1. Start at eur/usd =1 and we have $1000 (or 1000 euro), we buy 500 euros and 500 dollars. 2. eur/usd = 0.5, we have 1500 euro. profit of 500 euro! or if 2. eur/usd = 2.0, we have $1500. profit of $500! a truly riskless system!
Who said my formulas are newly created? I just used the simple formula for logarithmic returns, which is, in fact, in all the schoolbooks. But now you're contradicting your own assumptions by offering me a game that violates your own random walk definitions. Remember that the B&S paper says "...distribution of stock prices at the end of any finite interval is log-normal". If you want to play a game, let's design it in a consistent manner, with two outcomes, where I either double my money or halve it. Essentially, you're refuting my point by engaging in the same exact inconsistency that is your problem in the first place.
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 logarithms of our payoffs are equal. For some strange reason you decline it, while you still claim that expected values should be calculated using logarithms, not prices. But I'm ready to accept your proposal. Let's design a game in a consistent manner, with two outcomes, where I either double my money or halve it. Let's say that in the first flip I give you $10 and if a coin comes up heads, you give me $20, while if it comes up tails you give me $5. What is the expected value of my bet in dollars? It's 0.5*5+0.5*20 = 12.5. This is the expected value as everybody knows it. But you came up with the brilliant idea to calculate expected value of logarithms, not of dollars. Let's see where your logic can lead us: I bet $10, ln(10)=2.302585093 I have 0.5 probability to get ln(5)=1.609437912 and 0.5 probability to get ln(20)=2.995732274 0.5*ln(5)+0.5*ln(20)=2.302585093 So far so good. In this game the expected values of the natural logarithms of the outcomes will equal the natural logarithms of my bets. According to you, this means that I can not beat you at this game, except through luck. In the long run my expected value is 0, following your logic. But I still want to try this game. Actually I want to play it for as many coin flips as possible. I'm telling you in advance that I will bet half of my bankroll on each coin flip. Are you prepared to play this game with me?
Hi Sambian, So you started with $500 and â¬500 1-If â¬/$ = 1 then your portfolio is worth $1000 or â¬1000 2-If â¬/$ = 0.5 your portfolio is always $500 + â¬500 But is worth $500+$250=$750 or â¬1000+â¬500=â¬1500 Now âWe buy euros with half of our dollars, and keep the other half,â That means : portfolio= $250+â¬1000 ($250 is now â¬500) (its worth keeps being â¬1500 or $750) 3- if â¬/$ = 0.25 (4⬠equal $1) Portfolio is $250+â¬1000 Itâs now worth $250+ $(1000/4)=$250+$250=$500 Or â¬(250*4)+â¬1000=â¬1000+â¬1000=â¬2000 ⦠May I miss something obvious and I would be sorry for that but whatâs new ? Masteratwork
sambian, we shall play the game, let's first make sure we have an explicit understanding... Firstly, can you make sure you understand the notion of "logarithmic return"? Just like arithmetic return, t's a quantity that's expressed in percentage terms... Secondly, can you confirm that, in order for your strategy to work, you require eur/usd to be a random walk as defined in the B&S paper?
Our portfolio is worth $750, we buy euros with $375, not with $250. This means that we buy â¬750 and our portfolio consists of $375 and â¬750. Our portfolio is $375+â¬750. It is now worth $375+750/4=$375+$187.5=$562.5 Or 375*4+â¬750=â¬1500+â¬750=â¬2250
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.
I agree your datas If you want, but I still don't get your point. You got a portfolio that was worth $1000 ans is now $562.5. Where on earth did you make some profits ? I'm really sorry but don't get it. I hope that it's more subtle than "I make profit in euros, but a loss in $". So please, what'is your point ? Masteratwork
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 ask "Where on earth did you make some profits". I have written very clearly in the title and many times in the article that the system is profitable in the long run, if the price follows a random walk. It is also useful if markets are efficient and you can not predict future prices. If you can predict when eur/usd will be 0.25, of course the best is to bet all your money on it.