【专题研究】基于随机森林模型的智能选股策略

机器学习
策略分享
随机森林
专题报告
标签: #<Tag:0x00007fc829783e50> #<Tag:0x00007fc829783d10> #<Tag:0x00007fc829783bd0> #<Tag:0x00007fc829783a90>

(iQuant) #1

专题研究介绍:机器学习已经成为量化策略设计中的一大利器,了解各种机器学习算法的原理、特点、优劣,对于量化建模有着极大的帮助。因此,本系列【专题研究】介绍几种在资本市场中非常流行的机器学习算法及其在选股方面的相应应用,希望能对大家有所帮助。


$$目录$$
1、什么是随机森林
 1.1 决策树
 1.2 随机:Bagging
 1.3 森林:更精确
 1.4 随机森林的关键参数
 1.4 模型评价
2、随机森林智能选股
 2.1 策略步骤
 2.2 回测结果&特征重要性
 2.3 随机森林模型评价


随机森林是当前使用最广泛的机器学习集成算法之一。由于其简单灵活、不容易过拟合、准确率高的特性,随机森林在很多应用中都体现了较好的效果。

本文从单棵决策树讲起,逐步解释了随机森林的工作原理,然后将随机森林预测应用于二级市场,介绍了基于随机森林模型的智能选股策略。

1、什么是随机森林

随机森林是一种集成算法(Ensemble Learning),它属于Bagging类型,通过组合多个弱学习器(决策树),对弱学习器的结果投票或取均值得到整体模型的最终结果,使得整体模型的结果具有较高的精确度和泛化性能。其之可以取得不错成绩,主要归功于“随机”和“森林”,一个使它具有抗过拟合能力,一个使它更加精准

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$$图1:随机森林(分类)模型示意图$$

1.1 决策树

随机森林是多个决策树的集成。所以理解随机森林,首先要从理解决策树开始。

日常生活中,我们对于事物的认知都是基于特征的判断与分类,譬如通过胎生与否可判断哺乳动物,根据肚脐尖圆来挑选螃蟹公母。决策树就是采用这样的思想,基于多个特征进行分类决策。在树的每个结点处,根据特征的表现通过某种规则分裂出下一层的叶子节点,终端的叶子节点即为最终的分类结果。决策树学习的关键是选择最优划分属性。随着逐层划分,决策树分支结点所包含的样本类别会逐渐趋于一致,从而得到最终分类。

目前主流的决策树算法包括C4.5 和CART:C4.5 每个节点可分裂成多个子节点,不支持特征的组合,只能用于分类问题;CART 每个节点只分裂成两个子节点,支持特征的组合,可用于分类和回归问题。而在随机森林中,通常采用CART 算法来选择划分属性,所以以下主要介绍CART决策树。

(1)决策树如何分裂

答案是:基尼不纯度(Gini Impurity)的最大减少。
那么问题来了,什么是基尼不纯度?

节点的基尼不纯度是指,根据节点中样本的分布对样本分类时,从节点中随机选择的样本被分错的概率。因此,基尼不纯度越小,样本的纯度越高。

假设有K 个类,样本集D中的点属于第k 类的概率为𝑃𝑘,其基尼不纯度为:
$$Gini(D)=1-\sum_{k=1}^{K} {{P_k}^2}$$
根据特征A 分裂为𝐷1和𝐷2两不相交部分,则分裂后的
$$Gini(D,A)=\frac{|D_1|}{|D|}Gini(D_1)+\frac{|D_2|}{|D|}Gini(D_2)$$
以Gini(𝐷, A)最小的特征A 为划分属性,将训练集依特征分配到两个子结点中去。

说白了,决策树的分裂标准是:怎么分能让分类完的结果更“纯粹”,就怎么分。

(2)何时停止生长

从根节点开始,递归地在每个结点分裂时选取Gini(𝐷, A)最小的特征A 为划分属性,将训练集依特征分配到两个子结点中去。照此逐层划分,直至结点中样本个数小于预定阈值,或样本集的Gini 指数小于预定阈值,或者没有更多特征,即停止生长,形成了一棵可进行分类预测的决策树。

(3)决策树的效果

很容易理解,如果决策树一直分裂,终有一日可以将所有的训练样本精确分类,但是这也会造成过拟合
%E8%BF%87%E6%8B%9F%E5%90%88
$$图2:单颗决策树的过拟合现象$$
为了解决决策树的致命问题“过拟合”,随机森林闪亮登场。

1.2 随机:Bagging

Bagging 是一种并行的集成学习的方法。基于“自助采样法”(bootstrap sampling),主要关注降低方差,因此它在容易受到样本扰动的学习器(如不剪枝的决策树)中效果明显。

Bootstrap 就是从训练集里面有放回地采集固定个数的样本,形成对于每一个弱学习器的样本集。也就是说,被采集过的样本在放回后有可能不止一次被采集到。

Bagging 算法中,对有m 个样本训练集做T 次的随机采样,则由于随机性,一般来说T 个采样集各不相同。正是由于Bagging 每次利用不同采样集来训练模型,故其泛化能力较强,有助于降低模型的方差。但是不可避免地其对训练集的拟合程度就会差一些,即增大了模型的偏倚。这时,为了避免可能的过大的偏倚,我们需要将树组合成森林。


$$图3:Bagging示意图$$

1.3 森林:更精确

俗话说“三个臭皮匠顶个诸葛亮”,随机森林就是典型的“三个臭皮匠”。

每个树的预测结果可能都不尽如人意,但是如果有多个树,让这些树投票选出最有可能的分类结果或者对于所有树的结果取均值得到回归结果,那么森林的预测就会更准确。


$$图4:组成森林$$

1.4 随机森林的关键参数

  • n_estimators (int) – 树的个数,个数越多,则模型越复杂,计算速度越慢。
  • max_features (str) – 最多考虑特征个数,新建节点时,最多考虑的特征个数。
  • max_depth (int) – 每棵树的最大深度,数值大拟合能力强,数值小泛化能力强。
  • min_samples_leaf (int) – 每个叶子节点最少样本数,数值大泛化能力强,数值小拟合能力强。
  • n_jobs (int) – 并行度,同时使用多少个进程进行计算,最多是4。

1.5 模型评价

(1)特征重要性

随机森林模型可以在预测的同时通过特征划分过程来计算评估各个因子特征的重要性。特征影响力的计算需要借助于结点分裂时Gini 指数,方法如下:
$$ I_i(A)=Gini(D_i)-Gini(D_i,A) $$
$$S(A)=\sum_{i}I_i(A) $$
其中,𝐼𝑖 (𝐴)表示结点i 根据特征A 分裂为两个子结点后,Gini 指数相对于母结点分裂前的下降值。故而可定义特征A 的绝对重要性𝑆(𝐴)为所有按特征A 分裂的结点处的𝐼𝑖 (𝐴)之和。将所有特征的绝对重要性归一化,即可得到各个特征的重要性评分

(2)模型评价

a. 回归模型

  • 可解释方差 EVS:可以被解释的方差,越接近1越好
  • 平均绝对误差 MAE:预测值和真实值的差值。数值越小越好
  • 均方误差 MSE:预测值和实际值的平方误差。数值越小越好
  • 均方对数误差 lnMSE:取对数后预测值和实际值的平方误差。当目标具有指数增长的目标时,最适合使用这一指标
  • 中位数绝对误差 median absolute error:取目标和预测之间的所有绝对差值的中值来计算损失
  • 确定系数(r^2) r2:预测模型和真实数据的拟合程度,最佳值为1,同时可为负值

b. 分类模型

  • 准确率 accuracy:预测正确的的数据占所有数据的比例
  • 精确率 precision:预测正确的正例数据占预测为正例数据的比例
  • 召回率 recall:预测为正例的数据占实际为正例数据的比例
  • F1分 f1 score:综合指标。F值 = 正确率 * 召回率 * 2 / (正确率 + 召回率)

2、随机森林智能选股

%E6%B5%81%E7%A8%8B
$$图5:随机森林智能选股策略$$

2.1 策略步骤

如图5所示,随机森林的策略构建包含下列步骤:

  • 获取数据:A股所有股票。
  • 特征和标签提取:计算18个因子作为样本特征;计算未来5日的个股收益作为样本的标签。
  • 特征预处理:进行缺失值处理。
  • 模型训练与预测:使用随机森林模型进行训练和预测。
  • 策略回测:利用2010到2017年数据进行训练,预测2017到2019年的股票表现。每日买入预测排名最靠前的5只股票,至少持有五日,同时淘汰排名靠后的股票。具体而言,预测排名越靠前,分配到的资金越多且最大资金占用比例不超过20%;初始5日平均分配资金,之后,尽量使用剩余资金(这里设置最多用等量的1.5倍)。
  • 模型评价:查看特征重要性和模型回归结果。

2.2 回测结果&特征重要性

回测结果如下:


$$图6:策略回测结果$$
从回测结果可以看出,由于市场本身问题,随机森林策略在2017-2018年的表现并不很好,但是当市场风格趋于一致时,随机森林策略表现出了不错的选股效果。

随机森林模型可以按照重要性输出特征,有助于我们分析哪些因素对于预测的帮助更大,从而优化模型。使用特征重要性如下:
%E9%87%8D%E8%A6%81%E6%80%A7
$$图7:特征重要性结果节选$$

2.3 随机森林模型评价

下面进行模型评价。训练集和预测集上的情况分别如下:
%E8%AE%AD%E7%BB%83%E9%9B%86
$$图8:训练集评估$$

%E9%A2%84%E6%B5%8B%E9%9B%86
$$图9:预测集评估$$
可以看到,模型的整体误差和拟合程度还有进一步优化的空间,此策略仅抛砖引玉,欢迎继续探索。

策略原代码如下:

克隆策略

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    In [5]:
    # 本代码由可视化策略环境自动生成 2019年4月22日 19:42
    # 本代码单元只能在可视化模式下编辑。您也可以拷贝代码,粘贴到新建的代码单元或者策略,然后修改。
    
    
    # 回测引擎:每日数据处理函数,每天执行一次
    def m19_handle_data_bigquant_run(context, data):
        # 按日期过滤得到今日的预测数据
        ranker_prediction = context.ranker_prediction[
            context.ranker_prediction.date == data.current_dt.strftime('%Y-%m-%d')]
        
        ranker_prediction = ranker_prediction.sort_values('pred_label', ascending=False)
     
        
        # 1. 资金分配
        # 平均持仓时间是hold_days,每日都将买入股票,每日预期使用 1/hold_days 的资金
        # 实际操作中,会存在一定的买入误差,所以在前hold_days天,等量使用资金;之后,尽量使用剩余资金(这里设置最多用等量的1.5倍)
        is_staging = context.trading_day_index < context.options['hold_days'] # 是否在建仓期间(前 hold_days 天)
        cash_avg = context.portfolio.portfolio_value / context.options['hold_days']
        cash_for_buy = min(context.portfolio.cash, (1 if is_staging else 1.5) * cash_avg)
        cash_for_sell = cash_avg - (context.portfolio.cash - cash_for_buy)
        positions = {e.symbol: p.amount * p.last_sale_price
                     for e, p in context.portfolio.positions.items()}
    
        # 2. 生成卖出订单:hold_days天之后才开始卖出;对持仓的股票,按机器学习算法预测的排序末位淘汰
        if not is_staging and cash_for_sell > 0:
            equities = {e.symbol: e for e, p in context.portfolio.positions.items()}
            instruments = list(reversed(list(ranker_prediction.instrument[ranker_prediction.instrument.apply(
                    lambda x: x in equities)])))
    
            for instrument in instruments:
                context.order_target(context.symbol(instrument), 0)
                cash_for_sell -= positions[instrument]
                if cash_for_sell <= 0:
                    break
    
        # 3. 生成买入订单:按机器学习算法预测的排序,买入前面的stock_count只股票
        buy_cash_weights = context.stock_weights
        buy_instruments = list(ranker_prediction.instrument[:len(buy_cash_weights)])
        max_cash_per_instrument = context.portfolio.portfolio_value * context.max_cash_per_instrument
        for i, instrument in enumerate(buy_instruments):
            cash = cash_for_buy * buy_cash_weights[i]
            if cash > max_cash_per_instrument - positions.get(instrument, 0):
                # 确保股票持仓量不会超过每次股票最大的占用资金量
                cash = max_cash_per_instrument - positions.get(instrument, 0)
            if cash > 0:
                context.order_value(context.symbol(instrument), cash)
    
    # 回测引擎:准备数据,只执行一次
    def m19_prepare_bigquant_run(context):
        pass
    
    # 回测引擎:初始化函数,只执行一次
    def m19_initialize_bigquant_run(context):
        # 加载预测数据
        
        context.ranker_prediction = context.options['data'].read_df()
        
    
        # 系统已经设置了默认的交易手续费和滑点,要修改手续费可使用如下函数
        context.set_commission(PerOrder(buy_cost=0.0003, sell_cost=0.0013, min_cost=5))
        # 预测数据,通过options传入进来,使用 read_df 函数,加载到内存 (DataFrame)
        # 设置买入的股票数量,这里买入预测股票列表排名靠前的5只
        stock_count = 5
        # 每只的股票的权重,如下的权重分配会使得靠前的股票分配多一点的资金,[0.339160, 0.213986, 0.169580, ..]
        context.stock_weights = T.norm([1 / math.log(i + 2) for i in range(0, stock_count)])
        # 设置每只股票占用的最大资金比例
        context.max_cash_per_instrument = 0.2
        context.options['hold_days'] = 5
    
    
    m1 = M.instruments.v2(
        start_date='2010-01-01',
        end_date='2017-01-01',
        market='CN_STOCK_A',
        instrument_list='',
        max_count=0
    )
    
    m2 = M.advanced_auto_labeler.v2(
        instruments=m1.data,
        label_expr="""# #号开始的表示注释
    # 0. 每行一个,顺序执行,从第二个开始,可以使用label字段
    # 1. 可用数据字段见 https://bigquant.com/docs/develop/datasource/deprecated/history_data.html
    #   添加benchmark_前缀,可使用对应的benchmark数据
    # 2. 可用操作符和函数见 `表达式引擎 <https://bigquant.com/docs/develop/bigexpr/usage.html>`_
    
    # 计算收益:5日收盘价(作为卖出价格)除以明日开盘价(作为买入价格)
    shift(close, -5) / shift(open, -1)
    
    # 极值处理:用1%和99%分位的值做clip
    clip(label, all_quantile(label, 0.01), all_quantile(label, 0.99))
    
    # 将分数映射到分类,这里使用20个分类
    all_wbins(label, 20)
    
    # 过滤掉一字涨停的情况 (设置label为NaN,在后续处理和训练中会忽略NaN的label)
    where(shift(high, -1) == shift(low, -1), NaN, label)
    """,
        start_date='',
        end_date='',
        benchmark='000300.SHA',
        drop_na_label=True,
        cast_label_int=True
    )
    
    m3 = M.input_features.v1(
        features="""(close_0-mean(close_0,12))/mean(close_0,12)*100
    rank(std(amount_0,15))
    rank_avg_amount_0/rank_avg_amount_8
    ts_argmin(low_0,20)
    rank_return_30
    (low_1-close_0)/close_0
    ta_bbands_lowerband_14_0
    mean(mf_net_pct_s_0,4)
    amount_0/avg_amount_3
    return_0/return_5
    return_1/return_5
    rank_avg_amount_7/rank_avg_amount_10
    ta_sma_10_0/close_0
    sqrt(high_0*low_0)-amount_0/volume_0*adjust_factor_0
    avg_turn_15/(turn_0+1e-5)
    return_10
    mf_net_pct_s_0
    (close_0-open_0)/close_1"""
    )
    
    m15 = M.general_feature_extractor.v7(
        instruments=m1.data,
        features=m3.data,
        start_date='',
        end_date='',
        before_start_days=0
    )
    
    m16 = M.derived_feature_extractor.v3(
        input_data=m15.data,
        features=m3.data,
        date_col='date',
        instrument_col='instrument',
        drop_na=False,
        remove_extra_columns=False
    )
    
    m7 = M.join.v3(
        data1=m2.data,
        data2=m16.data,
        on='date,instrument',
        how='inner',
        sort=False
    )
    
    m13 = M.dropnan.v1(
        input_data=m7.data
    )
    
    m9 = M.instruments.v2(
        start_date=T.live_run_param('trading_date', '2017-01-01'),
        end_date=T.live_run_param('trading_date', '2019-04-19'),
        market='CN_STOCK_A',
        instrument_list='',
        max_count=0
    )
    
    m17 = M.general_feature_extractor.v7(
        instruments=m9.data,
        features=m3.data,
        start_date='',
        end_date='',
        before_start_days=0
    )
    
    m18 = M.derived_feature_extractor.v3(
        input_data=m17.data,
        features=m3.data,
        date_col='date',
        instrument_col='instrument',
        drop_na=False,
        remove_extra_columns=False
    )
    
    m14 = M.dropnan.v1(
        input_data=m18.data
    )
    
    m4 = M.random_forest_regressor.v1(
        training_ds=m13.data,
        features=m3.data,
        predict_ds=m14.data,
        iterations=10,
        feature_fraction=1,
        max_depth=30,
        min_samples_per_leaf=200,
        key_cols='date,instrument',
        workers=1,
        other_train_parameters={}
    )
    
    m19 = M.trade.v4(
        instruments=m9.data,
        options_data=m4.predictions,
        start_date='',
        end_date='',
        handle_data=m19_handle_data_bigquant_run,
        prepare=m19_prepare_bigquant_run,
        initialize=m19_initialize_bigquant_run,
        volume_limit=0.025,
        order_price_field_buy='open',
        order_price_field_sell='close',
        capital_base=1000000,
        auto_cancel_non_tradable_orders=True,
        data_frequency='daily',
        price_type='后复权',
        product_type='股票',
        plot_charts=True,
        backtest_only=False,
        benchmark='000300.SHA'
    )
    
    • 收益率66.26%
    • 年化收益率25.76%
    • 基准收益率24.49%
    • 阿尔法0.19
    • 贝塔0.59
    • 夏普比率0.86
    • 胜率0.54
    • 盈亏比1.09
    • 收益波动率27.73%
    • 信息比率0.04
    • 最大回撤23.26%
    bigcharts-data-start/{"__id":"bigchart-9870a6e796084a8e82aafec00239885b","__type":"tabs"}/bigcharts-data-end

    参考文献


    【专题研究】基于SVM支持向量机模型的选股策略
    【专题研究】基于XGBoost模型的智能选股策略
    (zdy0225) #4

    你好,为什么克隆代码重新运行后回测结果就不一样了


    (iQuant) #5

    您好,克隆后会模型会重新训练,每次重新训练结果都会或多或少有所不同。


    (zdy0225) #6

    想问一下这个代码里有选股部分的代码吗 就是策略步骤介绍的哪里。我重新运行之后收益率直接变成了负的,和原始的有很大出入,想问这是什么原因。


    (iQuant) #7

    可以参考学院板块,每一步都有详细教程帖:https://bigquant.com/tutorial/


    (xuehao) #8

    您好,请问是哪18个因子呢?


    (达达) #9

    策略中有,见输入特征列表