python Udacity：交易机器学习

Posted 2021-05-09

[Demystifying reinforcement learning](http://www.nervanasys.com/demystifying-deep-reinforcement-learning/)

[ML Algo in trading](http://francescopochetti.com/part-vii-backtest-portfolio-performance/)

Interview with Tammer Kamel

Build strategy that is:
1) Theoretically sound
2) Empirically testable
3) Simple

What a company is worth?
  INTRINSIC VALUE
    is based on future dividends. In other words, companies pay a certain amount
to their investors every year based on how many shares they own. And this is the
value of all future dividends going into the future.
    Future Value / Discount Rate
    = Total dividends per year / DR

  BOOK VALUE
    is the value of the company is we split it up into pieces and sold those
individual pieces.
    Total assets (ignoring intangible assets) minus liabilities

  MARKET CAPITALIZATON
    is the value the market is placing on the company.
    No shares * price
    

Many stock trading strategies look for deviations between intrinsic value and market cap.

Order: BUY,IBM,100,LIMIT,99.95  # BUY/SELL,stock,no shares,MARKET/LIMIT,price
* LIMIT is the max price you are willing to pay

then in the order book this will appear as (given this is the first order):
BID 99.95 100

SELL order will be reflected as ASK in the order book.

Market capitalization for a stock: # shares outstanding * price

ETFs have 4 or 3 letters
Mutual Funds usually have 5 letters
Hedge Funds don't have abbreviations

AUM - Assets Under Management - is the total amount of money being managed by the fund.

How fund managers are rewarded:
Expense ratio
  is typically a percentage of AUM, therefore higher the AUM value, greater the incentive.
Two & Twenty
  This structure actually motivates both AUM accumulation ("Two") as well as
Profits ("Twenty"). Here "Risk taking" is synonymous with aiming for greater
profits, which is motivated by the Two & Twenty model.


Hedge fund goals:
  - beat a benchmark* (portfolio may go down with the market)
  - absolute return (+ve returns no matter what; long/short positions)
Metrics:
  - cumulative return
  - volatility (std)
  - risk/reward (Sharpe Ratio)
  
*select benchmark that represent the type of your investment. E.g. if you invest
in European stocks, use European stock index as the benchmark, not SPY.

What is porfolio optimization?
  Given a set of assets and a time period, find an allocation of funds to 
assets that miximizes performance.

What is performance?
  We could choose from a number of metrics, including cumulative return,
volatility or risk, and risk adjusted return (Sharpe Ratio).

E.g cumulative return is the most trivial measure to use - simply investing all your money in the stock with maximum return (and none in others) would be your optimal portfolio, in this case. Hence, it is the easiest to solve for. But probably not the best for risk mitigation.


Framing the problem (optimise for Sharpe Ratio):
  minimise f(X) = SR * -1 (we want to maximise the SR)
  where X is the allocation vector eg [.1, .4., .4, .1]
  
  ranges: limits on values
    0 <= X <= 1
  
  constraints: properties of X that must be 'true'
    X.sum() = 1.0

How to use an optimizer:
1) Provide a function to optimize, e.g f(x) = x**2+4
2) Provide an initial guess
3) Call the optimizer
  import scipy.optimize as spo
  min_result = spo.minimize(f, guess, method='SLSQP', options={'disp': True})
  print min_result.x, min_result.fun

Functions with multiple minima, any discontinuities or zero slope can be hard
to minimize.

Parameterized model
e.g. f(x) = mx + b <-- model with two parameters m, b
     now we can use an optimizer to minimise the squared error
     to find the line of best fit for the model given the data

Daily Portfolio Value
Given:
  start_val = 1000000
  start_date = 2009-01-01
  end-date = 2011-12-31
  symbols = ['SPY', 'XOM', 'GOOG', 'GLD']
  allocs = [0.4, 0.4, 0.1, 0.1]
  
Pseude-algo:
  start with prices df
  normed = prices/prices[0]
  alloced = normed*allocs
  pos_vals = alloced*start_val  # position values
  port_val = pos_vals.sum(axis=1)


Portfolio Statistics
daily_rets = daily_rets[1:]  # ignore 0

4 key statistins:
1) cum_ret = (port_val[-1]/port_val[0])-1  # port_val == portfolio value
2) avg_daily_ret = daily_rets.mean()
3) std_daily_ret = daily_rets.std()  # volatility
4) sharpe_ratio


SHARPE RATIO: risk adjusted return
All else being equal:
- lower risk is better
- higher return is better
SR also considers risk free rate of return

Rp - portfolio return
Rf - risk free rate of return (return rate on a savings account in a bank)
sigma_p - std dev of portfolio return

The form of Sharpe Ratio: (Rp - Rf) / sigma_p

The value of a portfolio is directly proportional to the return
it generates over some baseline (here risk-free rate), and inversely
proportional to its volatility.

SR = mean(daily_rets - daily_rf) / std(daily_rets)

Note:
a) mean is the expected value
b) std(daily_rets - daily_rf) == std(daily_rets) since daily_rf is a const
c) daily_rf == risk free rate
   - LIBOR
   - interest rate on 3 month T-bill
   - 0% (value that's commonly been used in the past few years) - good approximation
   
   to convert annual risk free rate into daily rate
   e.g. annual rate 10% or 0.1
   then daily_rf = (1 + 0.1)**(1/252) - 1
   
   
SR can vary widely depending on how frequenty you sample (e.g. you sample prices
every year/month/week/day)
Original version of SR is that it's an annual measure, therefore if we sample
at frequencies other than annual we need to add an adjusment factor
SR_annualized = k * SR
where k = sqrt(no samples per year)
  - daily k sqrt(252)
  - weekly k sqrt(52)
  - monthly k sqrt(12)
  
Finally the SR = sqrt(252) * mean(daily_rets - daily_rf) / std(daily_rets)

WARNING: use daily_rets.std() or np.std(daily_rets, ddof=1)
Pandas uses the unbiased estimator (N-1 in the denominator), whereas Numpy by default does not. See http://stackoverflow.com/questions/24984178/different-std-in-pandas-vs-numpy

"""
kurtosis (quantifies whether the shape of the data distribution matches the Gaussian distribution)
  + fat tails
  - skinny tails
  
Scatterplots
  slope (Beta): how reactive a stock is to the market - higher Beta means
the stock is more reactive to the market

NOTE: slope != correlation
correlation is a measure of how tightly do the individual points fit the line
  
  intercept (alpha): +ve --> the stock on avg is performing a little bit better
than the market

In many cases in financial research we assume the daily returns are normally distributed,
but this can be dangerous because it ignores kurtosis or the probability in the
tails.
"""

# Compute daily returns
daily_returns = compute_daily_returns(df)

# Plot a histogram
daily_returns.hist(bins=20)

# Get mean as standard deviation
mean = daily_returns['SPY'].mean()
std = daily_returns['SPY'].std()

plt.axvline(mean, color='w', linestyle='dashed', linewidth=2)
plt.axvline(std, color='r', linestyle='dashed', linewidth=2)
plt.axvline(-std, color='r', linestyle='dashed', linewidth=2)
plt.show()

# Compute kurtosis
daily_returns.kurtosis()


# Compute and plot two histograms on the same chart
daily_returns['SPY'].hist(bins=20, label='SPY')
daily_returns['XOM'].hist(bins=20, label='XOM')
plt.legend(loc='upper right')
plt.show()


# Scatterplots
daily_returns.plot(kind='scatter', x='SPY', y='XOM')  # SPY vs XOM
beta_XOM, alpha_XOM = np.polyfit(daily_returns['SPY'], daily_returns['XOM'], 1)  # fit poly degree 1
plt.plot(daily_returns['SPY'], beta_XOM*daily_returns['SPY'] + alpha_XOM, '-', color='r')

daily_returns.plot(kind='scatter', x='SPY', y='GLD')  # SPY vs GLD
beta_GLD, alpha_GLD = np.polyfit(daily_returns['SPY'], daily_returns['GLD'], 1)  # fit poly degree 1
plt.plot(daily_returns['SPY'], beta_GLD*daily_returns['SPY'] + alpha_GLD, '-', color='r')

# Calculate correlation coefficient
daily_returns.corr(method='pearson')

"""
Dealing with missing data:
1. Fill forward (to avoid peeking into the future)
2. Fill backward
"""

def fill_missing_values(df_data):
    """Fill missing values in data frame, in place."""
    df_data.fillna(method='ffill', inplace=True)
    df_data.fillna(method='bfill', inplace=True)
    return df_data

"""
Daily returns
daily_ret[t] = (price[t]/price[t-1]) - 1

Cumulative returns
cumret[t] = (price[t]/price[0]) - 1
"""


import os
import pandas as pd
import matplotlib.pyplot as plt

def symbol_to_path(symbol, base_dir="data"):
    """Return CSV file path given ticker symbol."""
    return os.path.join(base_dir, "{}.csv".format(str(symbol)))


def get_data(symbols, dates):
    """Read stock data (adjusted close) for given symbols from CSV files."""
    df = pd.DataFrame(index=dates)
    if 'SPY' not in symbols:  # add SPY for reference, if absent
        symbols.insert(0, 'SPY')

    for symbol in symbols:
        df_temp = pd.read_csv(symbol_to_path(symbol), index_col='Date',
                parse_dates=True, usecols=['Date', 'Adj Close'], na_values=['nan'])
        df_temp = df_temp.rename(columns={'Adj Close': symbol})
        df = df.join(df_temp)
        if symbol == 'SPY':  # drop dates SPY did not trade
            df = df.dropna(subset=["SPY"])

    return df


def plot_data(df, title="Stock prices", xlabel="Date", ylabel="Price"):
    """Plot stock prices with a custom title and meaningful axis labels."""
    ax = df.plot(title=title, fontsize=12)
    ax.set_xlabel(xlabel)
    ax.set_ylabel(ylabel)
    plt.show()


def compute_daily_returns(df):
    """Compute and return the daily return values."""
    daily_returns = df.pct_change()
    # Daily return values for the first date cannot be calculated. Set these to zero.
    daily_returns.ix[0, :] = 0
    
    # Alternative method
    # daily_returns = (df / df.shift(1)) - 1
    # daily_returns.ix[0, :] = 0
    return daily_returns


def test_run():
    # Read data
    dates = pd.date_range('2012-07-01', '2012-07-31')  # one month only
    symbols = ['SPY','XOM']
    df = get_data(symbols, dates)
    plot_data(df)

    # Compute daily returns
    daily_returns = compute_daily_returns(df)
    plot_data(daily_returns, title="Daily returns", ylabel="Daily returns")


if __name__ == "__main__":
    test_run()

"""Bollinger Bands."""

import os
import pandas as pd
import matplotlib.pyplot as plt

def symbol_to_path(symbol, base_dir="data"):
    """Return CSV file path given ticker symbol."""
    return os.path.join(base_dir, "{}.csv".format(str(symbol)))


def get_data(symbols, dates):
    """Read stock data (adjusted close) for given symbols from CSV files."""
    df = pd.DataFrame(index=dates)
    if 'SPY' not in symbols:  # add SPY for reference, if absent
        symbols.insert(0, 'SPY')

    for symbol in symbols:
        df_temp = pd.read_csv(symbol_to_path(symbol), index_col='Date',
                parse_dates=True, usecols=['Date', 'Adj Close'], na_values=['nan'])
        df_temp = df_temp.rename(columns={'Adj Close': symbol})
        df = df.join(df_temp)
        if symbol == 'SPY':  # drop dates SPY did not trade
            df = df.dropna(subset=["SPY"])

    return df


def plot_data(df, title="Stock prices"):
    """Plot stock prices with a custom title and meaningful axis labels."""
    ax = df.plot(title=title, fontsize=12)
    ax.set_xlabel("Date")
    ax.set_ylabel("Price")
    plt.show()


def get_rolling_mean(values, window):
    """Return rolling mean of given values, using specified window size."""
    return pd.rolling_mean(values, window=window)


def get_rolling_std(values, window):
    """Return rolling standard deviation of given values, using specified window size."""
    return pd.rolling_std(values, window=window)


def get_bollinger_bands(rm, rstd):
    """Return upper and lower Bollinger Bands."""
    upper_band = rm + 2*rstd
    lower_band = rm - 2*rstd
    return upper_band, lower_band


def test_run():
    # Read data
    dates = pd.date_range('2012-01-01', '2012-12-31')
    symbols = ['SPY']
    df = get_data(symbols, dates)

    # Compute Bollinger Bands
    # 1. Compute rolling mean
    rm_SPY = get_rolling_mean(df['SPY'], window=20)

    # 2. Compute rolling standard deviation
    rstd_SPY = get_rolling_std(df['SPY'], window=20)

    # 3. Compute upper and lower bands
    upper_band, lower_band = get_bollinger_bands(rm_SPY, rstd_SPY)
    
    # Plot raw SPY values, rolling mean and Bollinger Bands
    ax = df['SPY'].plot(title="Bollinger Bands", label='SPY')
    rm_SPY.plot(label='Rolling mean', ax=ax)
    upper_band.plot(label='upper band', ax=ax)
    lower_band.plot(label='lower band', ax=ax)

    # Add axis labels and legend
    ax.set_xlabel("Date")
    ax.set_ylabel("Price")
    ax.legend(loc='upper left')
    plt.show()


if __name__ == "__main__":
    test_run()

# Timing Python operations

import time

t1 = time.time()
print 'Execute your function'
t2 = time.time()
print 'The time taken by print statement is {} seconds'.format(t2-t1)

# Working with multiple stocks

"""
SPY is used for reference - it's the market
Normalize by the first day's price to plot on "equal footing"
"""

import os
import pandas as pd
import matplotlib.pyplot as plt


def symbol_to_path(symbol, base_dir="data"):
    """Return CSV file path given ticker symbol."""
    return os.path.join(base_dir, "{}.csv".format(str(symbol)))


def get_data(symbols, dates):
    """Read stock data (adjusted close) for given symbols from CSV files."""
    df = pd.DataFrame(index=dates)
    if 'SPY' not in symbols:  # add SPY for reference, if absent
        symbols.insert(0, 'SPY')

    for symbol in symbols:
        df_temp = pd.read_csv(symbol_to_path(symbol), index_col='Date',
                parse_dates=True, usecols=['Date', 'Adj Close'], na_values=['nan'])
        df_temp.rename(columns={'Adj Close': symbol}, inplace=True)
        df = df.join(df_temp)
        if symbol == 'SPY':  # drop dates SPY did not trade
            df = df.dropna(subset=["SPY"])

    return df


def normalize_data(df):
  """Normalize stock prices using the first row of the dataframe."""
  return df / df.ix[0, :]


def plot_data(df, title="Stock prices"):
    """Plot stock prices with a custom title and meaningful axis labels."""
    ax = df.plot(title=title, fontsize=12)
    ax.set_xlabel("Date")
    ax.set_ylabel("Price")
    plt.show()
    

def plot_selected(df, columns, start_index, end_index):
    """Plot the desired columns over index values in the given range."""
    df = normalize_data(df)
    plot_data(df.ix[start_index:end_index, columns])


def test_run():
    # Define a date range
    dates = pd.date_range('2010-01-01', '2010-12-31')

    # Choose stock symbols to read
    symbols = ['GOOG', 'IBM', 'GLD']  # SPY will be added in get_data()
    
    # Get stock data
    df = get_data(symbols, dates)

    # Slice and plot
    plot_selected(df, ['SPY', 'IBM'], '2010-03-01', '2010-04-01')


if __name__ == "__main__":
    test_run()