Misinterpretation of correlation

问题如下：

Wuyan reports that after repeatedly searching the most recent 10 years of data, she eventually identified variables that had a statistically significant relationship with equity returns. Wuyan used these variables to forecast equity returns. She documented, in a separate section of the report, a high correlation between nominal GDP and equity returns. Based on this noted high correlation, Wuyan concludes that nominal GDP predicts equity returns. Based on her statistical results, Wuyan expects equities to underperform over the next 12 months and recommends that the firm underweight equities.

Commenting on the report, John Tommanson, an investment adviser for the firm, suggests extending the starting point of the historical data back another 20 years to obtain more robust statistical results. Doing so would enable the analysis to include different economic and central bank policy environments. Tommanson is reluctant to underweight equities for his clients, citing the strong performance of equities over the last quarter, and believes the most recent quarterly data should be weighted more heavily in setting capital market expectations.

Discuss how each of the following forecasting challenges evident in Wuyan’s report and in Tommanson’s comments affects the setting of capital market expectations:

i. Status quo bias

ii. Data-mining bias

iii. Risk of regime change

iv. Misinterpretation of correlation

Discuss how each of the following forecasting challenges evident in Wuyan’s report and in Tommanson’s comments affects the setting of capital market expectations:

Status quo bias

Data-mining bias

Risk of regime change

Misinterpretation of correlation

选项：

解释：

Status quo bias：

Tommanson’s statement that he is reluctant to underweight equities given the strong performance of equities over the last quarter is an example of status quo bias. His statement that the most recent quarterly data should be weighted more heavily in setting capital market expectations is also an example of this bias. Status quo bias reflects the tendency for forecasts to perpetuate recent observations and for managers to then avoid making changes. Status quo bias can be mitigated by a disciplined effort to avoid anchoring on the status quo.

Data-mining bias：

In Wuyan’s report, data-mining bias arises from repeatedly searching a data set until a statistically significant pattern emerges. Such a pattern will almost inevitably occur, but the statistical relationship cannot be expected to have predictive value. As a result, the modeling results are unreliable. Irrelevant variables are often included in the forecasting model. As a solution, the analyst should scrutinize the variables selected and provide an economic rationale for each variable selected in the forecasting model. A further test is to examine the forecasting relationship out of sample.

Risk of regime change：

The suggestion by Tommanson to extend the data series back increases the risk of the data representing more than one regime. A change in regime is a shift in the technological, political, legal, economic, or regulatory environments. Regime change alters the risk–return relationship since the asset’s risk and return characteristics vary with economic and market environments. Analysts can apply statistical techniques that account for the regime change or simply use only part of the whole data series.

Misinterpretation of correlation：

Wuyan states that the high correlation between nominal GDP and equity returns implies nominal GDP predicts equity returns. This statement is incorrect since high correlation does not imply causation. In this case, nominal GDP could predict equity returns, equity returns could predict nominal GDP, a third variable could predict both, or the relationship could merely be spurious. Correlation does not allow the analyst to distinguish between these cases. As a result, correlation relationships should not be used in a predictive model without understanding the underlying linkages between the variables.

Status quo bias
Tommanson表示，鉴于股市上一季度的强劲表现，他不愿减持股票，这是“现状偏见”的一个例子。他曾表示，在设定资本市场预期时，应该更重视最近的季度数据，这也是这种偏见的一个例子。现状偏差反映了一种趋势，即预测会延续最近的观察结果，而经理们则会避免做出改变。通过自律地努力避免固守现状，可以减轻现状偏见。


Data-mining bias：
在Wuyan的报告中，数据挖掘偏差产生于重复搜索数据集，直到出现统计上显著的模式。这样的模式几乎不可避免地会发生，但不能指望统计关系具有预测价值。因此，建模结果是不可靠的。预测模型中经常包含不相关的变量。作为一种解决方案，分析师应该仔细检查所选的变量，并为预测模型中所选的每个变量提供经济依据。进一步的检验是检验样本外的预测关系。



Risk of regime change：
Tommanson提出的将数据序列向后延伸的建议增加了代表不同时期的数据的风险。投资时期的变化是技术、政治、法律、经济或监管环境的变化。由于资产的风险和回报特征随经济和市场环境的变化而变化，制度变化改变了风险-回报关系。分析人员可以应用统计技术来解释政权的变化，或者仅仅使用整个数据系列的一部分。



Misinterpretation of correlation：
Wuyan认为，名义GDP与股权收益的高度相关意味着名义GDP可以预测股权收益。这种说法是不正确的，因为高相关性并不意味着因果关系。在这种情况下，名义GDP可以预测股票回报，股票回报也可以预测名义GDP，第三个变量也可以同时预测两者，或者两者之间的关系可能只是虚假的。相关性不允许分析人员区分这些情况。因此，如果不了解变量之间的潜在联系，就不应该在预测模型中使用相关关系。