股票Beta值计算代码问题：与Yahoo Finance/Zacks结果不符

我正基于SPY计算股票的Beta值，但计算结果与Yahoo Finance和Zacks上的数值始终不符。Beta值的标准计算公式为：Beta = 协方差（股票与指数） / 方差（指数）。

以下是调用get_beta(['AAPL'])的初始代码及输出：

初始代码 #

def covariance(self, SPY_hist, hist2):

        SPY_closes = SPY_hist['Close'].to_list()
        length = len(SPY_closes)

        SPY_average = 0
        for p in SPY_closes:
            SPY_average += p
        SPY_average = SPY_average / length

        hist2_closes = hist2['Close'].to_list()
        length = len(hist2_closes)

        hist2_average = 0
        for day in hist2_closes:
            hist2_average += day
        hist2_average = hist2_average / length

        total = 0
        for i in range(len(SPY_hist)):
            total += ((SPY_closes[i] - SPY_average) * (hist2_closes[i] - hist2_average))

        return total / (length - 1)

    def variance(self, SPY_hist):

        SPY_closes = SPY_hist['Close'].to_list()
        length = len(SPY_closes)

        SPY_average = 0
        for p in SPY_closes:
            SPY_average += p
        SPY_average = SPY_average / length

        sum = 0
        for i in SPY_closes:
            dif = i - SPY_average
            sum += (dif ** 2)

        return (sum / (length-1))


    def beta(self, SPY_hist, hist2):

        _covariance = self.covariance(SPY_hist=SPY_hist, hist2=hist2)

        _variance = self.variance(SPY_hist=SPY_hist)

        return (_covariance / _variance)

    def get_beta(self, securities):

        SPY_hist = yfinance.Ticker('SPY').history('1mo')
        betas = {}

        for security in securities:
            security_hist = yfinance.Ticker(security).history('1mo')
            b = self.beta(SPY_hist=SPY_hist, hist2=security_hist)
            betas[security] = b

        return betas

初始输出 #

{'AAPL': 0.6610297779078679}

我测试了苹果（AAPL）和特斯拉（TSLA）两只股票，计算出的Beta值均明显偏低——苹果的Beta值理应高于SPY。使用5年期数据时，预期苹果Beta约为1.27、特斯拉约为2.07，但实际计算值仅为0.66和1.5。

更新 #

我了解到Yahoo计算Beta时使用的是每日涨跌幅而非收盘价本身，公式为：Beta = （股票每日涨跌幅与指数每日涨跌幅的协方差） / （指数每日涨跌幅的方差）。我实现了涨跌幅计算函数并修改代码后，结果更接近预期但仍存在偏差：苹果的计算值为1.14，特斯拉为2.5。

更新后代码 #

def covariance(self, SPY_hist, hist2):

        #SPY_closes = SPY_hist['Close'].to_list()
        SPY_closes = SPY_hist
        length = len(SPY_closes)

        SPY_average = 0
        for p in SPY_closes:
            SPY_average += p
        SPY_average = SPY_average / length

        #hist2_closes = hist2['Close'].to_list()
        hist2_closes = hist2
        length = len(hist2_closes)

        hist2_average = 0
        for day in hist2_closes:
            hist2_average += day
        hist2_average = hist2_average / length

        total = 0
        for i in range(len(SPY_hist)):
            total += ((SPY_closes[i] - SPY_average) * (hist2_closes[i] - hist2_average))

        return total / (length - 1)

    def variance(self, SPY_hist):

        #SPY_closes = SPY_hist['Close'].to_list()
        SPY_closes = SPY_hist
        length = len(SPY_closes)

        SPY_average = 0
        for p in SPY_closes:
            SPY_average += p
        SPY_average = SPY_average / length

        sum = 0
        for i in SPY_closes:
            dif = i - SPY_average
            sum += (dif ** 2)

        return (sum / (length-1))


    def beta(self, SPY_hist, hist2):

        _covariance = self.covariance(SPY_hist=SPY_hist, hist2=hist2)

        _variance = self.variance(SPY_hist=SPY_hist)

        return (_covariance / _variance)

    def percent_change(self, hist):

        closes = hist['Close'].to_list()
        percent_change = []
        for i in range(len(closes)):
            if i != 0:
                percent_change.append(((closes[i-1] - closes[i]) / closes[i-1]) * 100)

        return percent_change

    def get_beta(self, securities):

        SPY_hist = yfinance.Ticker('SPY').history('1mo')
        SPY_pc = self.percent_change(hist=SPY_hist)
        betas = {}

        for security in securities:
            security_hist = yfinance.Ticker(security).history('1mo')
            security_pc = self.percent_change(hist=security_hist)
            b = self.beta(SPY_hist=SPY_pc, hist2=security_pc)
            betas[security] = b

        return betas

内容的提问来源于stack exchange，提问作者Alex Michael