from typing import Literal, Annotated
import numpy as np
from numpy.typing import NDArray
import numba as nb
[docs]
@nb.njit
def python_estimate_downside_risk(
ts: Annotated[NDArray[np.float64], Literal["1D array"]],
prices: Annotated[NDArray[np.float64], Literal["1D array"]],
target_return: float
) -> float:
"""Estimate the downside risk of an asset based on historical price data.
Downside risk measures the volatility of returns that fall below a target return,
focusing on negative deviations rather than total volatility.
Args:
ts: Array of time values (converted to specified unit)
prices: Array of asset prices corresponding to the time values
target_return: The target return threshold for calculating downside risk
Returns:
float: The estimated downside risk (standard deviation of returns below target)
"""
dlogS = np.log(prices[1:] / prices[:-1])
dt = ts[1:] - ts[:-1]
rms_rarray = dlogS / np.sqrt(dt)
less_return_array = target_return - rms_rarray
less_return_array[less_return_array < 0] = 0.
downside_risk = np.sqrt(np.mean(np.square(less_return_array)))
return downside_risk
[docs]
@nb.njit
def python_estimate_upside_risk(
ts: Annotated[NDArray[np.float64], Literal["1D array"]],
prices: Annotated[NDArray[np.float64], Literal["1D array"]],
target_return: float
) -> float:
"""Estimate the upside risk of an asset based on historical price data.
Upside risk measures the volatility of returns that exceed a target return,
focusing on positive deviations above a minimum acceptable return.
Args:
ts: Array of time values (converted to specified unit)
prices: Array of asset prices corresponding to the time values
target_return: The target return threshold for calculating upside risk
Returns:
float: The estimated upside risk (standard deviation of returns above target)
"""
dlogS = np.log(prices[1:] / prices[:-1])
dt = ts[1:] - ts[:-1]
rms_rarray = dlogS / np.sqrt(dt)
more_return_array = rms_rarray - target_return
more_return_array[more_return_array < 0] = 0.
upside_risk = np.sqrt(np.mean(np.square(more_return_array)))
return upside_risk