Published
Bohyun Yoo*
* Swiss Institute of Artificial Intelligence, Chaltenbodenstrasse 26, 8834 Schindellegi, Schwyz, Switzerland
This study discovers and analyzes price premium (discount/surcharge) factors in the real estate auction market. Unlike existing bottom-up studies based on individual auction cases, a top-down time-series analysis is conducted, assuming that the price premium factor varies over time. To overcome limitations such as the difference between the court appraisal time* and the auctioned time, and the difficulty of using external data on court appraisals and price premium factors, the Fourier transform is utilized to extract the court appraisals and price premium factors in reverse. The extracted components are verified to determine if they can play a role as each factor. The price premium factor is found to have a similar movement to the difference in past values of the auction sale rate, and, as it signifies the discounts/surcharges in the auction market compared to the general market, it is named the “momentum factor”. Furthermore, by leveraging the momentum factor, the price premium can be differentiated by region, and the extent of the price premium applied can be distinguished over various time periods compared to the general market. Given the clustering tendency, the momentum factor can be a significant indicator for auction market participants to detect market changes.
1. Introduction
The housing auction market in Korea is one of the real estate markets, and many stakeholders such as mortgage banks, arbitrage investors, and non-performing loan operators are deeply involved. In general, there is a perception that the auction market is surcharged or discounted compared to the general market. If the auction market is an efficient and fair-trading market, it will not be different from the general market price, but most housing auction cases are implemented by default, so it is known that have legal issues and that applies as a discount factor. However, the bottom-up analysis based on individual auction cases, which is a method mainly used in previous studies on discounts and surcharges, is limited in time and space, and the time-varying effect cannot be considered, and the results of the analysis are limited and dependent on the data held by the researcher.
To overcome these limitations, it should be carried out the analysis from the market perspective, but the time series data Auction Sale Rate is unreliable as an indicator because the court appraiser price, which is the standard, is performed at the past rather than at the time of the auctioned price. It is difficult to specify the time of court appraisal as a variable in the model because it varies from case to case of individual auction how much it is in the past at the time of successful bid, and even if the time is known, the court appraisal price cannot be accurately estimated. Individual cases can be investigated in a bottom-up manner to return the point of view based on the general market price, but it is a very vast task and likewise a study limited to time and space.
The target of this paper is the apartment auction market, and to overcome the limitations of the auction sale rate, the auction sale rate is decomposed into three components in a top-down manner using Fourier transform. The proof of the decomposed each component is performed. And the price premium effect at the auction market is presumed and the reason is analyzed and the section discrimination in which the price premium effect acts is attempted. In addition, the time-varying beta through the Kalman filter is used to support the price premium effect, and the analysis of how the price premium effect differs in each region's market is also performed.
2. Literature review
Shilling et al (1990) analyzed the apartment auction in 1985 in the baton lounge, Louisiana, USA, and found an auction discount rate of -24%, Forgey et al (1994) analyzed houses from 1991 to 1993 in the United States and found that they were traded at a -23% discount. Spring (1996) analyzed foreclosures in Texas from 1991 to 1993 and found a 4-6% discount, Clauretie and daneshvary (2009) analyzed the housing auctions from 2004 to 2007 and found that about 7.5% of foreclosures were discounted because of endogenous and autocorrelation.
Campbell et al (2011) analyzed about 1.8 million housing transactions in Massachusetts and found that the discount rates for foreclosures and deaths were different. Zhou et al (2015) found that on average, 16 cities in the United States were discounted by 14.7%, Arslan, Guler & Tasking (2015) analyzed that a 1% increase in risk-free interest rates led to a 27% drop in house prices and a 3% increase in foreclosure rates.Jin (2010) compared and analyzed the general sale price and the auction price of apartments in Dobong-gu, Seoul and Suji-gu, Yongin-si, Korea, and found that the auction price is more discounted than the general transaction price. Lee (2012) noted that the real estate market is not efficient and is one of the anomalies of the discount / surcharge phenomenon in the apartment auction market.
Lee (2009) and Oh (2021) pointed out the limitations that occurred when the court appraisal price and the auctioned price were different and estimated the auction sale rate by correcting the court appraisal price to the auctioned time.
However, previous studies mainly focus on the analysis of variables in the bottom-up method along with the limitation of space and time based on individual auction cases. In addition, it is difficult to see the analysis in the same environment as Korea because the cases other than Korea adopt the open bidding system.
3. Materials and method
3.1. Decomposition of auction sale rate
Configuration of the auction sale rate defined as
Where i is each auction case, t is each per month. If the auctioned price is discounted and surcharged compared to the general market price, the component can be separated as shown in (2), and if there is no discount and surcharge, it can be expressed as shown in (4). In order to estimate the price premium effect, which is the discount or surcharge, it can be defined in the Regression form as shown in (5), and it is assumed that the explanatory power of each component is as shown in (6).
In the Regression form in terms of effects,
3.2. The data
The empirical analysis in this paper is based on Auction Sale Rate and Market Price Index in nationwide 2012.03 ~ 2022.10 in month. The auction sale rate is calculated by collecting the sum of court appraiser prices and auctioned prices nationwide announced by the court from 2012.03 to 2022.10. The Market price index is an index of general market apartment prices nationwide and is provided by the Korea Real Estate Board. Log-Differencing is taken in the Market price index to match the forms of both data equally then Standardization, which translates to mean 0 and variance 1, take both data to match the same scale.
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skewness and kurtosis reported in Table 1 shows AuctionSaleRate and MarketPriceIndex has different peaks and tails compared to normal distribution. and the Lev results in Table 1 show that it is different from the leverage effect (Black 1976.) of the stock market. The auction market and the general sales market has a positive sign relationship with the future volatility. This means that volatility in the real estate market has a positive correlation with price.
3.3. Identification of variables
3.3.1. The effect of market price
Auction sale rate can be decomposed into three components in the regression form as shown in (5), and log-differencing market price index is used as the first variable, EoM's proxy variable. As shown in Table 2, EoM has the strongest explanatory power in auction sale rate.
3.3.2. Component identification
Where y_t is Auction sale rate at time t,
3.3.2.1. Fourier transform
Fourier transform is a mathematical transformation that decomposes a function into a frequency component, representing the output of the transformation as a frequency domain. In this paper, it is used to extract the orthogonal cycle of EoA and EoP as defined in (5). In terms of linear transformation, the orthogonal factor present in the signal can be extracted as a Forward and Inverse Discreate Fourier matrix, as shown in (9).
where
where
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3.3.2.2. Regression analysis
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where
Table 2 shows the results of using the extracted signals as a variable of regression by performing FFT in 4.3.2.1.
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3.3.3. Proof of the effect of appraisal price
Based on Table 2 and according to the assumption of (5),
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The analysis is conducted in two main aspects:
- Time interval between the time of court appraisal and the time of Auctioned (Table 4)
- Regression with the general market price at the time of court appraisal price (Table 4)
where
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As shown in Table 4, the time difference distribution has a right skewed shape and the range of 25% to 75% is about 7 to 11 months. Price difference has a long-tailed distribution, and it can be estimated that the court appraisal price and the housing price at the time of the court appraisal have a very high correlation and are almost the same value. To summarize the results of the two analyses, the court appraisal price is the lag variable of the housing price. In terms of the component (5) EoA can be assumed to have a lag relationship with
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Table 5 [1] shows the relationship between the lag variable of
Table 5 [2] is a confirmation of whether
Table 5 [3] confirms the relationship between
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To sum up with Result of Table 5, in Table 4
3.3.4. Proof of the effect of premium price
Based on result of Table 2 and according to the assumption of (5),
- Verify that
can distinguish between discount and surcharge points. (Figure 8) - Track what variables
is, name it, and verify it makes sense.
3.3.4.1. Distinguish to price premium pffect in auction sale rate
The
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3.3.4.2. Momentum factor
In 4.3.4.1, it is confirmed that
where c_0 is intercept, y is auction sale rate, v is volatility as differencing of auction sale rate.
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In Table 6, the volatility variable is significantly related to
the volatility variable (16)(17) and
In summary, the volatility variable of Auction sale rate can be explained as the main factor that creates the Price premium effect, and in particular, the reason why volatility causes the price premium effect can be interpreted as the reason that the volatility of the auction market has a positive correlation with the Auction sale rate. As a result, the volatility component can be named the momentum of the auction market.
3.3.5. Time varying beta to capture price premium section
In 4.3.4, it was confirmed that
3.3.5.1. Kalman filter
The Kalman filter is a model for describing dynamics based on measurements and recursive procedure for computing the estimator of the unobserved component or the state vector at time t.
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<Predict Step>
Calculate the optimal parameter of
Calculate the optimal parameter of
The random walk effect is considered by assuming that Q, R is the initial value near 0 (= diffuse prior) and F is the diag (1,1,1,1) unit matrix and the Kalman gain (K) determines the weight for the new information using the information of the error between the prediction and the observation.
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Table 8 shows that Time varying betas with Kalman filter performs better than the OLS with stable parameters. Figure 11 compares the change of the parameters of
auction market is more sensitive than the market price effect. This can be assumed to be an momentum interval, and the price premium effect is a sensitive interval.
3.3.5.2. Experiment
It is necessary to confirm whether the logic constructed so far works in the auction market in the region other than the whole country. Furthermore, when the model is performed by region, the characteristics of each region can be confirmed. The target areas of the empirical analysis are Seoul and gyeong-gi area where the auction market is most active.
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Table 8 and Figure 13 to Figure 18 are the results of the analysis of Seoul and Gyeonggi Province. Table 8 [2] Beta of
4. Conclusion
The previous auction market studies using bottom-up method mainly analyzed the variables affecting the Auction sale rate or had the disadvantage that the space and time were limited to the data they had. In this paper, time series analysis was carried out from the market perspective, and the top-down method using Fourier transform was attempted to solve the problem that the court appraiser price could not reflect the general market price at the time of the auction, and the price premium effect could be specified through the proof of each component.
In addition, it was found that the reason for making the price premium effect in the auction market is the momentum effect, and the time varying beta (Kalman filter) supports the above logic showing that the price premium effect can be divided by region. It is practically impossible to analyze a vast amount of auction cases for the analysis of the auction market, and this paper was very encouraging in that it provided many participants in the auction market with indicators that can be viewed from a market perspective.
However, it requires a deep understanding of the momentum factor. The sensitive activity of the momentum factor signifies not just market rises or falls, it indicates shifts in the price relationship between the auction and the general markets. Intuitively, when the real estate market heats up, high demand narrows the gap between general market prices and auction prices.
Therefore, the role of the momentum factor can be interpreted as representing the 'popularity' of the auction market compared to the general market. To elaborate further, it can serve as an indicator to judge whether the market is overheating or cooling down in comparison to the general market.
The additional insights of this study are as follows: Korea's apartment auction market has only momentum factors except for market prices under court appraiser control. Macro factors such as government regulations and interest rates are in the market price, so the third variable of the auction market is only the momentum factor, which can be very important information for many participants in the auction market.
This paper can be more rigorous if the following limitations are resolved. Since the monthly auction sale rate data may not be enough to support the rigor of the analysis, a wider analysis period or more time will further support the rigor of the analysis. In addition, the rigor of the analysis will be supported if more data on the unidentified area can be obtained in the process of proving the appraiser component of the court.
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