreading allocations across strategies, BUT you never get a better risk-adjusted return profile by including a strategy that has a negative risk-adjusted return profile. Its just statistically impossible, even if the strategy correlates with a coefficient of -1.
I don't really understand how this goes on for 17 pages... w*r1 + (1-w)*r2 < r1 if (r2 < r1) and w is between (0,1) where as (w,1-w)'C (w,1-w) might be less than C(1,1). So you can't have a higher expected return, but a better risk adjusted return. amazingIndustry has amazingPatience.
I wonder myself ;-) Even risk adjusted returns are only better under very special circumstances, not necessarily. Most would understand this rather simple concept if they started with the Portfolio Standard Deviation (PSD) formula. PSD is not always lower the more assets you add. The number of assets, pairwise correlations, weights, all play a significant role. Its just shocking to witness that those with the most outrageous claims blatantly ignore simple math and probability theory ....but enough said...