An extended fama-french multi-factor model in direct real estate investing

Yiu, Chung Yim; Xiong, Chuyi; Cheung, Ka Shing Article An extended fama-french multi-factor model in direct real estate investing Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Yiu, Chung Yim; Xiong, Chuyi; Cheung, Ka Shing (2022) : An extended famafrench multi-factor model in direct real estate investing, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 15, Iss. 9, pp. 1-14, https://doi.org/10.3390/jrfm15090390 This Version is available at: https://hdl.handle.net/10419/274911 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Journal of Risk and Financial Management 15: 390. https://doi.org/10.3390/jrfm15090390 Academic Editor: Riza Demirer Received: 1 August 2022 Accepted: 29 August 2022 Published: 2 September 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Journal of Risk and Financial Management Article An Extended Fama-French Multi-Factor Model in Direct Real Estate Investing Chung-Yim Yiu 1,* , Chuyi Xiong 2and Ka-Shing Cheung 1 1Department of Property, The University of Auckland Business School, Auckland 1010, New Zealand 2Three Gorges Finance Co., Ltd., Beijing 100197, China *Correspondence: edwar[email protected] Abstract: Understanding risk-adjusted returns in real estate investment are crucial, but little is known about the risk-adjusted returns for direct real estate. This paper examines risk-adjusted total returns by developing an extended capital asset pricing model (CAPM) to investigate whether direct real estate returns compensate for their risk levels. Based on a panel dataset of the residential property transaction in 62 Territorial Authorities of New Zealand from 2002Q1 to 2018Q4, a direct real estate portfolio performance in the single-factor CAPM model is compared with the national housing markets stock markets and REITs markets in New Zealand before the pandemic. The results demonstrate that the direct real estate returns outperform the market returns with a significant positive alpha and beta smaller than one but positive. The alpha is further evaluated by the five-factor CAPM model, which includes the factors of liquidity risk, value risk, time risk, credit-rating risk, and currency risk. The assessment shows that most of the excess return (alpha) can be attributed to direct real estate market risks. Keywords: direct real estate; total housing returns; CAPM; Fama-French five-factor model; New Zealand 1. Introduction Is there an excess risk-adjusted return in direct real estate investments? At the end of 2019, when most investment markets plummeted in the pandemic outbreak, housing prices rose in many countries. The United States Case-Shiller’s National Home Price Index and China’s 70 Major Cities New Home Price Index have uninterruptedly risen since November 2019, with their respective annual growth rates reaching 8.4% and 4.0% in October 2020. In terms of risk-return ratios, real estate investments outperform many other investment vehicles. In hindsight, if direct real estate, especially residential properties, had been included in an investment portfolio during the early pandemic, the portfolio’s investment returns might have made a real difference. Chong et al. (2009, p. 183) also found that “a higher allocation towards real estate will reduce portfolio risk in periods of high-interest rate volatility”. This paper uses New Zealand as a case to compare the risk-return relationships between a direct housing portfolio and other investment vehicles. During the pandemic, New Zealand has been one of the countries with the most substantial house price growth. In December 2020, the REINZ house price index of New Zealand showed a 19.2% year-on-year increase, regardless of the rental yield. Even before the pandemic, the average price return of housing investment in New Zealand achieved 7.93% from 2002 to 2018, compared to 3.42% for REITs, 4.85% for bonds, and 9.59% for stocks. In the meantime, the risk level of residential property investment, as measured by the standard deviation of the price swings, was only 8.57%, compared to 11.85% in REITs and 13.23% in stocks (Table 1). J. Risk Financial Manag. 2022,15, 390. https://doi.org/10.3390/jrfm15090390 https://www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2022,15, 390 2 of 14 Table 1. Annual price returns and standard deviations of various investment vehicles in New Zealand, 2002–2018. Annual Returns (%) Stocks REITs Bonds Houses Mean 9.59 3.42 4.85 7.93 Std. Dev. 12.84 11.85 1.33 7.14 Notes: The annual price returns of stocks, REITs, and houses are calculated by the year-on-year change of the NZX50 index and the REINZ house price index of New Zealand. The annual return of bonds is calculated by the average of 10-year secondary market government bond yields (RBNZ). Figure 1shows the time series of investment vehicles’ price returns, including stocks, REITs, bonds, and houses. Housing returns clearly show fewer occurrences of negative returns and are of lower volatility than stocks and REITs. J. Risk Financial Manag. 2022, 15, x FOR PEER REVIEW 2 of 14 Table 1. Annual price returns and standard deviations of various investment vehicles in New Zealand, 2002–2018. Annual Returns (%) Stocks REITs Bonds Houses Mean 9.59 3.42 4.85 7.93 Std. Dev. 12.84 11.85 1.33 7.14 Notes: The annual price returns of stocks, REITs, and houses are calculated by the year-on-year change of the NZX50 index and the REINZ house price index of New Zealand. The annual return of bonds is calculated by the average of 10-year secondary market government bond yields (RBNZ). Figure 1 shows the time series of investment vehicles’ price returns, including stocks, REITs, bonds, and houses. Housing returns clearly show fewer occurrences of negative returns and are of lower volatility than stocks and REITs. Figure 1. The Annual Price Returns of Stocks, REITs, Bonds and Houses in New Zealand, 2002– 2018. Comparing the risk-return performance of 21 forms of investment from 1989 to 2011 in New Zealand, Watson (2012) also found that direct real estate investment (i.e., farmland and residential property) earned the highest average return in excess of the risk-free rate, as indicated by the Sharp ratio, a standard metric of risk-adjusted return. The study further explained that such excess return per unit of risk is associated with liquidity risk and portfolio risk. A portfolio of property assets is expensive to acquire because the indivisibility and trading of properties also incur considerable transaction costs such as agency fees and search costs. Furthermore, the idiosyncratic risk associated with owning an individual property (non-uniformity) and owning properties within one specific region (spatial risk) also accounts for the excess returns of direct real estate. However, the study did not provide any empirical evidence of these omitted risks when national housing returns were analysed. This paper aims to empirically study the impacts of various types of risk on direct real estate excess returns. Traditionally, direct real estate is seldom considered in portfolio management. This is due to its ‘lumpiness’, illiquidity, and high transaction costs (Liao and Mei 1999). CAPM analyses on the REITs market do not represent direct real estate performance, as the movement of REITs returns is found essentially to follow stock markets (Glascock et al. 2000; Figure 1. The Annual Price Returns of Stocks, REITs, Bonds and Houses in New Zealand, 2002–2018. Comparing the risk-return performance of 21 forms of investment from 1989 to 2011 in New Zealand, Watson (2012) also found that direct real estate investment (i.e., farmland and residential property) earned the highest average return in excess of the risk-free rate, as indicated by the Sharp ratio, a standard metric of risk-adjusted return. The study further explained that such excess return per unit of risk is associated with liquidity risk and portfolio risk. A portfolio of property assets is expensive to acquire because the indivisibility and trading of properties also incur considerable transaction costs such as agency fees and search costs. Furthermore, the idiosyncratic risk associated with owning an individual property (non-uniformity) and owning properties within one specific region (spatial risk) also accounts for the excess returns of direct real estate. However, the study did not provide any empirical evidence of these omitted risks when national housing returns were analysed. This paper aims to empirically study the impacts of various types of risk on direct real estate excess returns. Traditionally, direct real estate is seldom considered in portfolio management. This is due to its ‘lumpiness’, illiquidity, and high transaction costs (Liao and Mei 1999). CAPM analyses on the REITs market do not represent direct real estate performance, as the movement of REITs returns is found essentially to follow stock markets (Glascock et al. 2000;Niskanen and Falkenbach 2010). However, with the recent PropTech (and FinTech) J. Risk Financial Manag. 2022,15, 390 3 of 14 advancement, investors can trade houses online via instant buyers platforms or invest in crowdfunded e-REIT markets (Montgomery et al. 2018). The former reduces transaction costs and improves liquidity, while the latter reduces lumpiness and facilitates diversification by including direct real estate in portfolios. According to a performance report of an e-REIT company, its returns continued to increase steadily, whereas the stock market and public REITs markets plunged by 48% and 37%, respectively. With the advancement of PropTech, risk-return analysis of direct real estate has become essential in portfolio management. Financial analyses, such as Markowitz’s (1952) portfolio theory and Sharpe’s (1964) CAPM model, emphasize the risk-return relationship. Fama and French (1995) developed a Fama-French model to explain size risk and value risk. Fama and French (2015) further advanced a five-factor Fama-French model to explain profitability and investment risks. With the development of real estate investment trusts (REITs) markets, risk-return analysis is commonly applied in indirect (or securitized) real estate investment. Yet there have been very few risk-return analyses on direct real estate. Some studies argued that risk-adjusted direct real estate returns should be analysed by considering liquidity risk, owner-occupied housing, segmented market structures, and leverage ratio. However, most of these studies do not provide empirical evidence (Liu et al. 1990). Almost all previous empirical studies considered price return instead of total return, and some were taking stock return as the market return (Cannon et al. 2006;Domian et al. 2015) or the national housing return as the market (Case et al. 2011;Huang 2021). While the importance of a stable and continuous rental yield is well recognized in both direct real estate (i.e., residential property purchases) and indirect real estate (i.e., REITs markets), relatively few studies compare the returns of these two markets in a unified framework. To better understand the risk-return relationship of direct real estate assets in a diversified portfolio, this study attempts to examine the risk-return performance of a spatial portfolio of direct real estate markets of 65 Territorial Authorities (TAs) in New Zealand by using both the CAPM model (Sharpe 1964) and Fama-French model (Fama and French 2015). By comparing the returns amongst the national housing market, stock market, and the REITs market, both market risk, and institutional risk factors are considered. Specifically, we would like to answer this question: can the excessive returns be attributable to market risk and institutional risk ? This study aims to identify the relationships between housing returns, market returns, and asset risk factors. Three proxies of market return are considered, viz. (1) the New Zealand National House Price Index, (2) the New Zealand Stock Price Index, and (3) the New Zealand REITs Price Index. Both price returns and total returns will be studied. The size risk (liquidity risk), value risk, time risk, default risk, and currency risk are further controlled in a Fama-French analysis. New Zealand is used as the case because the country has experienced one of the most substantial growths in housing prices over the past decade. Are the returns from its direct real estate commensurate with the risk levels? The Economist (2019) declares that New Zealand houses are vastly overvalued, and house markets entrench into the bubble territory “on an unsustainable path”. That also affects the affordability of homeownership (Cheung and Wong 2019). In the fourth quarter of 2018, houses in New Zealand were overvalued by 57% relative to incomes and 113% relative to rents. New Zealand’s house prices have more than trebled since 1990, while British and American house prices have less than doubled. Some have even warned that New Zealand’s house prices are the most vulnerable to correction (Kennedy 2019). During the outbreak of COVID-19, the year-on-year growth of house prices in New Zealand was one of the highest in the world. With the outbreak of COVID-19, asset markets are experiencing an unprecedented spike of risk and uncertainty worldwide; how does the risk factor into the urban housing markets (Cheung et al. 2021)? This paper is organized as follows. Section 2is a literature review. Section 3outlines the research design and data, and Section 4discusses empirical results. Section 5concludes. J. Risk Financial Manag. 2022,15, 390 4 of 14 2. Literature Review The Capital Asset Pricing Model (CAPM), which Sharpe (1964) and Lintner (1965) introduced based on the earlier work of Markowitz (1952) and Tobin (1958), is widely used in financial markets for relating the expected rate of return of a security to expected risk (Wu et al. 2017;Panwar 2016). The seminal papers developed by Fama and French (1992,1993,1995,2015) add non-market factors to address size risk, value risk, profitability risk, and investment risk. In order to predict risk-return, many studies have applied the multifactor model to the stock market (Taneja 2010;Hu et al. 2019;Sehgal and Balakrishnan 2013;Santhi and Gurunathan 2014;Alves 2013). As CAPM and the Fama-French models offer investors a new insight into investment under conditions of certainty in the stock market, more studies are extending the implications of these two models (Paliienko et al. 2020;Sehrawat et al. 2020). Ling and Naranjo (1999) applied a multifactor asset pricing model to test whether indirect real estate such as REITs integrates with stocks. Subsequently, an extensive body of research in literature has applied CAPM and the Fama-French model to REITs to explore the explanation for REITs’ risk-return relationship and illustrate the diversification benefit of REITs in portfolio management (Chun et al. 2004). Peterson and Hsieh (1997) showed that the three stock market factors and two bond market factors could explain REITs’ risk premium. Jackson (2020) also demonstrated a positive relationship between REITs’ risk and market capitalization. Many studies evidence the efficiency of CAPM and the Fama-French model for explaining the risk-return of REITs (Yusof and bin Mohd Nawawi 2012;Co¸skun et al. 2017), but not in direct real estate. Even if the studies applied CAPM analysis to direct real estate, most of them focused on the commercial real estate market and measured its risk and return using aggregate data at an index level or appraised property values (Brueggeman et al. 1984;Peng 2016). Some literature compares the risk and returns between REITs and the commercial real estate market (Ross and Zisler 1991;Neil Myer and Webb 1993). Wong and Cheung (2017) found that the magnitude of discounts/premiums of high-end commercial properties hinges on the tradeoff between asset specificity and search. However, the literature on the risk and return of residential real estate is very slender. Some theoretical studies have raised concerns about various types of risk impacts on direct real estate investment returns. Domian et al. (2015, p. 594) extended the crosssectional CAPM model by adding liquidity risk and leverage risk to estimate the risk and return for residential real estate. They found that residential real estate underperformed the bond and stock markets after considering liquidity and leverage, probably because their sample included the post-subprime mortgage crisis period. Furthermore, the assumed “12-month marketing period for a typical residential transaction, and a Time-on-Market (TOM) risk premium of 44 percent” was rather arbitrary. Besides comparing to the stock markets, another strand of studies compares individual housing returns to national housing returns. Case et al. (2011), for example, applied CAPMbased models on MSA-level housing returns to compare with the national housing return. They found strong support for a positive risk-return relationship in housing. Similarly, Huang (2021) used a Fama-French model on MSA-level housing return to compare with the national housing return and showed credit and liquidity risk effects. However, in the previous studies, all the housing returns considered are only price returns, not total returns. One of the significant differences between direct real estate investments and stocks or bonds is the stable and continuous rental income stream from the real estate assets. That is also one of the characteristics of investing in REITs. Therefore, this paper does not only compare housing returns with national housing and stock returns but also with the REITs market. Recent studies of residential real estate risk and return focus on total returns and trading momentum. Chambers et al. (2019) included rental yield in constructing real estate total returns and found that long-term real estate investment would be less profitable and rather risky. Jordàet al. (2019) also considered housing rental yield to study the total returns of various asset classes. Deng et al. (2022) estimated ‘real estate risk’ with and without J. Risk Financial Manag. 2022,15, 390 5 of 14 short-term trading based on return predictability, return volatility, and price dispersion. They show that as short-term investors exit the market, market returns are less predictable and less volatile, while prices are less dispersed cross-sectionally. This study attempts to apply CAPM and Fama-French models on both housing price return and total return to identify the effects of rental yield and risk factors on the excess returns of direct investment on residential real estate. The models are well-established in both financial and indirect real estate markets, providing a sound methodology for our study. 3. Research Design 3.1. Data Table 2summarises the variables with their sources, descriptions, and units of measurement. First, our sample contains 62 Territory Authorities (TAs) with data period from 2002Q1 to 2018Q4 (68 quarters) to avoid the COVID shock. These data form a panel dataset of 5,184 observations. The housing price return is defined as the annual price return and is derived from the year-on-year changes of the house price indices of the individual Territory Authorities (CoreLogic 2020). The total housing return is the sum of the annual price return and the rental yield (MBIE 2020). The rental yields are derived by taking a weighted average of the rent-to-price ratio of each meshblock and aggregating them to the Territory Authority levels, as shown in the Appendix A. Three proxies are used for market returns, viz. (a) New Zealand housing market total returns; (b) stock market returns from NZX50; and (c) New Zealand REITs returns (Datastream 2020). The first market return measures the average of the price returns of housing investment of all TAs—national housing return, which shares a similar institutional arrangement of the housing market of each TA. The second one refers to the returns of the stock market NZX50, which is the most commonly used metric in the literature but is not real estate specific. The price and total returns of New Zealand REITs (NZ_REITs) are also employed, reflecting the performance of the New Zealand real estate markets, with similar market risk factors, but different institutional risk factors. We have also derived five risk factors in the analysis, namely (1) liquidity risk (SMB), (2) value risk (HML), time risk (SML) (RBNZ 2020), default risk (GMB) (S&P 2020), and currency risk (CUR) (Datastream 2020). Detailed definitions of them are shown in Table 2. Table 2. Descriptions and Sources of the Variables. Variable Descriptions Units Sources Ri,t Price return of housing in New Zealand (Estimated by a hedonic pricing analysis on the transactions in Territory Authority iat time t) % p.a. See Appendix A RtNational Price return of housing in New Zealand (average of all Territory Authorities at time t)% p.a. Average of Ri,t Ti,t Total return of housing in New Zealand (Sum of price return and rental yield in Territory Authority iat time t) % p.a. See Appendix A Rf,tRisk-free rates (i.e., 10-year government bond yield rate from the Reserve Bank of New Zealand) % p.a. RBNZ Rm,t Market price return in year-on-year % change of the proxied index (Proxy 1: New Zealand Housing Price Return, Rt) (Proxy 2: New Zealand Stock Index, NZX 50) (Proxy 3: S&P New Zealand All REITs Return Index, NZ_REITs) % p.a. NZ_HTR = Rt NZX 50—S&P (Datastream); NZ_REITs—S&P (Datastream) Tm,t Market total return in year-on-year % change of the S&P New Zealand All REITs Total Return Index, NZ_REITs_TR) % p.a. NZ_REITs—S&P (Datastream) J. Risk Financial Manag. 2022,15, 390 6 of 14 Table 2. Cont. Variable Descriptions Units Sources SMBtLiquidity risk (Small Minus Big): Smallest 1/3 Price Index—Biggest 1/3 Price Index NA HMLtValue risk (High Minus Low): Highest 1/3 CV/P—Lowest 1/3 CV/P NA CV—CoreLogic (2020), P (See Appendix A) SMLtTime risk (Short-term Minus Long-term): 2-year yield minus the 10-year yield of government bonds % p.a. Govt Bond Yield (RBNZ 2020) GMBtDefault risk (Good-grade Minus Bad-grade): AA yield—BBB yield of corporate bond % p.a. S&P NZL AA & BBB Investment Grade Corporate B.D. Index (Datastream) CURtCurrency risk: NZD exchange rate against USD NA Datastream Notes: RBNZ stands for Reserve Bank of New Zealand. (RBNZ 2020). Table 3shows the summary statistics of the variables used. The average price and total returns of housing investment in New Zealand from 2001 to 2018 are about 9.7% and 14.2% per annum, higher than the market returns in the stock exchange (11.3%) and New Zealand REITs market (3.4%). The risk-free rate is about 5%, even higher than that of REITs in New Zealand. The “liquidity risk (SMB)” and “value risk (HML)” are about -2.4% and − 1.2% on average, whereas the time risk (SML) and the credit-rating risk (GMB) are about − 0.6% and − 0.8% on average. The exchange rate from New Zealand dollars to United States dollars is, on average, about 1.0 to 0.7. Table 3. Summary Statistics of the Panel Variables. Variables Mean Std. Dev. Minimum Maximum Ri,t9.71 13.04 −372.40 124.20 Ti,t14.17 13.01 −32.45 129.19 Rt14.17 8.38 −1.60 34.01 Rf,t4.94 1.33 2.29 6.77 Rm,t(NZX50) 11.24 13.13 −33.01 30.60 Rm,t(NZ_REITS) 3.42 11.76 −31.32 26.33 Tm,t (NZ_REITS_TR) 11.04 12.53 −25.04 35.14 SMBt−2.39 6.93 −18.72 12.85 HMLt−1.18 5.47 −11.45 10.13 SMLt−0.64 0.78 −2.02 0.92 GMBt−0.83 0.57 −2.70 0.53 CURt0.69 0.11 0.41 0.86 TA 62 (Territorial Authorities of New Zealand) Quarters 68 (2002Q1–2018Q4) 3.2. Model Setup Consider Jensen’s (1968) single-factor CAPM model as the baseline panel model (Model 1), as shown in Equation (1): Ri,t−Rf,t=α1,P+β1,PRm,t−Rf,t+ε1,i,t(1) where Ri,t is the price return of housing investment in each Territory Authority (TA) iat time t, which is calculated by the annual return Gi,t of the hedonic house price indices (details in the Appendix A). Rf,t is the risk-free rate at time tproxied by the ten-year government bond yield from the Reserve Bank of New Zealand. Rm,t is the market price return at time t. The total return model is similar to Equation (1) by replacing Ri,t with total return Ti,t, and Rm,twith the total market return Tm,t. Housing market risks include not only financial risks but also spatial-temporal risks. Spatial-temporally, different TAs will have different risk-return relationships due to various spatial and temporal reasons, such as ease of resale (liquidity risk, SMBt , Small Minus J. Risk Financial Manag. 2022,15, 390 7 of 14 Big), the predictive power of appraisal information (value risk, HMLt , High Minus Low), institutional costs, etc. Temporally, different periods will also have different risk-return associations due to various macroeconomic reasons, such as the time cost risk ( SMLt , Short-term Minus Long-term), the required compensations for default risk ( GMBt , Goodgrade Minus Bad-grade) and currency risk ( CURt ), etc. Thus, to further control other relevant temporal-risk and spatial-temporal-risk factors, we modify the baseline model to an extended Fama-French Five-Factor Model (Model 2, Equation (2)). Mathematically: Ri,t−Rf,t=α2,P+β2,PRm,t−Rf,t+γ1,PSMBt+γ2,PHMLt+γ3,PSMLt+γ4,PGMBt+γ5,PCURt+ε2,i,t(2) In the housing markets, SMBt is proxied by subtracting the average return of the smallest one-third of TAs in housing transaction amount from the average return of the largest one-third of TAs in housing transaction amount (Equation (3)). SMBt represents the liquidity risk as the transaction amount represents market activeness. Instead of using the book-to-value ratio used in stock market analysis, HMLt of the housing market is proxied by the appraisal-to-value ratio, which is the difference between the average return of the lowest one-third of TAs of housing appraised Capital Value to Market Price (CVTP) ratio and the average return of the highest one-third of TAs of housing CVTP ratio (Equation (4)) (Appendix A). HMLtcan be considered as an appraisal risk: SMBt=∑S i=sRi,t S−s−∑B i=bRi,t B−b(3) HMLt=∑H i=hRi,t H−h−∑L i=lRi,t L−l(4) where s,s+1, . . . , Sand b,b+1, . . . , Bare the smallest and the largest one-third of TAs in housing transaction amounts at time t; whereas h , h+ 1, . . . , H and l , l+ 1, . . . , L are the highest and the lowest one-third TAs in housing CV/P ratios at time t. SMLt=yg 2y,t−yg 10y,t(5) Equation (5) represents the time cost risk, which is proxied by the difference between short-term and long-term market required returns, SMLt (i.e., Short-term Minus Longterm). SMLt is calculated by subtracting the long-term risk-free 10-year New Zealand government bond yields yg 10y,t from the 2-year New Zealand government bond yields yg 2y,t at time t. GMBt=yc aa,t−yc bbb,t(6) Equation (6) shows GMBt (Good-grade Minus Bad-grade) that represents the default risk (3rd-party credit-rating risk). The risk is proxied by the difference of market required returns between good grade and bad grade corporate bonds, where yc aa,t and yc bbb,t are the AA-grade and BBB-grade corporate bond yields at time t, respectively. The currency risk factor CURt is also included in the model because of an argument that foreign funds influence house prices in New Zealand. Currency risk is proxied by the annual growth rate of the exchange rate between NZD and USD. 4. Empirical Results and Discussion Table 4presents the results of a panel data analysis of single-factor CAPM panel models on three different market risk proxies: NZ_HCR, NZX50, and NZ_REITs. The cross-sectional effect on each TA is fixed (fixed effects, F.E.). Jensen’s alpha αi in these models exhibits a significantly positive excess return, increasing from 3.7 to 9.2 from the national housing to the stock and the REITs markets. This reflects the fact that New Zealand’s housing price returns outperform the market price returns of NZ_HCR, NZX50, and NZ_REITs in the period when the risk factors of residential direct real estate markets are not considered. However, if the total return is considered, the excess return of housing J. Risk Financial Manag. 2022,15, 390 8 of 14 investment is almost 40% more than that measured by the price return model. All the beta ( β ) estimates are positive and far less than one, decreasing from 0.78 to 0.11 of the four market return proxies. The relatively larger beta of Model 1a and the smaller betas of other Models imply that the housing returns correlate strongly with the national housing market returns but correlate weakly with the stock or REITs’ market returns in the same direction. This implies that direct real estate can be a good candidate for portfolio diversification. The result also raises the question of the linkages between the real estate market and the REITs market (Gounopoulos et al. 2019). Table 4. Results of the Single-factor CAPM Models. Model 1a Model 2a Model 3a Model 4a Dep. Var Rm(NZ_HCR) Rm(NZX50) Rm(NZ_REIT) Tm(NZ_REIT_TR) αi3.695 (18.21) *** 6.618 (28.35) *** 9.166 (49.00) *** 12.710 (51.36) *** βi0.777 (39.35) *** 0.301 (17.77) *** 0.124 (6.12) *** 0.110 (5.83) *** F.E. Yes Yes Yes Yes Adj R-sq 0.36 0.14 0.07 0.07 Observations 72 ×62 68 ×62 68 ×62 68 ×62 Notes: *** represents estimate is significant at the 1% level. The figures in parentheses are the t-statistics. Models 1a, 2a, 3a, and 4a are for the four proxies of market returns, viz. NZ_HCR, NZX50, NZ_REIT, and NZ_REIT_TR, respectively. Figure 2shows the scatterplot of betas versus average price returns of 12 City-TAs in New Zealand, illustrating their beta-return relationships. The beta-return correlations in city-TA are primarily positive, which confirms the Security Market Line (Tang and Shum 2003). The small magnitudes of the betas reflect the diversification benefits of including direct real estate investment in the portfolio with NZX50 stocks. We further test the five-factor models to determine the risk factors that can explain the returns. J. Risk Financial Manag. 2022, 15, x FOR PEER REVIEW 9 of 14 Figure 2. Beta-return relationships of the 12 City-TAs of New Zealand. Notes: This beta-return scatterplot is based on the single-factor CAPM model taking NZX50 as the market returns on the 12 City-TAs of New Zealand (excluding three outliers—Invercargill City, Porirua City, and Nelson City). The vertical axis represents the betas 𝛽 estimated in Model 1b of the TA, and the horizontal axis represents the average total return 𝑅  of the TA housing market. The best fit line 𝑅 = 6.91𝛽 + 5.65 achieves an R-squared of 0.25. Table 5 presents the results of the five-factor models. First, all the alphas 𝛼 are substantially reduced compared to those in the single-factor model. The result indicates that the excess returns in the housing markets can partially be explained by other risk factors, regardless of which market returns are considered. However, when total return is considered, the magnitude of the excess return is almost 70% more than that in the price return model. It reflects that most of the five risk factors cannot explain most of the excess return in rental yield. Second, the similar magnitude of betas 𝛽 in all models reflect the independence of these specific risk factors from the market risk. Table 5. Results of the Five-factor Fama-French Models. Model 1b Model 2b Model 3b Model 4b Dep. Var 𝑅(NZ_HCR) 𝑅(NZX50) 𝑅(NZ_REIT) 𝑇(NZ_REIT_TR) 𝛼 2.673 (7.64) *** 4.038 (10.69) *** 4.950 (12.10) *** 8.359 (17.38) *** 𝛽 0.813 (31.21) *** 0.308 (18.92) *** 0.185 (8.57) *** 0.148 (7.35) *** 𝑆𝑀𝐵 −0.007 (−0.15) −0.206 (−4.25) *** −0.336 (−6.65) *** −0.315 (−6.26) *** 𝐻𝑀𝐿 −0.013 (−0.25) −0.017 (−0.29) −0.042 (−0.68) −0.009 (−0.16) 𝑆𝑀𝐿 −0.780 (−2.80) *** 3.28 (11.78) *** 1.986 (6.61) *** 2.201 (7.37) *** 𝐺𝑀𝐵 −0.489 (−1.41) −4.759 (−13.41) *** −5.098 (−13.34) *** −5.191 (−13.70) *** 𝐶𝑈𝑅 −0.027 (−1.72) * −0.057 (−3.36) *** −0.021 (−1.20) −0.015 (−0.85) North Shore City Waitakere City Auckland City Manukau City Hamilton City Napier City Palmerston North City Upper Hutt City Lower Hutt City Wellington City Christchurch City Dunedin City 7 7.5 8 8.5 9 9.5 10 0.25 0.30 0.35 0.40 0.45 0.50 0.55 Figure 2. Beta-return relationships of the 12 City-TAs of New Zealand. Notes: This beta-return scatterplot is based on the single-factor CAPM model taking NZX50 as the market returns on the 12 City-TAs of New Zealand (excluding three outliers—Invercargill City, Porirua City, and Nelson City). The vertical axis represents the betas βT estimated in Model 1b of the TA, and the horizontal axis represents the average total return Rt of the TA housing market. The best fit line Rt = 6.91 βT + 5.65 achieves an R-squared of 0.25.