def asymmetric_round_price_to_penny(price, prefer_round_down,
diff=(0.0095 - .005)):
"""
Asymmetric rounding function for adjusting prices to two places in a way
that "improves" the price. For limit prices, this means preferring to
round down on buys and preferring to round up on sells. For stop prices,
it means the reverse.
If prefer_round_down == True:
When .05 below to .95 above a penny, use that penny.
If prefer_round_down == False:
When .95 below to .05 above a penny, use that penny.
In math-speak:
If prefer_round_down: [<X-1>.0095, X.0195) -> round to X.01.
If not prefer_round_down: (<X-1>.0005, X.0105] -> round to X.01.
"""
# Subtracting an epsilon from diff to enforce the open-ness of the upper
# bound on buys and the lower bound on sells. Using the actual system
# epsilon doesn't quite get there, so use a slightly less epsilon-ey value.
epsilon = float_info.epsilon * 10
diff = diff - epsilon
# relies on rounding half away from zero, unlike numpy's bankers' rounding
rounded = round(price - (diff if prefer_round_down else -diff), 2)
if zp_math.tolerant_equals(rounded, 0.0):
return 0.0
return rounded
def information_ratio(algo_volatility, algorithm_return, benchmark_return):
"""
http://en.wikipedia.org/wiki/Information_ratio
Args:
algorithm_returns (np.array-like):
All returns during algorithm lifetime.
benchmark_returns (np.array-like):
All benchmark returns during algo lifetime.
Returns:
float. Information ratio.
"""
if zp_math.tolerant_equals(algo_volatility, 0):
return np.nan
# The square of the annualization factor is in the volatility,
# because the volatility is also annualized,
# i.e. the sqrt(annual factor) is in the volatility's numerator.
# So to have the the correct annualization factor for the
# Sharpe value's numerator, which should be the sqrt(annual factor).
# The square of the sqrt of the annual factor, i.e. the annual factor
# itself, is needed in the numerator to factor out the division by
# its square root.
return (algorithm_return - benchmark_return) / algo_volatility
def sharpe_ratio(algorithm_volatility, algorithm_return, treasury_return):
"""
http://en.wikipedia.org/wiki/Sharpe_ratio
Args:
algorithm_volatility (float): Algorithm volatility.
algorithm_return (float): Algorithm return percentage.
treasury_return (float): Treasury return percentage.
Returns:
float. The Sharpe ratio.
"""
if zp_math.tolerant_equals(algorithm_volatility, 0):
return np.nan
return (algorithm_return - treasury_return) / algorithm_volatility
def sharpe_ratio(algorithm_volatility, algorithm_return, treasury_return):
"""
http://en.wikipedia.org/wiki/Sharpe_ratio
Args:
algorithm_volatility (float): Algorithm volatility.
algorithm_return (float): Algorithm return percentage.
treasury_return (float): Treasury return percentage.
Returns:
float. The Sharpe ratio.
"""
if zp_math.tolerant_equals(algorithm_volatility, 0):
return np.nan
return (algorithm_return - treasury_return) / algorithm_volatility
def sortino_ratio(algorithm_period_return, treasury_period_return, mar):
"""
http://en.wikipedia.org/wiki/Sortino_ratio
Args:
algorithm_returns (np.array-like):
Returns from algorithm lifetime.
algorithm_period_return (float):
Algorithm return percentage from latest period.
mar (float): Minimum acceptable return.
Returns:
float. The Sortino ratio.
"""
if zp_math.tolerant_equals(mar, 0):
return 0.0
return (algorithm_period_return - treasury_period_return) / mar
def sortino_ratio(algorithm_period_return, treasury_period_return, mar):
"""
http://en.wikipedia.org/wiki/Sortino_ratio
Args:
algorithm_returns (np.array-like):
Returns from algorithm lifetime.
algorithm_period_return (float):
Algorithm return percentage from latest period.
mar (float): Minimum acceptable return.
Returns:
float. The Sortino ratio.
"""
if zp_math.tolerant_equals(mar, 0):
return 0.0
return (algorithm_period_return - treasury_period_return) / mar
def information_ratio(algorithm_returns, benchmark_returns):
"""
http://en.wikipedia.org/wiki/Information_ratio
Args:
algorithm_returns (np.array-like):
All returns during algorithm lifetime.
benchmark_returns (np.array-like):
All benchmark returns during algo lifetime.
Returns:
float. Information ratio.
"""
relative_returns = algorithm_returns - benchmark_returns
relative_deviation = relative_returns.std(ddof=1)
if zp_math.tolerant_equals(relative_deviation, 0) or \
np.isnan(relative_deviation):
return 0.0
return np.mean(relative_returns) / relative_deviation
def information_ratio(algorithm_returns, benchmark_returns):
"""
http://en.wikipedia.org/wiki/Information_ratio
Args:
algorithm_returns (np.array-like):
All returns during algorithm lifetime.
benchmark_returns (np.array-like):
All benchmark returns during algo lifetime.
Returns:
float. Information ratio.
"""
relative_returns = algorithm_returns - benchmark_returns
relative_deviation = relative_returns.std(ddof=1)
if zp_math.tolerant_equals(relative_deviation, 0) or \
np.isnan(relative_deviation):
return 0.0
return np.mean(relative_returns) / relative_deviation
