Trading fees and 1:1 risk/reward targets

Trading fees and 1:1 risk/reward targets

When trading the markets, whether it be forex, cryptocurrencies or traditional, the risk/reward ratio is used to compare the expected returns of an investment/trade with the amount of risk undertaken to capture these returns.

After entering a trade, one strategy for managing risk is to scale out half the position when the risk/reward ratio reaches 1:1. An advantage of this strategy is that the trade effectively becomes risk-free ie. the profits taken at 1:1 are equal to the potential loss if the remaining position hits the stop order.

Trading fees are often calculated as a percentage commission on each order. For larger positions, these can significantly reduce the returns. A trade that scales out half the position at 1:1 and is subsequently stopped out can result in a net loss if fees have not been considered.

To prevent this, the 1:1 target should account for fees as shown.

The 1:1 risk/reward target

When fees are either zero or not considered, the 1:1 target is the difference between the entry price and stop price, in the trade direction eg. given an entry price of $100 and a stop price of $90, the 1:1 target is $110.

For a long position, this is written as:

target price = entry price + (entry price - stop price)

And for a short position:

target price = entry price - (stop price - entry price)

This can be simplified for both long and short positions to:

target price = (entry price x 2) - stop price

Fees

For trades using a 50% scale out at 1:1, the following fees apply:

  • fees for the whole position at the entry price
  • fees for half the position at the target price
  • fees for half the position at the stop price (if the position is stopped out)

This is calculated as follows:

fees = (entry price x amount x commission rate) + (target price x amount/2 x commission rate) + (stop price x amount/2 x commission rate)

For a 50% scale out at 1:1 to cover fees, the additional price movement required is the total fees divided by half the position size. ie. fees / (amount / 2), or 2 x fees / amount

The 1:1 “risk including fees”/reward target

The 1:1 “risk including fees”/reward target can then be defined as follows:

  • target price = (entry price x 2) - stop price + (2 x fees / amount) for a long position, and
  • target price = (entry price x 2) - stop price - (2 x fees / amount) for a short position

Since the target price depends on the fees, and the fees depend on the target price, how can the 1:1 target be determined?

This is possible using linear algebra and simultaneous equations.

Given:

  • entry price e
  • stop price s
  • amount a
  • commission rate c (assuming the same rate for all orders)

fees f and target price t for a long position is defined as:

(1) f = eac + tac/2 + sac/2

(2) t = 2e - s + 2f/a

Substituting for t in (1) and solving for f:

f = eac + (2e - s + 2f/a)ac/2 + sac/2

f = eac + eac - sac/2 + fc + sac/2

f = 2eac + fc

f - fc = 2eac

f(1 - c) = 2eac

f = 2eac/(1 - c)

Substituting for f in (2) and solving for t:

t = 2e - s + 2(2eac/(1 - c))/a

t = 2e - s + 4ec/(1 - c)

Gives the fee-adjusted 1:1 target price for a long position:

target price = (2 x entry price) - stop price + (4 x entry price x commissionRate) / (1 - commissionRate)

Similarly, for a short position, fees f and target price t are defined as:

(1) f = eac + tac/2 + sac/2

(2) t = 2e - s - 2f/a

Substituting for t in (1) and solving for f:

f = eac + (2e - s - 2f/a)ac/2 + sac/2

f = eac + eac - sac/2 - fc + sac/2

f = 2eac - fc

f + fc = 2eac

f(1 + c) = 2eac

f = 2eac/(1 + c)

Substituting for f in (2) and solving for t:

t = 2e - s - 2(2eac/(1 + c))/a

t = 2e - s - 4ec/(1 + c)

Gives the fee-adjusted 1:1 target price for a short position:

target price = (2 x entry price) - stop price - (4 x entry price x commissionRate) / (1 + commissionRate)

Note on slippage

The above calculations do not factor in potential slippage on the stop order. At the time profit is taken at 1:1, it is not possible to know the price at which the stop order will be executed.

To account for this, the stop price in the calculations can be substituted with an estimated stop price including slippage as required.