druce

[
    {
	"quote": "When I use a word, it means just what I choose it to mean-neither more nor less.", 
	"author": "Humpty Dumpty"
    },
    {
	"quote": "You know the world is going crazy when the best rapper is a white guy, the best golfer is a black guy, the tallest guy in the NBA is Chinese, the Swiss hold the America's Cup, France is accusing the U.S. of arrogance, Germany doesn't want to go to war, and the three most powerful men in America are named 'Bush', 'Dick', and 'Colon.'", 
	"author": "Chris Rock"
    },
    {

druce

# number of stocks
n = 1000 
# random historical mean returns for each stock
mu = np.random.normal(0.1, 0.2, n)

# number of factors
m = 10

# factor covariance matrix - random symmetrical matrix
SigmaFactor = np.random.randn(m, m)/4

druce

vol_limit = cp.Parameter(nonneg=True)

prob = cp.Problem(cp.Maximize(ret), 
                  [cp.norm1(w) <= 1.5,  # 1-norm <= 1.5, i.e. gross exposure < 150%
                   cp.sum(w) == 1,
                   vol <= vol_limit]
                 )

# define function so we can solve many in parallel
def solve_vl(vl_val):

druce

vol_limit = cp.Parameter(nonneg=True)

prob = cp.Problem(cp.Maximize(ret),
                  [cp.sum(w) == 1, 
                   w >= 0,
                   vol <= vol_limit   # new constraint: vol <= vol_limit parameter
                  ]
                 )

# define helper function 

druce

# Solve max return portfolio (corner solution)
prob = cp.Problem(cp.Maximize(ret),  # maximize return
                  [cp.sum(w) == 1, 
                   w >= 0]
                 )
prob.solve()
wts = [float('%0.4f' % v) for v in w.value]
maxretvol = vol.value

druce

import cvxpy as cp

# compute covariance matrix (df being the dataframe of historical returns)
Sigma = np.cov(df.transpose())
# number of assets
n = Sigma.shape[0]
# average returns
mu = df.mean().values
# asset SDs
asset_vols = np.sqrt(Sigma.diagonal())

druce

import pandas_datareader as pdr
# load gold data from FRED API & save copy locally to CSV file
series = ['GOLDAMGBD228NLBM']
gold_download = pdr.data.DataReader(series, 
                                    'fred', 
                                    start='1968-12-31')
# convert daily to annual
gold_download = gold_download.resample('A').last().reset_index()
gold_download.set_index(pd.DatetimeIndex(gold_download['DATE']).year, inplace=True)
gold_download['return'] = gold_download['GOLDAMGBD228NLBM'].pct_change()

druce

data_xls = 'http://www.stern.nyu.edu/~adamodar/pc/datasets/histretSP.xls'
data_sheet = "Returns by year"
# these will change as rows get added on Damodaran website
skiprows = range(17)
skipfooter = 10
download_df = pd.read_excel('http://www.stern.nyu.edu/~adamodar/pc/datasets/histretSP.xls', 
                         sheet_name=data_sheet, 
                         skiprows=skiprows,
                         skipfooter=skipfooter)
download_df = download_df.set_index('Year')

druce

Return vol $$ \sigma_{1} $$	Return vol $$ \sigma_{2} $$	Return correlation $$ \rho_{12} $$	Portfolio volatility
$3	$4	1.0	$$ \sqrt{3^2 + 4^2 + 2 \cdot 3 \cdot 4 \cdot 1} = 3 + 4 = $7 $$
$3	$4	-1.0	$$ \sqrt{3^2 + 4^2 + 2 \cdot 3 \cdot 4 \cdot (-1)} = 4 - 3 = $1 $$
$3	$4	0.5	$$ \sqrt{3^2 + 4^2 + 2 \cdot 3 \cdot 4 \cdot 0.5} = \sqrt{37} = $6.08 $$
$3	$4	-0.5	$$ \sqrt{3^2 + 4^2 + 2 \cdot 3 \cdot 4 \

druce

ML Algo	Search algo	CV Error (RMSE in $)	Time mm::ss
Linear Regression	--	18192	0:01
ElasticNet	ElasticNetCV (Grid Search)	17964	0:02
ElasticNet	GridSearchCV	17964	0:05