Lump Sum vs. Dollar Cost Averaging

import quandl
vtsax = quandl.get("YAHOO/FUND_VTSAX")
print(vtsax.head())
print("")
print(vtsax.tail())

%matplotlib inline
import matplotlib.pyplot as plt
from matplotlib.ticker import FuncFormatter
from matplotlib import style
style.use('fivethirtyeight')

vtsax['Adjusted Close'].plot(figsize=(20,10))
ax = plt.subplot()
ax.yaxis.set_major_formatter(FuncFormatter(lambda x, pos: '${:,.0f}'.format(x))) # y-axis in dollars
plt.title('VTSAX Historical Stock Price')
plt.ylabel('Stock Price ($)')

today_price = vtsax['Adjusted Close'][-1] # The final value of our stock (Nov 28, 2016)
initial_investment = 100000 # Our $100,000 windfall

num_stocks_bought = initial_investment / vtsax['Adjusted Close']
lumpsum = num_stocks_bought * today_price

lumpsum.plot(figsize=(20,10), color='r')
ax = plt.subplot()
ax.yaxis.set_major_formatter(FuncFormatter(lambda x, pos: '${:,.0f}'.format(x)))
plt.title("Lump Sum - Today's value of $100,000 invested on date")
plt.ylabel('Stock Price ($)')

print("If we timed our lump-sum perfectetly, $100,000 invested on {} would be worth ${:,.2f} today.".format(lumpsum.idxmax().strftime('%b %d, %Y'), lumpsum.max()))
print("")
print("Alternatively, if we invested our lump-sum at the peak of the 2007-2009 crash, $100,000 invested on {} would still be worth ${:,.2f} today.".format(lumpsum[:-(9*252)].idxmin().strftime('%b %d, %Y'), lumpsum[:-(9*252)].min()))

import pandas as pd

def doDCA(investment, start_date):
    # gets dates of 10 investment dates (spaced 30 days apart) beginning on the day we receive our windfall
    investment_dates_all = pd.date_range(start_date,periods=10,freq='30D')
    
    # removes dates beyond the most recent data available
    investment_dates = investment_dates_all[investment_dates_all < vtsax.index[-1]]
    
    # since not all dates will be a business day, this returns the closest buseiness day
    closest_investment_dates = vtsax.index.searchsorted(investment_dates)
    
    # $10,000 investement every 30 days
    portion = investment/10.0
    
    # gets the number of stocks purchased over the 300 day investment period
    stocks_invested = sum(portion / vtsax['Adjusted Close'][closest_investment_dates])
    
    # adds cash value in for cash that has not yet been invested (start dates <300 days from today)
    uninvested_dollars = portion * sum(investment_dates_all >= vtsax.index[-1])
    
    # value of stocks today
    total_value = today_price*stocks_invested + uninvested_dollars
    return total_value

# Generates DCA series for every initial investment date
dca = pd.Series(vtsax.index.map(lambda x: doDCA(initial_investment, x)), index=vtsax.index)

dca.plot(figsize=(20,10), color='b')
ax = plt.subplot()
ax.yaxis.set_major_formatter(FuncFormatter(lambda x, pos: '${:,.0f}'.format(x)))
plt.title('Dollar-Cost Average - Value of $10,000 invested on date')
plt.ylabel('Investment Value ($)')

dca.plot(figsize=(20,10), color='b', label="DCA")
plt.plot(lumpsum, color='r', label="Lump-Sum")
plt.legend()
ax = plt.subplot()
ax.yaxis.set_major_formatter(FuncFormatter(lambda x, pos: '${:,.0f}'.format(x)))
plt.title('Lump-Sum vs Dollar-Cost Averaging')
plt.ylabel('Investment Value ($)')

# Difference between lump sum and DCA
diff = (lumpsum - dca)

fig, (ax1, ax2, ax3) = plt.subplots(3,1, sharex=True, figsize=(20,17))

# VTSAX Actual
vtsax['Adjusted Close'].plot(ax=ax1)
ax1.yaxis.set_major_formatter(FuncFormatter(lambda x, pos: '${:,.0f}'.format(x))) # Y axis in dollars
ax1.set_xlabel('')
ax1.set_title('VTSAX Historical Stock Price')
ax1.set_ylabel('Stock Value ($)')

# Comparison
dca.plot(ax=ax2, color='b')
lumpsum.plot(ax=ax2, color='r')
ax2.axhline(initial_investment, linestyle="--", color="black")
ax2.text(vtsax.index[50],initial_investment*1.1, "Initial Investment")
ax2.yaxis.set_major_formatter(FuncFormatter(lambda x, pos: '${:,.0f}K'.format(x*1e-3))) # Y axis $1,000s
ax2.legend(["DCA", "Lump-Sum"])
ax2.set_title('Comparison Lump Sum vs. Dollar Cost Averaging - Value of $100K invested on date')
ax2.set_ylabel('Investment Value ($)')

# Difference
ax3.fill_between(diff.index, y1=diff, y2=0, color='red', where=diff>0)
ax3.fill_between(diff.index, y1=diff, y2=0, color='blue', where=diff<0)

ax3.yaxis.set_major_formatter(FuncFormatter(lambda x, pos: '${:,.0f}K'.format(x*1e-3))) # Y axis $1,000s
ax3.set_ylabel('Difference ($)')
ax3.set_title('Difference (Lump Sum - Dollar Cost Average)')
ax3.legend(["Lump-Sum > DCA", "DCA > Lump-Sum"]);

print("Lump-sum returns more than DCA %.1f%% of all the days" % (100*sum(diff>0)/len(diff)))
print("DCA returns more than lump-sum %.1f%% of all the days" % (100*sum(diff<0)/len(diff)))

print("Mean difference: Average dollar improvement lump-sum returns vs. DCA: ${:,.0f}".format(sum(diff) / len(diff)))
print("Mean difference when lump-sum > DCA: ${:,.0f}".format(sum(diff[diff>0]) / sum(diff>0)))
print("Mean difference when DCA > lump-sum: ${:,.0f}".format(sum(-diff[diff<0]) / sum(diff<0)))

rel_area_lump_sum_wins = sum(diff[diff>0]) / sum(abs(diff))
print("A measure of risk to reward of lump sum would be to take the area above where the difference is greater than zero and divide it by the total area of the deviation from zero")
rel_area_lump_sum_wins