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Ok, if you can make a random walk as you understand it on Excel and send it to me, I can show you that my system will be profitable, if your random walk is really random. I'm worried that your examples include prices of 0 and negative prices, which is impossible in the real world. I'm...

There are no errors. If you have some amount of dollars = x and want to buy euros with half of it, how much euros can you buy? It's either (x/2)/eurusd or (x/2)*usdeur. For example: You have $4. eurusd = 2, usdeur = 0.5. How much euros can you buy with 4/2 = $2? Obviously the answer is 1...

MathAndLogic, here I have given examples with real prices, not with random walk models.

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...

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 :) )

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.

I will surely write what it has to do with options, but I need more time, which I don't have these days. Here is something briefly: Are you acquainted with the Cox-Ross-Rubinstein option pricing model? Those guys claim to calculate "probability" of up movement and down movement, but in their...

Ok, if your mother tongue is English and you say that I can't use "bet" in this sense, I agree with you :) This game exactly represents the payoffs of a person who buys something in a random walk world and waits until the price either rises 100% or decreases 50%. If you play that game all day...

The link to the calculations from my first posting can not be downloaded anymore due to restrictions from rapidshare. This is why I uploaded the file here: http://docs.google.com/fileview?id=0B3b6-3_7QGPuODZmZmI2ZjYtZWViZi00ZDMyLWFhYjQtNzBmNjc3NDhhNDFk&hl=en Please, before doing more...

Let's go ahead with the movements. The next 2 movements are up. We have $562.5, we buy euros with half of them = €1125 and keep the other half = $281.25 4. eur/usd = 0.5 Our portfolio is $281.25 and €1125. It is worth 281.25+1125/2=281.25+2500=$843.75 We buy euros with half of them =...

My portfolio is now $562.5, but if I just bought and held euros, it would be $250. And the idea of the system is that it's profitable in both currencies in the long run, when there are up and down movements. You take an example of only two movements, both of them are down movements, and then you...

I understand this notion. The returns in our game in percentage terms are +100% of my bet when I win and -50% of my bet when I lose. Yes.

Our portfolio is worth $750, we buy euros with $375, not with $250. This means that we buy €750 and our portfolio consists of $375 and €750. Our portfolio is $375+€750. It is now worth $375+750/4=$375+$187.5=$562.5 Or 375*4+€750=€1500+€750=€2250

You use logarithms to calculate expected value. I have never seen somebody using logarithms for calculating expected value of trades. And when I trade I don't expect to get logarithms, but dollars or euros. I was not contradicting my assumptions, I was just offering you a game where the...

You are starting to get it :)

I'm also more into real life trading value, I just don't post my real life systems online :) MathAndLogic posted the other thread in this forum, so I decided that here is the proper place to post this thread, so that people can follow the discussion. And actually this thread has a lot to do...

What do you think, would I post it online if it had big real life value? :) It has theorethical value, which you can not appreciate, and this is fine by me, I'm used to it. As I already said, I use prices which are available to me. If you have better database, I will appreaciate it if you send...

If you understand the probabilities of up and down movements, you will understand the reason for the "time decay". It is because those ETFs seek to replicate daily returns in proportions which are not in their favor (i.e. not the Kelly bet :) ). If you just short S&P, you will get -1...

Here should be written "the coin comes up heads" :) Another remark - the sequence of heads and tails doesn't matter, the end result is always the same. This is a property of the Kelly bet.

I'm just showing that the idea works when tested with real prices. This is how it's done. If you need examples of other people who didn't take into account comissions and slippage, but their work was appreciated, look at Black, Scholes, Merton etc. :) The moment in which the trades are done is...