NO.PZ202206070100000102
问题如下：
Brian O'Reilly Case Scenario
Brian O’Reilly is a capital markets consultant for the Tennessee Teachers’ Retirement System (TTRS). O’Reilly is meeting with the TTRS board to present his capital market expectations for the next year. Board member Kay Durden asks O’Reilly about the possibility that data measurement biases exist in historical data. O’Reilly responds:
“One bias results from the use of appraisal data in the absence of market transaction data. Appraisal values tend to be less volatile than market determined values for identical assets. As a result, measured volatilities are biased downward and correlations with other assets tend to be exaggerated.”
Board member Arnold Brown asks O’Reilly about the use of high-frequency (daily) data in developing capital market expectations. O’Reilly answers, “Sometimes it is necessary to use daily data to obtain a data series of the desired length. Ironically, high-frequency data improves the precision of sample variances, covariances, and correlations but not the precision of the sample mean. High-frequency data are more sensitive to asynchronism across variables.”
Durden states that he recently read an article on psychological biases related to making accurate and unbiased forecasts. She asks O’Reilly to inform the board about the anchoringand prudence biases. O’Reilly offers the following explanation:
“The anchoring bias is the tendency for forecasts to be overly influenced by the memory of catastrophic or dramatic past events that are anchored in a person’s memory. The confirming evidence trap is the bias that leads individuals to give greater weight to information that supports a preferred viewpoint than to evidence that contradicts it.”
The board asks about forecasting expected returns for major markets, given that price earnings ratios are not constant over time and that many companies are repurchasing shares instead of increasing cash dividends. O’Reilly responds that the Grinold–Kroner model accounts for those factors and then makes the following forecasts for the European equity market:
The dividend yield will be 1.95%.
Shares outstanding will decline 1.00%.
The long-term inflation rate will be 1.75% per year.
An expansion rate for P/E multiples will be 0.15% per year.
The long-term corporate earnings growth premium will be 1% above expected real GDP growth.
Expected real GDP growth will be 2.5% per year.
The risk-free rate will be 2.0%.
选项：
A.correct.
B.incorrect with respect to asynchronism.
C.incorrect with respect to variances and correlations.
解释：
Solution
A is correct. O’Reilly’s answer is entirely correct as stated.
B is incorrect. O’Reilly’s answer is entirely correct as stated. High-frequency data are more sensitive to asynchronism.
C is incorrect. O’Reilly’s answer is entirely correct as stated. High-frequency data produce more precise variances and co-variances (and less precise means).
A是正确的。O’Reilly的回答完全正确。
B是错误的。高频数据对异步更加敏感，即高频数据更容易产生异步性的问题。比如用每天的数据观测美国和欧洲股票市场，因为两地存有时差，所以就会出现异步性。但如果是用月度数据观测，这种时差就可以忽略不计。
C是错误的。高频数据产生了更大容量的样本数据，所以能估计出更精确的方差和协方差。但是对于均值而言，只要用的历史数据，估计的数值就不太精确。这也是根据实务观测到的结果。
1.appraisal data会高估还是低估correlation？
2.asynchronous会高估还是低估correlation？