I am trading Forex currencies. The platform I use charges a 0.25% fee for every trade I make.
For this example, let's assume $2USD is worth 1 Euro. Also, the fee only affects USD.
Now say I buy 1 Euro for 2USD. From that trade, I pay the 0.25% fee, making my buy actually worth $1.995USD, meaning I receive 0.9975 Euros from the trade.
Now, drastically, the price changes and the exchange rate is now $3 USD for 1 Euro. I decide to profit take, and my 0.9975 Euros is now worth $2.9925 USD. After I pay the fee ($2.9925 - $2.9925 * 0.0025), and from that trade, I now have $2.99 USD.
What I would like to do is find a formula that will allow me to calculate the minimum percentage of change in the exchange rate needed in order to profit from the trade after the fees. Ideally, I would have a function that would take the buy price (in this case $2) and calculate what percentage of increase I could sell at and still receive a profit after both fees.
If the fee is $x$, after the transaction you have $1-x$ of the amount you invested. When you make the return transaction you also have $1-x$ of the amount you had before the sale. The price has to rise $\frac 1{(1-x)^2}$ for you to break even. If the fee is $0.25\%=0.0025$ you need the price to rise from $1$ to about $1.0050188$ to break even. If the commission is small, the price rise you need is a little greater than two commissions.