Introduction to Financial Engineering - Project 3

import pandas as pd import numpy as np import matplotlib.pyplot as plt plt.style.use('ggplot') plt.rcParams["figure.figsize"] = (14, 8)

df = pd.read_parquet('algostrata_name.parquet')

train = df.iloc[:int(df.shape[0] / 2), ] test = df.iloc[int(df.shape[0] / 2):, ]

def calc_mean(returns): return (np.prod(1 + returns))**(1/len(returns)) - 1

ann_mean = (1+train.apply(calc_mean))**52-1 std = (train.std())*(52)**(0.5)

sharpe = ann_mean / std sharpe

strat_1_assets = sharpe.nlargest(5).index.tolist() strat_1_assets

train[strat_1_assets].cov()

def test_portfolio(assets, inital_investment=1000000): investment = inital_investment weights = 1 / len(assets) invest_over_time = [] for idx, row in test[assets].iterrows(): investment = (investment * (1 + row) * weights).sum() invest_over_time.append(investment) return pd.DataFrame(invest_over_time, index=test.index) def plot_investment(data, inital_investment=1000000): plt.plot(data) plt.axhline(y=inital_investment, color='b', linestyle='--') plt.legend(['Investment', f'Initial investment = {inital_investment}']) plt.title('Investment over time') plt.show()

plot_investment(test_portfolio(strat_1_assets))

top_200_assets = sharpe.nlargest(200).index.tolist()

from MST import MinimumSpanningTree

subset_df = train[top_200_assets] for i in range(5): subset, subset_df, corr_avg, PDI = MinimumSpanningTree(subset_df) subset_df

subset_df.cov()

strat_2_assets = subset_df.columns.tolist()

plot_investment(test_portfolio(strat_2_assets))

strat_1_mean = sum(test[strat_1_assets].apply(calc_mean) * 1 / len(strat_1_assets)) strat_1_std = sum(test[strat_1_assets].std() * 1 / len(strat_1_assets)) print('Strategy 1') print('Mean: ', strat_1_mean, "|", "std: ", strat_1_std)

strat_2_mean = sum(test[strat_2_assets].apply(calc_mean) * 1 / len(strat_2_assets)) strat_2_std = sum(test[strat_2_assets].std() * 1 / len(strat_2_assets)) print('Strategy 2') print('Mean: ', strat_2_mean, "|", "std: ", strat_2_std)

print('Strategy 1 sharpe ratio: ', strat_1_mean / strat_1_std) print('Strategy 2 sharpe ratio: ', strat_2_mean / strat_2_std)

def max_drawdown(data): local_min_max = np.diff(np.sign(np.diff(data))).nonzero()[0] + 1 peak = data[0] drawdown = 0 # For every min/max point for i in local_min_max: # If we find a peak, continue if data[i] > peak: peak = data[i] continue # Otherwise it must have gone down, so we calculate the drawdown current_drawdown = (data[i] - peak) / peak # If drawdown is larger than previously, replace if current_drawdown < drawdown: drawdown = current_drawdown return drawdown

strat_1_investment = test_portfolio(strat_1_assets) strat_2_investment = test_portfolio(strat_2_assets)

strat_1_drawdown = max_drawdown(strat_1_investment[0]) strat_2_drawdown = max_drawdown(strat_2_investment[0]) print('Strategy 1 drawdown:', strat_1_drawdown * 100, '%') print('Strategy 2 drawdown:', strat_2_drawdown * 100, '%')

def compare_strats(strat_1_assets, strat_2_assets): strat_1_mean = sum(test[strat_1_assets].apply(calc_mean) * 1 / len(strat_1_assets)) strat_1_std = sum(test[strat_1_assets].std() * 1 / len(strat_1_assets)) print('Strategy 1') print('Mean: ', strat_1_mean, "|", "std: ", strat_1_std) strat_2_mean = sum(test[strat_2_assets].apply(calc_mean) * 1 / len(strat_2_assets)) strat_2_std = sum(test[strat_2_assets].std() * 1 / len(strat_2_assets)) print('Strategy 2') print('Mean: ', strat_2_mean, "|", "std: ", strat_2_std) print('Strategy 1 sharpe ratio: ', strat_1_mean / strat_1_std) print('Strategy 2 sharpe ratio: ', strat_2_mean / strat_2_std) strat_1_investment = test_portfolio(strat_1_assets) strat_2_investment = test_portfolio(strat_2_assets) strat_1_drawdown = max_drawdown(strat_1_investment[0]) strat_2_drawdown = max_drawdown(strat_2_investment[0]) print('Strategy 1 drawdown:', strat_1_drawdown * 100, '%') print('Strategy 2 drawdown:', strat_2_drawdown * 100, '%')

from Clustering import Cluster

df_cluster = Cluster(train[top_200_assets], nClusters=3, dendogram=False)

df_cluster.groupby("Cluster").count()

strat_3_asset_small = sharpe[df_cluster[df_cluster['Cluster'] == 'Cluster 2'].index.tolist()].idxmax() strat_3_asset_small

subset_df = train[df_cluster[df_cluster['Cluster'] == 'Cluster 1'].index.tolist()] for i in range(5): subset, subset_df, corr_avg, PDI = MinimumSpanningTree(subset_df) subset_df

strat_3_assets = subset_df.columns.tolist() + [strat_3_asset_small] strat_3_assets

train[strat_3_assets].cov()

plot_investment(test_portfolio(strat_3_assets))

compare_strats(strat_2_assets, strat_3_assets)

stat_assets = list(set(strat_2_assets + strat_3_assets)) # Remove duplicates stat_assets

stats_assets=df[stat_assets]

pd.options.plotting.backend = "matplotlib"

stats_assets.hist(bins=100) plt.show()

stats_assets.plot.density() plt.xlim([-0.02, 0.02]) plt.plot()

import pylab import scipy.stats as stats

fig, axs = plt.subplots(2, 5, figsize=(16, 10), facecolor='w', edgecolor='k') k = 0 for i in range(2): for j in range(5): stats.probplot(stats_assets[stat_assets[k]], dist ="norm", plot=axs[i][j]) axs[i][j].set_title(stat_assets[k]) k += 1 fig.tight_layout() plt.show()

stat_assets

JB=pd.DataFrame(columns=stat_assets) for x in stat_assets: JB[x]=stats.jarque_bera(stats_assets[x])

JB

print('skewness for the selected assets is:') stats_assets.skew()

print('Kurtosis for the selected assets is:') stats_assets.kurtosis()