Office price index lagging in Singapore and Hong Kong.

As a result, there are a couple of problems when making use of the lagged appraisal returns data of real estate. Spurious volatility is one of them (Fisher and Geltner, 2000). Due to the prominent use of past appraisals in determining the estimates for real estate returns, naturally the change (volatility) of prices would be less than transaction-based prices. It is supported by a study from DeWit (1993), who explores that the In-house appraisals have a smaller volatility than common stock return volatility. Corgel and deRoos (1999) share similar conclusions as the appraisal-based return index understates return volatility. But they comment that the aim to inflate the return volatility may not work because changing the mean of returns would dis-magnify the effect of volatility changes on allocations. Surprisingly, Lai and Wang (1998) reach an opposite conclusion that appraisal returns are more volatile than "true" returns. But Geltner (1998) responds by stating that their definition of "true" returns is not that clear. So a different result may be obtained.

Another problem along with the appraisal-based data is seasonality. Unlike the stock market, where prices are adjusted practically in every minute, real estate prices are usually re-appraised once a year, mostly in the 4th quarter of a fiscal year. Even though the prices are released once every 3 months, the current news does not carry too much weight on the appraisals. The lagging error appears to be smaller in the 4th quarter when the prices are re-appraised (Fu, 2002). With the presence of seasonality in appraisal-based real estate returns, Fisher and Geltner (2000) state that the National Council of Real Estate Investment Fiduciaries (NCREIF) needs to provide accurate indicators of quarterly market directions, but it is a bit short of doing so due to the lag problems. In a sense, they are implying that the NCREIF lacks credibility as a representation of the market values of commercial real estate. Fu (2002) comments that the serial auto-correlation would be artificially "inflated" and the correlation with the returns of other investment goods would be understated.

The result of lags is a deviation of appraisal-based real estate returns from its "true" returns. A study by Geltner and Goetzmann (2000) found that there was about a 10% standard error in the appraisals for NCRELF properties. Another studies by Fisher, Miles and Webb (1999) reported that the transaction price was about 4.6% higher than the appraised value in the period of 1978-1985. Meanwhile, the percentage changed to -4.5% in 1988-1992. Then, the transaction prices were going back up, with a 3.8% discrepancy over the appraised value. It is also observed that the absolute mean difference between appraised value and the "true" value is around 9%-12.5%. Such discrepancies are enough for an individual to change his investment decision. They conclude that the reliability of appraisals is affected by the stability of the market which varies by property type over time. The lagging problem looks to be more serious in commercial real estate, due to fewer transactions. Also, a number of questions are arisen. The first question is that under what circumstances does the appraised value overstate the "true" value, or vice versa? Then, is that possible to find a pattern of that?

2.2. Ways to eliminate lags in appraisal-based returns

As concluded by Geltner (1991), appraisal-based returns can be useful in studying the risk characteristics of commercial real estates, once the smoothing problem is corrected. Similar to that, Ross and Zisler (1991) comment that appraisal values need to be "un-smoothed" in order to recover the total returns. Therefore, in order to get rid of the lagging/smoothing problem that causes the estimates of real estate returns deviating from its "true" returns, a number of methods have been used in previous studies. One of the methods is the application of cap rate time series to real estate income time series, as seen in Firstenburg, Ross, and Zisler, 1988; Wheaton and Torto, 1989; Liu, et al., 1990. Another method is to use the indices of real estate returns, grounded on hedonic models of real estate's fundamental value (see Hoag, 1980; Miles, Cole, and Guilkey, 1990). However, such methods are not able to tackle the "noise" as the returns generated from either the cap rates or hedonic models are subject to errors (Geltner, 1991).

A lagging-correction method has been utilized, called Reverse Engineering. Fisher and Geltner (2000) use this method in attempt to de-lag the NCRELF Index. However, Corgel and deRoos (1999) conclude that this method produces mixed implications for optimal portfolio allocation to real estate. In other words, it is implied that the de-lagged returns after using Reverse Engineering Method would either overstate or understate the "true" returns of real estate, thus not being able to eliminate the uncertainties incurred in such returns estimations. There are a couple of defects on Reverse Engineering (Fu, 2002). Firstly, Reverse Engineering is a reduced-form approach, which does not have the capacity to identify a dynamic lagging error structure. Then, the problem of seasonality is not addressed. Furthermore, it lacks the capacity to incorporate observable market information beyond the index itself. Fu concludes that this de-lagged index, via Reverse Engineering, is not necessarily more informative than the lagged index (the observed index).

Another method used to take care of the lagging problem in appraisal-based real estate returns is called the Repeated-Measures Regression (RMR). Geltner and Goetzmann (2000) utilize this method in attempt to de-lag the NCRELF Index. It is concluded that the RMR Index (the de-lagged index) is a better version of the NPI, which is more like an annual index than of quarterly index. They viewed the RMR Index as the NPI without "stale" valuations and artificial seasonality. Still, the downside of the RMR index is that it still lags behind the NAREIT index by about 3 years. As REITs are being traded on the stock market, the prices of REITs and the NAREIT should be the most updated values of real estate. In short, though some of the problems accompanying the lagged appraisal values are handled, it is not as close as informative as the stock market changes, granted the same current market information.

The State Space Model via Kalman Filter is introduced in Fu's (2002) study, in order to deal with the aforementioned problem. What makes the State Space Model via Kalman Filter better than the above methods? It is argued that this setting has the flexibility to allow the lagging error to be influenced by a variety of variables. That includes the latent appreciation return and seasonality. Moreover, it is, he asserts, capable of taking available market information, which can improve the forecast quality for latent appreciation return. His test on the NARELF Index shows that its return has greater volatility, improved cross-correlation with the returns of other indices affected by the same market news, and less serial auto-correlation returns, once the lag has been removed. This idea is further corroborated by Quan and Quigley (1991), saying that a full fledged Kalman filter algorithm can be employed to make the optimal updating rule more realistic.

However, most of the studies on the lagging problems of appraisal-based returns estimate focus on the data on the U.S. real estate market (i.e. NPI). There are yet studies focusing on such problems on the real estate markets in Asia. It would be worth studying the same problems in Asia, such as Hong Kong and Singapore, given their established economic structures. This study intends to bridge the knowledge gap in price discovery of commercial real estates in Asian countries/cities.

3. STUDY APPROACHES AND SINGAPORE TEST CASE

Using a case study on Singapore office price indices as a test case, a single-index model is constructed as the starting point of this study. The index is called the Synthetic Land Price Index (LPI). If the LPI is workable we then use it in the subsequent analysis in the Hong Kong case. If not, a more conventional multivariable approach is then introduced exclusively for the Hong Kong study. The advantage of such comparison approach is that we may clearly distinguish which approach can work better, or more precisely, which variables can best explain the overall price adjustments of office space.

3.1. Synthetic Office Land Price Index (LPI)

In the construction of a synthetic office land price index within the context of Singapore, the required data set is obtained from the URA Office Rental and Capital Value (CV) Indices and the JLL REIS-Asia real estate market indicators or variables. With the construction of this office land price index, it serves as a measure of the rate of CV appreciation of vacant office land in Singapore. The index can then be compared with the price indices of built up office assets that are maintained by URA, in order to determine to what extent would movement in the CV of office land explain the CV movement of built-up office assets. Essentially, the LPI is the difference between the supply price of capital (proxied by best lending rate) and the current rental return of an office asset (proxied by yield rate/capitalization rate). Calculations of the Synthetic Office Price Index are demonstrated in Table 1.

3.2. State Space Model & Kalman Filter

A State Space Model, with Kalman Filter, is deployed to find out how the observed Office Price Index deviates from its supposed "true" value, due to the lag structure in the appraisal values. Kalman Filter is a recursive algorithm for sequentially updating the 1-step-ahead estimate of the state mean and variance, once there is new information available (EViews Manual, p. 561). According to Kalman (1963), the signal value is equal to the message plus noise (random error term). If the error term is under Gaussian distribution, the Kalman filter provides an estimate of the state that is best available, which is in terms of a minimum mean estimator (Wells, 1996).

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