Vol.8 No.2 1 9 (July 2015) 1,a) 2 3 2012 1 5 2012 3 24, 2013 12 12 2 1 2 A Factor Model for Measuring Market Risk in Real Estate Investment Hiroshi Ishijima 1,a) Akira Maeda 2 Tomohiko Taniyama 3 Received: January 5, 2012, Revised: March 24, 2012, Accepted: December 12, 2013 Abstract: In this paper, we propose a two stage factor model for measuring market risks of real estate investment. The feature is as follows: The first stage factor model measures the market risk in real estate investment. The second stage factor model explains the market risk by a linear combination of attributes that characterize each piece of real estate. We then find that the model works well when applied to the Japanese real estate market. Keywords: real estate, market risk, factor model, financial engineering 1. 2 2 1 1 1 1 Graduate School of International Accounting, Chuo University, Shinjuku, Tokyo 162 8478, Japan 2 Graduate School of Arts and Sciences, The University of Tokyo, Meguro, Tokyo 153 8902, Japan 3 Nomura Research Institute, Ltd., Chiyoda, Tokyo 100 0005, Japan a) hiroshi ishijima@hi-ho.ne.jp 2 2 2 1 2 c 2015 Information Processing Society of Japan 1
Vol.8 No.2 1 9 (July 2015) 2/3 2008 1 [3] stratification / *1 2 J-REIT *2 *1 *2 J-REIT 1 2001 9 2000 70% J-REIT J-REIT 6 J-REIT J-REIT 10 J-REIT *3 J-REIT 2 2 2 3 4 2. 2 2 2.1 1 2.2 2 2.1 1 1 i R i r f = α i + β i (R M r f )+ε i (1) i R i r f R i r f TOPIX R M r f ε i 1 CAPM Luenberger [7] *3 J-REIT J-REIT [4] c 2015 Information Processing Society of Japan 2
Vol.8 No.2 1 9 (July 2015) β i 2 β i = Cov (R i,r M ) V [R M ] (2) 2 β i Cov (R M,ε i )=0 i V [R i ]=β 2 i V [R M ]+V [ε i ] (3) (3) i 2 1 β 2 i V [R M ] 2 i ρ 2 := β2 i V [R M ] V [R i ] (4) (4) i (4) 0 1 1 ρ 2 i β i 2.2 2 2.1 2 1 attributes [5], [8] 2 i β i K x i =(x i1...x ik...x ik ) K β i = γ k x ik (5) k=1 γ k k (5) 2 3. 2 2 4 3.1 J-REIT *4 J-REIT 6 2002 1 2009 1 1,400 J-REIT R i β i *4 ARES ARES J-REIT Property Index t i TR i,t IR i,t CR i,t TR i,t = IR i,t + CR i,t NOI i,t = V i,t 1 +0.5CI i,t 0.5PS i,t 0.471NOI i,t + (V i,t V i,t 1 )+PS i,t CI i,t V i,t 1 +0.5CI i,t 0.5PS i,t 0.471NOI i,t (6) NOI V CI PS CI PS NOI 1/6 c 2015 Information Processing Society of Japan 3
Vol.8 No.2 1 9 (July 2015) 1 β Fig. 1 Distribution and summary statistics of market risk β in real estate investment. 2 Fig. 2 Distribution of systematic risk in real estate investment. 3.3 x i r f 10 R M IPD Japan Monthly Indicator All Property 3.2 1 1 (1) 1 0 1 1 1,400 20% 1 (4) ρ 2 1 ρ 2 2 50% 47.6% J-REIT J-REIT 1 ρ 2 48.9% *5 4 (1) 3 *5 i j (1 ρ 2 i )(1 ρ2 j ) c 2015 Information Processing Society of Japan 4
Vol.8 No.2 1 9 (July 2015) 3 Fig. 3 Tradeoff between market risk (beta) and performance (alpha) in real estate investment. 3.3 2 (5) 2 (5) i x i x i J-REIT % 3.3.1 2 7 5 23 5 4 4 5 23 5 23 5 4 Fig. 4 Market risk (beta) and performance (alpha) for each area. 2012 2007 2005 2008 *6 5 *7 *6 2006 10 8 2009 10 9 *7 4 c 2015 Information Processing Society of Japan 5
Vol.8 No.2 1 9 (July 2015) 1 N β α α/β α/β Table 1 Number of observations (N), betas (β), alphas (α), alpha-beta ratios (α/β) and its ranking. 5 Fig. 5 Market risk (beta) and performance (alpha) for each use. 1 2012 J-REIT 1 1 α/β 3.3.2 2 2 7 5 23 5 4 4 (5) η i 2 2 AIC 5% Table 2 Comparison of AICs among second stage factor models. Also the ratios of the 5% significant independent variables are reported. K β i = γ k x ik + η i (7) k=1 i β i K x ik k =1,...,K γ k k (7) 2 7 No.1 No.7 SAS Proc Mixed [6] AIC AIC 1.38% 5% 2 3 c 2015 Information Processing Society of Japan 6
Vol.8 No.2 1 9 (July 2015) 3 2 No.5 5% Table 3 Estimated result for the second stage factor model No.5. ( : 5% significant). 4. 2 No.1 2 5 3.3.3 2 No.1 No.2 β i 4 5 β i β i 3.3.1 2 No.5 3 % 2 1 2 (1) (2) (3) (4) (5) (6) (7) 2 (a) (b) 2 2 [1] Elton, E.J., Gruber, M.J., Brown, S.J. and Goetzmann, W.N.: Modern Portfolio Theory and Investment Analysis: 8th Edition, John Wiley & Sons (2010). [2] Vol.8, No.2, pp.95 98 (2011). [3] Vol.2011- c 2015 Information Processing Society of Japan 7
Vol.8 No.2 1 9 (July 2015) MPS-85, No.11, pp.1 12 (2011). [4] J-REIT J-REIT J-REIT 5 (2007). [5] Lancaster, K.: A New Approach to Consumer Theory, Journal of Political Economy, Vol.74, pp.132 157 (1966). [6] Littell, R.C., Milliken, G.A., Stroup, W.W., Wolfinger, R.D. and Schabenberber, O.: SAS for Mixed Models: 2nd Edition, SAS Publishing (2006). [7] Luenberger, D.G.: Investment Science, Oxford University Press (1997). (2002). [8] Rosen, S.: Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition, Journal of Political Economy, Vol.82, pp.34 55 (1974). [2] 2 (5) [2] 1 3 1 2 3 1 [2] 1 [ (Pj,t+1 P j,t = E t + Dj,t+1 P ) ] M C t+1 (A.1) [ ] H i,t = L i,t Di,t H C + E t H i,t+1 M t+1 (A.2) D H i,t = b i,t M Z t (A.3) (j =1,...,N P ; i =1,...,N H ) P j,t t N P j Dj,t P t j M t+1 C := δ / u(c t+1, Z t+1 )/ C t+1 u(ct, Z t )/ C t u δ C t t Z t := (Z 1,t...Z k,t...z K,t ) t H i,t t N H i D i,t H t i L i,t t i 1 b i,t := (b i1,t...b ik,t...b ik,t ) t i K M k,t Z := u(c t, Z t )/ Z k,t / u(c t, Z t )/ C t k = 1,...,K ( M t Z := M Z 1,t... M k,t Z... M ) K,t Z (A.1) (A.2) (A.3) L i,t Dj,t P t F t F t E t [2] 1 2 (5) (A.2) (A.3) [ H i,t = E t δ τ L i,t+τ b i,t+τ Mt+τ Z ] (A.4) τ=0 M Z t+τ := u(c t+τ, Z t+τ ) / Z t+τ / u(ct, Z t ) / C t 1 b i,t = b i i, t (A.5) (A.4) [ ] H i,t = b i E t δ τ L i,t+τ Mt+τ Z (A.6) τ=0 H i,t+1 = δ 1 b i k=0 δ k [ E t+1 Li,t+k Mt+k Z ] δ 1 [ b i E t+1 Li,t Mt Z ]. (A.7) t E t [H i,t+1 ] H i,t H i,t = κ δ 1 b i L i,t M Z t H i,t. (A.8) κ := δ 1 1 2L i,t = L t (A.8) E t [H i,t+1 ] H i,t =κ + x i,t γ t H i,t (i =1,...,N H ) (A.9) c 2015 Information Processing Society of Japan 8
Vol.8 No.2 1 9 (July 2015) x i,t := b i /H i,t =(x i1,t...x ik,t...x ik,t ) γ t := δ 1 L t Mt Z =(γ 1,t...γ k,t...γ K,t ) i i ν i,t+1 (A.9) R i,t+1 := H i,t+1 H i,t H i,t = κ + x i,t γ t + ν i,t+1 (i =1,...,N H ) (A.10) ν i,t+1 (1) R M γ t t i (1) (2) β i,t := Cov t (R i,t+1,r M,t+1 ) / V t [R M,t+1 ] (2) (2) Cov V F t Cov t V t (2) (A.10) (2) β i,t = x i,t γ t = K x ik,t γ k,t k=1 γ t := Cov t ( γ t,r M,t+1 ) / V t [R M,t+1 ] =(γ 1,t...γ k,t...γ K,t ) (A.11) (A.12) (A.11) t (5) (5) η i (7) (A.11) Elton [1] (1) 2 (5) (7) 1971 1999 2004 10 2006 5 2007 4 2014 4 2013 9 2014 8 2010 FP 1963 1990 3 4 1999 4 Ph.D. 4 2004 4 2011 4 /2014 4 2004 10 2007 4 1978 2004 3 4 2010 3 2010 FP c 2015 Information Processing Society of Japan 9