Hi I am strangling to understand where is the mistake with the following strategy. Can anyone help me with the following argument?
Assuming a stock price follows geometric Brownian motion then the expected value, under the physical measure, is $S\exp(μt)$. If the forward price is $S\exp(rt)$ then if I always long the forward I will be profitable in the long run ( i understand there is a risk envolve and that this difference it can be explain by the market price of risk. I also understand that if the price of the forward is $S\exp(μt)$ there will be arbitrage by borrowing money buying the stock and selling it at the forward price.) But still under those assumptions if the price of forward is $S\exp(rt)$ by entering long I will be profitable in the long run.
Can anyone point out where my mistake is?