finds.recipes.finance
Financial functions
Copyright 2022, Terence Lim
MIT License
- finds.recipes.finance.bond_price(coupon: float, n: int, m: int, yields: float | List[float], par: float = 1, **kwargs) float[source]
Compute present value of bond given spot rates or yield-to-maturity
- Parameters:
coupon – Annual coupon rate
n – Number of remaining coupons
m – Number of compounding periods per year
yields – Simple annual yield-to-maturity or spot rates each period
par – face or par value of bond
- Returns:
Present value of bond
- finds.recipes.finance.bootstrap_risk(X: Series, alpha: float, n: int) DataFrame[source]
Returned bootstrapped risk statistics
- Parameters:
X – Series of observed returns
alpha – VaR level (e.g. 0.95)
n – Number of bootstrap samples
- Returns:
DataFrame of n bootstrapped samples of risk statistics
- finds.recipes.finance.bootstrap_spot(coupon: float, spots: List[float], m: int, price: float = 1) float[source]
Compute spot rate to maturity of par bond from yield and sequence of spots
- Parameters:
coupon – Annual coupon rate
spots – Simple annual spot rates each period (excl last period before maturity
m – Number of compounding periods per year
price – Present value of bond
- Returns:
Simple spot interest rate till maturity
- finds.recipes.finance.efficient_portfolio(mu: ndarray, sigma: ndarray, target: float)[source]
Returns weights of minimum variance portfolio that exceeds target return
- Parameters:
sigma – covariance matrix
mu – vector of expected excess (of the risk-free) returns
target – required minimum expected return of portfolio
- Returns:
Dict of weights, volatility and mean of efficient portfolio that achieves target
- finds.recipes.finance.forwards_from_spots(spots: List[float], m: int, skip: int = 0) List[float][source]
Compute forward rates given spot rates
- Parameters:
spots – Sequence of simple annual spot rates
m – Number of compounding periods per year
skip – Number of initial periods skipped
- Returns:
List of forward rates, excluding first period of spot rates input
- finds.recipes.finance.gmv_portfolio(sigma: ndarray, mu: ndarray | None = None)[source]
Returns position weights of global minimum variance portfolio
- Parameters:
sigma – covariance matrix
mu – vector of expected excess (of the risk-free) returns
- Returns:
Dict of weights, volatility and mean (if mu provided) of the GMV
- finds.recipes.finance.halflife(alpha)[source]
Returns halflife from alpha = -ln(2)/ln(lambda), where lambda=1-alpha
- finds.recipes.finance.historical_risk(X: Series, alpha: float)[source]
Calculate historical VaR, ES, and sample moments
- Parameters:
X – Series of observed returns
alpha – Var level (e.g. 0.95)
- finds.recipes.finance.hl_vol(high: DataFrame, low: DataFrame, last: DataFrame = None) DataFrame[source]
Compute Parkinson volatility from high and low prices
- Parameters:
high – DataFrame of high prices (observations x stocks)
low – DataFrame of low prices (observations x stocks)
last – DataFrame of last prices, for forward filling if high low missing
Returns – Estimated volatility
- finds.recipes.finance.kupiec(X: Series, VaR: Series, alpha: float) Dict[source]
Kupiec proportion of failures likelihood ratio test of VaR
- Parameters:
X – Series of observed returns
VaR – Series of predicted VaR
alpha – VaR level (e.g. 0.95)
- Returns:
Dict of likelihood statistic and pvalue
- finds.recipes.finance.kupiec_LR(alpha: float, s: int, n: int)[source]
Compute Kupiec likelihood ratio given s violations in n trials
- Parameters:
s – number of violations
n – number of observations
alpha – VaR level (e.g. 0.95)
- finds.recipes.finance.macaulay_duration(coupon: float, n: int, m: int, price: float, yields: float | List[float], par: float = 1, **kwargs) float[source]
Compute macaulay duration of a bond given spot rates or yield-to-maturity
- Parameters:
coupon – Annual coupon rate
n – Number of remaining coupons
m – Number of compounding periods per year
price – current market price of bond
yields – Simple annual yield-to-maturity or spot rates each period
par – face or par value of bond
- Returns:
Macaulay duration
- finds.recipes.finance.maximum_drawdown(x: Series, is_price_level: bool = False) Series[source]
Compute max drawdown (max loss from previous high) period and returns
- Parameters:
x – Returns or price level series
is_price_level – Whether input are price index levels, or returns
- Returns:
Series with start and end levels, keyed by dates, of maximum drawdown
Notes
MDD = (Trough - Peak) / Peak
- finds.recipes.finance.modified_convexity(coupon: float, n: int, m: int, price: float, yields: float | List[float], par: float = 1, **kwargs) float[source]
Compute mocified convexity of a bond given spot rates or yield-to-maturity
- Parameters:
coupon – Annual coupon rate
n – Number of remaining coupons
m – Number of compounding periods per year
price – current market price of bond
yields – Simple annual yield-to-maturity or spot rates each period
par – face or par value of bond
- Returns:
Modified convexity
- finds.recipes.finance.modified_duration(coupon: float, n: int, m: int, price: float, yields: float | List[float], par: float = 1, **kwargs) float[source]
Compute modified duration of a bond given spot rates or yield-to-maturity
- Parameters:
coupon – Annual coupon rate
n – Number of remaining coupons
m – Number of compounding periods per year
price – current market price of bond
yields – Simple annual yield-to-maturity or spot rates each period
par – face or par value of bond
- Returns:
Modified duration
- finds.recipes.finance.ohlc_vol(first: DataFrame, high: DataFrame, low: DataFrame, last: DataFrame, ffill: bool = False, zero_mean: bool = True) DataFrame[source]
Compute Garman-Klass or Rogers-Satchell (non zero mean) OHLC vol
- Parameters:
first – DataFrame of open prices (observations x stocks)
high – DataFrame of high prices (observations x stocks)
low – DataFrame of low prices (observations x stocks)
last – DataFrame of close prices (observations x stocks)
- Returns:
Estimated volatility
- finds.recipes.finance.parametric_risk(sigma: float | Series, alpha: float) Dict[source]
Calculate parametric gaussian VaR and ES
- Parameters:
sigma – predicted volatility, or a Series
alpha – Var level (e.g. 0.95)
- finds.recipes.finance.tangency_portfolio(mu: ndarray, sigma: ndarray)[source]
Returns weights of tangency portfolio with largest slope (sharpe ratio)
- Parameters:
sigma – covariance matrix
mu – vector of expected excess (of the risk-free) returns
- Returns:
Dict of weights, volatility and mean of the tangency portfolio