CME - 数据问答题

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

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.

中文解析：

现状偏见

Tommanson表示，鉴于股市在上一季度的强劲表现，他不愿减持股票，这是维持现状偏见的一个例子。他曾表示，在设定资本市场预期时，应更重视最新季度数据，这也是这种偏见的一个例子。现状偏见反映了预测倾向于延续最近的观察结果，而管理者则倾向于避免做出改变。通过有纪律的努力，避免固守现状，可以减轻对现状的偏见。



数据挖掘的偏见

在Wuyan的报告中，数据挖掘偏差源于反复搜索数据集，直到出现统计上显著的模式。这种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。作为解决方案，分析师应该仔细检查所选择的变量，并为预测模型中选择的每个变量提供经济基础。进一步的检验是检验样本外的预测关系。



政权更迭的风险

Tommanson提出的将数据序列往后延伸的建议，增加了数据代表多个政体的风险。制度的改变是指技术、政治、法律、经济或监管环境的转变。由于资产的风险和收益特征随着经济和市场环境的变化而变化，制度变化改变了风险-收益关系。分析人员可以应用统计技术来解释制度变化，或者仅仅使用整个数据系列的一部分。