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何时持有股票，何时持有黄金

学术论文

作者When to Own Stocks and When to Own Gold [点击查看论文]

论文链接https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3535152

策略概要

该策略的投资范围包括标普500指数和黄金。世俗市场指标（SMI）的构建方法是：席勒市盈率（C）除以黄金现货价格（A）。基于SMI的资产配置策略如下：当SMI向上穿过+1阈值时，超配黄金。保持超配黄金，直到SMI向下穿过-1阈值，此时切换到超配股票。保持超配股票，直到SMI再次向上穿过+1阈值，这标志着切换回黄金。该策略利用SMI，根据市场状况动态地在黄金和股票之间进行资产配置。

II. 策略合理性

该论文讨论了股票和黄金回报分布的差异，这些差异受到长期经济条件的影响。它批评了CAPE（周期性调整市盈率）作为长期市场指标，认为它未能提供及时信号，并存在参考和同质性问题。将黄金纳入分析是基于其长期的通胀对冲特性、其经通胀调整后的价格的均值回归，以及其与经济政策不确定性的相关性。为了解决这些问题，该论文引入了长期市场指标（SMI），该指标将CAPE比率与黄金现货价格进行比较。SMI提供了金融资产（股票）与实物资产（黄金）的相对比较，其中分子反映经济实力，分母反映经济疲软和不确定性。这种方法旨在更有效地为投资决策提供信息。

回测表现

波动率14%

夏普比率0.43

索提诺比率0.178

最大回撤-28%

胜率56%

完整 Python 代码

1import numpy as np
2from AlgorithmImports import *
3from scipy import stats
4from typing import List, Dict
5import data_tools
6class WhentoOwnStocksandWhentoOwnGold(QCAlgorithm):
7def Initialize(self) -> None:
8self.SetStartDate(1996, 1, 1)
9self.SetCash(100000)
10self.warmpup_period: int = 100*12*21
11data: Securities = self.AddEquity('SPY', Resolution.Daily)
12self.spy_symbol: Symbol = data.Symbol
13
14self.SetWarmUp(timedelta(self.warmpup_period), Resolution.Daily)    # Load data from 100 years ago.
15
16self.smi: List[float] = []       # SMI indicator historical values.
17self.cape_symbol: Symbol = self.AddData(data_tools.QuantpediaMonthlyData, 'SHILLER_PE_RATIO_MONTH', Resolution.Daily).Symbol
18
19data: Security = self.AddData(data_tools.QuantpediaFutures, 'CME_GC1', Resolution.Daily)
20data.SetFeeModel(data_tools.CustomFeeModel())
21self.gold_symbol: Symbol = data.Symbol
22
23stockPlot: Chart = Chart('SMI')
24stockPlot.AddSeries(Series('SMI', SeriesType.Line, 0))
25
26# self.last_month = 0
27self.rebalance_flag: bool = False
28self.Settings.MinimumOrderMarginPortfolioPercentage = 0.
29self.Schedule.On(self.DateRules.MonthStart(self.spy_symbol), self.TimeRules.AfterMarketOpen(self.spy_symbol), self.Rebalance)
30self.settings.daily_precise_end_time = False
31def OnData(self, data: Slice) -> None:
32custom_data_last_update_date: Dict[Symbol, datetime.date] = data_tools.LastDateHandler.get_last_update_date()
33if (self.Securities[self.cape_symbol].GetLastData() and self.Time.date() > custom_data_last_update_date[self.cape_symbol]) or \
34    (self.Securities[self.gold_symbol].GetLastData() and self.Time.date() > custom_data_last_update_date[self.gold_symbol]):
35    self.Liquidate()
36    return
37# Cape value comes at the start of the month
38if self.cape_symbol in data and data[self.cape_symbol] and self.gold_symbol in data and data[self.gold_symbol]:
39    gold_price: float = data[self.gold_symbol].Value
40    cape: float = data[self.cape_symbol].Value
41    
42    if cape == 0:
43        return
44    
45    if gold_price == 0:
46        gold_price = 19.25
47        
48    smi: float = cape / np.log(gold_price)
49    self.Plot('SMI', 'SMI', smi)
50    self.smi.append(smi)
51if not self.rebalance_flag:
52    return
53# if self.spy_symbol in data and data[self.spy_symbol] and self.gold_symbol in data and data[self.gold_symbol]:
54self.rebalance_flag = False 
55if len(self.smi) != 0:
56    data_points = [x for x in range(0, len(self.smi))]
57    slope, intercept, r_value, p_value, std_err = stats.linregress(data_points, self.smi)
58    # Linear regression - X = independent, Y = dependent
59    # y = alpha + beta.x
60    alpha = intercept
61    beta = slope
62    x = data_points[-1]
63    y = alpha + (beta*x)
64    
65    smi = self.smi[-1]
66    if self.spy_symbol in data and data[self.spy_symbol] and self.gold_symbol in data and data[self.gold_symbol]:
67        if smi > y + 1*std_err:
68            self.Liquidate(self.spy_symbol)
69            self.SetHoldings(self.gold_symbol, 1)
70        elif smi < y - 1*std_err:
71            self.Liquidate(self.gold_symbol)
72            self.SetHoldings(self.spy_symbol, 1)
73def Rebalance(self) -> None:
74self.rebalance_flag = True