基金定投能赚钱吗？

用随机函数模拟出一段四年的走势，在均匀的时间点买入走势基金：

import numpy as np
import matplotlib.pylab as plt

TOTALMONEY = 1e5

def genData():
    data = np.random.normal(0,1,2000).cumsum()[1000:]
    if data.min()<0:
        data+=-data.min()+1
    return data

def test_mindata():
    minData = 1
    for _ in range(10000):
        data = genData()
        if data.min()<minData:
            minData = data.min()
    assert minData>0 

test_mindata()

模拟出的走势大概是这样的：

plt.plot(genData())

模拟走势

三种不同的时间段投资策略：

def simulate_market():
#     无交易手续费，每日定投
    data = genData()
    money_for_each = TOTALMONEY/len(data)
    number_of_purchases = (money_for_each/data).sum()
    market_value = number_of_purchases*data[-1]
    growth_rate_of_funds = market_value/TOTALMONEY-1
#     plt.plot(data)
    return growth_rate_of_funds

def simulate_market_with_trading_fee(fee=0.0015):
#     有交易手续费，每日定投
    data = genData()
    money_for_each = TOTALMONEY/len(data)*(1-fee)
    number_of_purchases = (money_for_each/data).sum()
    market_value = number_of_purchases*data[-1]
    growth_rate_of_funds = market_value/TOTALMONEY-1
#     plt.plot(data)
    return growth_rate_of_funds

def simulate_market_with_trading_fee_months(fee=0.0015):
#     有交易手续费，每月定投
    data = genData()
    data_for_trading = data[::5]
    money_for_each = TOTALMONEY/len(data_for_trading)*(1-fee)
    number_of_purchases = (money_for_each/data_for_trading).sum()
    market_value = number_of_purchases*data[-1]
    growth_rate_of_funds = market_value/TOTALMONEY-1
    return growth_rate_of_funds

按照三种策略模拟十万次走势生成、投资操作：

ax1 = plt.subplot(311) #     无交易手续费，每日定投
ax2 = plt.subplot(312) #     有交易手续费，每日定投
ax3 = plt.subplot(313) #     有交易手续费，每月定投

growth_rate_of_funds_set = []
for _ in range(100000):
    growth_rate_of_funds_set.append(simulate_market())

ax1.hist(growth_rate_of_funds_set,bins=np.linspace(-7.5,7.5,300))

growth_rate_of_funds_set = []
for _ in range(100000):
    growth_rate_of_funds_set.append(simulate_market_with_trading_fee())

ax2.hist(growth_rate_of_funds_set,bins=np.linspace(-7.5,7.5,300))

growth_rate_of_funds_set = []
for _ in range(100000):
    growth_rate_of_funds_set.append(simulate_market_with_trading_fee_months())

ax3.hist(growth_rate_of_funds_set,bins=np.linspace(-7.5,7.5,300))

四年的总投资收益率是这样的：

定投收益率

注意有一半可能是负收益。