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2 Science for Open and Environmental Systems KIKUCHI, Atsushi Optimal Asset Allocation with Real Estate The institutional investors such as life insurance companies, trust banks, and pension funds, have to allocate their funds to several assets in order to obtain the higher but stable rate of return. Real estate is viewed as a portfolio diversifier, or risk reducer. Historically, real estate has been defined as only investments in private real estate equity and private real estate debt. The investors, who wanted to invest real estate, needed to buy and hold individual buildings directly. There were no secondary and securitized markets for private real estate debt or private real estate equity. Today, however, with the advent of securitization, the definition of real estate for institutional investors has broadened to cover many structures. We examine the relationship among the real estate index, stock index, and bond. index. We can find the difference among them. We examine that optimal asset allocation problem with real estate using mean-variance approach with the available data sets. We use the Sumitomo Life Research Index(SLRI), TOPIX, and Nikko Bond Performance Index. The results show that real estate can reduce risk on the asset mix. In our future research, we need to examine the model using additional data.
3 Optimal Asset Allocation with Real Estate
4 A Study of Funds Allocation on Decentralized Organization 2001
5 (I) (I) (I) MV MLPM (II) (II) (II) MV MLPM
6 1 2
7 J-REIT: J-REIT
8 4
9 1 2-1 optimal asset allocation optimal portfolio
10
11
12
13 2-4 ( ) ( ) : SPV : special purpose vehicle
14 debt CP equity 10
15 2-5 6 Topix National Council of Real Estate Investment Fiduciaries NCREIF :SLRI 6 SPC J-REIT 11
16 SLRI NOI 4 12
17 13
18 rp re Var(R) Minimize subject to n n Var( R) σ x x ( 3.1 ) P E j= 1 k = 1 jk j k r r ( 3.2 ) n j= 1 x j = 1 ( 3.3 ) x 0 ( j = 1,..., n) ( 3.4 ) j x X ( 3.5 ) σ jk : j k : j x = (x 1,, x n ) T x j r E r j rp : : j n : r = r x p j j= 1 (3.3) (3.4) (3.5) X (3.2)(3.4) x j 7 R 1, R n r 1t,, r nt, t = 1,, T r jt t j T p t p t = Pr{( R1,..., Rn ) = ( r1 t,..., rnt )} ( 3.6 ) p t 1/T 7 t t 14
19 jk r jt T 1 σ = ( r r )( r r ) ( 3.7 ) jk T t= 1 jt jk Var(R) n n j= 1 k = 1 j kt k Var( R) σ x x ( 3.8 ) jk j k (3.8) (3.7) (3.8) n n T 1 Var (R) = ( rjt rj )( rkt rk ) x jx j= k = T 1 1 t= 1 n 1 = T n n ( rjt rj ) x j ( rkt rk ) xk = j= k = T t = T n ( r r ) x k T jt j j T t= 1 j= 1 t= 1 j= 1 y = r x r t j= 1 jt j p 2 = 1 T n 2 r jtx j rp T 1 2 Var( R) = y t ( 3.9 ) T t= 1 Minimize 1 T T t= 1 2 y t ( 3.10 ) subject to n j= 1 r x y = r jt j t p ( t = 1,..., T ) ( 3.11 ) rp r E ( 3.12 ) n j= 1 x = 1 ( 3.13 ) j x 0 ( 3.14 ) j x X ( 3.15 ) 15
20 Bawa and Lindenberg Mean-Lower Partial Moments model : MLPM lower partial moments 3-1 r G rg rt 3-1 k LPM ( R ; r G ) (3.16) k T 1 k LPM k ( R ; rg ) rt rg ( 3.16 ) 8 T t= 1 d + d = r r ( 3.17 ) t t t G + d t d t 0 (3.17) (1) r r 0 t G d t = + t 0, d = r r ( 3.18 ) t G 8 a = max ( a, 0 ) 16
21 (2) r r 0 t G t + t d = ( r r ), d = 0 ( 3.19 ) d d + 0 t t t G t = rt rg d ( 3.20 ) + d t d t + t d t d 0, 0 ( 3.21 ) + (3.17) d t d t d = 5 t d d t t = 0 dt = 5 d t = 2 d t = t d t d = 0 ( 3.22 ) (3.21) + d t (3.22) d t d t 0 + (3.17) d d D + t d t d = r r + d 0 ( 3.23 ) t G d t t t { r + d r, d 0 ; t = 1 T } D = t t G t,..., ( 3.24 ) { d t dt D} = rt rg t min ( 3.25 ) k LPM ( R ; r G ) d t Minimize 1 T T t= 1 ( d t ) k ( 3.26 ) subject to n j=1 r jt x j + d t r G ( t = 1,..., T ) ( 3.27 ) d 0 ( 3.28 ) t (3.2)(3.5) k = 1 k = 2 2 k 3 k=2 17
22 NH FH OH F S 0 F 1+ rf = ( 3.29 ) 0 S 1 + r D r F r D : : (3.29) F t t+1 t t+1 t t+1 t t 9 (3.29) 9 :5 t t+1 t+1 18
23 j j NH j FH j NH j FH 1 2 njp NH 1NH 2NH nnh H 1FH 2FH nfh jnh : j jfh : j
24 20
25 -(I) -(II) NUOPT (I) 4-2 -(II) 10 NUOPT 21
26 -(I) { }7 { }
27 SLRI 90 NCREIF SLRI NCREIF 23
28 4-4 SLRI NikkoBPI GSBI NCREIF NikkoBPI GSBI SLRI NCREIF 4-4 NH FH
29 NH FH FH NH FH NikkoBPI SP500_NH NCREIF_NH SP500_NH 4-6 SLRI NCREIF_NH NikkoBPI NCREIF_NH SP500_NH TOPIX SLRI NCREIF_FH NikkoBPI NCREIF_FH SLRI NikkoBPI 25
30 4-5 SP500_NH NikkoCBPI NikkoBPI NCREIF_NH GSBI TOPIX SLRI NH 7 NikkoBPI NikkoCBPI SP500_NH
31 4-6 SP500_FH NikkoCBPI NikkoBPI NCREIF_FH GSBI_FH TOPIX SLRI FH 7 NCREIF_FH NikkoBPI NikkoCBPI SP500_FH
32 MV 2 MLPM MLPM 6.22%15.94%NH0.02% 5.22%13.84%FH0.02% 5.22%15.94%OH0.02% NHMV
33 FHMV
34 OHMV 4-9 NH FH OH
35 NHMV 4-11 NHMV
36 FHMV 4-13 FHMV
37 OHMV 4-15 OHMV
38 %8.00% % %10.66% NCREIF_NH 4-9 TOPIX GSBI_FH %10.66% NCREIF_NH 4-10 TOPIX GSBI_FH
39 NHMLPM 4-16 LPM 35
40 FHMLPM
41 OHMLPM 4-18 NH FH OH
42 NHMLPM 4-20 NHMLPM
43 FHMLPM 4-22 FHMLPM
44 OHMLPM 4-24 OHMLPM
45 %8.78% NCREIF_NH 4-8 NikkoBPI 11.00% NikkoCBPI SP500_NH %10.78% NCREIF_FH 4-9 TOPIX GSBI_FH NikkoBPI SP500_FH NCREIF_FH %10.78% NCREIF_NH 4-10 TOPIX GSBI_FH NikkoBPI SP500_FH NCREIF_FH
46 -(II) { }4 { }
47 NikkoBPI NikkoBPI 4-8 SLRI TOPIX NikkoBPI NikkoBPI NikkoCBPI SLRI TOPIX
48 MV 2 MLPM MLPM 6.36%8.56% 0.02% MV -(II)
49
50 %7.38% SLRI 4-27 NikkoBPI NikkoBPI MLPM -(II)
51 MLPM 4-32 MLPM
52 %8.54% SLRI
53 49
54
55 [1] J.L.Pagliari Jr., J.R.Webb, J.J.Del Casino1995 Applying MPT to Institutional Real Estate Portfolios : The Good, The Bad and Uncertain, Journal of Real Estate Portfolio Management, Vol.1, No.1, p [2] 1998,, Vol.36, No.12, p [3] , [4] 2001, [5] 1999, [6] , [7] 1998SPC, BP [8], /NTT 1991, 51
56
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183 04 022 J-REIT J-REIT Debt Equity 90 Equity Equity Equity Equity Equity Equity J-REIT 20019 28 2600 28000 J-REIT The National Council of Real Estate Investment Fiduciaries NOI BMV + 0.5* CI
AT A GLANCE INDIVIDUAL GROUP 63.72% 1, % At a Glance INSTITUTIONAL GROUP 34.26% % GLOBAL MARKETS GROUP 5.56% % 2
214 At a Glance 32 36 38 4 42 43 31 AT A GLANCE INDIVIDUAL GROUP 63.72% 1,293 32.4% 226 214 At a Glance INSTITUTIONAL GROUP 34.26% 695 76.26% 532 32 GLOBAL MARKETS GROUP 5.56% 112 4.2% 28 3 1% 1,5 5 1,
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2011 Vol.60 No.2 p.138 147 Performance of the Japanese long-term care benefit: An International comparison based on OECD health data Mie MORIKAWA[1] Takako TSUTSUI[2] [1]National Institute of Public Health,
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SUMMARY There might be no other business that has high uncertainty like Live Entertainment Business. This is because the success and failure of this business depend a great deal on the unscientific element
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Housing Purchase by Single Women in Tokyo Yoshilehl YUI* Recently some single women purchase their houses and the number of houses owned by single women are increasing in Tokyo. And their housing demands