[PYTHON] Try to model the cumulative return of rollovers in futures trading

Modeling futures trading

It is basically a continuation of last time and previous.

Today, the standard "[[] in Futures Trading Fri](http://www.comtex.co.jp/www/?module=Default&action=meigara&page=sheet1&article=T-kin) ”actually builds continuous returns from rollovers, helping to predict and model It is a story to use for.

Rollover is simply a shift from a contract with an imminent deadline for futures trading to a contract that is soon or long ahead. That is. In order to model the continuous transition of the transaction balance, various conditions of the market and the transaction must be taken into consideration, but here we will consider a simple model that transitions linearly.

Brand selection

Refer to Gold Futures Rollover Dates 2013 and select an appropriate stock. At the time of writing, it is 3/13, so let's aim at GCJ14 and GCM14, which will soon reach the contract expiration date (Last Trade).

Random walk

[Random Walk](http://ja.wikipedia.org/wiki/%E3%83%A9%E3%83%B3%E3%83%80%E3%83%A0%E3%83%BB%E3% Simulate futures contracts with 82% A6% E3% 82% A9% E3% 83% BC% E3% 82% AF% E7% 90% 86% E8% AB% 96).

def random_walk(px, n, f):
    np.random.seed(34567)
    N = 200
    _walk = (np.random.randint(0, 200, size=N) - 100) * 0.25
    perturb = (np.random.randint(0, 20, size=N) - 10) * 0.25
    walk = _walk.cumsum()
    rng = pd.date_range(px.index[0], periods=len(px) + N, freq='B')
    near = np.concatenate([px.values, px.values[-1] + walk])
    far = np.concatenate([px.values, px.values[-1] + walk + perturb])
    prices = pd.DataFrame({n: near, f: far}, index=rng)
    return prices

You now have a random walk function. Let's pass Yahoo! Finance data to this.

#SPY investment trust base price S&Used as an approximate price for the P 500 index
px = web.get_data_yahoo('SPY')['Adj Close'] * 10
#Specify the brand and contract expiration date
expiries = {
    'GCJ14': datetime(2014,4,28),
    'GCM14': datetime(2014,6,26)
}
expiry = pd.Series(expiries).order()

print( px.tail(5) )
# => 
# Date
# 2014-03-06    1881.8
# 2014-03-07    1882.6
# 2014-03-10    1881.6
# 2014-03-11    1872.3
# 2014-03-12    1872.8

print( expiry )
# =>
# GCJ14   2014-04-28
# GCM14   2014-06-26

prices = random_walk(px, 'GCJ14', 'GCM14')
print( prices.tail(5) )
# =>
#               GCJ14    GCM14
# 2014-10-17  1618.80  1621.05
# 2014-10-20  1634.80  1632.55
# 2014-10-21  1622.55  1623.80
# 2014-10-22  1638.55  1639.30
# 2014-10-23  1637.55  1638.30

Weighting

Next, build a model that calculates the weights. The code is the same as the O'Reilly book.

def get_roll_weights(start, expiry, items, roll_periods=5):
    dates = pd.date_range(start, expiry[-1], freq='B')
    weights = pd.DataFrame(np.zeros((len(dates), len(items))),
                        index=dates, columns=items)
    prev_date = weights.index[0]
    for i, (item, ex_date) in enumerate( expiry.iteritems() ):
        if i < len(expiry) - 1:
            weights.ix[prev_date:ex_date - pd.offsets.BDay(), item] = 1
            roll_rng = pd.date_range(end=ex_date - pd.offsets.BDay(),
                                     periods=roll_periods + 1, freq='B')
            decay_weights = np.linspace(0, 1, roll_periods + 1)
            weights.ix[roll_rng, item] = 1 - decay_weights
            weights.ix[roll_rng, expiry.index[i + 1]] = decay_weights
        else:
            weights.ix[prev_date:, item] = 1
        prev_date = ex_date
    return weights

Calculation of continuous returns

Finally, use these functions to find the continuous return index.

weights = get_roll_weights('3/11/2014', expiry, prices.columns)

sample_prices  = prices.ix['2014-04-17' : '2014-04-28']
sample_weights = weights.ix['2014-04-17' : '2014-04-28']
sample = sample_prices * sample_weights

#Build a new data frame
result = pd.DataFrame({'GCJ14': sample['GCJ14'], 'GCM14': sample['GCM14'], 'GOLD': sample['GCJ14'] + sample['GCM14'] })

#Get a return on rolled up futures contracts
print( result )
# =>
#               GCJ14    GCM14     GOLD
# 2014-04-17  1663.30     0.00  1663.30
# 2014-04-18  1687.55     0.00  1687.55
# 2014-04-21  1348.24   337.16  1685.40
# 2014-04-22  1017.78   678.42  1696.20
# 2014-04-23   676.62  1015.53  1692.15
# 2014-04-24   338.01  1351.84  1689.85
# 2014-04-25     0.00  1705.55  1705.55
# 2014-04-28     0.00  1723.05  1723.05

That's about it for analyzing stock portfolios, and from the next time onward, we will apply it to other fields.

reference

Introduction to data analysis with Python-Data processing using NumPy and pandas http://www.oreilly.co.jp/books/9784873116556/