英文标题：
《A Stock Market Model Based on CAPM and Market Size》
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作者：
Andrey Sarantsev, Blessing Ofori-Atta, Brandon Flores
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最新提交年份：
2021
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英文摘要：
We introduce a new system of stochastic differential equations which models dependence of market beta and unsystematic risk upon size, measured by market capitalization. We fit our model using size deciles data from Kenneth French\'s data library. This model is somewhat similar to generalized volatility-stabilized models in (Pal, 2011; Pickova, 2013). The novelty of our work is twofold. First, we take into account the difference between price and total returns (in other words, between market size and wealth processes). Second, we work with actual market data. We study the long-term properties of this system of equations, and reproduce observed linearity of the capital distribution curve. Our model has two modifications: for price returns and for equity premium. Somewhat surprisingly, they exhibit the same fit, with very similar coefficients. In the Appendix, we analyze size-based real-world index funds.
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中文摘要：
我们引入了一个新的随机微分方程系统，该系统模拟了市场贝塔和非系统风险对规模的依赖性，以市值衡量。我们使用肯尼思·弗伦奇（KennethFrench）数据库中的大小十分位数数据来拟合我们的模型。该模型在某种程度上类似于（Pal，2011；Pickova，2013）中的广义波动率稳定模型。我们工作的新颖性是双重的。首先，我们考虑了价格和总回报之间的差异（换句话说，市场规模和财富过程之间的差异）。其次，我们使用实际的市场数据。我们研究了这一方程组的长期性质，并再现了观察到的资本分布曲线的线性。我们的模型有两个修改：价格回报和股权溢价。令人惊讶的是，它们表现出相同的拟合，系数非常相似。在附录中，我们分析了基于规模的真实指数基金。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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