python金融风控模型模型和数据分析微专业课
（微信二维码扫一扫报名）
Updated March 5, 2021
Overview
US interest rates are currently near all-time lows. Broadly speaking, this suggests that investments made in debt products (e.g., bonds) are paying very little in returns, and so are not highly demanded by investors. Investors have little else to do with cash right now other than to put it into equities, which drives the stock market higher. As of March 5, 2021, we observe that relative to a normal interest rate environment the US stock market is Fairly Valued.
Below is our composite chart showing the position of the S&P500 relative to its average position, and adjusted for average interest rates. Read the detail below to understand in inputs and limitations of this model.
Theory & Data
There are two core reasons that stock markets and interest rates tend to move inversely with one another.
- Lower Profits. As market interest rates rise, that means that firms who wish to borrow money in order to fund profitable projects will need to pay more in interest payments. This will necessarily lower profits. In some cases, it means the firms will not be able to do the project at all. Lower profits mean lower stock prices, since stock prices are fundamentally a measure of all future profits of a firm. The opposite is true as well - as rates fall firms are able to borrow more, which increases profits and expands economic output.
- Less Demand. As market interest rates rise investors are able to earn higher yields by investing in debt instruments (bonds, etc) rather than equities (stocks). This lowers the demand for stocks, which lowers their prices. Likewise, when interest rates are very low, investors seeking a return on their cash don't have many available choices, and tend to get pushed into riskier assets (lower quality bonds, stocks), in order to make a return. This drives those prices higher.
There is plenty more to know about the inverse correlation between stocks and bonds. Check out these resources for more info.
Suffice it to say here that what we are primarily concerned with is the question: Is the current market fairly valued when considering current interest rates?
Current Values & Analysis
Interest Rates
Figure 1 below shows the Ten Year Treasury Bond rate over the last ~60 years, from 1962 to present day. Rates spiked in the '70s and '80s as a response to high inflation at the time, and since then have been on a pretty steady downward trajectory.
Figure 1. Ten Year Treasury Bond Interest Rates
Trendlines
The average (arithmetic mean) of this rate over the entire timeframe is roughly 6%. Rates haven't been in that neighborhood for about 20 years, but history does suggest that a healthy economy should revert back up to higher rates eventually. ("Eventually" here is quite a loaded term, and speculating on future Fed monetary policy decisions, or on fundamental changes to Fed policy and philosophy, are outside of the scope of this article, but only a Google search away).
Figure 2A below shows the same chart as above, only this time with the 6% average trendline drawn in. Figure 2B in blue shows the real S&P500 over the same time frame, as well is its corresponding trendline. [This comes directly from our S&P500 Model detail, so look there for more detail on the data and trendline.]
Figures 2A & 2B
Detrending the Data
Instead of looking at the raw values for each of these charts, we can instead think about each of them in terms of their performance relative to their respective trendlines. Are they above or below the respective trend? In the two charts below we map each chart in terms of the number of standard deviations above/below the value of its respective trendline.
You can see in the left chart that the most current 10Year interest rate is about ~1.75 standard deviations below normal. Likewise, you can see in the chart to the right that the S&P500 is currently ~1.6 standard deviations above its trendline. As explained above, it is not surprising that this is the case. We should generally expect that when interest rates are relatively high, stocks should be relatively low, and vice versa.
Figures 3A & 3B
Comparison
As mentioned above, we should generally expect that when interest rates are relatively high, stocks should be relatively low. What ought to be very interesting to us is when interest rates and stock prices are in the same phase (both high or both low, relative to their trendlines). Since we are already expressing data in both charts in terms of standard deviations above/below trend, we can just sum the two charts together to see where they are out of phase.
Figure 4. Composite Sum - S&P500 vs 10Y Rates, Std Devs from Trendline
Summary
Figure 4 above shows our final chart. The two relative performance indicators for interest rates (red) and stocks (blue) have been combined, showing a composite value in purple. When greater than zero, this indicates that rates are high, and stocks are also high. The peak here is during the 2000 internet bubble. During this time stocks prices were very high, but bond prices were right around average... meaning that even though investors had other good options to invest in, and despite the high interest rates firms needed to pay in order to borrow money, stocks were still very high. That's a clear bubble - which we all know in retrospect popped loudly and abruptly.
On those merits, we are not in a similar bubble today. As of March 5, 2021, the 10Y Treasury bond rate was 1.54%, which is 1.5 standard deviations below normal. Likewise, the S&P500 value of $3,842 is 1.8 standard deviations above its own respective trendline. Summed together, this gives a composite value of 0.3 standard deviations above normal, indicating that stocks are currently Fairly Valued.
Data Sources
The below table cites all data and sources used in constructing the charts, or otherwise referred to, on this page.
2021年3月5日更新
概述
美国利率目前接近历史最低点。从广义上讲，这表明对债务产品（例如债券）的投资所获得的回报很少，因此对投资者的要求不高。投资者现在除了将现金投入股票外，与现金几乎没有关系，这推动了股市的上涨。截至2021年3月5日，我们观察到相对于正常利率环境，美国股票市场价值合理。
以下是我们的综合图表，显示了S＆P500相对于其平均头寸的头寸，并根据平均利率进行了调整。阅读以下详细信息，以了解此模型的输入和限制。
参考https://www.currentmarketvaluation.com/models/10y-interest-rates.php
理论与数据
股市和利率倾向于相互逆向移动有两个核心原因。
- 降低利润。随着市场利率的上升，这意味着希望借钱来为盈利项目提供资金的公司将需要支付更多的利息。这必然会降低利润。在某些情况下，这意味着公司将根本无法执行该项目。较低的利润意味着较低的股价，因为股价从根本上衡量了公司所有未来利润。反之亦然-随着利率下降，企业能够借入更多贷款，从而增加利润并扩大经济产出。
- 需求减少。随着市场利率上升，投资者可以通过投资债务工具（债券等）而不是股票（股票）来获得更高的收益。这降低了对股票的需求，从而降低了价格。同样，在利率非常低的情况下，寻求现金回报的投资者没有太多可用选择，他们往往会被压入风险较高的资产（劣质债券，股票）以获取回报。这将推动这些价格上涨。
关于股票和债券之间的逆相关性，还有更多的知识要知道。查看这些 资源以获取更多信息。
在这里可以简单地说，我们主要关心的问题是：在考虑当前利率时，当前市场的估值是否合理？
当前值与分析
利率
下面的图1显示了从1962年至今的过去60年间的十年期国债利率。由于当时的高通货膨胀率，70年代和80年代的利率飙升，此后一直处于相当稳定的下降轨道。
图1.十年期国债利率
趋势线
在整个时间范围内，此速率的平均值（算术平均值）约为6％。房价已不存在该区域约20年的历史，但历史确实表明，健康的经济最终应恢复到更高的利率。（“最终”在这里是一个很繁琐的术语，并且对未来的美联储货币政策决定或对美联储政策和理念的根本变化进行推测，不在本文讨论范围之内，只是谷歌搜索不到）。
下面的图2A显示了与上面相同的图表，只是这次绘制了6％的平均趋势线。蓝色的图2B显示了在同一时间范围内的真实S＆P500，以及其对应的趋势线。[这直接来自我们的S＆P500模型详细信息，因此请查看此处以获取有关数据和趋势线的更多详细信息。]
图2A和2B
数据去趋势
不用查看每个图表的原始值，而是可以根据它们相对于各自趋势线的性能来考虑它们。它们是高于还是低于各自的趋势？在下面的两个图表中，我们根据高于或低于其各自趋势线值的标准偏差的数量来绘制每个图表。
您可以在左图中看到，最新的10年期利率大约比正常水平低约1.75个标准差。同样，您可以在右边的图表中看到S＆P500当前在其趋势线上方约1.6个标准差。如上所述，这种情况并不奇怪。我们通常应该期望，当利率相对较高时，库存应该相对较低，反之亦然。
图3A和3B
比较
如上所述，我们通常应该期望，当利率相对较高时，库存应该相对较低。当利率和股票价格处于同一阶段时（相对于趋势线而言，两者都高或低）时，对我们来说应该非常有趣。由于我们已经在两个图表中以高于/低于趋势的标准偏差表示数据，因此我们可以将两个图表相加在一起，以查看它们的异相位置。
图4.综合总和-S＆P500与10年利率，趋势线的标准偏差
概括
上面的图4显示了我们的最终图表。利率（红色）和股票（蓝色）的两个相对绩效指标已合并，以紫色显示复合值。大于零时，表示利率很高，库存也很高。这里的高峰是在2000年互联网泡沫期间。在此期间，股票价格非常高，但债券价格却接*均水平……这意味着，即使投资者还有其他良好的投资选择，尽管公司需要支付高利率才能借钱，但股票仍然是仍然很高。那是一个明显的泡沫-回顾过去，我们都知道它突然大声地弹出了。
基于这些优点，我们今天不在类似的泡沫中。截至2021年3月5日，10年期美国国债利率为1.54％，比正常水平低1.5个标准差。同样，S＆P500的3,842美元值比其各自的趋势线高1.8个标准差。总计起来，得出的复合值为正常水平之上的0.3个标准差，表明股票目前处于公允价值状态。
数据源
下表引用了在此页面上用于构建图表或以其他方式引用的所有数据和来源。
| 物品 | 来源 |
|---|---|
| 10年期国债利率 | 从圣路易斯联邦储备银行FRED取得的10年期国库债券固定利率（DGS10），美国联邦储备系统（美国）理事会； |
| SP500价格 | 雅虎！财务S＆P500每日收盘价 |
| 消费物价指数 | 美国劳动统计局，《所有城市消费者的消费物价指数：所有项目》 [CPIAUCNS]，取自圣路易斯联邦储备银行FRED； |
作者总结：这篇文章论点利率暗示美国股市是合理价值，这还值得商榷。作者并不同意这观点。美国接近0的低利率是人为调整，并非市场行为。合理利率应该在2%左右，0利率或负利率本来都不正常。
为了避免被割韭菜，做好价值投资，我们需要识别优质企业，欢迎各位同学学习python信用评分卡建模视频系列教程（附代码， 博主录制），学习企业信用评级模型知识 ：
（微信二维码扫一扫报名）
（原创课程，版权所有，项目合作QQ：231469242，微信公众号：pythonEducation）