[Strategy] Sector Rotation with Dual Momentum

개요

미국 섹터 ETF로 듀얼 모멘텀 전략을 구현해 봅니다.

미국 섹터 ETF로 듀얼 모멘텀 전략을 구현해 볼 것입니다. 듀얼 모멘텀은 상대적으로 모멘텀이 좋은 자산을 편입하는 상대 모멘텀과 현금보다 수익이 나쁘면 현금으로 대체하는 절대 모멘텀을 혼합한 것입니다. 우선 필요한 라이브러리를 가져옵니다.

import pandas as pd
import pandas_datareader as pdr
from datetime import datetime, timedelta
import backtrader as bt
import numpy as np
%matplotlib inline
import matplotlib.pyplot as plt
import pyfolio as pf
import quantstats
import math
import seaborn
plt.rcParams["figure.figsize"] = (10, 6) # (w, h)

섹터는 StateStreet의 ETF 중 상장 기간이 긴 9개 섹터로 합니다. Consumer Discretionary, Consumer Staples, Financial, Energy, Health Care, Industrial, Materials, Technology, Utilities가 있습니다. 절대 모멘텀 판정을 위해 단기 국채 ETF인 SHY를 사용합니다.

# XLY (Consumer Discretionary), XLP (Consumer Staples), XLF (Financial), XLE (Energy), XLV (Health Care), XLI (Industrial)
# XLB (Materials), XLK (Technology), XLU (Utilities)
# SHY (1-3 year treasury: cash)

# shy starts: 2002-07-30
start = datetime(2002,8,1)
end = datetime(2021,5,31)

tickers = ['XLB','XLE','XLF','XLI','XLK','XLP','XLU','XLV','XLY','SHY']

def get_price_data(tickers):
    df_sector = pd.DataFrame(columns=tickers)
    
    for ticker in tickers:
        df_sector[ticker] = pdr.get_data_yahoo(ticker, start, end)['Adj Close']  
         
    return df_sector

SHY의 데이터가 2002년 7월 30일부터 시작되므로 2002년 8월부터 2021년 5월까지로 해 봅니다. Yahoo Finance에서 가져옵니다. tickers 리스트로 열을 설정한 데이터프레임을 만들고 각 열에 섹터 ETF 가격 데이터 다운받은 것을 넣습니다.

df_sector = get_price_data(tickers)
df_sector

	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY	SHY
Date
2002-07-31	13.538386	14.196311	12.657179	15.610104	11.063435	13.371263	10.526128	19.728098	19.041368	59.007946
2002-08-01	13.452792	13.359758	12.344178	15.263207	10.576707	13.245712	10.373425	19.177660	18.458864	59.124153
2002-08-02	12.886496	13.208796	12.031182	14.708185	10.352652	13.220597	10.169827	19.023533	17.640223	59.240341
2002-08-05	12.445313	12.718184	11.558938	14.222539	9.904553	13.038550	9.991673	18.208862	17.230904	59.334690
2002-08-06	12.972098	13.177356	11.937830	14.708185	10.321753	13.051109	10.403966	18.656561	17.742558	59.189507
...	...	...	...	...	...	...	...	...	...	...
2021-05-24	87.370003	52.680000	37.759998	103.680000	138.610001	71.230003	66.040001	124.480003	170.220001	86.288010
2021-05-25	86.629997	51.610001	37.380001	103.370003	138.649994	71.250000	65.239998	124.110001	170.759995	86.288010
2021-05-26	86.660004	52.070000	37.490002	103.699997	138.639999	71.099998	65.250000	123.389999	172.389999	86.307999
2021-05-27	87.349998	52.110001	37.919998	105.120003	137.910004	70.660004	64.809998	123.120003	173.080002	86.307999
2021-05-28	87.260002	52.209999	37.990002	105.120003	138.399994	70.809998	65.160004	123.599998	172.839996	86.307999

4741 rows × 10 columns

9개 섹터 중 12개월 누적 수익률 상위 5개 섹터를 동일 비중으로 가져가고, 누적 수익률이 -인 경우는 SHY etf로 대체합니다. 그러기 위해서는 12개월 모멘텀이 필요합니다. 현재 주가 x에 대해서 섹터별로 현재 시점보다 365~370일 이전 값 중 가장 최근 값을 12개월 이전 주가로 놓고 모멘텀을 구합니다.

def get_momentum(x):
    temp = [0 for _ in range(len(x.index))]
    momentum = pd.Series(temp, index=x.index)
    
    try:
        before_12m = df_sector[x.name-timedelta(days=370):x.name-timedelta(days=365)].iloc[-1]
        momentum = x / before_12m - 1
        
    except:
        pass
    
    return momentum

momentum_col = [col + '_m' for col in df_sector.columns]
df_sector[momentum_col] = df_sector.apply(lambda x: get_momentum(x), axis=1)
df_sector

	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY	SHY	XLB_m	XLE_m	XLF_m	XLI_m	XLK_m	XLP_m	XLU_m	XLV_m	XLY_m	SHY_m
Date
2002-07-31	13.538386	14.196311	12.657179	15.610104	11.063435	13.371263	10.526128	19.728098	19.041368	59.007946	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
2002-08-01	13.452792	13.359758	12.344178	15.263207	10.576707	13.245712	10.373425	19.177660	18.458864	59.124153	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
2002-08-02	12.886496	13.208796	12.031182	14.708185	10.352652	13.220597	10.169827	19.023533	17.640223	59.240341	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
2002-08-05	12.445313	12.718184	11.558938	14.222539	9.904553	13.038550	9.991673	18.208862	17.230904	59.334690	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
2002-08-06	12.972098	13.177356	11.937830	14.708185	10.321753	13.051109	10.403966	18.656561	17.742558	59.189507	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2021-05-24	87.370003	52.680000	37.759998	103.680000	138.610001	71.230003	66.040001	124.480003	170.220001	86.288010	0.682965	0.443394	0.760269	0.649446	0.451031	0.273896	0.208169	0.269416	0.415237	0.001353
2021-05-25	86.629997	51.610001	37.380001	103.370003	138.649994	71.250000	65.239998	124.110001	170.759995	86.288010	0.668710	0.414077	0.742554	0.644514	0.451450	0.274254	0.193534	0.265643	0.419726	0.001353
2021-05-26	86.660004	52.070000	37.490002	103.699997	138.639999	71.099998	65.250000	123.389999	172.389999	86.307999	0.624778	0.388083	0.661283	0.583297	0.452851	0.264749	0.185948	0.260579	0.410932	0.001585
2021-05-27	87.349998	52.110001	37.919998	105.120003	137.910004	70.660004	64.809998	123.120003	173.080002	86.307999	0.621316	0.371464	0.610498	0.553144	0.437001	0.238278	0.164027	0.244925	0.392717	0.001816
2021-05-28	87.260002	52.209999	37.990002	105.120003	138.399994	70.809998	65.160004	123.599998	172.839996	86.307999	0.604747	0.413618	0.639363	0.567971	0.444939	0.230001	0.136724	0.233693	0.407870	0.001354

4741 rows × 20 columns

모멘텀 데이터가 구해진 구간에서만 해야 합니다. 넉넉하게 2003년 9월부터로 합니다. 월말 리밸런싱을 가정하여 월말 데이터만 뽑을 것입니다.

df_sector = df_sector.loc[df_sector.index >= '2003-09-01']
df_sector

	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY	SHY	XLB_m	XLE_m	XLF_m	XLI_m	XLK_m	XLP_m	XLU_m	XLV_m	XLY_m	SHY_m
Date
2003-09-02	15.675874	15.949609	14.443469	17.174885	14.594810	13.280826	11.393372	20.984875	23.290251	60.545948	0.164111	0.106830	0.120231	0.117627	0.330342	-0.014628	0.041108	0.053515	0.187309	0.021664
2003-09-03	15.682619	15.956034	14.471502	17.315781	14.749743	13.312909	11.430570	20.903135	23.282331	60.590282	0.199814	0.153077	0.180209	0.167377	0.414177	0.009859	0.073979	0.095002	0.230865	0.019995
2003-09-04	15.541031	15.930345	14.409845	17.301693	14.889193	13.377061	11.435885	20.955162	23.353628	60.671680	0.184210	0.153843	0.153485	0.155082	0.384475	0.006577	0.081200	0.064972	0.211939	0.021741
2003-09-05	15.480347	15.859716	14.342584	17.111485	14.811721	13.235914	11.414631	20.903135	23.123890	60.878826	0.212436	0.146638	0.165520	0.162850	0.425399	-0.003573	0.082316	0.074755	0.222488	0.024101
2003-09-08	15.615194	16.078033	14.482710	17.196020	15.082846	13.274407	11.499658	21.274691	23.131823	60.804867	0.198884	0.143698	0.159318	0.153906	0.404500	-0.000675	0.090378	0.093859	0.185895	0.024863
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2021-05-24	87.370003	52.680000	37.759998	103.680000	138.610001	71.230003	66.040001	124.480003	170.220001	86.288010	0.682965	0.443394	0.760269	0.649446	0.451031	0.273896	0.208169	0.269416	0.415237	0.001353
2021-05-25	86.629997	51.610001	37.380001	103.370003	138.649994	71.250000	65.239998	124.110001	170.759995	86.288010	0.668710	0.414077	0.742554	0.644514	0.451450	0.274254	0.193534	0.265643	0.419726	0.001353
2021-05-26	86.660004	52.070000	37.490002	103.699997	138.639999	71.099998	65.250000	123.389999	172.389999	86.307999	0.624778	0.388083	0.661283	0.583297	0.452851	0.264749	0.185948	0.260579	0.410932	0.001585
2021-05-27	87.349998	52.110001	37.919998	105.120003	137.910004	70.660004	64.809998	123.120003	173.080002	86.307999	0.621316	0.371464	0.610498	0.553144	0.437001	0.238278	0.164027	0.244925	0.392717	0.001816
2021-05-28	87.260002	52.209999	37.990002	105.120003	138.399994	70.809998	65.160004	123.599998	172.839996	86.307999	0.604747	0.413618	0.639363	0.567971	0.444939	0.230001	0.136724	0.233693	0.407870	0.001354

4467 rows × 20 columns

df_sector = df_sector.resample(rule='M').last()
df_sector

	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY	SHY	XLB_m	XLE_m	XLF_m	XLI_m	XLK_m	XLP_m	XLU_m	XLV_m	XLY_m	SHY_m
Date
2003-09-30	14.795932	15.520121	14.317087	16.465275	14.161002	13.081612	11.742328	20.726589	21.877050	61.204376	0.262647	0.159783	0.254630	0.211224	0.549396	0.046216	0.220763	0.109258	0.224424	0.025187
2003-10-31	16.205723	15.668549	15.308742	17.483309	15.199060	13.673891	11.822752	20.868189	23.868029	60.954796	0.308261	0.149684	0.229142	0.225826	0.332856	0.052628	0.258101	0.055298	0.251398	0.018522
2003-11-30	16.571718	15.791162	15.252403	17.829716	15.415970	13.834840	11.849562	21.315365	24.082193	60.918385	0.220937	0.126278	0.170652	0.185293	0.160100	0.088849	0.230594	0.041464	0.195446	0.022362
2003-12-31	18.196249	17.858601	15.944183	19.011400	15.899339	14.080931	12.625952	22.548845	25.046740	61.580399	0.374128	0.258117	0.304918	0.318576	0.386755	0.111733	0.264659	0.149301	0.372001	0.022204
2004-01-31	17.391766	18.260498	16.465641	19.203211	16.578060	14.080931	12.885720	23.169601	24.903564	61.655003	0.397179	0.346110	0.391883	0.431284	0.478930	0.181031	0.336749	0.208711	0.423282	0.023939
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2021-01-31	70.342949	38.907192	28.822254	84.509895	128.574844	63.745312	61.689369	114.632141	161.753036	86.304970	0.225154	-0.239690	-0.029353	0.041759	0.331888	0.031193	-0.070859	0.156782	0.310609	0.025973
2021-02-28	73.240715	47.644489	32.167427	90.331978	130.330002	62.959564	57.927460	112.220512	160.894394	86.254997	0.410367	0.133454	0.212918	0.242024	0.508937	0.100085	-0.060249	0.221042	0.397808	0.018839
2021-03-31	78.800003	49.060001	34.049999	98.449997	132.809998	68.309998	64.040001	116.739998	168.070007	86.207031	0.783784	0.779943	0.671183	0.694440	0.669173	0.288959	0.194204	0.338860	0.727183	0.002123
2021-04-30	83.040001	49.389999	36.259998	101.930000	139.699997	69.580002	66.720001	121.330002	178.919998	86.256012	0.631931	0.370344	0.625815	0.612261	0.543715	0.227514	0.203983	0.235929	0.546639	-0.000034
2021-05-31	87.260002	52.209999	37.990002	105.120003	138.399994	70.809998	65.160004	123.599998	172.839996	86.307999	0.604747	0.413618	0.639363	0.567971	0.444939	0.230001	0.136724	0.233693	0.407870	0.001354

213 rows × 20 columns

9개 섹터 중 모멘텀이 좋은 5개 섹터를 선택합니다. 선택된 5개 섹터는 동일 비중으로 투자합니다. 모멘텀이 음수이거나 SHY보다 못하면 SHY로 대체합니다. 선택한 섹터와 그 섹터 ETF의 가격을 데이터프레임에 담습니다. 모멘텀 값들을 추출해서 sorting하고 크기 순으로 5개를 잡아줍니다.

def select_sector(x):
    selected_sector = pd.Series([0,0,0,0,0,0,0,0,0,0], index=['SECTOR1','PRICE1','SECTOR2','PRICE2','SECTOR3','PRICE3','SECTOR4','PRICE4','SECTOR5','PRICE5'])
    
    momentum1 = None
    momentum2 = None
    momentum3 = None
    momentum4 = None
    momentum5 = None
    
    sorted_momentum = x[['XLB_m','XLE_m','XLF_m','XLI_m','XLK_m','XLP_m','XLU_m','XLV_m','XLY_m','SHY_m']].sort_values(ascending=False)
    
    # SHY가 가장 좋을 경우
    if x['SHY_m'] == sorted_momentum[0]:
        momentum1 = sorted_momentum[0]
        momentum2 = sorted_momentum[0]
        momentum3 = sorted_momentum[0]
        momentum4 = sorted_momentum[0]
        momentum5 = sorted_momentum[0]

        selected_sector['SECTOR1'] = x[x==momentum1].index[0][:3]
        selected_sector['PRICE1'] = x[selected_sector['SECTOR1']]
        selected_sector['SECTOR2'] = x[x==momentum2].index[0][:3]
        selected_sector['PRICE2'] = x[selected_sector['SECTOR2']]
        selected_sector['SECTOR3'] = x[x==momentum3].index[0][:3]
        selected_sector['PRICE3'] = x[selected_sector['SECTOR3']]
        selected_sector['SECTOR4'] = x[x==momentum4].index[0][:3]
        selected_sector['PRICE4'] = x[selected_sector['SECTOR4']]
        selected_sector['SECTOR5'] = x[x==momentum5].index[0][:3]
        selected_sector['PRICE5'] = x[selected_sector['SECTOR5']]
        
    # SHY가 두번째 좋을 경우
    if x['SHY_m'] == sorted_momentum[1]:
        momentum1 = sorted_momentum[0]
        momentum2 = sorted_momentum[1]
        momentum3 = sorted_momentum[1]
        momentum4 = sorted_momentum[1]
        momentum5 = sorted_momentum[1]

        selected_sector['SECTOR1'] = x[x==momentum1].index[0][:3]
        selected_sector['PRICE1'] = x[selected_sector['SECTOR1']]
        selected_sector['SECTOR2'] = x[x==momentum2].index[0][:3]
        selected_sector['PRICE2'] = x[selected_sector['SECTOR2']]
        selected_sector['SECTOR3'] = x[x==momentum3].index[0][:3]
        selected_sector['PRICE3'] = x[selected_sector['SECTOR3']]
        selected_sector['SECTOR4'] = x[x==momentum4].index[0][:3]
        selected_sector['PRICE4'] = x[selected_sector['SECTOR4']]
        selected_sector['SECTOR5'] = x[x==momentum5].index[0][:3]
        selected_sector['PRICE5'] = x[selected_sector['SECTOR5']]
        
    # SHY가 세번째 좋을 경우
    if x['SHY_m'] == sorted_momentum[2]:
        momentum1 = sorted_momentum[0]
        momentum2 = sorted_momentum[1]
        momentum3 = sorted_momentum[2]
        momentum4 = sorted_momentum[2]
        momentum5 = sorted_momentum[2]

        selected_sector['SECTOR1'] = x[x==momentum1].index[0][:3]
        selected_sector['PRICE1'] = x[selected_sector['SECTOR1']]
        selected_sector['SECTOR2'] = x[x==momentum2].index[0][:3]
        selected_sector['PRICE2'] = x[selected_sector['SECTOR2']]
        selected_sector['SECTOR3'] = x[x==momentum3].index[0][:3]
        selected_sector['PRICE3'] = x[selected_sector['SECTOR3']]
        selected_sector['SECTOR4'] = x[x==momentum4].index[0][:3]
        selected_sector['PRICE4'] = x[selected_sector['SECTOR4']]
        selected_sector['SECTOR5'] = x[x==momentum5].index[0][:3]
        selected_sector['PRICE5'] = x[selected_sector['SECTOR5']]
        
    # SHY가 네번째 좋을 경우
    if x['SHY_m'] == sorted_momentum[3]:
        momentum1 = sorted_momentum[0]
        momentum2 = sorted_momentum[1]
        momentum3 = sorted_momentum[2]
        momentum4 = sorted_momentum[3]
        momentum5 = sorted_momentum[3]

        selected_sector['SECTOR1'] = x[x==momentum1].index[0][:3]
        selected_sector['PRICE1'] = x[selected_sector['SECTOR1']]
        selected_sector['SECTOR2'] = x[x==momentum2].index[0][:3]
        selected_sector['PRICE2'] = x[selected_sector['SECTOR2']]
        selected_sector['SECTOR3'] = x[x==momentum3].index[0][:3]
        selected_sector['PRICE3'] = x[selected_sector['SECTOR3']]
        selected_sector['SECTOR4'] = x[x==momentum4].index[0][:3]
        selected_sector['PRICE4'] = x[selected_sector['SECTOR4']]
        selected_sector['SECTOR5'] = x[x==momentum5].index[0][:3]
        selected_sector['PRICE5'] = x[selected_sector['SECTOR5']]
        
    # SHY가 다섯번째 이하일 경우
    else:
        momentum1 = sorted_momentum[0]
        momentum2 = sorted_momentum[1]
        momentum3 = sorted_momentum[2]
        momentum4 = sorted_momentum[3]
        momentum5 = sorted_momentum[4]

        selected_sector['SECTOR1'] = x[x==momentum1].index[0][:3]
        selected_sector['PRICE1'] = x[selected_sector['SECTOR1']]
        selected_sector['SECTOR2'] = x[x==momentum2].index[0][:3]
        selected_sector['PRICE2'] = x[selected_sector['SECTOR2']]
        selected_sector['SECTOR3'] = x[x==momentum3].index[0][:3]
        selected_sector['PRICE3'] = x[selected_sector['SECTOR3']]
        selected_sector['SECTOR4'] = x[x==momentum4].index[0][:3]
        selected_sector['PRICE4'] = x[selected_sector['SECTOR4']]
        selected_sector['SECTOR5'] = x[x==momentum5].index[0][:3]
        selected_sector['PRICE5'] = x[selected_sector['SECTOR5']]

    return selected_sector

df_sector[['SECTOR1','PRICE1','SECTOR2','PRICE2','SECTOR3','PRICE3','SECTOR4','PRICE4','SECTOR5','PRICE5']] = df_sector.apply(lambda x: select_sector(x), axis=1) 
df_sector

	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY	SHY	...	SECTOR1	PRICE1	SECTOR2	PRICE2	SECTOR3	PRICE3	SECTOR4	PRICE4	SECTOR5	PRICE5
Date
2003-09-30	14.795932	15.520121	14.317087	16.465275	14.161002	13.081612	11.742328	20.726589	21.877050	61.204376	...	XLK	14.161002	XLB	14.795932	XLF	14.317087	XLY	21.877050	XLU	11.742328
2003-10-31	16.205723	15.668549	15.308742	17.483309	15.199060	13.673891	11.822752	20.868189	23.868029	60.954796	...	XLK	15.199060	XLB	16.205723	XLU	11.822752	XLY	23.868029	XLF	15.308742
2003-11-30	16.571718	15.791162	15.252403	17.829716	15.415970	13.834840	11.849562	21.315365	24.082193	60.918385	...	XLU	11.849562	XLB	16.571718	XLY	24.082193	XLI	17.829716	XLF	15.252403
2003-12-31	18.196249	17.858601	15.944183	19.011400	15.899339	14.080931	12.625952	22.548845	25.046740	61.580399	...	XLK	15.899339	XLB	18.196249	XLY	25.046740	XLI	19.011400	XLF	15.944183
2004-01-31	17.391766	18.260498	16.465641	19.203211	16.578060	14.080931	12.885720	23.169601	24.903564	61.655003	...	XLK	16.578060	XLI	19.203211	XLY	24.903564	XLB	17.391766	XLF	16.465641
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2021-01-31	70.342949	38.907192	28.822254	84.509895	128.574844	63.745312	61.689369	114.632141	161.753036	86.304970	...	XLK	128.574844	XLY	161.753036	XLB	70.342949	XLV	114.632141	XLI	84.509895
2021-02-28	73.240715	47.644489	32.167427	90.331978	130.330002	62.959564	57.927460	112.220512	160.894394	86.254997	...	XLK	130.330002	XLB	73.240715	XLY	160.894394	XLI	90.331978	XLV	112.220512
2021-03-31	78.800003	49.060001	34.049999	98.449997	132.809998	68.309998	64.040001	116.739998	168.070007	86.207031	...	XLB	78.800003	XLE	49.060001	XLY	168.070007	XLI	98.449997	XLF	34.049999
2021-04-30	83.040001	49.389999	36.259998	101.930000	139.699997	69.580002	66.720001	121.330002	178.919998	86.256012	...	XLB	83.040001	XLF	36.259998	XLI	101.930000	XLY	178.919998	XLK	139.699997
2021-05-31	87.260002	52.209999	37.990002	105.120003	138.399994	70.809998	65.160004	123.599998	172.839996	86.307999	...	XLF	37.990002	XLB	87.260002	XLI	105.120003	XLK	138.399994	XLE	52.209999

213 rows × 30 columns

각각의 수익률을 계산합니다.

return_col = [ticker + '_r' for ticker in tickers]
df_sector[return_col] = df_sector[tickers].pct_change()
df_sector

	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY	SHY	...	XLB_r	XLE_r	XLF_r	XLI_r	XLK_r	XLP_r	XLU_r	XLV_r	XLY_r	SHY_r
Date
2003-09-30	14.795932	15.520121	14.317087	16.465275	14.161002	13.081612	11.742328	20.726589	21.877050	61.204376	...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2003-10-31	16.205723	15.668549	15.308742	17.483309	15.199060	13.673891	11.822752	20.868189	23.868029	60.954796	...	0.095282	0.009564	0.069264	0.061829	0.073304	0.045276	0.006849	0.006832	0.091008	-0.004078
2003-11-30	16.571718	15.791162	15.252403	17.829716	15.415970	13.834840	11.849562	21.315365	24.082193	60.918385	...	0.022584	0.007825	-0.003680	0.019814	0.014271	0.011771	0.002268	0.021429	0.008973	-0.000597
2003-12-31	18.196249	17.858601	15.944183	19.011400	15.899339	14.080931	12.625952	22.548845	25.046740	61.580399	...	0.098030	0.130924	0.045355	0.066276	0.031355	0.017788	0.065521	0.057868	0.040052	0.010867
2004-01-31	17.391766	18.260498	16.465641	19.203211	16.578060	14.080931	12.885720	23.169601	24.903564	61.655003	...	-0.044211	0.022504	0.032705	0.010089	0.042689	0.000000	0.020574	0.027529	-0.005716	0.001211
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2021-01-31	70.342949	38.907192	28.822254	84.509895	128.574844	63.745312	61.689369	114.632141	161.753036	86.304970	...	-0.024175	0.037467	-0.017978	-0.042688	-0.008383	-0.049815	-0.008772	0.014016	0.007650	0.000232
2021-02-28	73.240715	47.644489	32.167427	90.331978	130.330002	62.959564	57.927460	112.220512	160.894394	86.254997	...	0.041195	0.224568	0.116062	0.068892	0.013651	-0.012326	-0.060981	-0.021038	-0.005308	-0.000579
2021-03-31	78.800003	49.060001	34.049999	98.449997	132.809998	68.309998	64.040001	116.739998	168.070007	86.207031	...	0.075904	0.029710	0.058524	0.089869	0.019029	0.084982	0.105521	0.040273	0.044598	-0.000556
2021-04-30	83.040001	49.389999	36.259998	101.930000	139.699997	69.580002	66.720001	121.330002	178.919998	86.256012	...	0.053807	0.006726	0.064905	0.035348	0.051879	0.018592	0.041849	0.039318	0.064556	0.000568
2021-05-31	87.260002	52.209999	37.990002	105.120003	138.399994	70.809998	65.160004	123.599998	172.839996	86.307999	...	0.050819	0.057097	0.047711	0.031296	-0.009306	0.017677	-0.023381	0.018709	-0.033982	0.000603

213 rows × 40 columns

섹터 로테이션 전략의 월별 수익률을 구합니다. 직전 달 모멘텀 값 기준으로 이번 달 투자 대상을 결정하는 것이니 주의합니다.

df_sector['RETURN'] = 0
df_sector['RETURN_ACC'] = 0
df_sector['LOG_RETURN'] = 0
df_sector['LOG_RETURN_ACC'] = 0

for i in range(len(df_sector)):
    strat_return = 0
    log_strat_return = 0
    
    # 직전 달 모멘텀이 좋은 것으로 리밸런싱해서 앞으로 한 달 가져가는 것
    if i > 0:
        strat_return = (df_sector[df_sector.iloc[i-1]['SECTOR1']+'_r'].iloc[i]+df_sector[df_sector.iloc[i-1]['SECTOR2']+'_r'].iloc[i]+df_sector[df_sector.iloc[i-1]['SECTOR3']+'_r'].iloc[i]+df_sector[df_sector.iloc[i-1]['SECTOR4']+'_r'].iloc[i]+df_sector[df_sector.iloc[i-1]['SECTOR5']+'_r'].iloc[i])/5
        log_strat_return = math.log(strat_return + 1)
        
    df_sector.loc[df_sector.index[i], 'RETURN'] = strat_return
    # 누적 = 직전 누적 * 현재
    df_sector.loc[df_sector.index[i], 'RETURN_ACC'] = (1+df_sector.loc[df_sector.index[i-1], 'RETURN_ACC'])*(1+strat_return)-1
    df_sector.loc[df_sector.index[i], 'LOG_RETURN'] = log_strat_return
    # 로그누적 = 직전 로그누적 + 현재 로그
    df_sector.loc[df_sector.index[i], 'LOG_RETURN_ACC'] = df_sector.loc[df_sector.index[i-1], 'LOG_RETURN_ACC'] + log_strat_return
    
# 수익률 * 100
df_sector[['RETURN','RETURN_ACC','LOG_RETURN','LOG_RETURN_ACC']] = df_sector[['RETURN','RETURN_ACC','LOG_RETURN','LOG_RETURN_ACC']]*100
df_sector[return_col] = df_sector[return_col] * 100

df_sector

	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY	SHY	...	XLK_r	XLP_r	XLU_r	XLV_r	XLY_r	SHY_r	RETURN	RETURN_ACC	LOG_RETURN	LOG_RETURN_ACC
Date
2003-09-30	14.795932	15.520121	14.317087	16.465275	14.161002	13.081612	11.742328	20.726589	21.877050	61.204376	...	NaN	NaN	NaN	NaN	NaN	NaN	0.000000	0.000000	0.000000	0.000000
2003-10-31	16.205723	15.668549	15.308742	17.483309	15.199060	13.673891	11.822752	20.868189	23.868029	60.954796	...	7.330401	4.527572	0.684909	0.683179	9.100762	-0.407782	6.714135	6.714135	6.498344	6.498344
2003-11-30	16.571718	15.791162	15.252403	17.829716	15.415970	13.834840	11.849562	21.315365	24.082193	60.918385	...	1.427124	1.177052	0.226764	2.142860	0.897287	-0.059735	0.888319	7.662097	0.884396	7.382740
2003-12-31	18.196249	17.858601	15.944183	19.011400	15.899339	14.080931	12.625952	22.548845	25.046740	61.580399	...	3.135507	1.778777	6.552057	5.786814	4.005226	1.086723	6.304695	14.449864	6.113927	13.496667
2004-01-31	17.391766	18.260498	16.465641	19.203211	16.578060	14.080931	12.885720	23.169601	24.903564	61.655003	...	4.268866	0.000000	2.057417	2.752940	-0.571632	0.121149	0.711106	15.263723	0.708589	14.205256
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2021-01-31	70.342949	38.907192	28.822254	84.509895	128.574844	63.745312	61.689369	114.632141	161.753036	86.304970	...	-0.838339	-4.981469	-0.877195	1.401617	0.765016	0.023166	-1.071591	413.258151	-1.077374	163.560875
2021-02-28	73.240715	47.644489	32.167427	90.331978	130.330002	62.959564	57.927460	112.220512	160.894394	86.254997	...	1.365086	-1.232636	-6.098149	-2.103798	-0.530836	-0.057902	1.947834	423.255565	1.929106	165.489981
2021-03-31	78.800003	49.060001	34.049999	98.449997	132.809998	68.309998	64.040001	116.739998	168.070007	86.207031	...	1.902859	8.498206	10.552062	4.027326	4.459828	-0.055610	5.393464	451.477164	5.253043	170.743024
2021-04-30	83.040001	49.389999	36.259998	101.930000	139.699997	69.580002	66.720001	121.330002	178.919998	86.256012	...	5.187862	1.859178	4.184885	3.931818	6.455638	0.056818	4.506847	476.331393	4.408240	175.151264
2021-05-31	87.260002	52.209999	37.990002	105.120003	138.399994	70.809998	65.160004	123.599998	172.839996	86.307999	...	-0.930568	1.767743	-2.338126	1.870928	-3.398168	0.060270	1.730772	486.306378	1.715965	176.867230

213 rows × 44 columns

# MDD

df_sector['BALANCE'] = (1+df_sector['RETURN']/100).cumprod()
df_sector['DRAWDOWN'] = -(df_sector['BALANCE'].cummax() - df_sector['BALANCE']) / df_sector['BALANCE'].cummax()

df_sector[['BALANCE','DRAWDOWN']] = df_sector[['BALANCE','DRAWDOWN']] * 100
df_sector

	XLB	XLE	XLF	XLI	XLK	XLP	XLU	XLV	XLY	SHY	...	XLU_r	XLV_r	XLY_r	SHY_r	RETURN	RETURN_ACC	LOG_RETURN	LOG_RETURN_ACC	BALANCE	DRAWDOWN
Date
2003-09-30	14.795932	15.520121	14.317087	16.465275	14.161002	13.081612	11.742328	20.726589	21.877050	61.204376	...	NaN	NaN	NaN	NaN	0.000000	0.000000	0.000000	0.000000	100.000000	-0.000000
2003-10-31	16.205723	15.668549	15.308742	17.483309	15.199060	13.673891	11.822752	20.868189	23.868029	60.954796	...	0.684909	0.683179	9.100762	-0.407782	6.714135	6.714135	6.498344	6.498344	106.714135	-0.000000
2003-11-30	16.571718	15.791162	15.252403	17.829716	15.415970	13.834840	11.849562	21.315365	24.082193	60.918385	...	0.226764	2.142860	0.897287	-0.059735	0.888319	7.662097	0.884396	7.382740	107.662097	-0.000000
2003-12-31	18.196249	17.858601	15.944183	19.011400	15.899339	14.080931	12.625952	22.548845	25.046740	61.580399	...	6.552057	5.786814	4.005226	1.086723	6.304695	14.449864	6.113927	13.496667	114.449864	-0.000000
2004-01-31	17.391766	18.260498	16.465641	19.203211	16.578060	14.080931	12.885720	23.169601	24.903564	61.655003	...	2.057417	2.752940	-0.571632	0.121149	0.711106	15.263723	0.708589	14.205256	115.263723	-0.000000
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2021-01-31	70.342949	38.907192	28.822254	84.509895	128.574844	63.745312	61.689369	114.632141	161.753036	86.304970	...	-0.877195	1.401617	0.765016	0.023166	-1.071591	413.258151	-1.077374	163.560875	513.258151	-1.071591
2021-02-28	73.240715	47.644489	32.167427	90.331978	130.330002	62.959564	57.927460	112.220512	160.894394	86.254997	...	-6.098149	-2.103798	-0.530836	-0.057902	1.947834	423.255565	1.929106	165.489981	523.255565	-0.000000
2021-03-31	78.800003	49.060001	34.049999	98.449997	132.809998	68.309998	64.040001	116.739998	168.070007	86.207031	...	10.552062	4.027326	4.459828	-0.055610	5.393464	451.477164	5.253043	170.743024	551.477164	-0.000000
2021-04-30	83.040001	49.389999	36.259998	101.930000	139.699997	69.580002	66.720001	121.330002	178.919998	86.256012	...	4.184885	3.931818	6.455638	0.056818	4.506847	476.331393	4.408240	175.151264	576.331393	-0.000000
2021-05-31	87.260002	52.209999	37.990002	105.120003	138.399994	70.809998	65.160004	123.599998	172.839996	86.307999	...	-2.338126	1.870928	-3.398168	0.060270	1.730772	486.306378	1.715965	176.867230	586.306378	-0.000000

213 rows × 46 columns

기본적인 성과 분석 지표를 직접 구해봅니다.

total_month = len(df_sector)
profit_month = len(df_sector[df_sector['RETURN'] >= 0])
loss_month = len(df_sector[df_sector['RETURN'] < 0])
win_rate = profit_month / total_month * 100
CAGR = ((1+df_sector['RETURN_ACC'][-1]/100)**(1/(total_month/12)))-1
STDEV = np.std(df_sector['RETURN'][1:])*math.sqrt(12)
RRR = CAGR * 100 / STDEV

print(total_month, "개월 중 수익 월 :", profit_month, "개월")
print(total_month, "개월 중 손실 월 :", loss_month, "개월")
print("승률 :", round(win_rate, 2))

print('CAGR : ', round(CAGR*100, 2))
print('MDD : ', round(df_sector['DRAWDOWN'].min(), 2))
print('STDEV :', round(STDEV, 2))
print('Return-Risk Ratio: ', round(RRR, 2))

213 개월 중 수익 월 : 147 개월
213 개월 중 손실 월 : 66 개월
승률 : 69.01
CAGR :  10.48
MDD :  -34.98
STDEV : 12.51
Return-Risk Ratio:  0.84

CAGR 10.48%, 변동성 12.51%, MDD -35% 정도입니다. 동일 기간 S&P 500 ETF인 SPY 100%를 투자한다면 거의 동일한 CAGR에 14.2% 변동성, -50% MDD로 섹터 로테이션 듀얼 모멘텀 전략이 벤치마크인 SPY ETF보다 좋습니다.

plt.figure(figsize=(15,5))
seaborn.lineplot(data=df_sector, x=df_sector.index, y=df_sector['LOG_RETURN_ACC'])

<matplotlib.axes._subplots.AxesSubplot at 0x25066016c08>

output_21_1

plt.figure(figsize=(15,5))
seaborn.lineplot(data=df_sector, x=df_sector.index, y=df_sector['DRAWDOWN'])

<matplotlib.axes._subplots.AxesSubplot at 0x250660ad608>

output_22_1

아래 그림의 샤프 비율은 월간 데이터로 구해진 것이라 왜곡되어 있습니다. 환산시킨 0.86이나 Return-Risk Ratio 0.84가 더 믿을 만 합니다. 월간 수익률 차트는 참고할 만 합니다. 2008-2009 구간에 크게 당한 것 말고는 2020 코로나 구간도 괜찮은 방어력을 보여주었습니다.

quantstats.stats.sharpe(df_sector['RETURN'])/math.sqrt(252/12)

0.8624672303343784

quantstats.reports.plots(df_sector['RETURN']/100, mode='basic')

output_25_0 output_25_1

개요

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