No strategy will do better than buy-and-hold, according to the believers in the efficient market hypothesis. You can see this in the papers of Eugene Fama. Here I present a strategy which beats buy-and-hold. It has theoretical value, I'm not using it in real life and I don't intend to use it.
Can you explain more what do you mean with this? I don't know anything about the second order of taylor expansion. And I have serious doubts that it can make any profits (joking )
well...I followed sambians threads for a while and although there was alot of hating, I think he mentioned something important every trader should understand. his strategy is not riskless, not even in the long run, because markets are not random. the strategy is pretty useless, when traded alone, however it can make you a pretty descent profit, if you use it in basket trading. basically, it is nothing else then a bet on chop, while a trend will kill the portfolio (the more chop you have, the more then you can rebalance, the more profit. when the market is going in one direction, without the whipsaws, you will be in trouble) however, if you look at leveraged ETF´s or short ETF´s, their risk profiles are just the opposite: they are killed by chop and profit from monotone directional movements. so if you trade sambias "strategy" via a basket of the 30 DOW stocks and hedge with a long UltraShort ETF - position, you might have some good riskarb in place. even if the "strategy" outperforms buy and hold, why not just buy the portfolio and rebalance and sell an index etf against it. when something is always better, then the other thing, you have a perfect pairs trade in place.
Actually, I don't recommend my strategy for any kind trading, except for people who believe that markets are efficient and that prices follow a random walk. I don't think there are many of those people in this forum, so you can look at my system just as a theoretical argument against the random walks. The idea which you describe (combining my strategy with a leveraged ETF) will not perform very good. The profits from my strategy are miniscule. If a price is choppy, just sell options and profit from the time decay.
you are right in saying, that your strategy won´t show a brilliant performance, not even in combination with leveraged ETF´s I just wanted to point out, that the concept behind your strategy is very usefull when you use it in a basket trading approach. basically I know a CTA who uses this exact idea to manage FX - accounts. there is more behind his strategy, but your asumptions are the basis. the funny thing is, that your strategy provides a framework, just like BSM - model for options. you cannot make profits, by trading according to BSM option valuation, as well as you cannot make profits trading your strategy. However, and here most should perk their ears, when you have something, that only works under perfect random walk conditions...perhaps you can use it as a tool for finding nonrandom behaviour
I also replied in another thread: The problem here is your random walk model. I think you are mixing continuous processes with discreet ones. In your model, each step of the random walk is 1. If each step is that big, everyone will make money. You flip a fair coin that has two discreet events and you get paid more than you lose, even though it is random whether the outcome of each flipping is head or tail. You have positive expectancy. But if you really want to talk about random price movement, you must use much smaller steps, like one pip (0.0001) instead of 1. In this case, price goes up or down by 0.0001 instead of 1. You will find that the price will cause you more losses than you have appetite for. In other words, it is much much much harder for a random walk whose steps are of size 0.0001 to reach your winning price target than a walk with step size of 1 (10000 times larger). In your original article, it is unrealistic to use 1 for the movement of EUR/USD. Let's make an analogy in the spirit of your original article. You start at 0, and set your profit target at 1 and stop loss at -0.5. If each step of the move of EURUSD is of magnitude 1 and each step for USDEUR is 0.5 (let's not even talk about the problem with linking 2 variables here), then it is very easy to make money. But if you make the random walk of step size 0.0001, then you will realize the probability of loss is far greater. Let me simplify this even more. Consider an asset X priced at 0, and you set profit target at 1 and stop loss at 0.5. Now consider the following 2 situations: (A) X is uniformly and randomly distributed between -a and a, a>=1. With each passing unit of time, you are give a value of X between -a and a. You have positive expectancy. (B) X moves randomly up or down by an infinitesimal step and makes one move with each passing unit of time from its previous location. In this case, the probability of X hitting your stop loss in any period of time overwhelms the probability of X hitting your profit target in the same period of time. Bypassing the numerous tiny little steps X needs to make is your critical flaw. Reality is represented by (B), and your model is represented by (A). It is simple to verify the above by either mathematical proof, but I think it is best if you could convince yourself by running a Monte Carlo. Regards, M&L
Of course if the efficient market hypothesis was true then it would have been perfectly rational to buy internet stocks in 2000 when the Nasdaq was above 4000. After all, everybody else was, and the aggregate market can't be wrong according to the efficient market hypothesis. I don't think there is a single successful trader alive who believes in the efficient market hypothesis, since his whole career proves otherwise.