 Library "FunctionKellyCriterion"
Kelly criterion methods.
the kelly criterion helps with the decision of how much one should invest in
a asset as long as you know the odds and expected return of said asset.

simplified(win_p, rr)
simplified version of the kelly criterion formula.
Parameters:
win_p: float, probability of winning.
rr: float, reward to risk rate.
Returns: float, optimal fraction to risk.
usage:
simplified(0.55, 1.0)

partial(win_p, loss_p, win_rr, loss_rr)
general form of the kelly criterion formula.
Parameters:
win_p: float, probability of the investment returns a positive outcome.
loss_p: float, probability of the investment returns a negative outcome.
win_rr: float, reward on a positive outcome.
loss_rr: float, reward on a negative outcome.
Returns: float, optimal fraction to risk.
usage:
partial(0.6, 0.4, 0.6, 0.1)

from_returns(returns)
Calculate the fraction to invest from a array of returns.
Parameters:
returns: array<float> trade/asset/strategy returns.
Returns: float, optimal fraction to risk.
usage:
from_returns(array.from(0.1,0.2,0.1,-0.1,-0.05,0.05))

final_f(fraction, max_expected_loss)
Final fraction, eg. if fraction is 0.2 and expected max loss is 10%
then you should size your position as 0.2/0.1=2 (leverage, 200% position size).
Parameters:
fraction: float, aproximate percent fraction invested.
max_expected_loss: float, maximum expected percent on a loss (ex 10% = 0.1).
Returns: float, final fraction to invest.
usage:
final_f(0.2, 0.5)

Holding Period Return function
Parameters:
fraction: float, aproximate percent fraction invested.
trade: float, profit or loss in a trade.
biggest_loss: float, value of the biggest loss on record.
Returns: float, multiplier of effect on equity so that a win of 5% is 1.05 and loss of 5% is 0.95.
usage:
hpr (fraction=0.05, trade=0.1, biggest_loss=-0.2)

twr(returns, rr, eps )
Terminal Wealth Relative, returns a multiplier that can be applied
to the initial capital that leadds to the final balance.
Parameters:
returns: array<float>, list of trade returns.
rr: float , reward to risk rate.
eps: float , minimum resolution to void zero division.
Returns: float, optimal fraction to invest.
usage:
twr (returns=array.from(0.1,-0.2,0.3), rr=0.6)

ghpr(returns, rr, eps )
Geometric mean Holding Period Return, represents the average multiple made on the stake.
Parameters:
returns: array<float>, list of trade returns.
rr: float , reward to risk rate.
eps: float , minimum resolution to void zero division.
Returns: float, multiplier of effect on equity so that a win of 5% is 1.05 and loss of 5% is 0.95.
usage:
ghpr(returns=array.from(0.1,-0.2,0.3), rr=0.6)

run_coin_simulation(fraction, initial_capital, n_series, n_periods)
run multiple coin flipping (binary outcome) simulations.
Parameters:
fraction: float, fraction of capital to bet.
initial_capital: float, capital at the start of simulation.
n_series: int , number of simulation series.
n_periods: int , number of periods in each simulation series.
Returns: matrix<float>(n_series, n_periods), matrix with simulation results per row.
usage:
run_coin_simulation(fraction=0.1)

run_asset_simulation(returns, fraction, initial_capital)
run a simulation over provided returns.
Parameters:
returns: array<float>, trade, asset or strategy percent returns.
fraction: float , fraction of capital to bet.
initial_capital: float , capital at the start of simulation.
Returns: array<float>, array with simulation results.
usage:
run_asset_simulation(returns=array.from(0.1,-0.2,0.-3,0.4), fraction=0.1)

strategy_win_probability()
calculate strategy() current probability of positive outcome in a trade.

strategy_avg_won()
calculate strategy() current average won on a trade with positive outcome.

strategy_avg_loss()
calculate strategy() current average lost on a trade with negative outcome.

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