# Source code for qf_lib.common.utils.miscellaneous.kelly

```
# Copyright 2016-present CERN – European Organization for Nuclear Research
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
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from qf_lib.containers.series.qf_series import QFSeries
from qf_lib.containers.series.simple_returns_series import SimpleReturnsSeries
[docs]def kelly(qf_series: QFSeries) -> float:
"""
Calculates the value of the Kelly Criterion (the fraction of money that should be invested) for the series
of returns/prices.
Kelly Criterion assumptions:
1. You trade the same way you traded in the past.
2. Each return corresponds to one trade.
3. Returns are normally distributed (calculated value will be close to the ideal kelly value even for highly skewed
returns. Test showed that the difference of up to 10% (relative) might occur for extremely skewed distributions.
Parameters
----------
qf_series: QFSeries
timeseries of returns/prices. Each return/price must correspond to one trade.
Returns
-------
float
fraction of money that should be invested
"""
# it is important to convert a series to simple returns and not log returns
returns_tms = qf_series.to_simple_returns() # type: SimpleReturnsSeries
mean = returns_tms.mean()
variance = returns_tms.var()
kelly_criterion_value = mean / variance
return kelly_criterion_value
[docs]def kelly_binary(win_probability: float, win_size: float, lose_size: float) -> float:
"""
Calculates the value of the Kelly Criterion (the fraction of money that should be invested) for a bet
that has two possible outcomes.
NOTE: This method should not be used to estimate the kelly value for a timeseries.
Parameters
----------
win_probability:float
probability of winning. Assumes that probability of losing is 1 - win_probability.
win_size: float
gain if we win.
For example: 0.7 means that we get additional 70% of what we bet. (if we bet 10$ and we win we now have 17$)
new_value = old_value * (1 + win_size)
lose_size: float
lose if we lose. This value should be negative.
For example: -0.2 means that we lose 20% of what we bet. (if we bet 10$ and we lose we now have 8$)
new_value = old_value * (1 + lose_size)
Returns
-------
float
fraction of money that should be invested
"""
kelly_value = (-win_size * win_probability + lose_size * win_probability - lose_size) / (win_size * lose_size)
return kelly_value
```