Introduction

When buying stocks and investment trusts, there is a dollar cost averaging method as a buying method. Risk can be reduced by purchasing products such as stocks and mutual funds ** on a regular basis ** at a fixed price **.

In the slides I often see, I felt that I was not convinced because it was written assuming an arbitrary transition of stock price / base price and the number of data was small. Obviously, the risk is reduced in theory. Therefore, it is an attempt to simulate based on the standard price data of actual investment trusts.

Simulation assumptions

Investment trust used for simulation

Sumitomo Mitsui Trust Assetment's Foreign Stock Index e

Evaluation index

In this simulation, we will compare the ROI one year after the start of purchase.

ROI = \frac{Assets held one year later-1 year investment amount}{1 year investment amount}

Method 1 (Bulk purchase)

I will purchase a certain amount (100,000 yen) at a certain timing.

Method 2 (Regular purchase of a certain number of units)

From a certain timing, we will purchase a certain number of units (10,000 yen) on the 25th of every month for one year.

Method 3 (fixed amount subscription)

From a certain timing, I will purchase a fixed amount (10,000 yen) on the 25th of every month for one year.

simulation

Risk evaluation is performed by changing the purchase start time in 100 ways and comparing the resulting ROI distribution.

import pandas as pd
df = pd.read_csv('http://www.smtam.jp/fund_data/csv/110057.csv', 
                 names=['day', 'price', 'income', 'asset'], skiprows=1)
df.loc[:, 'day'] = pd.to_datetime(df.day)
print df.shape
df.head(10)

import matplotlib
import seaborn as sns
%matplotlib inline
import matplotlib.pyplot as plt

fig, ax = plt.subplots(1, figsize=(12, 8))
df.plot('day', 'price', ax =ax, label=u'Base price')
ax.set_ylabel(u'Base price')
ax.set_xlabel(u'date')

import  numpy as np
def package(timing):
    num = []
    invest = []
    price = 100000
    for i, r in df.iterrows():
        if i == timing:
            num_add = int(10000.0 * price/ r.price)
            num.append(num[i-1] + num_add  if len(num) > 0 else num_add)
            invest.append(invest[i-1] + price if len(invest) > 0 else price)
        else:
            num.append(num[i-1] if len(num) > 0 else 0)
            invest.append(invest[i-1] if len(invest) > 0 else 0)
    return num, invest

def constant_num(start_timing):
    num = []
    invest = []
    for i, r in df.iterrows():
        if r.day.day == 25 and i >= start_timing:
            num_add = 10000
            invest_add = r.price 
            num.append(num[i-1] + num_add  if len(num) > 0 else num_add)
            invest.append(invest[i-1] + invest_add if len(invest) > 0 else invest_add)
        else:
            num.append(num[i-1] if len(num) > 0 else 0)
            invest.append(invest[i-1] if len(invest) > 0 else 0)
    return num, invest


def doller_cost(start_timing):
    num = []
    invest = []
    price = 10000
    for i, r in df.iterrows():
        if r.day.day == 25 and i >= start_timing:
            num_add = int(10000.0 * price/ r.price)
            num.append(num[i-1] + num_add  if len(num) > 0 else num_add)
            invest.append(invest[i-1] + price if len(invest) > 0 else price)
        else:
            num.append(num[i-1] if len(num) > 0 else 0)
            invest.append(invest[i-1] if len(invest) > 0 else 0)
    return num, invest


def sim(function, label, color):
    fig, ax = plt.subplots(1, figsize=(12, 8))
    final_ratio = []
    for i in np.arange(0, 100) * 10:
        num, invest = function(i)
        num = pd.Series(num)
        invest = pd.Series(invest)
        df.loc[:, 'ratio'] = (num * df.price / 10000.0 - invest.astype(float)) / invest.astype(float)
        df.plot('day', 'ratio', ax=ax,alpha=0.1, color=color)
        
        final_ratio.append(df.iloc[i + 365].ratio)
    ax.set_title(label)
    ax.set_ylabel('ROI')
    ax.set_xlabel(u'date')
    ax.legend_.remove()
    return final_ratio

package_ratio = sim(package, u'Bulk purchase', 'blue')
constant_ratio = sim(constant_num, u'Fixed number of subscriptions', 'green')
dc_ratio = sim(doller_cost, u'Fixed amount subscription', 'red')

fig, ax = plt.subplots(1, figsize=(12, 8))
pd.Series(package_ratio).hist(ax=ax, color='blue', alpha=0.3, normed=True, label=u'Bulk purchase')
pd.Series(constant_ratio).hist(ax=ax, color='green', alpha=0.3, normed=True, label=u'Fixed number of subscriptions')
pd.Series(dc_ratio).hist(ax=ax, color='red', alpha=0.3, normed=True, label=u'Fixed amount subscription')
ax.set_xlabel('ROI')
ax.set_ylabel('freq(normed)')
ax.legend()

What I found

It was possible to simulate that the bulk purchase has a large distribution of ROI.
The difference between regular flat-rate purchase and regular fixed-price purchase was not so big

I tried to simulate the dollar cost averaging method