import numpy as np from numpy.fft import fft, ifft import scipy.signal as sig class Security: """ This can be a list of stocks, bonds, or otherinvestment vehicles. price - Pandas DataFrame with datetime as index sorted to chronical order """ def __init__(self, sym, price, volume=None, rfr: float = 0.01, sf: float = 252.0): """ Parameters ---------- price : TYPE pandas.DataFrame DESCRIPTION. historical adj. daily close prices of stocks under consideration volume : TYPE pandas.DataFrame DESCRIPTION. daily trading volume. The default is none. rfr : TYPE float, optional DESCRIPTION. annualized risk free rate. The default is 0.01. sf : TYPE sample frequency, optional DESCRIPTION. The default is 252 (daily). there are 252 trading days in a year. Monthly sampling frequency would be 12. And weekly sampling frequenc is 52. """ self._symbol = sym self._price = price self._volume = volume # self._symbol = price.columns.values self._rfr = rfr self._sf = sf @property def symbol(self): return self._symbol @symbol.setter def symbol(self, value): raise AttributeError('security symbol is read only') @property def price(self): return self._price @price.setter def price(self, value): raise AttributeError('security price is read only') @property def volume(self): if self._volume is None: raise ValueError('trading volume information not available') return self._volume @volume.setter def volume(self, value): raise AttributeError('security volume is read only') def sma(self, window): return self.price.rolling(window).mean() def vwma(self, window): """ Volume weighted moving average. When plotted against sma, it gives an early indicator when VWMA crosses SMA. When VWMA is above SMA, it indicates a strong upward trend and vice versa. """ price_vol = self.price * self.volume return price_vol.rolling(window).sum() / self.volume.rolling(window).sum() def vosma(self, window): return self.volume.rolling(window).mean() def ema(self, window): # default to 14 day window # EMA pre-process the first point price = self.price temp = price.iloc[0:window].mean() price.iloc[window-1] = temp price.iloc[0:(window-1)] = np.nan # process the EMA avg = price.ewm(span=window, adjust=False).mean() return avg def voema(self, window): # default to 14 day window # EMA pre-process the first point vol = self.volume temp = vol.iloc[0:window].mean() vol.iloc[window-1] = temp vol.iloc[0:(window-1)] = np.nan # process the EMA avg = vol.ewm(span=window, adjust=False).mean() return avg def rsi(self, window = 14): """ Traditional interpretation and usage of the RSI are that values of 70 or above indicate that a security is becoming overbought or overvalued and may be primed for a trend reversal or corrective pullback in price. An RSI reading of 30 or below indicates an oversold or undervalued condition. """ # use exponential averaging d_chg = self.price.diff() d_up, d_dn = d_chg.copy(), d_chg.copy() d_up[d_up < 0] = 0 d_dn[d_dn > 0] = 0 # EMA pre-process the first point temp = d_up.iloc[1:(window+1)].mean() d_up.iloc[window] = temp d_up.iloc[1:window] = np.nan temp = d_dn.iloc[1:(window+1)].mean() d_dn.iloc[window] = temp d_dn.iloc[1:window] = np.nan # process the EMA avg_up = d_up.ewm(span=window, adjust=False).mean() avg_dn = d_dn.ewm(span=window, adjust=False).mean() rs = avg_up / abs(avg_dn.values) exp_rsi = 100 - 100 / (1+rs) return exp_rsi def volume_rsi(self, window = 14): """ The volume RSI (Relative Strength Index) is quite similar to the price based RSI with difference that up-volume and down-volume are used in the RSI formula instead changes in price. If price RSI shows relation between up-moves and down-moves within an analyzed period of time by revealing which moves are stronger, the volume RSI indicator shows the relation between volume traded during these price up-moves and down-moves respectfully by revealing whether up-volume (bullish money flow) or down-volume (bearish money flow) is stronger. The same as price RSI, volume RSI oscillates around 50% center-line in the range from 0 to 100%. In technical analysis this indicator could be used in the same way as well. The simplest way of using the volume RSI would be to generate trading signals on the crossovers of the indicator and 50% center-line around which it oscillates. Here you have to remember following: volume RSI reading above 50% are considered bullish as bullish volume dominates over bearish volume; volume RSI readings below 50% are considered bearish as bearish volume overcomes bullish volume. Respectfully, technical analysis would suggest to generate buy/sell signals by following rules: Buy when indicators moves above 50% line after being below it; Sell when indicator drops below 50% line after being above it. """ # use exponential averaging volume = self.volume up_vol, dn_vol = volume.copy(), volume.copy() d_chg = self.price.diff() up_vol[d_chg < 0] = 0 dn_vol[d_chg > 0] = 0 up_vol.iloc[0] = np.nan dn_vol.iloc[0] = np.nan # EMA pre-process the first point temp = up_vol.iloc[1:(window+1)].mean() up_vol.iloc[window] = temp up_vol.iloc[1:window] = np.nan temp = dn_vol.iloc[1:(window+1)].mean() dn_vol.iloc[window] = temp dn_vol.iloc[1:window] = np.nan # EMA processing avg_up = up_vol.ewm(span=window, adjust=False).mean() avg_dn = dn_vol.ewm(span=window, adjust=False).mean() rs = avg_up / avg_dn.values exp_rsi = 100 - 100 / (1+rs) return exp_rsi def daily_returns(self): return self.price.pct_change() @property def annualized_return(self): dr = self.daily_returns() return self._sf * dr.mean() @property def annualized_stdev(self): dr = self.daily_returns() return np.sqrt(self._sf) * dr.std() @property def sharpe(self): return (self.annualized_return - self._rfr) / self.annualize_stdev def rolling_stdev(self, window): return self.price.rolling(window).std() def bollinger(self, window): """ Parameters ---------- window : TYPE int, optional DESCRIPTION - averaging window in days. Returns ------- lower, upper : TYPE pandas.DataFrame DESCRIPTION - lower band (minus 2 sigma) and the upper band. """ avg = self.sma(window) sdd2 = self.rolling_stdev(window).mul(2) lower = avg.sub(sdd2.values) upper = avg.add(sdd2.values) # low_up = lower.join(upper, lsuffix='_L', rsuffix='_U') return lower, upper def macd(self, short_wd = 12, long_wd = 26, sig_wd = 9): """ MACD Line: (12-day EMA - 26-day EMA) Signal Line: 9-day EMA of MACD Line MACD Histogram: MACD Line - Signal Line MACD is calculated by subtracting the 26-period EMA from the 12-period EMA. MACD triggers technical signals when it crosses above (to buy) or below (to sell) its signal line. The speed of crossovers is also taken as a signal of a market is overbought or oversold. MACD helps investors understand whether the bullish or bearish movement in the price is strengthening or weakening MACD historgram represents signal line crossovers that are the most common MACD signals. The signal line is a 9-day EMA of the MACD line. As a moving average of the indicator, it trails the MACD and makes it easier to spot MACD turns. A bullish crossover occurs when the MACD turns up and crosses above the signal line. A bearish crossover occurs when the MACD turns down and crosses below the signal line. Crossovers can last a few days or a few weeks, depending on the strength of the move. """ macd_short = self.ema(short_wd) macd_long = self.ema(long_wd) macd_line = macd_short - macd_long.values macd_sig = macd_line.ewm(span=sig_wd, adjust=False).mean() macd_hist = macd_line - macd_sig.values norm_hist = macd_hist.div(macd_long.values) return macd_line, macd_sig, macd_hist, norm_hist def get_crossing(stocks): """ Parameters ---------- stocks : TYPE instance of class 'security' Returns ------- cross : TYPE pandas DataFrame DESCRIPTION - +1 when 50 day moving average is above 200 day moving average. -1 when vice versa. transition days are of value +3 and -3 respectively. """ sma50 = stocks.sma(50) sma200 = stocks.sma(200) cross = np.sign(sma50.sub(sma200.values)) cross_diff = cross.diff() cross = cross.add(cross_diff.values) cross.columns = stocks.price.columns return cross def get_sma_slope(stocks, wd = 50): """ Parameters ---------- stocks : TYPE DESCRIPTION. wd : TYPE, optional DESCRIPTION. The default is 50. Returns ------- slope : TYPE pandas DataFrame DESCRIPTION - +1 when n day moving average is positive. -1 when negative. transition days are of value +3 and -3 respectively. """ sma = stocks.sma(wd) slope = np.sign(sma.diff()) slope_diff = slope.diff() slope = slope.add(slope_diff.values) return slope def fill_missing_data(df): df.ffill(inplace=True) df.bfilln(inplace=True) def fft_convolve(signal, window): fft_signal = fft(signal) fft_window = fft(window) return ifft(fft_signal * fft_window) def zero_pad(array, n): """Extends an array with zeros. array: numpy array n: length of result returns: new NumPy array """ res = np.zeros(n) res[: len(array)] = array return res def smooth(price, hsize=10, sigma=3): """ Parameters ---------- price : TYPE DataFrame. DESCRIPTION - with time index and no invalid values hsize : TYPE integer DESCRIPTION - this adds phase delay. similar to SMA window sigma : TYPE float DESCRIPTION - gaussian standard deviation affects smoothness Returns ------- TYPE DataFrame DESCRIPTION - smoothed price Doesn't offer much benefit over sma. Only theoretical values. For future different smooth functiona experiments """ data = price.copy() window = sig.gaussian(M=hsize, std=sigma) window /= window.sum() padded = zero_pad(window, data.shape[0]) for col in data.columns: ys = data[col].values smoo = abs(fft_convolve(ys, padded)) smoo[0:hsize-1] = np.nan data[col] = smoo return data