老师，想问下我这么理解对吗？ true variance是用REIT的数据，所以是平滑过得，会低估variance，因此true variance会比observed小？

问题如下：

Richard Martin is chief investment officer for the Trunch Foundation (the foundation), which has a large, globally diversified investment portfolio. Martin meets with the foundation’s fixed-income and real estate portfolio managers to review expected return forecasts and potential investments, as well as to consider short-term modifications to asset weights within the total fund strategic asset allocation.

Martin asks the real estate portfolio manager to discuss the performance characteristics of real estate. The real estate portfolio manager makes the following statements:

Statement 1: Adding traded REIT securities to an equity portfolio should substantially improve the portfolio’s diversification over the next year.

Statement 2: Traded REIT securities are more highly correlated with direct real estate and less highly correlated with equities over multi-year horizons.

Martin looks over the long-run valuation metrics the manager is using for commercial real estate, shown in Exhibit 1.

The real estate team uses an in-house model for private real estate to estimate the true volatility of returns over time. The model assumes that the current observed return equals the weighted average of the current true return and the previous observed return. Because the true return is not observable, the model assumes a relationship between true returns and observable REIT index returns; therefore, it uses REIT index returns as proxies for both the unobservable current true return and the previous observed return.

Martin asks the fixed-income portfolio manager to review the foundation’s bond portfolios. The existing aggregate bond portfolio is broadly diversified in domestic and international developed markets. The first segment of the portfolio to be reviewed is the domestic sovereign portfolio. The bond manager notes that there is a market consensus that the domestic yield curve will likely experience a single 20 bp increase in the near term as a result of monetary tightening and then remain relatively flat and stable for the next three years. Martin then reviews duration and yield measures for the short-term domestic sovereign bond portfolio in Exhibit 2.

The discussion turns to the international developed fixed-income market. The foundation invested in bonds issued by Country XYZ, a foreign developed country. XYZ’s sovereign yield curve is currently upward sloping, and the yield spread between 2-year and 10-year XYZ bonds is 100 bps.

The fixed-income portfolio manager tells Martin that he is interested in a domestic market corporate bond issued by Zeus Manufacturing Corporation (ZMC). ZMC has just been downgraded two steps by a major credit rating agency. In addition to expected monetary actions that will raise short-term rates, the yield spread between three-year sovereign bonds and the next highest-quality government agency bond widened by 10 bps.

Although the foundation’s fixed-income portfolios have focused primarily on developed markets, the portfolio manager presents data in Exhibit 3 on two emerging markets for Martin to consider. Both economies increased exports of their mineral resources over the last decade.

The fixed-income portfolio manager also presents information on a new investment opportunity in an international developed market. The team is considering the bonds of Xdelp, a large energy exploration and production company. Both the domestic and international markets are experiencing synchronized growth in GDP midway between the trough and the peak of the business cycle. The foreign country’s government has displayed a disciplined approach to maintaining stable monetary and fiscal policies and has experienced a rising current account surplus and an appreciating currency. It is expected that with the improvements in free cash flow and earnings, the credit rating of the Xdelp bonds will be upgraded. Martin refers to the foundation’s asset allocation policy in Exhibit 4 before making any changes to either the fixed-income or real estate portfolios.

Based on the private real estate model developed to estimate return volatility, the true variance is most likely:

选项：

A.lower than the variance of the observed data. B.approximately equal to the variance of the observed data. C.greater than the variance of the observed data.

解释：

C is correct.

The in-house model assumes that the current observed return equals the weighted average of the current true return and the previous observed return. The model uses REIT index returns as proxies for the returns in the model. The smoothed nature of most published (observed) real estate returns is a major contributor to the appearance of low correlation with financial assets. This smoothing dampens the volatility of the observed data and distorts correlations with other assets. Thus, the raw observable data tend to understate the risk and overstate the diversification benefits of these asset classes. It is generally accepted that the true variance of real estate returns is greater than the variance of the observed data.

内部模型假设当前的观测收益等于当前真实收益和之前观测收益的加权平均值。该模型使用REIT指数回报作为模型中的回报。大多数公布的(观察到的)房地产回报的平滑性质是其与金融资产相关性较低的主要原因。这种平滑降低了观测数据的波动性，扭曲了与其他资产的相关性。因此，原始的可观察数据往往低估了这些资产类别的风险，而高估了这些资产类别的多元化收益。一般认为，房地产收益的真实方差大于观测数据的方差。